commit 7b10741be4280d84a7ac9f41c54380cbc1f09c1b Author: Yawning Angel yawning@schwanenlied.me Date: Wed Jun 24 14:51:00 2015 +0000
Import Andrew Moon's ed25519-donna.
This is a clean copy of ed25519-donna as of commit:
8757bd4cd209cb032853ece0ce413f122eef212c
https://github.com/floodyberry/ed25519-donna --- src/ext/README | 5 + src/ext/ed25519/donna/README.md | 183 + src/ext/ed25519/donna/curve25519-donna-32bit.h | 579 +++ src/ext/ed25519/donna/curve25519-donna-64bit.h | 413 ++ src/ext/ed25519/donna/curve25519-donna-helpers.h | 67 + src/ext/ed25519/donna/curve25519-donna-sse2.h | 1112 +++++ src/ext/ed25519/donna/ed25519-donna-32bit-sse2.h | 513 +++ src/ext/ed25519/donna/ed25519-donna-32bit-tables.h | 61 + src/ext/ed25519/donna/ed25519-donna-64bit-sse2.h | 436 ++ src/ext/ed25519/donna/ed25519-donna-64bit-tables.h | 53 + .../ed25519/donna/ed25519-donna-64bit-x86-32bit.h | 435 ++ src/ext/ed25519/donna/ed25519-donna-64bit-x86.h | 351 ++ .../ed25519/donna/ed25519-donna-basepoint-table.h | 259 ++ src/ext/ed25519/donna/ed25519-donna-batchverify.h | 275 ++ src/ext/ed25519/donna/ed25519-donna-impl-base.h | 364 ++ src/ext/ed25519/donna/ed25519-donna-impl-sse2.h | 390 ++ .../donna/ed25519-donna-portable-identify.h | 103 + src/ext/ed25519/donna/ed25519-donna-portable.h | 135 + src/ext/ed25519/donna/ed25519-donna.h | 115 + src/ext/ed25519/donna/ed25519-hash-custom.h | 11 + src/ext/ed25519/donna/ed25519-hash.h | 219 + src/ext/ed25519/donna/ed25519-randombytes-custom.h | 8 + src/ext/ed25519/donna/ed25519-randombytes.h | 91 + src/ext/ed25519/donna/ed25519.c | 150 + src/ext/ed25519/donna/ed25519.h | 30 + src/ext/ed25519/donna/fuzz/README.md | 173 + src/ext/ed25519/donna/fuzz/build-nix.php | 134 + src/ext/ed25519/donna/fuzz/curve25519-ref10.c | 1272 ++++++ src/ext/ed25519/donna/fuzz/curve25519-ref10.h | 8 + src/ext/ed25519/donna/fuzz/ed25519-donna-sse2.c | 3 + src/ext/ed25519/donna/fuzz/ed25519-donna.c | 1 + src/ext/ed25519/donna/fuzz/ed25519-donna.h | 34 + src/ext/ed25519/donna/fuzz/ed25519-ref10.c | 4647 ++++++++++++++++++++ src/ext/ed25519/donna/fuzz/ed25519-ref10.h | 9 + src/ext/ed25519/donna/fuzz/fuzz-curve25519.c | 172 + src/ext/ed25519/donna/fuzz/fuzz-ed25519.c | 219 + src/ext/ed25519/donna/modm-donna-32bit.h | 469 ++ src/ext/ed25519/donna/modm-donna-64bit.h | 361 ++ src/ext/ed25519/donna/regression.h | 1024 +++++ src/ext/ed25519/donna/test-internals.c | 176 + src/ext/ed25519/donna/test-ticks.h | 50 + src/ext/ed25519/donna/test.c | 260 ++ 42 files changed, 15370 insertions(+)
diff --git a/src/ext/README b/src/ext/README index b52c74d..5501aba 100644 --- a/src/ext/README +++ b/src/ext/README @@ -60,6 +60,11 @@ ed25519/ref10/* Daniel Bernsten's portable ref10 implementation of ed25519. Public domain.
+ed25519/donna/* + + Andrew Moon's semi-portable ed25519-donna implementation of + ed25519. Public domain. + readpassphrase.[ch]
Portable readpassphrase implementation from OpenSSH portable, version diff --git a/src/ext/ed25519/donna/README.md b/src/ext/ed25519/donna/README.md new file mode 100644 index 0000000..e09fc27 --- /dev/null +++ b/src/ext/ed25519/donna/README.md @@ -0,0 +1,183 @@ +[ed25519](http://ed25519.cr.yp.to/) is an +[Elliptic Curve Digital Signature Algortithm](http://en.wikipedia.org/wiki/Elliptic_Curve_DSA), +developed by [Dan Bernstein](http://cr.yp.to/djb.html), +[Niels Duif](http://www.nielsduif.nl/), +[Tanja Lange](http://hyperelliptic.org/tanja), +[Peter Schwabe](http://www.cryptojedi.org/users/peter/), +and [Bo-Yin Yang](http://www.iis.sinica.edu.tw/pages/byyang/). + +This project provides performant, portable 32-bit & 64-bit implementations. All implementations are +of course constant time in regard to secret data. + +#### Performance + +SSE2 code and benches have not been updated yet. I will do those next. + +Compilers versions are gcc 4.6.3, icc 13.1.1, clang 3.4-1~exp1. + +Batch verification time (in parentheses) is the average time per 1 verification in a batch of 64 signatures. Counts are in thousands of cycles. + +Note that SSE2 performance may be less impressive on AMD & older CPUs with slower SSE ops! + +Visual Studio performance for `ge25519_scalarmult_base_niels` will lag behind a bit until optimized assembler versions of `ge25519_scalarmult_base_choose_niels` +are made. + +##### E5200 @ 2.5ghz, march=core2 + +<table> +<thead><tr><th>Implementation</th><th>Sign</th><th>gcc</th><th>icc</th><th>clang</th><th>Verify</th><th>gcc</th><th>icc</th><th>clang</th></tr></thead> +<tbody> +<tr><td>ed25519-donna 64bit </td><td></td><td>100k</td><td>110k</td><td>137k</td><td></td><td>327k (144k) </td><td>342k (163k) </td><td>422k (194k) </td></tr> +<tr><td>amd64-64-24k </td><td></td><td>102k</td><td> </td><td> </td><td></td><td>355k (158k) </td><td> </td><td> </td></tr> +<tr><td>ed25519-donna-sse2 64bit</td><td></td><td>108k</td><td>111k</td><td>116k</td><td></td><td>353k (155k) </td><td>345k (154k) </td><td>360k (161k) </td></tr> +<tr><td>amd64-51-32k </td><td></td><td>116k</td><td> </td><td> </td><td></td><td>380k (175k) </td><td> </td><td> </td></tr> +<tr><td>ed25519-donna-sse2 32bit</td><td></td><td>147k</td><td>147k</td><td>156k</td><td></td><td>380k (178k) </td><td>381k (173k) </td><td>430k (192k) </td></tr> +<tr><td>ed25519-donna 32bit </td><td></td><td>597k</td><td>335k</td><td>380k</td><td></td><td>1693k (720k)</td><td>1052k (453k)</td><td>1141k (493k)</td></tr> +</tbody> +</table> + +##### E3-1270 @ 3.4ghz, march=corei7-avx + +<table> +<thead><tr><th>Implementation</th><th>Sign</th><th>gcc</th><th>icc</th><th>clang</th><th>Verify</th><th>gcc</th><th>icc</th><th>clang</th></tr></thead> +<tbody> +<tr><td>amd64-64-24k </td><td></td><td> 68k</td><td> </td><td> </td><td></td><td>225k (104k) </td><td> </td><td> </td></tr> +<tr><td>ed25519-donna 64bit </td><td></td><td> 71k</td><td> 75k</td><td> 90k</td><td></td><td>226k (105k) </td><td>226k (112k) </td><td>277k (125k) </td></tr> +<tr><td>amd64-51-32k </td><td></td><td> 72k</td><td> </td><td> </td><td></td><td>218k (107k) </td><td> </td><td> </td></tr> +<tr><td>ed25519-donna-sse2 64bit</td><td></td><td> 79k</td><td> 82k</td><td> 92k</td><td></td><td>252k (122k) </td><td>259k (124k) </td><td>282k (131k) </td></tr> +<tr><td>ed25519-donna-sse2 32bit</td><td></td><td> 94k</td><td> 95k</td><td>103k</td><td></td><td>296k (146k) </td><td>294k (137k) </td><td>306k (147k) </td></tr> +<tr><td>ed25519-donna 32bit </td><td></td><td>525k</td><td>299k</td><td>316k</td><td></td><td>1502k (645k)</td><td>959k (418k) </td><td>954k (416k) </td></tr> +</tbody> +</table> + +#### Compilation + +No configuration is needed **if you are compiling against OpenSSL**. + +##### Hash Options + +If you are not compiling aginst OpenSSL, you will need a hash function. + +To use a simple/**slow** implementation of SHA-512, use `-DED25519_REFHASH` when compiling `ed25519.c`. +This should never be used except to verify the code works when OpenSSL is not available. + +To use a custom hash function, use `-DED25519_CUSTOMHASH` when compiling `ed25519.c` and put your +custom hash implementation in ed25519-hash-custom.h. The hash must have a 512bit digest and implement + + struct ed25519_hash_context; + + void ed25519_hash_init(ed25519_hash_context *ctx); + void ed25519_hash_update(ed25519_hash_context *ctx, const uint8_t *in, size_t inlen); + void ed25519_hash_final(ed25519_hash_context *ctx, uint8_t *hash); + void ed25519_hash(uint8_t *hash, const uint8_t *in, size_t inlen); + +##### Random Options + +If you are not compiling aginst OpenSSL, you will need a random function for batch verification. + +To use a custom random function, use `-DED25519_CUSTOMRANDOM` when compiling `ed25519.c` and put your +custom hash implementation in ed25519-randombytes-custom.h. The random function must implement: + + void ED25519_FN(ed25519_randombytes_unsafe) (void *p, size_t len); + +Use `-DED25519_TEST` when compiling `ed25519.c` to use a deterministically seeded, non-thread safe CSPRNG +variant of Bob Jenkins [ISAAC](http://en.wikipedia.org/wiki/ISAAC_%28cipher%29) + +##### Minor options + +Use `-DED25519_INLINE_ASM` to disable the use of custom assembler routines and instead rely on portable C. + +Use `-DED25519_FORCE_32BIT` to force the use of 32 bit routines even when compiling for 64 bit. + +##### 32-bit + + gcc ed25519.c -m32 -O3 -c + +##### 64-bit + + gcc ed25519.c -m64 -O3 -c + +##### SSE2 + + gcc ed25519.c -m32 -O3 -c -DED25519_SSE2 -msse2 + gcc ed25519.c -m64 -O3 -c -DED25519_SSE2 + +clang and icc are also supported + + +#### Usage + +To use the code, link against `ed25519.o -mbits` and: + + #include "ed25519.h" + +Add `-lssl -lcrypto` when using OpenSSL (Some systems don't need -lcrypto? It might be trial and error). + +To generate a private key, simply generate 32 bytes from a secure +cryptographic source: + + ed25519_secret_key sk; + randombytes(sk, sizeof(ed25519_secret_key)); + +To generate a public key: + + ed25519_public_key pk; + ed25519_publickey(sk, pk); + +To sign a message: + + ed25519_signature sig; + ed25519_sign(message, message_len, sk, pk, signature); + +To verify a signature: + + int valid = ed25519_sign_open(message, message_len, pk, signature) == 0; + +To batch verify signatures: + + const unsigned char *mp[num] = {message1, message2..} + size_t ml[num] = {message_len1, message_len2..} + const unsigned char *pkp[num] = {pk1, pk2..} + const unsigned char *sigp[num] = {signature1, signature2..} + int valid[num] + + /* valid[i] will be set to 1 if the individual signature was valid, 0 otherwise */ + int all_valid = ed25519_sign_open_batch(mp, ml, pkp, sigp, num, valid) == 0; + +**Note**: Batch verification uses `ed25519_randombytes_unsafe`, implemented in +`ed25519-randombytes.h`, to generate random scalars for the verification code. +The default implementation now uses OpenSSLs `RAND_bytes`. + +Unlike the [SUPERCOP](http://bench.cr.yp.to/supercop.html) version, signatures are +not appended to messages, and there is no need for padding in front of messages. +Additionally, the secret key does not contain a copy of the public key, so it is +32 bytes instead of 64 bytes, and the public key must be provided to the signing +function. + +##### Curve25519 + +Curve25519 public keys can be generated thanks to +[Adam Langley](http://www.imperialviolet.org/2013/05/10/fastercurve25519.html) +leveraging Ed25519's precomputed basepoint scalar multiplication. + + curved25519_key sk, pk; + randombytes(sk, sizeof(curved25519_key)); + curved25519_scalarmult_basepoint(pk, sk); + +Note the name is curved25519, a combination of curve and ed25519, to prevent +name clashes. Performance is slightly faster than short message ed25519 +signing due to both using the same code for the scalar multiply. + +#### Testing + +Fuzzing against reference implemenations is now available. See [fuzz/README](fuzz/README.md). + +Building `ed25519.c` with `-DED25519_TEST` and linking with `test.c` will run basic sanity tests +and benchmark each function. `test-batch.c` has been incorporated in to `test.c`. + +`test-internals.c` is standalone and built the same way as `ed25519.c`. It tests the math primitives +with extreme values to ensure they function correctly. SSE2 is now supported. + +#### Papers + +[Available on the Ed25519 website](http://ed25519.cr.yp.to/papers.html) \ No newline at end of file diff --git a/src/ext/ed25519/donna/curve25519-donna-32bit.h b/src/ext/ed25519/donna/curve25519-donna-32bit.h new file mode 100644 index 0000000..b0861ac --- /dev/null +++ b/src/ext/ed25519/donna/curve25519-donna-32bit.h @@ -0,0 +1,579 @@ +/* + Public domain by Andrew M. liquidsun@gmail.com + See: https://github.com/floodyberry/curve25519-donna + + 32 bit integer curve25519 implementation +*/ + +typedef uint32_t bignum25519[10]; +typedef uint32_t bignum25519align16[12]; + +static const uint32_t reduce_mask_25 = (1 << 25) - 1; +static const uint32_t reduce_mask_26 = (1 << 26) - 1; + + +/* out = in */ +DONNA_INLINE static void +curve25519_copy(bignum25519 out, const bignum25519 in) { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + out[4] = in[4]; + out[5] = in[5]; + out[6] = in[6]; + out[7] = in[7]; + out[8] = in[8]; + out[9] = in[9]; +} + +/* out = a + b */ +DONNA_INLINE static void +curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) { + out[0] = a[0] + b[0]; + out[1] = a[1] + b[1]; + out[2] = a[2] + b[2]; + out[3] = a[3] + b[3]; + out[4] = a[4] + b[4]; + out[5] = a[5] + b[5]; + out[6] = a[6] + b[6]; + out[7] = a[7] + b[7]; + out[8] = a[8] + b[8]; + out[9] = a[9] + b[9]; +} + +DONNA_INLINE static void +curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) { + uint32_t c; + out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; + out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; + out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; + out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; + out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; + out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; + out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; + out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; + out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; + out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; + out[0] += 19 * c; +} + +DONNA_INLINE static void +curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) { + uint32_t c; + out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; + out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; + out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; + out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; + out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; + out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; + out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; + out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; + out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; + out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; + out[0] += 19 * c; +} + +/* multiples of p */ +static const uint32_t twoP0 = 0x07ffffda; +static const uint32_t twoP13579 = 0x03fffffe; +static const uint32_t twoP2468 = 0x07fffffe; +static const uint32_t fourP0 = 0x0fffffb4; +static const uint32_t fourP13579 = 0x07fffffc; +static const uint32_t fourP2468 = 0x0ffffffc; + +/* out = a - b */ +DONNA_INLINE static void +curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) { + uint32_t c; + out[0] = twoP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; + out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; + out[2] = twoP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; + out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; + out[4] = twoP2468 + a[4] - b[4] + c; + out[5] = twoP13579 + a[5] - b[5] ; + out[6] = twoP2468 + a[6] - b[6] ; + out[7] = twoP13579 + a[7] - b[7] ; + out[8] = twoP2468 + a[8] - b[8] ; + out[9] = twoP13579 + a[9] - b[9] ; +} + +/* out = a - b, where a is the result of a basic op (add,sub) */ +DONNA_INLINE static void +curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) { + uint32_t c; + out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; + out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; + out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; + out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; + out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; + out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; + out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; + out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; + out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; + out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; + out[0] += 19 * c; +} + +DONNA_INLINE static void +curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) { + uint32_t c; + out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; + out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; + out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; + out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; + out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; + out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; + out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; + out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; + out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; + out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; + out[0] += 19 * c; +} + +/* out = -a */ +DONNA_INLINE static void +curve25519_neg(bignum25519 out, const bignum25519 a) { + uint32_t c; + out[0] = twoP0 - a[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; + out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; + out[2] = twoP2468 - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; + out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; + out[4] = twoP2468 - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; + out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; + out[6] = twoP2468 - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; + out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; + out[8] = twoP2468 - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; + out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; + out[0] += 19 * c; +} + +/* out = a * b */ +#define curve25519_mul_noinline curve25519_mul +static void +curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) { + uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9; + uint32_t s0,s1,s2,s3,s4,s5,s6,s7,s8,s9; + uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c; + uint32_t p; + + r0 = b[0]; + r1 = b[1]; + r2 = b[2]; + r3 = b[3]; + r4 = b[4]; + r5 = b[5]; + r6 = b[6]; + r7 = b[7]; + r8 = b[8]; + r9 = b[9]; + + s0 = a[0]; + s1 = a[1]; + s2 = a[2]; + s3 = a[3]; + s4 = a[4]; + s5 = a[5]; + s6 = a[6]; + s7 = a[7]; + s8 = a[8]; + s9 = a[9]; + + m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0); + m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0); + m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0); + m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0); + m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0); + + r1 *= 2; + r3 *= 2; + r5 *= 2; + r7 *= 2; + + m0 = mul32x32_64(r0, s0); + m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0); + m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0); + m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0); + m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0); + + r1 *= 19; + r2 *= 19; + r3 = (r3 / 2) * 19; + r4 *= 19; + r5 = (r5 / 2) * 19; + r6 *= 19; + r7 = (r7 / 2) * 19; + r8 *= 19; + r9 *= 19; + + m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9)); + m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9)); + m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9)); + m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9)); + + r3 *= 2; + r5 *= 2; + r7 *= 2; + r9 *= 2; + + m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9)); + m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9)); + m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9)); + m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9)); + m8 += (mul32x32_64(r9, s9)); + + r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26); + m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25); + m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26); + m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25); + m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26); + m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25); + m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26); + m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25); + m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26); + m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25); + m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26); + r1 += p; + + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + out[4] = r4; + out[5] = r5; + out[6] = r6; + out[7] = r7; + out[8] = r8; + out[9] = r9; +} + +/* out = in*in */ +static void +curve25519_square(bignum25519 out, const bignum25519 in) { + uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9; + uint32_t d6,d7,d8,d9; + uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c; + uint32_t p; + + r0 = in[0]; + r1 = in[1]; + r2 = in[2]; + r3 = in[3]; + r4 = in[4]; + r5 = in[5]; + r6 = in[6]; + r7 = in[7]; + r8 = in[8]; + r9 = in[9]; + + m0 = mul32x32_64(r0, r0); + r0 *= 2; + m1 = mul32x32_64(r0, r1); + m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2); + r1 *= 2; + m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 ); + m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2); + r2 *= 2; + m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3); + m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2); + r3 *= 2; + m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 ); + m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 ); + m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2); + + d6 = r6 * 19; + d7 = r7 * 2 * 19; + d8 = r8 * 19; + d9 = r9 * 2 * 19; + + m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19)); + m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2)); + m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 )); + m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 )); + m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 )); + m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2)); + m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 )); + m7 += (mul32x32_64(d9, r8 )); + m8 += (mul32x32_64(d9, r9 )); + + r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26); + m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25); + m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26); + m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25); + m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26); + m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25); + m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26); + m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25); + m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26); + m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25); + m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26); + r1 += p; + + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + out[4] = r4; + out[5] = r5; + out[6] = r6; + out[7] = r7; + out[8] = r8; + out[9] = r9; +} + + +/* out = in ^ (2 * count) */ +static void +curve25519_square_times(bignum25519 out, const bignum25519 in, int count) { + uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9; + uint32_t d6,d7,d8,d9; + uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c; + uint32_t p; + + r0 = in[0]; + r1 = in[1]; + r2 = in[2]; + r3 = in[3]; + r4 = in[4]; + r5 = in[5]; + r6 = in[6]; + r7 = in[7]; + r8 = in[8]; + r9 = in[9]; + + do { + m0 = mul32x32_64(r0, r0); + r0 *= 2; + m1 = mul32x32_64(r0, r1); + m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2); + r1 *= 2; + m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 ); + m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2); + r2 *= 2; + m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3); + m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2); + r3 *= 2; + m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 ); + m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 ); + m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2); + + d6 = r6 * 19; + d7 = r7 * 2 * 19; + d8 = r8 * 19; + d9 = r9 * 2 * 19; + + m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19)); + m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2)); + m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 )); + m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 )); + m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 )); + m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2)); + m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 )); + m7 += (mul32x32_64(d9, r8 )); + m8 += (mul32x32_64(d9, r9 )); + + r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26); + m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25); + m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26); + m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25); + m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26); + m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25); + m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26); + m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25); + m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26); + m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25); + m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26); + r1 += p; + } while (--count); + + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + out[4] = r4; + out[5] = r5; + out[6] = r6; + out[7] = r7; + out[8] = r8; + out[9] = r9; +} + +/* Take a little-endian, 32-byte number and expand it into polynomial form */ +static void +curve25519_expand(bignum25519 out, const unsigned char in[32]) { + static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}}; + uint32_t x0,x1,x2,x3,x4,x5,x6,x7; + + if (endian_check.s == 1) { + x0 = *(uint32_t *)(in + 0); + x1 = *(uint32_t *)(in + 4); + x2 = *(uint32_t *)(in + 8); + x3 = *(uint32_t *)(in + 12); + x4 = *(uint32_t *)(in + 16); + x5 = *(uint32_t *)(in + 20); + x6 = *(uint32_t *)(in + 24); + x7 = *(uint32_t *)(in + 28); + } else { + #define F(s) \ + ((((uint32_t)in[s + 0]) ) | \ + (((uint32_t)in[s + 1]) << 8) | \ + (((uint32_t)in[s + 2]) << 16) | \ + (((uint32_t)in[s + 3]) << 24)) + x0 = F(0); + x1 = F(4); + x2 = F(8); + x3 = F(12); + x4 = F(16); + x5 = F(20); + x6 = F(24); + x7 = F(28); + #undef F + } + + out[0] = ( x0 ) & 0x3ffffff; + out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & 0x1ffffff; + out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & 0x3ffffff; + out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & 0x1ffffff; + out[4] = (( x3) >> 6) & 0x3ffffff; + out[5] = ( x4 ) & 0x1ffffff; + out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & 0x3ffffff; + out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & 0x1ffffff; + out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & 0x3ffffff; + out[9] = (( x7) >> 6) & 0x1ffffff; +} + +/* Take a fully reduced polynomial form number and contract it into a + * little-endian, 32-byte array + */ +static void +curve25519_contract(unsigned char out[32], const bignum25519 in) { + bignum25519 f; + curve25519_copy(f, in); + + #define carry_pass() \ + f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \ + f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \ + f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \ + f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \ + f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \ + f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \ + f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \ + f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \ + f[9] += f[8] >> 26; f[8] &= reduce_mask_26; + + #define carry_pass_full() \ + carry_pass() \ + f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25; + + #define carry_pass_final() \ + carry_pass() \ + f[9] &= reduce_mask_25; + + carry_pass_full() + carry_pass_full() + + /* now t is between 0 and 2^255-1, properly carried. */ + /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */ + f[0] += 19; + carry_pass_full() + + /* now between 19 and 2^255-1 in both cases, and offset by 19. */ + f[0] += (reduce_mask_26 + 1) - 19; + f[1] += (reduce_mask_25 + 1) - 1; + f[2] += (reduce_mask_26 + 1) - 1; + f[3] += (reduce_mask_25 + 1) - 1; + f[4] += (reduce_mask_26 + 1) - 1; + f[5] += (reduce_mask_25 + 1) - 1; + f[6] += (reduce_mask_26 + 1) - 1; + f[7] += (reduce_mask_25 + 1) - 1; + f[8] += (reduce_mask_26 + 1) - 1; + f[9] += (reduce_mask_25 + 1) - 1; + + /* now between 2^255 and 2^256-20, and offset by 2^255. */ + carry_pass_final() + + #undef carry_pass + #undef carry_full + #undef carry_final + + f[1] <<= 2; + f[2] <<= 3; + f[3] <<= 5; + f[4] <<= 6; + f[6] <<= 1; + f[7] <<= 3; + f[8] <<= 4; + f[9] <<= 6; + + #define F(i, s) \ + out[s+0] |= (unsigned char )(f[i] & 0xff); \ + out[s+1] = (unsigned char )((f[i] >> 8) & 0xff); \ + out[s+2] = (unsigned char )((f[i] >> 16) & 0xff); \ + out[s+3] = (unsigned char )((f[i] >> 24) & 0xff); + + out[0] = 0; + out[16] = 0; + F(0,0); + F(1,3); + F(2,6); + F(3,9); + F(4,12); + F(5,16); + F(6,19); + F(7,22); + F(8,25); + F(9,28); + #undef F +} + + +/* out = (flag) ? in : out */ +DONNA_INLINE static void +curve25519_move_conditional_bytes(uint8_t out[96], const uint8_t in[96], uint32_t flag) { + const uint32_t nb = flag - 1, b = ~nb; + const uint32_t *inl = (const uint32_t *)in; + uint32_t *outl = (uint32_t *)out; + outl[0] = (outl[0] & nb) | (inl[0] & b); + outl[1] = (outl[1] & nb) | (inl[1] & b); + outl[2] = (outl[2] & nb) | (inl[2] & b); + outl[3] = (outl[3] & nb) | (inl[3] & b); + outl[4] = (outl[4] & nb) | (inl[4] & b); + outl[5] = (outl[5] & nb) | (inl[5] & b); + outl[6] = (outl[6] & nb) | (inl[6] & b); + outl[7] = (outl[7] & nb) | (inl[7] & b); + outl[8] = (outl[8] & nb) | (inl[8] & b); + outl[9] = (outl[9] & nb) | (inl[9] & b); + outl[10] = (outl[10] & nb) | (inl[10] & b); + outl[11] = (outl[11] & nb) | (inl[11] & b); + outl[12] = (outl[12] & nb) | (inl[12] & b); + outl[13] = (outl[13] & nb) | (inl[13] & b); + outl[14] = (outl[14] & nb) | (inl[14] & b); + outl[15] = (outl[15] & nb) | (inl[15] & b); + outl[16] = (outl[16] & nb) | (inl[16] & b); + outl[17] = (outl[17] & nb) | (inl[17] & b); + outl[18] = (outl[18] & nb) | (inl[18] & b); + outl[19] = (outl[19] & nb) | (inl[19] & b); + outl[20] = (outl[20] & nb) | (inl[20] & b); + outl[21] = (outl[21] & nb) | (inl[21] & b); + outl[22] = (outl[22] & nb) | (inl[22] & b); + outl[23] = (outl[23] & nb) | (inl[23] & b); + +} + +/* if (iswap) swap(a, b) */ +DONNA_INLINE static void +curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint32_t iswap) { + const uint32_t swap = (uint32_t)(-(int32_t)iswap); + uint32_t x0,x1,x2,x3,x4,x5,x6,x7,x8,x9; + + x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0; + x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1; + x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2; + x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3; + x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4; + x5 = swap & (a[5] ^ b[5]); a[5] ^= x5; b[5] ^= x5; + x6 = swap & (a[6] ^ b[6]); a[6] ^= x6; b[6] ^= x6; + x7 = swap & (a[7] ^ b[7]); a[7] ^= x7; b[7] ^= x7; + x8 = swap & (a[8] ^ b[8]); a[8] ^= x8; b[8] ^= x8; + x9 = swap & (a[9] ^ b[9]); a[9] ^= x9; b[9] ^= x9; +} diff --git a/src/ext/ed25519/donna/curve25519-donna-64bit.h b/src/ext/ed25519/donna/curve25519-donna-64bit.h new file mode 100644 index 0000000..2941d1b --- /dev/null +++ b/src/ext/ed25519/donna/curve25519-donna-64bit.h @@ -0,0 +1,413 @@ +/* + Public domain by Adam Langley agl@imperialviolet.org & + Andrew M. liquidsun@gmail.com + See: https://github.com/floodyberry/curve25519-donna + + 64bit integer curve25519 implementation +*/ + +typedef uint64_t bignum25519[5]; + +static const uint64_t reduce_mask_40 = ((uint64_t)1 << 40) - 1; +static const uint64_t reduce_mask_51 = ((uint64_t)1 << 51) - 1; +static const uint64_t reduce_mask_56 = ((uint64_t)1 << 56) - 1; + +/* out = in */ +DONNA_INLINE static void +curve25519_copy(bignum25519 out, const bignum25519 in) { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + out[4] = in[4]; +} + +/* out = a + b */ +DONNA_INLINE static void +curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) { + out[0] = a[0] + b[0]; + out[1] = a[1] + b[1]; + out[2] = a[2] + b[2]; + out[3] = a[3] + b[3]; + out[4] = a[4] + b[4]; +} + +/* out = a + b, where a and/or b are the result of a basic op (add,sub) */ +DONNA_INLINE static void +curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) { + out[0] = a[0] + b[0]; + out[1] = a[1] + b[1]; + out[2] = a[2] + b[2]; + out[3] = a[3] + b[3]; + out[4] = a[4] + b[4]; +} + +DONNA_INLINE static void +curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) { + uint64_t c; + out[0] = a[0] + b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51; + out[1] = a[1] + b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51; + out[2] = a[2] + b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51; + out[3] = a[3] + b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51; + out[4] = a[4] + b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51; + out[0] += c * 19; +} + +/* multiples of p */ +static const uint64_t twoP0 = 0x0fffffffffffda; +static const uint64_t twoP1234 = 0x0ffffffffffffe; +static const uint64_t fourP0 = 0x1fffffffffffb4; +static const uint64_t fourP1234 = 0x1ffffffffffffc; + +/* out = a - b */ +DONNA_INLINE static void +curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) { + out[0] = a[0] + twoP0 - b[0]; + out[1] = a[1] + twoP1234 - b[1]; + out[2] = a[2] + twoP1234 - b[2]; + out[3] = a[3] + twoP1234 - b[3]; + out[4] = a[4] + twoP1234 - b[4]; +} + +/* out = a - b, where a and/or b are the result of a basic op (add,sub) */ +DONNA_INLINE static void +curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) { + out[0] = a[0] + fourP0 - b[0]; + out[1] = a[1] + fourP1234 - b[1]; + out[2] = a[2] + fourP1234 - b[2]; + out[3] = a[3] + fourP1234 - b[3]; + out[4] = a[4] + fourP1234 - b[4]; +} + +DONNA_INLINE static void +curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) { + uint64_t c; + out[0] = a[0] + fourP0 - b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51; + out[1] = a[1] + fourP1234 - b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51; + out[2] = a[2] + fourP1234 - b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51; + out[3] = a[3] + fourP1234 - b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51; + out[4] = a[4] + fourP1234 - b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51; + out[0] += c * 19; +} + +/* out = -a */ +DONNA_INLINE static void +curve25519_neg(bignum25519 out, const bignum25519 a) { + uint64_t c; + out[0] = twoP0 - a[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51; + out[1] = twoP1234 - a[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51; + out[2] = twoP1234 - a[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51; + out[3] = twoP1234 - a[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51; + out[4] = twoP1234 - a[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51; + out[0] += c * 19; +} + +/* out = a * b */ +DONNA_INLINE static void +curve25519_mul(bignum25519 out, const bignum25519 in2, const bignum25519 in) { +#if !defined(HAVE_NATIVE_UINT128) + uint128_t mul; +#endif + uint128_t t[5]; + uint64_t r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c; + + r0 = in[0]; + r1 = in[1]; + r2 = in[2]; + r3 = in[3]; + r4 = in[4]; + + s0 = in2[0]; + s1 = in2[1]; + s2 = in2[2]; + s3 = in2[3]; + s4 = in2[4]; + +#if defined(HAVE_NATIVE_UINT128) + t[0] = ((uint128_t) r0) * s0; + t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0; + t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1; + t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1; + t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2; +#else + mul64x64_128(t[0], r0, s0) + mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul) + mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul) + mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul) + mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul) +#endif + + r1 *= 19; + r2 *= 19; + r3 *= 19; + r4 *= 19; + +#if defined(HAVE_NATIVE_UINT128) + t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2; + t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3; + t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4; + t[3] += ((uint128_t) r4) * s4; +#else + mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul) + mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul) + mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul) + mul64x64_128(mul, r4, s4) add128(t[3], mul) +#endif + + + r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51); + add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51); + add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51); + add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51); + add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51); + r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51; + r1 += c; + + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + out[4] = r4; +} + +DONNA_NOINLINE static void +curve25519_mul_noinline(bignum25519 out, const bignum25519 in2, const bignum25519 in) { + curve25519_mul(out, in2, in); +} + +/* out = in^(2 * count) */ +DONNA_NOINLINE static void +curve25519_square_times(bignum25519 out, const bignum25519 in, uint64_t count) { +#if !defined(HAVE_NATIVE_UINT128) + uint128_t mul; +#endif + uint128_t t[5]; + uint64_t r0,r1,r2,r3,r4,c; + uint64_t d0,d1,d2,d4,d419; + + r0 = in[0]; + r1 = in[1]; + r2 = in[2]; + r3 = in[3]; + r4 = in[4]; + + do { + d0 = r0 * 2; + d1 = r1 * 2; + d2 = r2 * 2 * 19; + d419 = r4 * 19; + d4 = d419 * 2; + +#if defined(HAVE_NATIVE_UINT128) + t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 )); + t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19)); + t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 )); + t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 )); + t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 )); +#else + mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul) + mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul) + mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul) + mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul) + mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul) +#endif + + r0 = lo128(t[0]) & reduce_mask_51; + r1 = lo128(t[1]) & reduce_mask_51; shl128(c, t[0], 13); r1 += c; + r2 = lo128(t[2]) & reduce_mask_51; shl128(c, t[1], 13); r2 += c; + r3 = lo128(t[3]) & reduce_mask_51; shl128(c, t[2], 13); r3 += c; + r4 = lo128(t[4]) & reduce_mask_51; shl128(c, t[3], 13); r4 += c; + shl128(c, t[4], 13); r0 += c * 19; + c = r0 >> 51; r0 &= reduce_mask_51; + r1 += c ; c = r1 >> 51; r1 &= reduce_mask_51; + r2 += c ; c = r2 >> 51; r2 &= reduce_mask_51; + r3 += c ; c = r3 >> 51; r3 &= reduce_mask_51; + r4 += c ; c = r4 >> 51; r4 &= reduce_mask_51; + r0 += c * 19; + } while(--count); + + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + out[4] = r4; +} + +DONNA_INLINE static void +curve25519_square(bignum25519 out, const bignum25519 in) { +#if !defined(HAVE_NATIVE_UINT128) + uint128_t mul; +#endif + uint128_t t[5]; + uint64_t r0,r1,r2,r3,r4,c; + uint64_t d0,d1,d2,d4,d419; + + r0 = in[0]; + r1 = in[1]; + r2 = in[2]; + r3 = in[3]; + r4 = in[4]; + + d0 = r0 * 2; + d1 = r1 * 2; + d2 = r2 * 2 * 19; + d419 = r4 * 19; + d4 = d419 * 2; + +#if defined(HAVE_NATIVE_UINT128) + t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 )); + t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19)); + t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 )); + t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 )); + t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 )); +#else + mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul) + mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul) + mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul) + mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul) + mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul) +#endif + + r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51); + add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51); + add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51); + add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51); + add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51); + r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51; + r1 += c; + + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + out[4] = r4; +} + +/* Take a little-endian, 32-byte number and expand it into polynomial form */ +DONNA_INLINE static void +curve25519_expand(bignum25519 out, const unsigned char *in) { + static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}}; + uint64_t x0,x1,x2,x3; + + if (endian_check.s == 1) { + x0 = *(uint64_t *)(in + 0); + x1 = *(uint64_t *)(in + 8); + x2 = *(uint64_t *)(in + 16); + x3 = *(uint64_t *)(in + 24); + } else { + #define F(s) \ + ((((uint64_t)in[s + 0]) ) | \ + (((uint64_t)in[s + 1]) << 8) | \ + (((uint64_t)in[s + 2]) << 16) | \ + (((uint64_t)in[s + 3]) << 24) | \ + (((uint64_t)in[s + 4]) << 32) | \ + (((uint64_t)in[s + 5]) << 40) | \ + (((uint64_t)in[s + 6]) << 48) | \ + (((uint64_t)in[s + 7]) << 56)) + + x0 = F(0); + x1 = F(8); + x2 = F(16); + x3 = F(24); + } + + out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13); + out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26); + out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39); + out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12); + out[4] = x3 & reduce_mask_51; +} + +/* Take a fully reduced polynomial form number and contract it into a + * little-endian, 32-byte array + */ +DONNA_INLINE static void +curve25519_contract(unsigned char *out, const bignum25519 input) { + uint64_t t[5]; + uint64_t f, i; + + t[0] = input[0]; + t[1] = input[1]; + t[2] = input[2]; + t[3] = input[3]; + t[4] = input[4]; + + #define curve25519_contract_carry() \ + t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \ + t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \ + t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \ + t[4] += t[3] >> 51; t[3] &= reduce_mask_51; + + #define curve25519_contract_carry_full() curve25519_contract_carry() \ + t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51; + + #define curve25519_contract_carry_final() curve25519_contract_carry() \ + t[4] &= reduce_mask_51; + + curve25519_contract_carry_full() + curve25519_contract_carry_full() + + /* now t is between 0 and 2^255-1, properly carried. */ + /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */ + t[0] += 19; + curve25519_contract_carry_full() + + /* now between 19 and 2^255-1 in both cases, and offset by 19. */ + t[0] += (reduce_mask_51 + 1) - 19; + t[1] += (reduce_mask_51 + 1) - 1; + t[2] += (reduce_mask_51 + 1) - 1; + t[3] += (reduce_mask_51 + 1) - 1; + t[4] += (reduce_mask_51 + 1) - 1; + + /* now between 2^255 and 2^256-20, and offset by 2^255. */ + curve25519_contract_carry_final() + + #define write51full(n,shift) \ + f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \ + for (i = 0; i < 8; i++, f >>= 8) *out++ = (unsigned char)f; + #define write51(n) write51full(n,13*n) + write51(0) + write51(1) + write51(2) + write51(3) +} + +#if !defined(ED25519_GCC_64BIT_CHOOSE) + +/* out = (flag) ? in : out */ +DONNA_INLINE static void +curve25519_move_conditional_bytes(uint8_t out[96], const uint8_t in[96], uint64_t flag) { + const uint64_t nb = flag - 1, b = ~nb; + const uint64_t *inq = (const uint64_t *)in; + uint64_t *outq = (uint64_t *)out; + outq[0] = (outq[0] & nb) | (inq[0] & b); + outq[1] = (outq[1] & nb) | (inq[1] & b); + outq[2] = (outq[2] & nb) | (inq[2] & b); + outq[3] = (outq[3] & nb) | (inq[3] & b); + outq[4] = (outq[4] & nb) | (inq[4] & b); + outq[5] = (outq[5] & nb) | (inq[5] & b); + outq[6] = (outq[6] & nb) | (inq[6] & b); + outq[7] = (outq[7] & nb) | (inq[7] & b); + outq[8] = (outq[8] & nb) | (inq[8] & b); + outq[9] = (outq[9] & nb) | (inq[9] & b); + outq[10] = (outq[10] & nb) | (inq[10] & b); + outq[11] = (outq[11] & nb) | (inq[11] & b); +} + +/* if (iswap) swap(a, b) */ +DONNA_INLINE static void +curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint64_t iswap) { + const uint64_t swap = (uint64_t)(-(int64_t)iswap); + uint64_t x0,x1,x2,x3,x4; + + x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0; + x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1; + x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2; + x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3; + x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4; +} + +#endif /* ED25519_GCC_64BIT_CHOOSE */ + +#define ED25519_64BIT_TABLES + diff --git a/src/ext/ed25519/donna/curve25519-donna-helpers.h b/src/ext/ed25519/donna/curve25519-donna-helpers.h new file mode 100644 index 0000000..e4058ff --- /dev/null +++ b/src/ext/ed25519/donna/curve25519-donna-helpers.h @@ -0,0 +1,67 @@ +/* + Public domain by Andrew M. liquidsun@gmail.com + See: https://github.com/floodyberry/curve25519-donna + + Curve25519 implementation agnostic helpers +*/ + +/* + * In: b = 2^5 - 2^0 + * Out: b = 2^250 - 2^0 + */ +static void +curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) { + bignum25519 ALIGN(16) t0,c; + + /* 2^5 - 2^0 */ /* b */ + /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5); + /* 2^10 - 2^0 */ curve25519_mul_noinline(b, t0, b); + /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10); + /* 2^20 - 2^0 */ curve25519_mul_noinline(c, t0, b); + /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20); + /* 2^40 - 2^0 */ curve25519_mul_noinline(t0, t0, c); + /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10); + /* 2^50 - 2^0 */ curve25519_mul_noinline(b, t0, b); + /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50); + /* 2^100 - 2^0 */ curve25519_mul_noinline(c, t0, b); + /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100); + /* 2^200 - 2^0 */ curve25519_mul_noinline(t0, t0, c); + /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50); + /* 2^250 - 2^0 */ curve25519_mul_noinline(b, t0, b); +} + +/* + * z^(p - 2) = z(2^255 - 21) + */ +static void +curve25519_recip(bignum25519 out, const bignum25519 z) { + bignum25519 ALIGN(16) a,t0,b; + + /* 2 */ curve25519_square_times(a, z, 1); /* a = 2 */ + /* 8 */ curve25519_square_times(t0, a, 2); + /* 9 */ curve25519_mul_noinline(b, t0, z); /* b = 9 */ + /* 11 */ curve25519_mul_noinline(a, b, a); /* a = 11 */ + /* 22 */ curve25519_square_times(t0, a, 1); + /* 2^5 - 2^0 = 31 */ curve25519_mul_noinline(b, t0, b); + /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b); + /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5); + /* 2^255 - 21 */ curve25519_mul_noinline(out, b, a); +} + +/* + * z^((p-5)/8) = z^(2^252 - 3) + */ +static void +curve25519_pow_two252m3(bignum25519 two252m3, const bignum25519 z) { + bignum25519 ALIGN(16) b,c,t0; + + /* 2 */ curve25519_square_times(c, z, 1); /* c = 2 */ + /* 8 */ curve25519_square_times(t0, c, 2); /* t0 = 8 */ + /* 9 */ curve25519_mul_noinline(b, t0, z); /* b = 9 */ + /* 11 */ curve25519_mul_noinline(c, b, c); /* c = 11 */ + /* 22 */ curve25519_square_times(t0, c, 1); + /* 2^5 - 2^0 = 31 */ curve25519_mul_noinline(b, t0, b); + /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b); + /* 2^252 - 2^2 */ curve25519_square_times(b, b, 2); + /* 2^252 - 3 */ curve25519_mul_noinline(two252m3, b, z); +} diff --git a/src/ext/ed25519/donna/curve25519-donna-sse2.h b/src/ext/ed25519/donna/curve25519-donna-sse2.h new file mode 100644 index 0000000..1dbfd44 --- /dev/null +++ b/src/ext/ed25519/donna/curve25519-donna-sse2.h @@ -0,0 +1,1112 @@ +/* + Public domain by Andrew M. liquidsun@gmail.com + See: https://github.com/floodyberry/curve25519-donna + + SSE2 curve25519 implementation +*/ + +#include <emmintrin.h> +typedef __m128i xmmi; + +typedef union packedelem8_t { + unsigned char u[16]; + xmmi v; +} packedelem8; + +typedef union packedelem32_t { + uint32_t u[4]; + xmmi v; +} packedelem32; + +typedef union packedelem64_t { + uint64_t u[2]; + xmmi v; +} packedelem64; + +/* 10 elements + an extra 2 to fit in 3 xmm registers */ +typedef uint32_t bignum25519[12]; +typedef packedelem32 packed32bignum25519[5]; +typedef packedelem64 packed64bignum25519[10]; + +static const packedelem32 bot32bitmask = {{0xffffffff, 0x00000000, 0xffffffff, 0x00000000}}; +static const packedelem32 top32bitmask = {{0x00000000, 0xffffffff, 0x00000000, 0xffffffff}}; +static const packedelem32 top64bitmask = {{0x00000000, 0x00000000, 0xffffffff, 0xffffffff}}; +static const packedelem32 bot64bitmask = {{0xffffffff, 0xffffffff, 0x00000000, 0x00000000}}; + +/* reduction masks */ +static const packedelem64 packedmask26 = {{0x03ffffff, 0x03ffffff}}; +static const packedelem64 packedmask25 = {{0x01ffffff, 0x01ffffff}}; +static const packedelem32 packedmask2625 = {{0x3ffffff,0,0x1ffffff,0}}; +static const packedelem32 packedmask26262626 = {{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff}}; +static const packedelem32 packedmask25252525 = {{0x01ffffff, 0x01ffffff, 0x01ffffff, 0x01ffffff}}; + +/* multipliers */ +static const packedelem64 packednineteen = {{19, 19}}; +static const packedelem64 packednineteenone = {{19, 1}}; +static const packedelem64 packedthirtyeight = {{38, 38}}; +static const packedelem64 packed3819 = {{19*2,19}}; +static const packedelem64 packed9638 = {{19*4,19*2}}; + +/* 121666,121665 */ +static const packedelem64 packed121666121665 = {{121666, 121665}}; + +/* 2*(2^255 - 19) = 0 mod p */ +static const packedelem32 packed2p0 = {{0x7ffffda,0x3fffffe,0x7fffffe,0x3fffffe}}; +static const packedelem32 packed2p1 = {{0x7fffffe,0x3fffffe,0x7fffffe,0x3fffffe}}; +static const packedelem32 packed2p2 = {{0x7fffffe,0x3fffffe,0x0000000,0x0000000}}; + +static const packedelem32 packed32packed2p0 = {{0x7ffffda,0x7ffffda,0x3fffffe,0x3fffffe}}; +static const packedelem32 packed32packed2p1 = {{0x7fffffe,0x7fffffe,0x3fffffe,0x3fffffe}}; + +/* 4*(2^255 - 19) = 0 mod p */ +static const packedelem32 packed4p0 = {{0xfffffb4,0x7fffffc,0xffffffc,0x7fffffc}}; +static const packedelem32 packed4p1 = {{0xffffffc,0x7fffffc,0xffffffc,0x7fffffc}}; +static const packedelem32 packed4p2 = {{0xffffffc,0x7fffffc,0x0000000,0x0000000}}; + +static const packedelem32 packed32packed4p0 = {{0xfffffb4,0xfffffb4,0x7fffffc,0x7fffffc}}; +static const packedelem32 packed32packed4p1 = {{0xffffffc,0xffffffc,0x7fffffc,0x7fffffc}}; + +/* out = in */ +DONNA_INLINE static void +curve25519_copy(bignum25519 out, const bignum25519 in) { + xmmi x0,x1,x2; + x0 = _mm_load_si128((xmmi*)in + 0); + x1 = _mm_load_si128((xmmi*)in + 1); + x2 = _mm_load_si128((xmmi*)in + 2); + _mm_store_si128((xmmi*)out + 0, x0); + _mm_store_si128((xmmi*)out + 1, x1); + _mm_store_si128((xmmi*)out + 2, x2); +} + +/* out = a + b */ +DONNA_INLINE static void +curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) { + xmmi a0,a1,a2,b0,b1,b2; + a0 = _mm_load_si128((xmmi*)a + 0); + a1 = _mm_load_si128((xmmi*)a + 1); + a2 = _mm_load_si128((xmmi*)a + 2); + b0 = _mm_load_si128((xmmi*)b + 0); + b1 = _mm_load_si128((xmmi*)b + 1); + b2 = _mm_load_si128((xmmi*)b + 2); + a0 = _mm_add_epi32(a0, b0); + a1 = _mm_add_epi32(a1, b1); + a2 = _mm_add_epi32(a2, b2); + _mm_store_si128((xmmi*)out + 0, a0); + _mm_store_si128((xmmi*)out + 1, a1); + _mm_store_si128((xmmi*)out + 2, a2); +} + +#define curve25519_add_after_basic curve25519_add_reduce +DONNA_INLINE static void +curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) { + xmmi a0,a1,a2,b0,b1,b2; + xmmi c1,c2,c3; + xmmi r0,r1,r2,r3,r4,r5; + + a0 = _mm_load_si128((xmmi*)a + 0); + a1 = _mm_load_si128((xmmi*)a + 1); + a2 = _mm_load_si128((xmmi*)a + 2); + b0 = _mm_load_si128((xmmi*)b + 0); + b1 = _mm_load_si128((xmmi*)b + 1); + b2 = _mm_load_si128((xmmi*)b + 2); + a0 = _mm_add_epi32(a0, b0); + a1 = _mm_add_epi32(a1, b1); + a2 = _mm_add_epi32(a2, b2); + + r0 = _mm_and_si128(_mm_unpacklo_epi64(a0, a1), bot32bitmask.v); + r1 = _mm_srli_epi64(_mm_unpacklo_epi64(a0, a1), 32); + r2 = _mm_and_si128(_mm_unpackhi_epi64(a0, a1), bot32bitmask.v); + r3 = _mm_srli_epi64(_mm_unpackhi_epi64(a0, a1), 32); + r4 = _mm_and_si128(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), bot32bitmask.v); + r5 = _mm_srli_epi64(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), 32); + + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8); + c1 = _mm_srli_epi64(r4, 26); r4 = _mm_and_si128(r4, packedmask26.v); r5 = _mm_add_epi64(r5, c1); + c1 = _mm_srli_epi64(r5, 25); r5 = _mm_and_si128(r5, packedmask25.v); r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3)); + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + + _mm_store_si128((xmmi*)out + 0, _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpacklo_epi32(r2, r3))); + _mm_store_si128((xmmi*)out + 1, _mm_unpacklo_epi64(_mm_unpackhi_epi32(r0, r1), _mm_unpackhi_epi32(r2, r3))); + _mm_store_si128((xmmi*)out + 2, _mm_unpackhi_epi32(r4, r5)); +} + +DONNA_INLINE static void +curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) { + xmmi a0,a1,a2,b0,b1,b2; + xmmi c1,c2; + xmmi r0,r1; + + a0 = _mm_load_si128((xmmi*)a + 0); + a1 = _mm_load_si128((xmmi*)a + 1); + a2 = _mm_load_si128((xmmi*)a + 2); + a0 = _mm_add_epi32(a0, packed2p0.v); + a1 = _mm_add_epi32(a1, packed2p1.v); + a2 = _mm_add_epi32(a2, packed2p2.v); + b0 = _mm_load_si128((xmmi*)b + 0); + b1 = _mm_load_si128((xmmi*)b + 1); + b2 = _mm_load_si128((xmmi*)b + 2); + a0 = _mm_sub_epi32(a0, b0); + a1 = _mm_sub_epi32(a1, b1); + a2 = _mm_sub_epi32(a2, b2); + + r0 = _mm_and_si128(_mm_shuffle_epi32(a0, _MM_SHUFFLE(2,2,0,0)), bot32bitmask.v); + r1 = _mm_and_si128(_mm_shuffle_epi32(a0, _MM_SHUFFLE(3,3,1,1)), bot32bitmask.v); + + c1 = _mm_srli_epi32(r0, 26); + c2 = _mm_srli_epi32(r1, 25); + r0 = _mm_and_si128(r0, packedmask26.v); + r1 = _mm_and_si128(r1, packedmask25.v); + r0 = _mm_add_epi32(r0, _mm_slli_si128(c2, 8)); + r1 = _mm_add_epi32(r1, c1); + + a0 = _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpackhi_epi32(r0, r1)); + a1 = _mm_add_epi32(a1, _mm_srli_si128(c2, 8)); + + _mm_store_si128((xmmi*)out + 0, a0); + _mm_store_si128((xmmi*)out + 1, a1); + _mm_store_si128((xmmi*)out + 2, a2); +} + +DONNA_INLINE static void +curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) { + xmmi a0,a1,a2,b0,b1,b2; + xmmi c1,c2,c3; + xmmi r0,r1,r2,r3,r4,r5; + + a0 = _mm_load_si128((xmmi*)a + 0); + a1 = _mm_load_si128((xmmi*)a + 1); + a2 = _mm_load_si128((xmmi*)a + 2); + a0 = _mm_add_epi32(a0, packed4p0.v); + a1 = _mm_add_epi32(a1, packed4p1.v); + a2 = _mm_add_epi32(a2, packed4p2.v); + b0 = _mm_load_si128((xmmi*)b + 0); + b1 = _mm_load_si128((xmmi*)b + 1); + b2 = _mm_load_si128((xmmi*)b + 2); + a0 = _mm_sub_epi32(a0, b0); + a1 = _mm_sub_epi32(a1, b1); + a2 = _mm_sub_epi32(a2, b2); + + r0 = _mm_and_si128(_mm_unpacklo_epi64(a0, a1), bot32bitmask.v); + r1 = _mm_srli_epi64(_mm_unpacklo_epi64(a0, a1), 32); + r2 = _mm_and_si128(_mm_unpackhi_epi64(a0, a1), bot32bitmask.v); + r3 = _mm_srli_epi64(_mm_unpackhi_epi64(a0, a1), 32); + r4 = _mm_and_si128(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), bot32bitmask.v); + r5 = _mm_srli_epi64(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), 32); + + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8); + c1 = _mm_srli_epi64(r4, 26); r4 = _mm_and_si128(r4, packedmask26.v); r5 = _mm_add_epi64(r5, c1); + c1 = _mm_srli_epi64(r5, 25); r5 = _mm_and_si128(r5, packedmask25.v); r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3)); + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + + _mm_store_si128((xmmi*)out + 0, _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpacklo_epi32(r2, r3))); + _mm_store_si128((xmmi*)out + 1, _mm_unpacklo_epi64(_mm_unpackhi_epi32(r0, r1), _mm_unpackhi_epi32(r2, r3))); + _mm_store_si128((xmmi*)out + 2, _mm_unpackhi_epi32(r4, r5)); +} + +DONNA_INLINE static void +curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) { + xmmi a0,a1,a2,b0,b1,b2; + xmmi c1,c2,c3; + xmmi r0,r1,r2,r3,r4,r5; + + a0 = _mm_load_si128((xmmi*)a + 0); + a1 = _mm_load_si128((xmmi*)a + 1); + a2 = _mm_load_si128((xmmi*)a + 2); + a0 = _mm_add_epi32(a0, packed2p0.v); + a1 = _mm_add_epi32(a1, packed2p1.v); + a2 = _mm_add_epi32(a2, packed2p2.v); + b0 = _mm_load_si128((xmmi*)b + 0); + b1 = _mm_load_si128((xmmi*)b + 1); + b2 = _mm_load_si128((xmmi*)b + 2); + a0 = _mm_sub_epi32(a0, b0); + a1 = _mm_sub_epi32(a1, b1); + a2 = _mm_sub_epi32(a2, b2); + + r0 = _mm_and_si128(_mm_unpacklo_epi64(a0, a1), bot32bitmask.v); + r1 = _mm_srli_epi64(_mm_unpacklo_epi64(a0, a1), 32); + r2 = _mm_and_si128(_mm_unpackhi_epi64(a0, a1), bot32bitmask.v); + r3 = _mm_srli_epi64(_mm_unpackhi_epi64(a0, a1), 32); + r4 = _mm_and_si128(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), bot32bitmask.v); + r5 = _mm_srli_epi64(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), 32); + + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8); + c1 = _mm_srli_epi64(r4, 26); r4 = _mm_and_si128(r4, packedmask26.v); r5 = _mm_add_epi64(r5, c1); + c1 = _mm_srli_epi64(r5, 25); r5 = _mm_and_si128(r5, packedmask25.v); r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3)); + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + + _mm_store_si128((xmmi*)out + 0, _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpacklo_epi32(r2, r3))); + _mm_store_si128((xmmi*)out + 1, _mm_unpacklo_epi64(_mm_unpackhi_epi32(r0, r1), _mm_unpackhi_epi32(r2, r3))); + _mm_store_si128((xmmi*)out + 2, _mm_unpackhi_epi32(r4, r5)); +} + + +DONNA_INLINE static void +curve25519_neg(bignum25519 out, const bignum25519 b) { + xmmi a0,a1,a2,b0,b1,b2; + xmmi c1,c2,c3; + xmmi r0,r1,r2,r3,r4,r5; + + a0 = packed2p0.v; + a1 = packed2p1.v; + a2 = packed2p2.v; + b0 = _mm_load_si128((xmmi*)b + 0); + b1 = _mm_load_si128((xmmi*)b + 1); + b2 = _mm_load_si128((xmmi*)b + 2); + a0 = _mm_sub_epi32(a0, b0); + a1 = _mm_sub_epi32(a1, b1); + a2 = _mm_sub_epi32(a2, b2); + + r0 = _mm_and_si128(_mm_unpacklo_epi64(a0, a1), bot32bitmask.v); + r1 = _mm_srli_epi64(_mm_unpacklo_epi64(a0, a1), 32); + r2 = _mm_and_si128(_mm_unpackhi_epi64(a0, a1), bot32bitmask.v); + r3 = _mm_srli_epi64(_mm_unpackhi_epi64(a0, a1), 32); + r4 = _mm_and_si128(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), bot32bitmask.v); + r5 = _mm_srli_epi64(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), 32); + + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8); + c1 = _mm_srli_epi64(r4, 26); r4 = _mm_and_si128(r4, packedmask26.v); r5 = _mm_add_epi64(r5, c1); + c1 = _mm_srli_epi64(r5, 25); r5 = _mm_and_si128(r5, packedmask25.v); r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3)); + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + + _mm_store_si128((xmmi*)out + 0, _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpacklo_epi32(r2, r3))); + _mm_store_si128((xmmi*)out + 1, _mm_unpacklo_epi64(_mm_unpackhi_epi32(r0, r1), _mm_unpackhi_epi32(r2, r3))); + _mm_store_si128((xmmi*)out + 2, _mm_unpackhi_epi32(r4, r5)); +} + + +/* Multiply two numbers: out = in2 * in */ +static void +curve25519_mul(bignum25519 out, const bignum25519 r, const bignum25519 s) { + xmmi m01,m23,m45,m67,m89; + xmmi m0123,m4567; + xmmi s0123,s4567; + xmmi s01,s23,s45,s67,s89; + xmmi s12,s34,s56,s78,s9; + xmmi r0,r2,r4,r6,r8; + xmmi r1,r3,r5,r7,r9; + xmmi r119,r219,r319,r419,r519,r619,r719,r819,r919; + xmmi c1,c2,c3; + + s0123 = _mm_load_si128((xmmi*)s + 0); + s01 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,1,2,0)); + s12 = _mm_shuffle_epi32(s0123, _MM_SHUFFLE(2,2,1,1)); + s23 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,3,2,2)); + s4567 = _mm_load_si128((xmmi*)s + 1); + s34 = _mm_unpacklo_epi64(_mm_srli_si128(s0123,12),s4567); + s45 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,1,2,0)); + s56 = _mm_shuffle_epi32(s4567, _MM_SHUFFLE(2,2,1,1)); + s67 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,3,2,2)); + s89 = _mm_load_si128((xmmi*)s + 2); + s78 = _mm_unpacklo_epi64(_mm_srli_si128(s4567,12),s89); + s89 = _mm_shuffle_epi32(s89,_MM_SHUFFLE(3,1,2,0)); + s9 = _mm_shuffle_epi32(s89, _MM_SHUFFLE(3,3,2,2)); + + r0 = _mm_load_si128((xmmi*)r + 0); + r1 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(1,1,1,1)); + r1 = _mm_add_epi64(r1, _mm_and_si128(r1, top64bitmask.v)); + r2 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(2,2,2,2)); + r3 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(3,3,3,3)); + r3 = _mm_add_epi64(r3, _mm_and_si128(r3, top64bitmask.v)); + r0 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(0,0,0,0)); + r4 = _mm_load_si128((xmmi*)r + 1); + r5 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(1,1,1,1)); + r5 = _mm_add_epi64(r5, _mm_and_si128(r5, top64bitmask.v)); + r6 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(2,2,2,2)); + r7 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(3,3,3,3)); + r7 = _mm_add_epi64(r7, _mm_and_si128(r7, top64bitmask.v)); + r4 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(0,0,0,0)); + r8 = _mm_load_si128((xmmi*)r + 2); + r9 = _mm_shuffle_epi32(r8, _MM_SHUFFLE(3,1,3,1)); + r9 = _mm_add_epi64(r9, _mm_and_si128(r9, top64bitmask.v)); + r8 = _mm_shuffle_epi32(r8, _MM_SHUFFLE(3,0,3,0)); + + m01 = _mm_mul_epu32(r1,s01); + m23 = _mm_mul_epu32(r1,s23); + m45 = _mm_mul_epu32(r1,s45); + m67 = _mm_mul_epu32(r1,s67); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r3,s01)); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r3,s23)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r3,s45)); + m89 = _mm_mul_epu32(r1,s89); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r5,s01)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r5,s23)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r3,s67)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r7,s01)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r5,s45)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r7,s23)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r9,s01)); + + /* shift up */ + m89 = _mm_unpackhi_epi64(m67,_mm_slli_si128(m89,8)); + m67 = _mm_unpackhi_epi64(m45,_mm_slli_si128(m67,8)); + m45 = _mm_unpackhi_epi64(m23,_mm_slli_si128(m45,8)); + m23 = _mm_unpackhi_epi64(m01,_mm_slli_si128(m23,8)); + m01 = _mm_unpackhi_epi64(_mm_setzero_si128(),_mm_slli_si128(m01,8)); + + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r0,s01)); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r0,s23)); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r0,s45)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r0,s67)); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r2,s01)); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r2,s23)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r4,s23)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r0,s89)); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r4,s01)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r2,s45)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r2,s67)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r6,s01)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r4,s45)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r6,s23)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r8,s01)); + + r219 = _mm_mul_epu32(r2, packednineteen.v); + r419 = _mm_mul_epu32(r4, packednineteen.v); + r619 = _mm_mul_epu32(r6, packednineteen.v); + r819 = _mm_mul_epu32(r8, packednineteen.v); + r119 = _mm_shuffle_epi32(r1,_MM_SHUFFLE(0,0,2,2)); r119 = _mm_mul_epu32(r119, packednineteen.v); + r319 = _mm_shuffle_epi32(r3,_MM_SHUFFLE(0,0,2,2)); r319 = _mm_mul_epu32(r319, packednineteen.v); + r519 = _mm_shuffle_epi32(r5,_MM_SHUFFLE(0,0,2,2)); r519 = _mm_mul_epu32(r519, packednineteen.v); + r719 = _mm_shuffle_epi32(r7,_MM_SHUFFLE(0,0,2,2)); r719 = _mm_mul_epu32(r719, packednineteen.v); + r919 = _mm_shuffle_epi32(r9,_MM_SHUFFLE(0,0,2,2)); r919 = _mm_mul_epu32(r919, packednineteen.v); + + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r919,s12)); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r919,s34)); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r919,s56)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r919,s78)); + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r719,s34)); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r719,s56)); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r719,s78)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r719,s9)); + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r519,s56)); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r519,s78)); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r519,s9)); + m67 = _mm_add_epi64(m67,_mm_mul_epu32(r819,s89)); + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r319,s78)); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r319,s9)); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r619,s89)); + m89 = _mm_add_epi64(m89,_mm_mul_epu32(r919,s9)); + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r819,s23)); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r819,s45)); + m45 = _mm_add_epi64(m45,_mm_mul_epu32(r819,s67)); + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r619,s45)); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r619,s67)); + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r419,s67)); + m23 = _mm_add_epi64(m23,_mm_mul_epu32(r419,s89)); + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r219,s89)); + m01 = _mm_add_epi64(m01,_mm_mul_epu32(r119,s9)); + + r0 = _mm_unpacklo_epi64(m01, m45); + r1 = _mm_unpackhi_epi64(m01, m45); + r2 = _mm_unpacklo_epi64(m23, m67); + r3 = _mm_unpackhi_epi64(m23, m67); + r4 = _mm_unpacklo_epi64(m89, m89); + r5 = _mm_unpackhi_epi64(m89, m89); + + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8); + c1 = _mm_srli_epi64(r4, 26); r4 = _mm_and_si128(r4, packedmask26.v); r5 = _mm_add_epi64(r5, c1); + c1 = _mm_srli_epi64(r5, 25); r5 = _mm_and_si128(r5, packedmask25.v); r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3)); + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + + m0123 = _mm_unpacklo_epi32(r0, r1); + m4567 = _mm_unpackhi_epi32(r0, r1); + m0123 = _mm_unpacklo_epi64(m0123, _mm_unpacklo_epi32(r2, r3)); + m4567 = _mm_unpacklo_epi64(m4567, _mm_unpackhi_epi32(r2, r3)); + m89 = _mm_unpackhi_epi32(r4, r5); + + _mm_store_si128((xmmi*)out + 0, m0123); + _mm_store_si128((xmmi*)out + 1, m4567); + _mm_store_si128((xmmi*)out + 2, m89); +} + +DONNA_NOINLINE static void +curve25519_mul_noinline(bignum25519 out, const bignum25519 r, const bignum25519 s) { + curve25519_mul(out, r, s); +} + +#define curve25519_square(r, n) curve25519_square_times(r, n, 1) +static void +curve25519_square_times(bignum25519 r, const bignum25519 in, int count) { + xmmi m01,m23,m45,m67,m89; + xmmi r0,r1,r2,r3,r4,r5,r6,r7,r8,r9; + xmmi r0a,r1a,r2a,r3a,r7a,r9a; + xmmi r0123,r4567; + xmmi r01,r23,r45,r67,r6x,r89,r8x; + xmmi r12,r34,r56,r78,r9x; + xmmi r5619; + xmmi c1,c2,c3; + + r0123 = _mm_load_si128((xmmi*)in + 0); + r01 = _mm_shuffle_epi32(r0123,_MM_SHUFFLE(3,1,2,0)); + r23 = _mm_shuffle_epi32(r0123,_MM_SHUFFLE(3,3,2,2)); + r4567 = _mm_load_si128((xmmi*)in + 1); + r45 = _mm_shuffle_epi32(r4567,_MM_SHUFFLE(3,1,2,0)); + r67 = _mm_shuffle_epi32(r4567,_MM_SHUFFLE(3,3,2,2)); + r89 = _mm_load_si128((xmmi*)in + 2); + r89 = _mm_shuffle_epi32(r89,_MM_SHUFFLE(3,1,2,0)); + + do { + r12 = _mm_unpackhi_epi64(r01, _mm_slli_si128(r23, 8)); + r0 = _mm_shuffle_epi32(r01, _MM_SHUFFLE(0,0,0,0)); + r0 = _mm_add_epi64(r0, _mm_and_si128(r0, top64bitmask.v)); + r0a = _mm_shuffle_epi32(r0,_MM_SHUFFLE(3,2,1,2)); + r1 = _mm_shuffle_epi32(r01, _MM_SHUFFLE(2,2,2,2)); + r2 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(0,0,0,0)); + r2 = _mm_add_epi64(r2, _mm_and_si128(r2, top64bitmask.v)); + r2a = _mm_shuffle_epi32(r2,_MM_SHUFFLE(3,2,1,2)); + r3 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(2,2,2,2)); + r34 = _mm_unpackhi_epi64(r23, _mm_slli_si128(r45, 8)); + r4 = _mm_shuffle_epi32(r45, _MM_SHUFFLE(0,0,0,0)); + r4 = _mm_add_epi64(r4, _mm_and_si128(r4, top64bitmask.v)); + r56 = _mm_unpackhi_epi64(r45, _mm_slli_si128(r67, 8)); + r5619 = _mm_mul_epu32(r56, packednineteen.v); + r5 = _mm_shuffle_epi32(r5619, _MM_SHUFFLE(1,1,1,0)); + r6 = _mm_shuffle_epi32(r5619, _MM_SHUFFLE(3,2,3,2)); + r78 = _mm_unpackhi_epi64(r67, _mm_slli_si128(r89, 8)); + r6x = _mm_unpacklo_epi64(r67, _mm_setzero_si128()); + r7 = _mm_shuffle_epi32(r67, _MM_SHUFFLE(2,2,2,2)); + r7 = _mm_mul_epu32(r7, packed3819.v); + r7a = _mm_shuffle_epi32(r7, _MM_SHUFFLE(3,3,3,2)); + r8x = _mm_unpacklo_epi64(r89, _mm_setzero_si128()); + r8 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(0,0,0,0)); + r8 = _mm_mul_epu32(r8, packednineteen.v); + r9 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(2,2,2,2)); + r9x = _mm_slli_epi32(_mm_shuffle_epi32(r89, _MM_SHUFFLE(3,3,3,2)), 1); + r9 = _mm_mul_epu32(r9, packed3819.v); + r9a = _mm_shuffle_epi32(r9, _MM_SHUFFLE(2,2,2,2)); + + m01 = _mm_mul_epu32(r01, r0); + m23 = _mm_mul_epu32(r23, r0a); + m45 = _mm_mul_epu32(r45, r0a); + m45 = _mm_add_epi64(m45, _mm_mul_epu32(r23, r2)); + r23 = _mm_slli_epi32(r23, 1); + m67 = _mm_mul_epu32(r67, r0a); + m67 = _mm_add_epi64(m67, _mm_mul_epu32(r45, r2a)); + m89 = _mm_mul_epu32(r89, r0a); + m89 = _mm_add_epi64(m89, _mm_mul_epu32(r67, r2a)); + r67 = _mm_slli_epi32(r67, 1); + m89 = _mm_add_epi64(m89, _mm_mul_epu32(r45, r4)); + r45 = _mm_slli_epi32(r45, 1); + + r1 = _mm_slli_epi32(r1, 1); + r3 = _mm_slli_epi32(r3, 1); + r1a = _mm_add_epi64(r1, _mm_and_si128(r1, bot64bitmask.v)); + r3a = _mm_add_epi64(r3, _mm_and_si128(r3, bot64bitmask.v)); + + m23 = _mm_add_epi64(m23, _mm_mul_epu32(r12, r1)); + m45 = _mm_add_epi64(m45, _mm_mul_epu32(r34, r1a)); + m67 = _mm_add_epi64(m67, _mm_mul_epu32(r56, r1a)); + m67 = _mm_add_epi64(m67, _mm_mul_epu32(r34, r3)); + r34 = _mm_slli_epi32(r34, 1); + m89 = _mm_add_epi64(m89, _mm_mul_epu32(r78, r1a)); + r78 = _mm_slli_epi32(r78, 1); + m89 = _mm_add_epi64(m89, _mm_mul_epu32(r56, r3a)); + r56 = _mm_slli_epi32(r56, 1); + + m01 = _mm_add_epi64(m01, _mm_mul_epu32(_mm_slli_epi32(r12, 1), r9)); + m01 = _mm_add_epi64(m01, _mm_mul_epu32(r34, r7)); + m23 = _mm_add_epi64(m23, _mm_mul_epu32(r34, r9)); + m01 = _mm_add_epi64(m01, _mm_mul_epu32(r56, r5)); + m23 = _mm_add_epi64(m23, _mm_mul_epu32(r56, r7)); + m45 = _mm_add_epi64(m45, _mm_mul_epu32(r56, r9)); + m01 = _mm_add_epi64(m01, _mm_mul_epu32(r23, r8)); + m01 = _mm_add_epi64(m01, _mm_mul_epu32(r45, r6)); + m23 = _mm_add_epi64(m23, _mm_mul_epu32(r45, r8)); + m23 = _mm_add_epi64(m23, _mm_mul_epu32(r6x, r6)); + m45 = _mm_add_epi64(m45, _mm_mul_epu32(r78, r7a)); + m67 = _mm_add_epi64(m67, _mm_mul_epu32(r78, r9)); + m45 = _mm_add_epi64(m45, _mm_mul_epu32(r67, r8)); + m67 = _mm_add_epi64(m67, _mm_mul_epu32(r8x, r8)); + m89 = _mm_add_epi64(m89, _mm_mul_epu32(r9x, r9a)); + + r0 = _mm_unpacklo_epi64(m01, m45); + r1 = _mm_unpackhi_epi64(m01, m45); + r2 = _mm_unpacklo_epi64(m23, m67); + r3 = _mm_unpackhi_epi64(m23, m67); + r4 = _mm_unpacklo_epi64(m89, m89); + r5 = _mm_unpackhi_epi64(m89, m89); + + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8); + c1 = _mm_srli_epi64(r4, 26); r4 = _mm_and_si128(r4, packedmask26.v); r5 = _mm_add_epi64(r5, c1); + c1 = _mm_srli_epi64(r5, 25); r5 = _mm_and_si128(r5, packedmask25.v); r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3)); + c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2); + + r01 = _mm_unpacklo_epi64(r0, r1); + r45 = _mm_unpackhi_epi64(r0, r1); + r23 = _mm_unpacklo_epi64(r2, r3); + r67 = _mm_unpackhi_epi64(r2, r3); + r89 = _mm_unpackhi_epi64(r4, r5); + } while (--count); + + r0123 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(2,0,3,3)); + r4567 = _mm_shuffle_epi32(r67, _MM_SHUFFLE(2,0,3,3)); + r0123 = _mm_or_si128(r0123, _mm_shuffle_epi32(r01, _MM_SHUFFLE(3,3,2,0))); + r4567 = _mm_or_si128(r4567, _mm_shuffle_epi32(r45, _MM_SHUFFLE(3,3,2,0))); + r89 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(3,3,2,0)); + + _mm_store_si128((xmmi*)r + 0, r0123); + _mm_store_si128((xmmi*)r + 1, r4567); + _mm_store_si128((xmmi*)r + 2, r89); +} + +DONNA_INLINE static void +curve25519_tangle32(packedelem32 *out, const bignum25519 x, const bignum25519 z) { + xmmi x0,x1,x2,z0,z1,z2; + + x0 = _mm_load_si128((xmmi *)(x + 0)); + x1 = _mm_load_si128((xmmi *)(x + 4)); + x2 = _mm_load_si128((xmmi *)(x + 8)); + z0 = _mm_load_si128((xmmi *)(z + 0)); + z1 = _mm_load_si128((xmmi *)(z + 4)); + z2 = _mm_load_si128((xmmi *)(z + 8)); + + out[0].v = _mm_unpacklo_epi32(x0, z0); + out[1].v = _mm_unpackhi_epi32(x0, z0); + out[2].v = _mm_unpacklo_epi32(x1, z1); + out[3].v = _mm_unpackhi_epi32(x1, z1); + out[4].v = _mm_unpacklo_epi32(x2, z2); +} + +DONNA_INLINE static void +curve25519_untangle32(bignum25519 x, bignum25519 z, const packedelem32 *in) { + xmmi t0,t1,t2,t3,t4,zero; + + t0 = _mm_shuffle_epi32(in[0].v, _MM_SHUFFLE(3,1,2,0)); + t1 = _mm_shuffle_epi32(in[1].v, _MM_SHUFFLE(3,1,2,0)); + t2 = _mm_shuffle_epi32(in[2].v, _MM_SHUFFLE(3,1,2,0)); + t3 = _mm_shuffle_epi32(in[3].v, _MM_SHUFFLE(3,1,2,0)); + t4 = _mm_shuffle_epi32(in[4].v, _MM_SHUFFLE(3,1,2,0)); + zero = _mm_setzero_si128(); + _mm_store_si128((xmmi *)x + 0, _mm_unpacklo_epi64(t0, t1)); + _mm_store_si128((xmmi *)x + 1, _mm_unpacklo_epi64(t2, t3)); + _mm_store_si128((xmmi *)x + 2, _mm_unpacklo_epi64(t4, zero)); + _mm_store_si128((xmmi *)z + 0, _mm_unpackhi_epi64(t0, t1)); + _mm_store_si128((xmmi *)z + 1, _mm_unpackhi_epi64(t2, t3)); + _mm_store_si128((xmmi *)z + 2, _mm_unpackhi_epi64(t4, zero)); +} + +DONNA_INLINE static void +curve25519_add_reduce_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) { + xmmi r0,r1,r2,r3,r4; + xmmi s0,s1,s2,s3,s4,s5; + xmmi c1,c2; + + r0 = _mm_add_epi32(r[0].v, s[0].v); + r1 = _mm_add_epi32(r[1].v, s[1].v); + r2 = _mm_add_epi32(r[2].v, s[2].v); + r3 = _mm_add_epi32(r[3].v, s[3].v); + r4 = _mm_add_epi32(r[4].v, s[4].v); + + s0 = _mm_unpacklo_epi64(r0, r2); /* 00 44 */ + s1 = _mm_unpackhi_epi64(r0, r2); /* 11 55 */ + s2 = _mm_unpacklo_epi64(r1, r3); /* 22 66 */ + s3 = _mm_unpackhi_epi64(r1, r3); /* 33 77 */ + s4 = _mm_unpacklo_epi64(_mm_setzero_si128(), r4); /* 00 88 */ + s5 = _mm_unpackhi_epi64(_mm_setzero_si128(), r4); /* 00 99 */ + + c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2); + c1 = _mm_srli_epi32(s1, 25); c2 = _mm_srli_epi32(s3, 25); s1 = _mm_and_si128(s1, packedmask25252525.v); s3 = _mm_and_si128(s3, packedmask25252525.v); s2 = _mm_add_epi32(s2, c1); s4 = _mm_add_epi32(s4, _mm_unpackhi_epi64(_mm_setzero_si128(), c2)); s0 = _mm_add_epi32(s0, _mm_unpacklo_epi64(_mm_setzero_si128(), c2)); + c1 = _mm_srli_epi32(s2, 26); c2 = _mm_srli_epi32(s4, 26); s2 = _mm_and_si128(s2, packedmask26262626.v); s4 = _mm_and_si128(s4, packedmask26262626.v); s3 = _mm_add_epi32(s3, c1); s5 = _mm_add_epi32(s5, c2); + c1 = _mm_srli_epi32(s3, 25); c2 = _mm_srli_epi32(s5, 25); s3 = _mm_and_si128(s3, packedmask25252525.v); s5 = _mm_and_si128(s5, packedmask25252525.v); s4 = _mm_add_epi32(s4, c1); s0 = _mm_add_epi32(s0, _mm_or_si128(_mm_slli_si128(c1, 8), _mm_srli_si128(_mm_add_epi32(_mm_add_epi32(_mm_slli_epi32(c2, 4), _mm_slli_epi32(c2, 1)), c2), 8))); + c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2); + + out[0].v = _mm_unpacklo_epi64(s0, s1); /* 00 11 */ + out[1].v = _mm_unpacklo_epi64(s2, s3); /* 22 33 */ + out[2].v = _mm_unpackhi_epi64(s0, s1); /* 44 55 */ + out[3].v = _mm_unpackhi_epi64(s2, s3); /* 66 77 */ + out[4].v = _mm_unpackhi_epi64(s4, s5); /* 88 99 */ +} + +DONNA_INLINE static void +curve25519_add_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) { + out[0].v = _mm_add_epi32(r[0].v, s[0].v); + out[1].v = _mm_add_epi32(r[1].v, s[1].v); + out[2].v = _mm_add_epi32(r[2].v, s[2].v); + out[3].v = _mm_add_epi32(r[3].v, s[3].v); + out[4].v = _mm_add_epi32(r[4].v, s[4].v); +} + +DONNA_INLINE static void +curve25519_sub_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) { + xmmi r0,r1,r2,r3,r4; + xmmi s0,s1,s2,s3; + xmmi c1,c2; + + r0 = _mm_add_epi32(r[0].v, packed32packed2p0.v); + r1 = _mm_add_epi32(r[1].v, packed32packed2p1.v); + r2 = _mm_add_epi32(r[2].v, packed32packed2p1.v); + r3 = _mm_add_epi32(r[3].v, packed32packed2p1.v); + r4 = _mm_add_epi32(r[4].v, packed32packed2p1.v); + r0 = _mm_sub_epi32(r0, s[0].v); /* 00 11 */ + r1 = _mm_sub_epi32(r1, s[1].v); /* 22 33 */ + r2 = _mm_sub_epi32(r2, s[2].v); /* 44 55 */ + r3 = _mm_sub_epi32(r3, s[3].v); /* 66 77 */ + r4 = _mm_sub_epi32(r4, s[4].v); /* 88 99 */ + + s0 = _mm_unpacklo_epi64(r0, r2); /* 00 44 */ + s1 = _mm_unpackhi_epi64(r0, r2); /* 11 55 */ + s2 = _mm_unpacklo_epi64(r1, r3); /* 22 66 */ + s3 = _mm_unpackhi_epi64(r1, r3); /* 33 77 */ + + c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2); + c1 = _mm_srli_epi32(s1, 25); c2 = _mm_srli_epi32(s3, 25); s1 = _mm_and_si128(s1, packedmask25252525.v); s3 = _mm_and_si128(s3, packedmask25252525.v); s2 = _mm_add_epi32(s2, c1); r4 = _mm_add_epi32(r4, _mm_srli_si128(c2, 8)); s0 = _mm_add_epi32(s0, _mm_slli_si128(c2, 8)); + + out[0].v = _mm_unpacklo_epi64(s0, s1); /* 00 11 */ + out[1].v = _mm_unpacklo_epi64(s2, s3); /* 22 33 */ + out[2].v = _mm_unpackhi_epi64(s0, s1); /* 44 55 */ + out[3].v = _mm_unpackhi_epi64(s2, s3); /* 66 77 */ + out[4].v = r4; +} + +DONNA_INLINE static void +curve25519_sub_after_basic_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) { + xmmi r0,r1,r2,r3,r4; + xmmi s0,s1,s2,s3,s4,s5; + xmmi c1,c2; + + r0 = _mm_add_epi32(r[0].v, packed32packed4p0.v); + r1 = _mm_add_epi32(r[1].v, packed32packed4p1.v); + r2 = _mm_add_epi32(r[2].v, packed32packed4p1.v); + r3 = _mm_add_epi32(r[3].v, packed32packed4p1.v); + r4 = _mm_add_epi32(r[4].v, packed32packed4p1.v); + r0 = _mm_sub_epi32(r0, s[0].v); /* 00 11 */ + r1 = _mm_sub_epi32(r1, s[1].v); /* 22 33 */ + r2 = _mm_sub_epi32(r2, s[2].v); /* 44 55 */ + r3 = _mm_sub_epi32(r3, s[3].v); /* 66 77 */ + r4 = _mm_sub_epi32(r4, s[4].v); /* 88 99 */ + + s0 = _mm_unpacklo_epi64(r0, r2); /* 00 44 */ + s1 = _mm_unpackhi_epi64(r0, r2); /* 11 55 */ + s2 = _mm_unpacklo_epi64(r1, r3); /* 22 66 */ + s3 = _mm_unpackhi_epi64(r1, r3); /* 33 77 */ + s4 = _mm_unpacklo_epi64(_mm_setzero_si128(), r4); /* 00 88 */ + s5 = _mm_unpackhi_epi64(_mm_setzero_si128(), r4); /* 00 99 */ + + c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2); + c1 = _mm_srli_epi32(s1, 25); c2 = _mm_srli_epi32(s3, 25); s1 = _mm_and_si128(s1, packedmask25252525.v); s3 = _mm_and_si128(s3, packedmask25252525.v); s2 = _mm_add_epi32(s2, c1); s4 = _mm_add_epi32(s4, _mm_unpackhi_epi64(_mm_setzero_si128(), c2)); s0 = _mm_add_epi32(s0, _mm_unpacklo_epi64(_mm_setzero_si128(), c2)); + c1 = _mm_srli_epi32(s2, 26); c2 = _mm_srli_epi32(s4, 26); s2 = _mm_and_si128(s2, packedmask26262626.v); s4 = _mm_and_si128(s4, packedmask26262626.v); s3 = _mm_add_epi32(s3, c1); s5 = _mm_add_epi32(s5, c2); + c1 = _mm_srli_epi32(s3, 25); c2 = _mm_srli_epi32(s5, 25); s3 = _mm_and_si128(s3, packedmask25252525.v); s5 = _mm_and_si128(s5, packedmask25252525.v); s4 = _mm_add_epi32(s4, c1); s0 = _mm_add_epi32(s0, _mm_or_si128(_mm_slli_si128(c1, 8), _mm_srli_si128(_mm_add_epi32(_mm_add_epi32(_mm_slli_epi32(c2, 4), _mm_slli_epi32(c2, 1)), c2), 8))); + c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2); + + out[0].v = _mm_unpacklo_epi64(s0, s1); /* 00 11 */ + out[1].v = _mm_unpacklo_epi64(s2, s3); /* 22 33 */ + out[2].v = _mm_unpackhi_epi64(s0, s1); /* 44 55 */ + out[3].v = _mm_unpackhi_epi64(s2, s3); /* 66 77 */ + out[4].v = _mm_unpackhi_epi64(s4, s5); /* 88 99 */ +} + +DONNA_INLINE static void +curve25519_tangle64_from32(packedelem64 *a, packedelem64 *b, const packedelem32 *c, const packedelem32 *d) { + xmmi c0,c1,c2,c3,c4,c5,t; + xmmi d0,d1,d2,d3,d4,d5; + xmmi t0,t1,t2,t3,t4,zero; + + t0 = _mm_shuffle_epi32(c[0].v, _MM_SHUFFLE(3,1,2,0)); + t1 = _mm_shuffle_epi32(c[1].v, _MM_SHUFFLE(3,1,2,0)); + t2 = _mm_shuffle_epi32(d[0].v, _MM_SHUFFLE(3,1,2,0)); + t3 = _mm_shuffle_epi32(d[1].v, _MM_SHUFFLE(3,1,2,0)); + c0 = _mm_unpacklo_epi64(t0, t1); + c3 = _mm_unpackhi_epi64(t0, t1); + d0 = _mm_unpacklo_epi64(t2, t3); + d3 = _mm_unpackhi_epi64(t2, t3); + t = _mm_unpacklo_epi64(c0, d0); a[0].v = t; a[1].v = _mm_srli_epi64(t, 32); + t = _mm_unpackhi_epi64(c0, d0); a[2].v = t; a[3].v = _mm_srli_epi64(t, 32); + t = _mm_unpacklo_epi64(c3, d3); b[0].v = t; b[1].v = _mm_srli_epi64(t, 32); + t = _mm_unpackhi_epi64(c3, d3); b[2].v = t; b[3].v = _mm_srli_epi64(t, 32); + + t0 = _mm_shuffle_epi32(c[2].v, _MM_SHUFFLE(3,1,2,0)); + t1 = _mm_shuffle_epi32(c[3].v, _MM_SHUFFLE(3,1,2,0)); + t2 = _mm_shuffle_epi32(d[2].v, _MM_SHUFFLE(3,1,2,0)); + t3 = _mm_shuffle_epi32(d[3].v, _MM_SHUFFLE(3,1,2,0)); + c1 = _mm_unpacklo_epi64(t0, t1); + c4 = _mm_unpackhi_epi64(t0, t1); + d1 = _mm_unpacklo_epi64(t2, t3); + d4 = _mm_unpackhi_epi64(t2, t3); + t = _mm_unpacklo_epi64(c1, d1); a[4].v = t; a[5].v = _mm_srli_epi64(t, 32); + t = _mm_unpackhi_epi64(c1, d1); a[6].v = t; a[7].v = _mm_srli_epi64(t, 32); + t = _mm_unpacklo_epi64(c4, d4); b[4].v = t; b[5].v = _mm_srli_epi64(t, 32); + t = _mm_unpackhi_epi64(c4, d4); b[6].v = t; b[7].v = _mm_srli_epi64(t, 32); + + t4 = _mm_shuffle_epi32(c[4].v, _MM_SHUFFLE(3,1,2,0)); + zero = _mm_setzero_si128(); + c2 = _mm_unpacklo_epi64(t4, zero); + c5 = _mm_unpackhi_epi64(t4, zero); + t4 = _mm_shuffle_epi32(d[4].v, _MM_SHUFFLE(3,1,2,0)); + d2 = _mm_unpacklo_epi64(t4, zero); + d5 = _mm_unpackhi_epi64(t4, zero); + t = _mm_unpacklo_epi64(c2, d2); a[8].v = t; a[9].v = _mm_srli_epi64(t, 32); + t = _mm_unpacklo_epi64(c5, d5); b[8].v = t; b[9].v = _mm_srli_epi64(t, 32); +} + +DONNA_INLINE static void +curve25519_tangle64(packedelem64 *out, const bignum25519 x, const bignum25519 z) { + xmmi x0,x1,x2,z0,z1,z2,t; + + x0 = _mm_load_si128((xmmi *)x + 0); + x1 = _mm_load_si128((xmmi *)x + 1); + x2 = _mm_load_si128((xmmi *)x + 2); + z0 = _mm_load_si128((xmmi *)z + 0); + z1 = _mm_load_si128((xmmi *)z + 1); + z2 = _mm_load_si128((xmmi *)z + 2); + + t = _mm_unpacklo_epi64(x0, z0); out[0].v = t; out[1].v = _mm_srli_epi64(t, 32); + t = _mm_unpackhi_epi64(x0, z0); out[2].v = t; out[3].v = _mm_srli_epi64(t, 32); + t = _mm_unpacklo_epi64(x1, z1); out[4].v = t; out[5].v = _mm_srli_epi64(t, 32); + t = _mm_unpackhi_epi64(x1, z1); out[6].v = t; out[7].v = _mm_srli_epi64(t, 32); + t = _mm_unpacklo_epi64(x2, z2); out[8].v = t; out[9].v = _mm_srli_epi64(t, 32); +} + +DONNA_INLINE static void +curve25519_tangleone64(packedelem64 *out, const bignum25519 x) { + xmmi x0,x1,x2; + + x0 = _mm_load_si128((xmmi *)(x + 0)); + x1 = _mm_load_si128((xmmi *)(x + 4)); + x2 = _mm_load_si128((xmmi *)(x + 8)); + + out[0].v = _mm_shuffle_epi32(x0, _MM_SHUFFLE(0,0,0,0)); + out[1].v = _mm_shuffle_epi32(x0, _MM_SHUFFLE(1,1,1,1)); + out[2].v = _mm_shuffle_epi32(x0, _MM_SHUFFLE(2,2,2,2)); + out[3].v = _mm_shuffle_epi32(x0, _MM_SHUFFLE(3,3,3,3)); + out[4].v = _mm_shuffle_epi32(x1, _MM_SHUFFLE(0,0,0,0)); + out[5].v = _mm_shuffle_epi32(x1, _MM_SHUFFLE(1,1,1,1)); + out[6].v = _mm_shuffle_epi32(x1, _MM_SHUFFLE(2,2,2,2)); + out[7].v = _mm_shuffle_epi32(x1, _MM_SHUFFLE(3,3,3,3)); + out[8].v = _mm_shuffle_epi32(x2, _MM_SHUFFLE(0,0,0,0)); + out[9].v = _mm_shuffle_epi32(x2, _MM_SHUFFLE(1,1,1,1)); +} + +DONNA_INLINE static void +curve25519_swap64(packedelem64 *out) { + out[0].v = _mm_shuffle_epi32(out[0].v, _MM_SHUFFLE(1,0,3,2)); + out[1].v = _mm_shuffle_epi32(out[1].v, _MM_SHUFFLE(1,0,3,2)); + out[2].v = _mm_shuffle_epi32(out[2].v, _MM_SHUFFLE(1,0,3,2)); + out[3].v = _mm_shuffle_epi32(out[3].v, _MM_SHUFFLE(1,0,3,2)); + out[4].v = _mm_shuffle_epi32(out[4].v, _MM_SHUFFLE(1,0,3,2)); + out[5].v = _mm_shuffle_epi32(out[5].v, _MM_SHUFFLE(1,0,3,2)); + out[6].v = _mm_shuffle_epi32(out[6].v, _MM_SHUFFLE(1,0,3,2)); + out[7].v = _mm_shuffle_epi32(out[7].v, _MM_SHUFFLE(1,0,3,2)); + out[8].v = _mm_shuffle_epi32(out[8].v, _MM_SHUFFLE(1,0,3,2)); + out[9].v = _mm_shuffle_epi32(out[9].v, _MM_SHUFFLE(1,0,3,2)); +} + +DONNA_INLINE static void +curve25519_untangle64(bignum25519 x, bignum25519 z, const packedelem64 *in) { + _mm_store_si128((xmmi *)(x + 0), _mm_unpacklo_epi64(_mm_unpacklo_epi32(in[0].v, in[1].v), _mm_unpacklo_epi32(in[2].v, in[3].v))); + _mm_store_si128((xmmi *)(x + 4), _mm_unpacklo_epi64(_mm_unpacklo_epi32(in[4].v, in[5].v), _mm_unpacklo_epi32(in[6].v, in[7].v))); + _mm_store_si128((xmmi *)(x + 8), _mm_unpacklo_epi32(in[8].v, in[9].v) ); + _mm_store_si128((xmmi *)(z + 0), _mm_unpacklo_epi64(_mm_unpackhi_epi32(in[0].v, in[1].v), _mm_unpackhi_epi32(in[2].v, in[3].v))); + _mm_store_si128((xmmi *)(z + 4), _mm_unpacklo_epi64(_mm_unpackhi_epi32(in[4].v, in[5].v), _mm_unpackhi_epi32(in[6].v, in[7].v))); + _mm_store_si128((xmmi *)(z + 8), _mm_unpackhi_epi32(in[8].v, in[9].v) ); +} + +DONNA_INLINE static void +curve25519_mul_packed64(packedelem64 *out, const packedelem64 *r, const packedelem64 *s) { + xmmi r1,r2,r3,r4,r5,r6,r7,r8,r9; + xmmi r1_2,r3_2,r5_2,r7_2,r9_2; + xmmi c1,c2; + + out[0].v = _mm_mul_epu32(r[0].v, s[0].v); + out[1].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[1].v), _mm_mul_epu32(r[1].v, s[0].v)); + r1_2 = _mm_slli_epi32(r[1].v, 1); + out[2].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r1_2 , s[1].v), _mm_mul_epu32(r[2].v, s[0].v))); + out[3].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[1].v), _mm_mul_epu32(r[3].v, s[0].v)))); + r3_2 = _mm_slli_epi32(r[3].v, 1); + out[4].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r1_2 , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r3_2 , s[1].v), _mm_mul_epu32(r[4].v, s[0].v))))); + out[5].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[1].v), _mm_mul_epu32(r[5].v, s[0].v)))))); + r5_2 = _mm_slli_epi32(r[5].v, 1); + out[6].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r1_2 , s[5].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r3_2 , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r5_2 , s[1].v), _mm_mul_epu32(r[6].v, s[0].v))))))); + out[7].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[7].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[5].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[1].v), _mm_mul_epu32(r[7].v , s[0].v)))))))); + r7_2 = _mm_slli_epi32(r[7].v, 1); + out[8].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[8].v), _mm_add_epi64(_mm_mul_epu32(r1_2 , s[7].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r3_2 , s[5].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r5_2 , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r7_2 , s[1].v), _mm_mul_epu32(r[8].v, s[0].v))))))))); + out[9].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[9].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[8].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[7].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[5].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[7].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[8].v, s[1].v), _mm_mul_epu32(r[9].v, s[0].v)))))))))); + + r1 = _mm_mul_epu32(r[1].v, packednineteen.v); + r2 = _mm_mul_epu32(r[2].v, packednineteen.v); + r1_2 = _mm_slli_epi32(r1, 1); + r3 = _mm_mul_epu32(r[3].v, packednineteen.v); + r4 = _mm_mul_epu32(r[4].v, packednineteen.v); + r3_2 = _mm_slli_epi32(r3, 1); + r5 = _mm_mul_epu32(r[5].v, packednineteen.v); + r6 = _mm_mul_epu32(r[6].v, packednineteen.v); + r5_2 = _mm_slli_epi32(r5, 1); + r7 = _mm_mul_epu32(r[7].v, packednineteen.v); + r8 = _mm_mul_epu32(r[8].v, packednineteen.v); + r7_2 = _mm_slli_epi32(r7, 1); + r9 = _mm_mul_epu32(r[9].v, packednineteen.v); + r9_2 = _mm_slli_epi32(r9, 1); + + out[0].v = _mm_add_epi64(out[0].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[1].v), _mm_add_epi64(_mm_mul_epu32(r8, s[2].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[3].v), _mm_add_epi64(_mm_mul_epu32(r6, s[4].v), _mm_add_epi64(_mm_mul_epu32(r5_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r4, s[6].v), _mm_add_epi64(_mm_mul_epu32(r3_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r2, s[8].v), _mm_mul_epu32(r1_2, s[9].v)))))))))); + out[1].v = _mm_add_epi64(out[1].v, _mm_add_epi64(_mm_mul_epu32(r9 , s[2].v), _mm_add_epi64(_mm_mul_epu32(r8, s[3].v), _mm_add_epi64(_mm_mul_epu32(r7 , s[4].v), _mm_add_epi64(_mm_mul_epu32(r6, s[5].v), _mm_add_epi64(_mm_mul_epu32(r5 , s[6].v), _mm_add_epi64(_mm_mul_epu32(r4, s[7].v), _mm_add_epi64(_mm_mul_epu32(r3 , s[8].v), _mm_mul_epu32(r2, s[9].v))))))))); + out[2].v = _mm_add_epi64(out[2].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[3].v), _mm_add_epi64(_mm_mul_epu32(r8, s[4].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r6, s[6].v), _mm_add_epi64(_mm_mul_epu32(r5_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r4, s[8].v), _mm_mul_epu32(r3_2, s[9].v)))))))); + out[3].v = _mm_add_epi64(out[3].v, _mm_add_epi64(_mm_mul_epu32(r9 , s[4].v), _mm_add_epi64(_mm_mul_epu32(r8, s[5].v), _mm_add_epi64(_mm_mul_epu32(r7 , s[6].v), _mm_add_epi64(_mm_mul_epu32(r6, s[7].v), _mm_add_epi64(_mm_mul_epu32(r5 , s[8].v), _mm_mul_epu32(r4, s[9].v))))))); + out[4].v = _mm_add_epi64(out[4].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r8, s[6].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r6, s[8].v), _mm_mul_epu32(r5_2, s[9].v)))))); + out[5].v = _mm_add_epi64(out[5].v, _mm_add_epi64(_mm_mul_epu32(r9 , s[6].v), _mm_add_epi64(_mm_mul_epu32(r8, s[7].v), _mm_add_epi64(_mm_mul_epu32(r7 , s[8].v), _mm_mul_epu32(r6, s[9].v))))); + out[6].v = _mm_add_epi64(out[6].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r8, s[8].v), _mm_mul_epu32(r7_2, s[9].v)))); + out[7].v = _mm_add_epi64(out[7].v, _mm_add_epi64(_mm_mul_epu32(r9 , s[8].v), _mm_mul_epu32(r8, s[9].v))); + out[8].v = _mm_add_epi64(out[8].v, _mm_mul_epu32(r9_2, s[9].v)); + + c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2); + c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2); + c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2); + c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2); + c2 = _mm_srli_epi64(out[8].v, 26); out[8].v = _mm_and_si128(out[8].v, packedmask26.v); out[9].v = _mm_add_epi64(out[9].v, c2); + c2 = _mm_srli_epi64(out[9].v, 25); out[9].v = _mm_and_si128(out[9].v, packedmask25.v); out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v)); + c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2); +} + +DONNA_INLINE static void +curve25519_square_packed64(packedelem64 *out, const packedelem64 *r) { + xmmi r0,r1,r2,r3; + xmmi r1_2,r3_2,r4_2,r5_2,r6_2,r7_2; + xmmi d5,d6,d7,d8,d9; + xmmi c1,c2; + + r0 = r[0].v; + r1 = r[1].v; + r2 = r[2].v; + r3 = r[3].v; + + out[0].v = _mm_mul_epu32(r0, r0); + r0 = _mm_slli_epi32(r0, 1); + out[1].v = _mm_mul_epu32(r0, r1); + r1_2 = _mm_slli_epi32(r1, 1); + out[2].v = _mm_add_epi64(_mm_mul_epu32(r0, r2 ), _mm_mul_epu32(r1, r1_2)); + r1 = r1_2; + out[3].v = _mm_add_epi64(_mm_mul_epu32(r0, r3 ), _mm_mul_epu32(r1, r2 )); + r3_2 = _mm_slli_epi32(r3, 1); + out[4].v = _mm_add_epi64(_mm_mul_epu32(r0, r[4].v), _mm_add_epi64(_mm_mul_epu32(r1, r3_2 ), _mm_mul_epu32(r2, r2))); + r2 = _mm_slli_epi32(r2, 1); + out[5].v = _mm_add_epi64(_mm_mul_epu32(r0, r[5].v), _mm_add_epi64(_mm_mul_epu32(r1, r[4].v), _mm_mul_epu32(r2, r3))); + r5_2 = _mm_slli_epi32(r[5].v, 1); + out[6].v = _mm_add_epi64(_mm_mul_epu32(r0, r[6].v), _mm_add_epi64(_mm_mul_epu32(r1, r5_2 ), _mm_add_epi64(_mm_mul_epu32(r2, r[4].v), _mm_mul_epu32(r3, r3_2 )))); + r3 = r3_2; + out[7].v = _mm_add_epi64(_mm_mul_epu32(r0, r[7].v), _mm_add_epi64(_mm_mul_epu32(r1, r[6].v), _mm_add_epi64(_mm_mul_epu32(r2, r[5].v), _mm_mul_epu32(r3, r[4].v)))); + r7_2 = _mm_slli_epi32(r[7].v, 1); + out[8].v = _mm_add_epi64(_mm_mul_epu32(r0, r[8].v), _mm_add_epi64(_mm_mul_epu32(r1, r7_2 ), _mm_add_epi64(_mm_mul_epu32(r2, r[6].v), _mm_add_epi64(_mm_mul_epu32(r3, r5_2 ), _mm_mul_epu32(r[4].v, r[4].v))))); + out[9].v = _mm_add_epi64(_mm_mul_epu32(r0, r[9].v), _mm_add_epi64(_mm_mul_epu32(r1, r[8].v), _mm_add_epi64(_mm_mul_epu32(r2, r[7].v), _mm_add_epi64(_mm_mul_epu32(r3, r[6].v), _mm_mul_epu32(r[4].v, r5_2 ))))); + + d5 = _mm_mul_epu32(r[5].v, packedthirtyeight.v); + d6 = _mm_mul_epu32(r[6].v, packednineteen.v); + d7 = _mm_mul_epu32(r[7].v, packedthirtyeight.v); + d8 = _mm_mul_epu32(r[8].v, packednineteen.v); + d9 = _mm_mul_epu32(r[9].v, packedthirtyeight.v); + + r4_2 = _mm_slli_epi32(r[4].v, 1); + r6_2 = _mm_slli_epi32(r[6].v, 1); + out[0].v = _mm_add_epi64(out[0].v, _mm_add_epi64(_mm_mul_epu32(d9, r1 ), _mm_add_epi64(_mm_mul_epu32(d8, r2 ), _mm_add_epi64(_mm_mul_epu32(d7, r3 ), _mm_add_epi64(_mm_mul_epu32(d6, r4_2), _mm_mul_epu32(d5, r[5].v)))))); + out[1].v = _mm_add_epi64(out[1].v, _mm_add_epi64(_mm_mul_epu32(d9, _mm_srli_epi32(r2, 1)), _mm_add_epi64(_mm_mul_epu32(d8, r3 ), _mm_add_epi64(_mm_mul_epu32(d7, r[4].v), _mm_mul_epu32(d6, r5_2 ))))); + out[2].v = _mm_add_epi64(out[2].v, _mm_add_epi64(_mm_mul_epu32(d9, r3 ), _mm_add_epi64(_mm_mul_epu32(d8, r4_2), _mm_add_epi64(_mm_mul_epu32(d7, r5_2 ), _mm_mul_epu32(d6, r[6].v))))); + out[3].v = _mm_add_epi64(out[3].v, _mm_add_epi64(_mm_mul_epu32(d9, r[4].v ), _mm_add_epi64(_mm_mul_epu32(d8, r5_2), _mm_mul_epu32(d7, r[6].v)))); + out[4].v = _mm_add_epi64(out[4].v, _mm_add_epi64(_mm_mul_epu32(d9, r5_2 ), _mm_add_epi64(_mm_mul_epu32(d8, r6_2), _mm_mul_epu32(d7, r[7].v)))); + out[5].v = _mm_add_epi64(out[5].v, _mm_add_epi64(_mm_mul_epu32(d9, r[6].v ), _mm_mul_epu32(d8, r7_2 ))); + out[6].v = _mm_add_epi64(out[6].v, _mm_add_epi64(_mm_mul_epu32(d9, r7_2 ), _mm_mul_epu32(d8, r[8].v))); + out[7].v = _mm_add_epi64(out[7].v, _mm_mul_epu32(d9, r[8].v)); + out[8].v = _mm_add_epi64(out[8].v, _mm_mul_epu32(d9, r[9].v)); + + c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2); + c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2); + c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2); + c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2); + c2 = _mm_srli_epi64(out[8].v, 26); out[8].v = _mm_and_si128(out[8].v, packedmask26.v); out[9].v = _mm_add_epi64(out[9].v, c2); + c2 = _mm_srli_epi64(out[9].v, 25); out[9].v = _mm_and_si128(out[9].v, packedmask25.v); out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v)); + c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2); +} + + +/* Take a little-endian, 32-byte number and expand it into polynomial form */ +static void +curve25519_expand(bignum25519 out, const unsigned char in[32]) { + uint32_t x0,x1,x2,x3,x4,x5,x6,x7; + + x0 = *(uint32_t *)(in + 0); + x1 = *(uint32_t *)(in + 4); + x2 = *(uint32_t *)(in + 8); + x3 = *(uint32_t *)(in + 12); + x4 = *(uint32_t *)(in + 16); + x5 = *(uint32_t *)(in + 20); + x6 = *(uint32_t *)(in + 24); + x7 = *(uint32_t *)(in + 28); + + out[0] = ( x0 ) & 0x3ffffff; + out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & 0x1ffffff; + out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & 0x3ffffff; + out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & 0x1ffffff; + out[4] = (( x3) >> 6) & 0x3ffffff; + out[5] = ( x4 ) & 0x1ffffff; + out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & 0x3ffffff; + out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & 0x1ffffff; + out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & 0x3ffffff; + out[9] = (( x7) >> 6) & 0x1ffffff; + out[10] = 0; + out[11] = 0; +} + +/* Take a fully reduced polynomial form number and contract it into a + * little-endian, 32-byte array + */ +static void +curve25519_contract(unsigned char out[32], const bignum25519 in) { + bignum25519 ALIGN(16) f; + curve25519_copy(f, in); + + #define carry_pass() \ + f[1] += f[0] >> 26; f[0] &= 0x3ffffff; \ + f[2] += f[1] >> 25; f[1] &= 0x1ffffff; \ + f[3] += f[2] >> 26; f[2] &= 0x3ffffff; \ + f[4] += f[3] >> 25; f[3] &= 0x1ffffff; \ + f[5] += f[4] >> 26; f[4] &= 0x3ffffff; \ + f[6] += f[5] >> 25; f[5] &= 0x1ffffff; \ + f[7] += f[6] >> 26; f[6] &= 0x3ffffff; \ + f[8] += f[7] >> 25; f[7] &= 0x1ffffff; \ + f[9] += f[8] >> 26; f[8] &= 0x3ffffff; + + #define carry_pass_full() \ + carry_pass() \ + f[0] += 19 * (f[9] >> 25); f[9] &= 0x1ffffff; + + #define carry_pass_final() \ + carry_pass() \ + f[9] &= 0x1ffffff; + + carry_pass_full() + carry_pass_full() + + /* now t is between 0 and 2^255-1, properly carried. */ + /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */ + f[0] += 19; + carry_pass_full() + + /* now between 19 and 2^255-1 in both cases, and offset by 19. */ + f[0] += (1 << 26) - 19; + f[1] += (1 << 25) - 1; + f[2] += (1 << 26) - 1; + f[3] += (1 << 25) - 1; + f[4] += (1 << 26) - 1; + f[5] += (1 << 25) - 1; + f[6] += (1 << 26) - 1; + f[7] += (1 << 25) - 1; + f[8] += (1 << 26) - 1; + f[9] += (1 << 25) - 1; + + /* now between 2^255 and 2^256-20, and offset by 2^255. */ + carry_pass_final() + + #undef carry_pass + #undef carry_full + #undef carry_final + + f[1] <<= 2; + f[2] <<= 3; + f[3] <<= 5; + f[4] <<= 6; + f[6] <<= 1; + f[7] <<= 3; + f[8] <<= 4; + f[9] <<= 6; + + #define F(i, s) \ + out[s+0] |= (unsigned char )(f[i] & 0xff); \ + out[s+1] = (unsigned char )((f[i] >> 8) & 0xff); \ + out[s+2] = (unsigned char )((f[i] >> 16) & 0xff); \ + out[s+3] = (unsigned char )((f[i] >> 24) & 0xff); + + out[0] = 0; + out[16] = 0; + F(0,0); + F(1,3); + F(2,6); + F(3,9); + F(4,12); + F(5,16); + F(6,19); + F(7,22); + F(8,25); + F(9,28); + #undef F +} + +/* if (iswap) swap(a, b) */ +DONNA_INLINE static void +curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint32_t iswap) { + const uint32_t swap = (uint32_t)(-(int32_t)iswap); + xmmi a0,a1,a2,b0,b1,b2,x0,x1,x2; + xmmi mask = _mm_cvtsi32_si128(swap); + mask = _mm_shuffle_epi32(mask, 0); + a0 = _mm_load_si128((xmmi *)a + 0); + a1 = _mm_load_si128((xmmi *)a + 1); + b0 = _mm_load_si128((xmmi *)b + 0); + b1 = _mm_load_si128((xmmi *)b + 1); + b0 = _mm_xor_si128(a0, b0); + b1 = _mm_xor_si128(a1, b1); + x0 = _mm_and_si128(b0, mask); + x1 = _mm_and_si128(b1, mask); + x0 = _mm_xor_si128(x0, a0); + x1 = _mm_xor_si128(x1, a1); + a0 = _mm_xor_si128(x0, b0); + a1 = _mm_xor_si128(x1, b1); + _mm_store_si128((xmmi *)a + 0, x0); + _mm_store_si128((xmmi *)a + 1, x1); + _mm_store_si128((xmmi *)b + 0, a0); + _mm_store_si128((xmmi *)b + 1, a1); + + a2 = _mm_load_si128((xmmi *)a + 2); + b2 = _mm_load_si128((xmmi *)b + 2); + b2 = _mm_xor_si128(a2, b2); + x2 = _mm_and_si128(b2, mask); + x2 = _mm_xor_si128(x2, a2); + a2 = _mm_xor_si128(x2, b2); + _mm_store_si128((xmmi *)b + 2, a2); + _mm_store_si128((xmmi *)a + 2, x2); +} + +/* out = (flag) ? out : in */ +DONNA_INLINE static void +curve25519_move_conditional_bytes(uint8_t out[96], const uint8_t in[96], uint32_t flag) { + xmmi a0,a1,a2,a3,a4,a5,b0,b1,b2,b3,b4,b5; + const uint32_t nb = flag - 1; + xmmi masknb = _mm_shuffle_epi32(_mm_cvtsi32_si128(nb),0); + a0 = _mm_load_si128((xmmi *)in + 0); + a1 = _mm_load_si128((xmmi *)in + 1); + a2 = _mm_load_si128((xmmi *)in + 2); + b0 = _mm_load_si128((xmmi *)out + 0); + b1 = _mm_load_si128((xmmi *)out + 1); + b2 = _mm_load_si128((xmmi *)out + 2); + a0 = _mm_andnot_si128(masknb, a0); + a1 = _mm_andnot_si128(masknb, a1); + a2 = _mm_andnot_si128(masknb, a2); + b0 = _mm_and_si128(masknb, b0); + b1 = _mm_and_si128(masknb, b1); + b2 = _mm_and_si128(masknb, b2); + a0 = _mm_or_si128(a0, b0); + a1 = _mm_or_si128(a1, b1); + a2 = _mm_or_si128(a2, b2); + _mm_store_si128((xmmi*)out + 0, a0); + _mm_store_si128((xmmi*)out + 1, a1); + _mm_store_si128((xmmi*)out + 2, a2); + + a3 = _mm_load_si128((xmmi *)in + 3); + a4 = _mm_load_si128((xmmi *)in + 4); + a5 = _mm_load_si128((xmmi *)in + 5); + b3 = _mm_load_si128((xmmi *)out + 3); + b4 = _mm_load_si128((xmmi *)out + 4); + b5 = _mm_load_si128((xmmi *)out + 5); + a3 = _mm_andnot_si128(masknb, a3); + a4 = _mm_andnot_si128(masknb, a4); + a5 = _mm_andnot_si128(masknb, a5); + b3 = _mm_and_si128(masknb, b3); + b4 = _mm_and_si128(masknb, b4); + b5 = _mm_and_si128(masknb, b5); + a3 = _mm_or_si128(a3, b3); + a4 = _mm_or_si128(a4, b4); + a5 = _mm_or_si128(a5, b5); + _mm_store_si128((xmmi*)out + 3, a3); + _mm_store_si128((xmmi*)out + 4, a4); + _mm_store_si128((xmmi*)out + 5, a5); +} + diff --git a/src/ext/ed25519/donna/ed25519-donna-32bit-sse2.h b/src/ext/ed25519/donna/ed25519-donna-32bit-sse2.h new file mode 100644 index 0000000..db04a13 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-32bit-sse2.h @@ -0,0 +1,513 @@ +#if defined(ED25519_GCC_32BIT_SSE_CHOOSE) + +#define HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS + +DONNA_NOINLINE static void +ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) { + int32_t breg = (int32_t)b; + uint32_t sign = (uint32_t)breg >> 31; + uint32_t mask = ~(sign - 1); + uint32_t u = (breg + mask) ^ mask; + + __asm__ __volatile__ ( + /* ysubx+xaddy */ + "movl %0, %%eax ;\n" + "movd %%eax, %%xmm6 ;\n" + "pshufd $0x00, %%xmm6, %%xmm6 ;\n" + "pxor %%xmm0, %%xmm0 ;\n" + "pxor %%xmm1, %%xmm1 ;\n" + "pxor %%xmm2, %%xmm2 ;\n" + "pxor %%xmm3, %%xmm3 ;\n" + + /* 0 */ + "movl $0, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movl $1, %%ecx ;\n" + "movd %%ecx, %%xmm4 ;\n" + "pxor %%xmm5, %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm0 ;\n" + "por %%xmm5, %%xmm1 ;\n" + "por %%xmm4, %%xmm2 ;\n" + "por %%xmm5, %%xmm3 ;\n" + + /* 1 */ + "movl $1, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 0(%1), %%xmm4 ;\n" + "movdqa 16(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm0 ;\n" + "por %%xmm5, %%xmm1 ;\n" + "movdqa 32(%1), %%xmm4 ;\n" + "movdqa 48(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm2 ;\n" + "por %%xmm5, %%xmm3 ;\n" + + /* 2 */ + "movl $2, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 96(%1), %%xmm4 ;\n" + "movdqa 112(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm0 ;\n" + "por %%xmm5, %%xmm1 ;\n" + "movdqa 128(%1), %%xmm4 ;\n" + "movdqa 144(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm2 ;\n" + "por %%xmm5, %%xmm3 ;\n" + + /* 3 */ + "movl $3, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 192(%1), %%xmm4 ;\n" + "movdqa 208(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm0 ;\n" + "por %%xmm5, %%xmm1 ;\n" + "movdqa 224(%1), %%xmm4 ;\n" + "movdqa 240(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm2 ;\n" + "por %%xmm5, %%xmm3 ;\n" + + /* 4 */ + "movl $4, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 288(%1), %%xmm4 ;\n" + "movdqa 304(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm0 ;\n" + "por %%xmm5, %%xmm1 ;\n" + "movdqa 320(%1), %%xmm4 ;\n" + "movdqa 336(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm2 ;\n" + "por %%xmm5, %%xmm3 ;\n" + + /* 5 */ + "movl $5, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 384(%1), %%xmm4 ;\n" + "movdqa 400(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm0 ;\n" + "por %%xmm5, %%xmm1 ;\n" + "movdqa 416(%1), %%xmm4 ;\n" + "movdqa 432(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm2 ;\n" + "por %%xmm5, %%xmm3 ;\n" + + /* 6 */ + "movl $6, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 480(%1), %%xmm4 ;\n" + "movdqa 496(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm0 ;\n" + "por %%xmm5, %%xmm1 ;\n" + "movdqa 512(%1), %%xmm4 ;\n" + "movdqa 528(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm2 ;\n" + "por %%xmm5, %%xmm3 ;\n" + + /* 7 */ + "movl $7, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 576(%1), %%xmm4 ;\n" + "movdqa 592(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm0 ;\n" + "por %%xmm5, %%xmm1 ;\n" + "movdqa 608(%1), %%xmm4 ;\n" + "movdqa 624(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm2 ;\n" + "por %%xmm5, %%xmm3 ;\n" + + /* 8 */ + "movl $8, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 672(%1), %%xmm4 ;\n" + "movdqa 688(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm0 ;\n" + "por %%xmm5, %%xmm1 ;\n" + "movdqa 704(%1), %%xmm4 ;\n" + "movdqa 720(%1), %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "por %%xmm4, %%xmm2 ;\n" + "por %%xmm5, %%xmm3 ;\n" + + /* conditional swap based on sign */ + "movl %3, %%ecx ;\n" + "movl %2, %%eax ;\n" + "xorl $1, %%ecx ;\n" + "movd %%ecx, %%xmm6 ;\n" + "pxor %%xmm7, %%xmm7 ;\n" + "pshufd $0x00, %%xmm6, %%xmm6 ;\n" + "pxor %%xmm0, %%xmm2 ;\n" + "pxor %%xmm1, %%xmm3 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa %%xmm2, %%xmm4 ;\n" + "movdqa %%xmm3, %%xmm5 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "pand %%xmm7, %%xmm5 ;\n" + "pxor %%xmm4, %%xmm0 ;\n" + "pxor %%xmm5, %%xmm1 ;\n" + "pxor %%xmm0, %%xmm2 ;\n" + "pxor %%xmm1, %%xmm3 ;\n" + + /* store ysubx */ + "movd %%xmm0, %%ecx ;\n" + "movl %%ecx, %%edx ;\n" + "pshufd $0x39, %%xmm0, %%xmm0 ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 0(%%eax) ;\n" + "movd %%xmm0, %%ecx ;\n" + "pshufd $0x39, %%xmm0, %%xmm0 ;\n" + "shrdl $26, %%ecx, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 4(%%eax) ;\n" + "movd %%xmm0, %%edx ;\n" + "pshufd $0x39, %%xmm0, %%xmm0 ;\n" + "shrdl $19, %%edx, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 8(%%eax) ;\n" + "movd %%xmm0, %%ecx ;\n" + "shrdl $13, %%ecx, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 12(%%eax) ;\n" + "movd %%xmm1, %%edx ;\n" + "pshufd $0x39, %%xmm1, %%xmm1 ;\n" + "shrl $6, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 16(%%eax) ;\n" + "movl %%edx, %%ecx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 20(%%eax) ;\n" + "movd %%xmm1, %%edx ;\n" + "pshufd $0x39, %%xmm1, %%xmm1 ;\n" + "shrdl $25, %%edx, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 24(%%eax) ;\n" + "movd %%xmm1, %%ecx ;\n" + "pshufd $0x39, %%xmm1, %%xmm1 ;\n" + "shrdl $19, %%ecx, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 28(%%eax) ;\n" + "movd %%xmm1, %%edx ;\n" + "shrdl $12, %%edx, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 32(%%eax) ;\n" + "shrl $6, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "xorl %%ecx, %%ecx ;\n" + "movl %%edx, 36(%%eax) ;\n" + "movl %%ecx, 40(%%eax) ;\n" + "movl %%ecx, 44(%%eax) ;\n" + + /* store xaddy */ + "addl $48, %%eax ;\n" + "movdqa %%xmm2, %%xmm0 ;\n" + "movdqa %%xmm3, %%xmm1 ;\n" + "movd %%xmm0, %%ecx ;\n" + "movl %%ecx, %%edx ;\n" + "pshufd $0x39, %%xmm0, %%xmm0 ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 0(%%eax) ;\n" + "movd %%xmm0, %%ecx ;\n" + "pshufd $0x39, %%xmm0, %%xmm0 ;\n" + "shrdl $26, %%ecx, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 4(%%eax) ;\n" + "movd %%xmm0, %%edx ;\n" + "pshufd $0x39, %%xmm0, %%xmm0 ;\n" + "shrdl $19, %%edx, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 8(%%eax) ;\n" + "movd %%xmm0, %%ecx ;\n" + "shrdl $13, %%ecx, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 12(%%eax) ;\n" + "movd %%xmm1, %%edx ;\n" + "pshufd $0x39, %%xmm1, %%xmm1 ;\n" + "shrl $6, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 16(%%eax) ;\n" + "movl %%edx, %%ecx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 20(%%eax) ;\n" + "movd %%xmm1, %%edx ;\n" + "pshufd $0x39, %%xmm1, %%xmm1 ;\n" + "shrdl $25, %%edx, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 24(%%eax) ;\n" + "movd %%xmm1, %%ecx ;\n" + "pshufd $0x39, %%xmm1, %%xmm1 ;\n" + "shrdl $19, %%ecx, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 28(%%eax) ;\n" + "movd %%xmm1, %%edx ;\n" + "shrdl $12, %%edx, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 32(%%eax) ;\n" + "shrl $6, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "xorl %%ecx, %%ecx ;\n" + "movl %%edx, 36(%%eax) ;\n" + "movl %%ecx, 40(%%eax) ;\n" + "movl %%ecx, 44(%%eax) ;\n" + + /* t2d */ + "movl %0, %%eax ;\n" + "movd %%eax, %%xmm6 ;\n" + "pshufd $0x00, %%xmm6, %%xmm6 ;\n" + "pxor %%xmm0, %%xmm0 ;\n" + "pxor %%xmm1, %%xmm1 ;\n" + + /* 0 */ + "movl $0, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "pxor %%xmm0, %%xmm0 ;\n" + "pxor %%xmm1, %%xmm1 ;\n" + + /* 1 */ + "movl $1, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 64(%1), %%xmm3 ;\n" + "movdqa 80(%1), %%xmm4 ;\n" + "pand %%xmm7, %%xmm3 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "por %%xmm3, %%xmm0 ;\n" + "por %%xmm4, %%xmm1 ;\n" + + /* 2 */ + "movl $2, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 160(%1), %%xmm3 ;\n" + "movdqa 176(%1), %%xmm4 ;\n" + "pand %%xmm7, %%xmm3 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "por %%xmm3, %%xmm0 ;\n" + "por %%xmm4, %%xmm1 ;\n" + + /* 3 */ + "movl $3, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 256(%1), %%xmm3 ;\n" + "movdqa 272(%1), %%xmm4 ;\n" + "pand %%xmm7, %%xmm3 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "por %%xmm3, %%xmm0 ;\n" + "por %%xmm4, %%xmm1 ;\n" + + /* 4 */ + "movl $4, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 352(%1), %%xmm3 ;\n" + "movdqa 368(%1), %%xmm4 ;\n" + "pand %%xmm7, %%xmm3 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "por %%xmm3, %%xmm0 ;\n" + "por %%xmm4, %%xmm1 ;\n" + + /* 5 */ + "movl $5, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 448(%1), %%xmm3 ;\n" + "movdqa 464(%1), %%xmm4 ;\n" + "pand %%xmm7, %%xmm3 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "por %%xmm3, %%xmm0 ;\n" + "por %%xmm4, %%xmm1 ;\n" + + /* 6 */ + "movl $6, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 544(%1), %%xmm3 ;\n" + "movdqa 560(%1), %%xmm4 ;\n" + "pand %%xmm7, %%xmm3 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "por %%xmm3, %%xmm0 ;\n" + "por %%xmm4, %%xmm1 ;\n" + + /* 7 */ + "movl $7, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 640(%1), %%xmm3 ;\n" + "movdqa 656(%1), %%xmm4 ;\n" + "pand %%xmm7, %%xmm3 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "por %%xmm3, %%xmm0 ;\n" + "por %%xmm4, %%xmm1 ;\n" + + /* 8 */ + "movl $8, %%eax ;\n" + "movd %%eax, %%xmm7 ;\n" + "pshufd $0x00, %%xmm7, %%xmm7 ;\n" + "pcmpeqd %%xmm6, %%xmm7 ;\n" + "movdqa 736(%1), %%xmm3 ;\n" + "movdqa 752(%1), %%xmm4 ;\n" + "pand %%xmm7, %%xmm3 ;\n" + "pand %%xmm7, %%xmm4 ;\n" + "por %%xmm3, %%xmm0 ;\n" + "por %%xmm4, %%xmm1 ;\n" + + /* store t2d */ + "movl %2, %%eax ;\n" + "addl $96, %%eax ;\n" + "movd %%xmm0, %%ecx ;\n" + "movl %%ecx, %%edx ;\n" + "pshufd $0x39, %%xmm0, %%xmm0 ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 0(%%eax) ;\n" + "movd %%xmm0, %%ecx ;\n" + "pshufd $0x39, %%xmm0, %%xmm0 ;\n" + "shrdl $26, %%ecx, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 4(%%eax) ;\n" + "movd %%xmm0, %%edx ;\n" + "pshufd $0x39, %%xmm0, %%xmm0 ;\n" + "shrdl $19, %%edx, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 8(%%eax) ;\n" + "movd %%xmm0, %%ecx ;\n" + "shrdl $13, %%ecx, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 12(%%eax) ;\n" + "movd %%xmm1, %%edx ;\n" + "pshufd $0x39, %%xmm1, %%xmm1 ;\n" + "shrl $6, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 16(%%eax) ;\n" + "movl %%edx, %%ecx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 20(%%eax) ;\n" + "movd %%xmm1, %%edx ;\n" + "pshufd $0x39, %%xmm1, %%xmm1 ;\n" + "shrdl $25, %%edx, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 24(%%eax) ;\n" + "movd %%xmm1, %%ecx ;\n" + "pshufd $0x39, %%xmm1, %%xmm1 ;\n" + "shrdl $19, %%ecx, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "movl %%edx, 28(%%eax) ;\n" + "movd %%xmm1, %%edx ;\n" + "movd %%xmm1, %%edx ;\n" + "shrdl $12, %%edx, %%ecx ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "movl %%ecx, 32(%%eax) ;\n" + "shrl $6, %%edx ;\n" + "andl $0x1ffffff, %%edx ;\n" + "xorl %%ecx, %%ecx ;\n" + "movl %%edx, 36(%%eax) ;\n" + "movl %%ecx, 40(%%eax) ;\n" + "movl %%ecx, 44(%%eax) ;\n" + "movdqa 0(%%eax), %%xmm0 ;\n" + "movdqa 16(%%eax), %%xmm1 ;\n" + "movdqa 32(%%eax), %%xmm2 ;\n" + + /* conditionally negate t2d */ + + /* set up 2p in to 3/4 */ + "movl $0x7ffffda, %%ecx ;\n" + "movl $0x3fffffe, %%edx ;\n" + "movd %%ecx, %%xmm3 ;\n" + "movd %%edx, %%xmm5 ;\n" + "movl $0x7fffffe, %%ecx ;\n" + "movd %%ecx, %%xmm4 ;\n" + "punpckldq %%xmm5, %%xmm3 ;\n" + "punpckldq %%xmm5, %%xmm4 ;\n" + "punpcklqdq %%xmm4, %%xmm3 ;\n" + "movdqa %%xmm4, %%xmm5 ;\n" + "punpcklqdq %%xmm4, %%xmm4 ;\n" + + /* subtract and conditionally move */ + "movl %3, %%ecx ;\n" + "sub $1, %%ecx ;\n" + "movd %%ecx, %%xmm6 ;\n" + "pshufd $0x00, %%xmm6, %%xmm6 ;\n" + "movdqa %%xmm6, %%xmm7 ;\n" + "psubd %%xmm0, %%xmm3 ;\n" + "psubd %%xmm1, %%xmm4 ;\n" + "psubd %%xmm2, %%xmm5 ;\n" + "pand %%xmm6, %%xmm0 ;\n" + "pand %%xmm6, %%xmm1 ;\n" + "pand %%xmm6, %%xmm2 ;\n" + "pandn %%xmm3, %%xmm6 ;\n" + "movdqa %%xmm7, %%xmm3 ;\n" + "pandn %%xmm4, %%xmm7 ;\n" + "pandn %%xmm5, %%xmm3 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm3, %%xmm2 ;\n" + + /* store */ + "movdqa %%xmm0, 0(%%eax) ;\n" + "movdqa %%xmm1, 16(%%eax) ;\n" + "movdqa %%xmm2, 32(%%eax) ;\n" + : + : "m"(u), "r"(&table[pos * 8]), "m"(t), "m"(sign) /* %0 = u, %1 = table, %2 = t, %3 = sign */ + : "%eax", "%ecx", "%edx", "%xmm0", "%xmm1", "%xmm2", "%xmm3", "%xmm4", "%xmm5", "%xmm6", "%xmm7", "cc", "memory" + ); +} + +#endif /* defined(ED25519_GCC_32BIT_SSE_CHOOSE) */ + diff --git a/src/ext/ed25519/donna/ed25519-donna-32bit-tables.h b/src/ext/ed25519/donna/ed25519-donna-32bit-tables.h new file mode 100644 index 0000000..c977c26 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-32bit-tables.h @@ -0,0 +1,61 @@ +static const ge25519 ALIGN(16) ge25519_basepoint = { + {0x0325d51a,0x018b5823,0x00f6592a,0x0104a92d,0x01a4b31d,0x01d6dc5c,0x027118fe,0x007fd814,0x013cd6e5,0x0085a4db}, + {0x02666658,0x01999999,0x00cccccc,0x01333333,0x01999999,0x00666666,0x03333333,0x00cccccc,0x02666666,0x01999999}, + {0x00000001,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000}, + {0x01b7dda3,0x01a2ace9,0x025eadbb,0x0003ba8a,0x0083c27e,0x00abe37d,0x01274732,0x00ccacdd,0x00fd78b7,0x019e1d7c} +}; + +/* + d +*/ + +static const bignum25519 ALIGN(16) ge25519_ecd = { + 0x035978a3,0x00d37284,0x03156ebd,0x006a0a0e,0x0001c029,0x0179e898,0x03a03cbb,0x01ce7198,0x02e2b6ff,0x01480db3 +}; + +static const bignum25519 ALIGN(16) ge25519_ec2d = { + 0x02b2f159,0x01a6e509,0x022add7a,0x00d4141d,0x00038052,0x00f3d130,0x03407977,0x019ce331,0x01c56dff,0x00901b67 +}; + +/* + sqrt(-1) +*/ + +static const bignum25519 ALIGN(16) ge25519_sqrtneg1 = { + 0x020ea0b0,0x0186c9d2,0x008f189d,0x0035697f,0x00bd0c60,0x01fbd7a7,0x02804c9e,0x01e16569,0x0004fc1d,0x00ae0c92 +}; + +static const ge25519_niels ALIGN(16) ge25519_niels_sliding_multiples[32] = { + {{0x0340913e,0x000e4175,0x03d673a2,0x002e8a05,0x03f4e67c,0x008f8a09,0x00c21a34,0x004cf4b8,0x01298f81,0x0113f4be},{0x018c3b85,0x0124f1bd,0x01c325f7,0x0037dc60,0x033e4cb7,0x003d42c2,0x01a44c32,0x014ca4e1,0x03a33d4b,0x001f3e74},{0x037aaa68,0x00448161,0x0093d579,0x011e6556,0x009b67a0,0x0143598c,0x01bee5ee,0x00b50b43,0x0289f0c6,0x01bc45ed}}, + {{0x00fcd265,0x0047fa29,0x034faacc,0x01ef2e0d,0x00ef4d4f,0x014bd6bd,0x00f98d10,0x014c5026,0x007555bd,0x00aae456},{0x00ee9730,0x016c2a13,0x017155e4,0x01874432,0x00096a10,0x01016732,0x01a8014f,0x011e9823,0x01b9a80f,0x01e85938},{0x01d0d889,0x01a4cfc3,0x034c4295,0x0110e1ae,0x0162508c,0x00f2db4c,0x0072a2c6,0x0098da2e,0x02f12b9b,0x0168a09a}}, + {{0x0047d6ba,0x0060b0e9,0x0136eff2,0x008a5939,0x03540053,0x0064a087,0x02788e5c,0x00be7c67,0x033eb1b5,0x005529f9},{0x00a5bb33,0x00af1102,0x01a05442,0x001e3af7,0x02354123,0x00bfec44,0x01f5862d,0x00dd7ba3,0x03146e20,0x00a51733},{0x012a8285,0x00f6fc60,0x023f9797,0x003e85ee,0x009c3820,0x01bda72d,0x01b3858d,0x00d35683,0x0296b3bb,0x010eaaf9}}, + {{0x023221b1,0x01cb26aa,0x0074f74d,0x0099ddd1,0x01b28085,0x00192c3a,0x013b27c9,0x00fc13bd,0x01d2e531,0x0075bb75},{0x004ea3bf,0x00973425,0x001a4d63,0x01d59cee,0x01d1c0d4,0x00542e49,0x01294114,0x004fce36,0x029283c9,0x01186fa9},{0x01b8b3a2,0x00db7200,0x00935e30,0x003829f5,0x02cc0d7d,0x0077adf3,0x0220dd2c,0x0014ea53,0x01c6a0f9,0x01ea7eec}}, + {{0x039d8064,0x01885f80,0x00337e6d,0x01b7a902,0x02628206,0x015eb044,0x01e30473,0x0191f2d9,0x011fadc9,0x01270169},{0x02a8632f,0x0199e2a9,0x00d8b365,0x017a8de2,0x02994279,0x0086f5b5,0x0119e4e3,0x01eb39d6,0x0338add7,0x00d2e7b4},{0x0045af1b,0x013a2fe4,0x0245e0d6,0x014538ce,0x038bfe0f,0x01d4cf16,0x037e14c9,0x0160d55e,0x0021b008,0x01cf05c8}}, + {{0x01864348,0x01d6c092,0x0070262b,0x014bb844,0x00fb5acd,0x008deb95,0x003aaab5,0x00eff474,0x00029d5c,0x0062ad66},{0x02802ade,0x01c02122,0x01c4e5f7,0x00781181,0x039767fb,0x01703406,0x0342388b,0x01f5e227,0x022546d8,0x0109d6ab},{0x016089e9,0x00cb317f,0x00949b05,0x01099417,0x000c7ad2,0x011a8622,0x0088ccda,0x01290886,0x022b53df,0x00f71954}}, + {{0x027fbf93,0x01c04ecc,0x01ed6a0d,0x004cdbbb,0x02bbf3af,0x00ad5968,0x01591955,0x0094f3a2,0x02d17602,0x00099e20},{0x02007f6d,0x003088a8,0x03db77ee,0x00d5ade6,0x02fe12ce,0x0107ba07,0x0107097d,0x00482a6f,0x02ec346f,0x008d3f5f},{0x032ea378,0x0028465c,0x028e2a6c,0x018efc6e,0x0090df9a,0x01a7e533,0x039bfc48,0x010c745d,0x03daa097,0x0125ee9b}}, + {{0x028ccf0b,0x00f36191,0x021ac081,0x012154c8,0x034e0a6e,0x01b25192,0x00180403,0x01d7eea1,0x00218d05,0x010ed735},{0x03cfeaa0,0x01b300c4,0x008da499,0x0068c4e1,0x0219230a,0x01f2d4d0,0x02defd60,0x00e565b7,0x017f12de,0x018788a4},{0x03d0b516,0x009d8be6,0x03ddcbb3,0x0071b9fe,0x03ace2bd,0x01d64270,0x032d3ec9,0x01084065,0x0210ae4d,0x01447584}}, + {{0x0020de87,0x00e19211,0x01b68102,0x00b5ac97,0x022873c0,0x01942d25,0x01271394,0x0102073f,0x02fe2482,0x01c69ff9},{0x010e9d81,0x019dbbe5,0x0089f258,0x006e06b8,0x02951883,0x018f1248,0x019b3237,0x00bc7553,0x024ddb85,0x01b4c964},{0x01c8c854,0x0060ae29,0x01406d8e,0x01cff2f9,0x00cff451,0x01778d0c,0x03ac8c41,0x01552e59,0x036559ee,0x011d1b12}}, + {{0x00741147,0x0151b219,0x01092690,0x00e877e6,0x01f4d6bb,0x0072a332,0x01cd3b03,0x00dadff2,0x0097db5e,0x0086598d},{0x01c69a2b,0x01decf1b,0x02c2fa6e,0x013b7c4f,0x037beac8,0x013a16b5,0x028e7bda,0x01f6e8ac,0x01e34fe9,0x01726947},{0x01f10e67,0x003c73de,0x022b7ea2,0x010f32c2,0x03ff776a,0x00142277,0x01d38b88,0x00776138,0x03c60822,0x01201140}}, + {{0x0236d175,0x0008748e,0x03c6476d,0x013f4cdc,0x02eed02a,0x00838a47,0x032e7210,0x018bcbb3,0x00858de4,0x01dc7826},{0x00a37fc7,0x0127b40b,0x01957884,0x011d30ad,0x02816683,0x016e0e23,0x00b76be4,0x012db115,0x02516506,0x0154ce62},{0x00451edf,0x00bd749e,0x03997342,0x01cc2c4c,0x00eb6975,0x01a59508,0x03a516cf,0x00c228ef,0x0168ff5a,0x01697b47}}, + {{0x00527359,0x01783156,0x03afd75c,0x00ce56dc,0x00e4b970,0x001cabe9,0x029e0f6d,0x0188850c,0x0135fefd,0x00066d80},{0x02150e83,0x01448abf,0x02bb0232,0x012bf259,0x033c8268,0x00711e20,0x03fc148f,0x005e0e70,0x017d8bf9,0x0112b2e2},{0x02134b83,0x001a0517,0x0182c3cc,0x00792182,0x0313d799,0x001a3ed7,0x0344547e,0x01f24a0d,0x03de6ad2,0x00543127}}, + {{0x00dca868,0x00618f27,0x015a1709,0x00ddc38a,0x0320fd13,0x0036168d,0x0371ab06,0x01783fc7,0x0391e05f,0x01e29b5d},{0x01471138,0x00fca542,0x00ca31cf,0x01ca7bad,0x0175bfbc,0x01a708ad,0x03bce212,0x01244215,0x0075bb99,0x01acad68},{0x03a0b976,0x01dc12d1,0x011aab17,0x00aba0ba,0x029806cd,0x0142f590,0x018fd8ea,0x01a01545,0x03c4ad55,0x01c971ff}}, + {{0x00d098c0,0x000afdc7,0x006cd230,0x01276af3,0x03f905b2,0x0102994c,0x002eb8a4,0x015cfbeb,0x025f855f,0x01335518},{0x01cf99b2,0x0099c574,0x01a69c88,0x00881510,0x01cd4b54,0x0112109f,0x008abdc5,0x0074647a,0x0277cb1f,0x01e53324},{0x02ac5053,0x01b109b0,0x024b095e,0x016997b3,0x02f26bb6,0x00311021,0x00197885,0x01d0a55a,0x03b6fcc8,0x01c020d5}}, + {{0x02584a34,0x00e7eee0,0x03257a03,0x011e95a3,0x011ead91,0x00536202,0x00b1ce24,0x008516c6,0x03669d6d,0x004ea4a8},{0x00773f01,0x0019c9ce,0x019f6171,0x01d4afde,0x02e33323,0x01ad29b6,0x02ead1dc,0x01ed51a5,0x01851ad0,0x001bbdfa},{0x00577de5,0x00ddc730,0x038b9952,0x00f281ae,0x01d50390,0x0002e071,0x000780ec,0x010d448d,0x01f8a2af,0x00f0a5b7}}, + {{0x031f2541,0x00d34bae,0x0323ff9d,0x003a056d,0x02e25443,0x00a1ad05,0x00d1bee8,0x002f7f8e,0x03007477,0x002a24b1},{0x0114a713,0x01457e76,0x032255d5,0x01cc647f,0x02a4bdef,0x0153d730,0x00118bcf,0x00f755ff,0x013490c7,0x01ea674e},{0x02bda3e8,0x00bb490d,0x00f291ea,0x000abf40,0x01dea321,0x002f9ce0,0x00b2b193,0x00fa54b5,0x0128302f,0x00a19d8b}}, + {{0x022ef5bd,0x01638af3,0x038c6f8a,0x01a33a3d,0x039261b2,0x01bb89b8,0x010bcf9d,0x00cf42a9,0x023d6f17,0x01da1bca},{0x00e35b25,0x000d824f,0x0152e9cf,0x00ed935d,0x020b8460,0x01c7b83f,0x00c969e5,0x01a74198,0x0046a9d9,0x00cbc768},{0x01597c6a,0x0144a99b,0x00a57551,0x0018269c,0x023c464c,0x0009b022,0x00ee39e1,0x0114c7f2,0x038a9ad2,0x01584c17}}, + {{0x03b0c0d5,0x00b30a39,0x038a6ce4,0x01ded83a,0x01c277a6,0x01010a61,0x0346d3eb,0x018d995e,0x02f2c57c,0x000c286b},{0x0092aed1,0x0125e37b,0x027ca201,0x001a6b6b,0x03290f55,0x0047ba48,0x018d916c,0x01a59062,0x013e35d4,0x0002abb1},{0x003ad2aa,0x007ddcc0,0x00c10f76,0x0001590b,0x002cfca6,0x000ed23e,0x00ee4329,0x00900f04,0x01c24065,0x0082fa70}}, + {{0x02025e60,0x003912b8,0x0327041c,0x017e5ee5,0x02c0ecec,0x015a0d1c,0x02b1ce7c,0x0062220b,0x0145067e,0x01a5d931},{0x009673a6,0x00e1f609,0x00927c2a,0x016faa37,0x01650ef0,0x016f63b5,0x03cd40e1,0x003bc38f,0x0361f0ac,0x01d42acc},{0x02f81037,0x008ca0e8,0x017e23d1,0x011debfe,0x01bcbb68,0x002e2563,0x03e8add6,0x000816e5,0x03fb7075,0x0153e5ac}}, + {{0x02b11ecd,0x016bf185,0x008f22ef,0x00e7d2bb,0x0225d92e,0x00ece785,0x00508873,0x017e16f5,0x01fbe85d,0x01e39a0e},{0x01669279,0x017c810a,0x024941f5,0x0023ebeb,0x00eb7688,0x005760f1,0x02ca4146,0x0073cde7,0x0052bb75,0x00f5ffa7},{0x03b8856b,0x00cb7dcd,0x02f14e06,0x001820d0,0x01d74175,0x00e59e22,0x03fba550,0x00484641,0x03350088,0x01c3c9a3}}, + {{0x00dcf355,0x0104481c,0x0022e464,0x01f73fe7,0x00e03325,0x0152b698,0x02ef769a,0x00973663,0x00039b8c,0x0101395b},{0x01805f47,0x019160ec,0x03832cd0,0x008b06eb,0x03d4d717,0x004cb006,0x03a75b8f,0x013b3d30,0x01cfad88,0x01f034d1},{0x0078338a,0x01c7d2e3,0x02bc2b23,0x018b3f05,0x0280d9aa,0x005f3d44,0x0220a95a,0x00eeeb97,0x0362aaec,0x00835d51}}, + {{0x01b9f543,0x013fac4d,0x02ad93ae,0x018ef464,0x0212cdf7,0x01138ba9,0x011583ab,0x019c3d26,0x028790b4,0x00e2e2b6},{0x033bb758,0x01f0dbf1,0x03734bd1,0x0129b1e5,0x02b3950e,0x003bc922,0x01a53ec8,0x018c5532,0x006f3cee,0x00ae3c79},{0x0351f95d,0x0012a737,0x03d596b8,0x017658fe,0x00ace54a,0x008b66da,0x0036c599,0x012a63a2,0x032ceba1,0x00126bac}}, + {{0x03dcfe7e,0x019f4f18,0x01c81aee,0x0044bc2b,0x00827165,0x014f7c13,0x03b430f0,0x00bf96cc,0x020c8d62,0x01471997},{0x01fc7931,0x001f42dd,0x00ba754a,0x005bd339,0x003fbe49,0x016b3930,0x012a159c,0x009f83b0,0x03530f67,0x01e57b85},{0x02ecbd81,0x0096c294,0x01fce4a9,0x017701a5,0x0175047d,0x00ee4a31,0x012686e5,0x008efcd4,0x0349dc54,0x01b3466f}}, + {{0x02179ca3,0x01d86414,0x03f0afd0,0x00305964,0x015c7428,0x0099711e,0x015d5442,0x00c71014,0x01b40b2e,0x01d483cf},{0x01afc386,0x01984859,0x036203ff,0x0045c6a8,0x0020a8aa,0x00990baa,0x03313f10,0x007ceede,0x027429e4,0x017806ce},{0x039357a1,0x0142f8f4,0x0294a7b6,0x00eaccf4,0x0259edb3,0x01311e6e,0x004d326f,0x0130c346,0x01ccef3c,0x01c424b2}}, + {{0x0364918c,0x00148fc0,0x01638a7b,0x01a1fd5b,0x028ad013,0x0081e5a4,0x01a54f33,0x0174e101,0x003d0257,0x003a856c},{0x00051dcf,0x00f62b1d,0x0143d0ad,0x0042adbd,0x000fda90,0x01743ceb,0x0173e5e4,0x017bc749,0x03b7137a,0x0105ce96},{0x00f9218a,0x015b8c7c,0x00e102f8,0x0158d7e2,0x0169a5b8,0x00b2f176,0x018b347a,0x014cfef2,0x0214a4e3,0x017f1595}}, + {{0x006d7ae5,0x0195c371,0x0391e26d,0x0062a7c6,0x003f42ab,0x010dad86,0x024f8198,0x01542b2a,0x0014c454,0x0189c471},{0x0390988e,0x00b8799d,0x02e44912,0x0078e2e6,0x00075654,0x01923eed,0x0040cd72,0x00a37c76,0x0009d466,0x00c8531d},{0x02651770,0x00609d01,0x0286c265,0x0134513c,0x00ee9281,0x005d223c,0x035c760c,0x00679b36,0x0073ecb8,0x016faa50}}, + {{0x02c89be4,0x016fc244,0x02f38c83,0x018beb72,0x02b3ce2c,0x0097b065,0x034f017b,0x01dd957f,0x00148f61,0x00eab357},{0x0343d2f8,0x003398fc,0x011e368e,0x00782a1f,0x00019eea,0x00117b6f,0x0128d0d1,0x01a5e6bb,0x01944f1b,0x012b41e1},{0x03318301,0x018ecd30,0x0104d0b1,0x0038398b,0x03726701,0x019da88c,0x002d9769,0x00a7a681,0x031d9028,0x00ebfc32}}, + {{0x0220405e,0x0171face,0x02d930f8,0x017f6d6a,0x023b8c47,0x0129d5f9,0x02972456,0x00a3a524,0x006f4cd2,0x004439fa},{0x00c53505,0x0190c2fd,0x00507244,0x009930f9,0x01a39270,0x01d327c6,0x0399bc47,0x01cfe13d,0x0332bd99,0x00b33e7d},{0x0203f5e4,0x003627b5,0x00018af8,0x01478581,0x004a2218,0x002e3bb7,0x039384d0,0x0146ea62,0x020b9693,0x0017155f}}, + {{0x03c97e6f,0x00738c47,0x03b5db1f,0x01808fcf,0x01e8fc98,0x01ed25dd,0x01bf5045,0x00eb5c2b,0x0178fe98,0x01b85530},{0x01c20eb0,0x01aeec22,0x030b9eee,0x01b7d07e,0x0187e16f,0x014421fb,0x009fa731,0x0040b6d7,0x00841861,0x00a27fbc},{0x02d69abf,0x0058cdbf,0x0129f9ec,0x013c19ae,0x026c5b93,0x013a7fe7,0x004bb2ba,0x0063226f,0x002a95ca,0x01abefd9}}, + {{0x02f5d2c1,0x00378318,0x03734fb5,0x01258073,0x0263f0f6,0x01ad70e0,0x01b56d06,0x01188fbd,0x011b9503,0x0036d2e1},{0x0113a8cc,0x01541c3e,0x02ac2bbc,0x01d95867,0x01f47459,0x00ead489,0x00ab5b48,0x01db3b45,0x00edb801,0x004b024f},{0x00b8190f,0x011fe4c2,0x00621f82,0x010508d7,0x001a5a76,0x00c7d7fd,0x03aab96d,0x019cd9dc,0x019c6635,0x00ceaa1e}}, + {{0x01085cf2,0x01fd47af,0x03e3f5e1,0x004b3e99,0x01e3d46a,0x0060033c,0x015ff0a8,0x0150cdd8,0x029e8e21,0x008cf1bc},{0x00156cb1,0x003d623f,0x01a4f069,0x00d8d053,0x01b68aea,0x01ca5ab6,0x0316ae43,0x0134dc44,0x001c8d58,0x0084b343},{0x0318c781,0x0135441f,0x03a51a5e,0x019293f4,0x0048bb37,0x013d3341,0x0143151e,0x019c74e1,0x00911914,0x0076ddde}}, + {{0x006bc26f,0x00d48e5f,0x00227bbe,0x00629ea8,0x01ea5f8b,0x0179a330,0x027a1d5f,0x01bf8f8e,0x02d26e2a,0x00c6b65e},{0x01701ab6,0x0051da77,0x01b4b667,0x00a0ce7c,0x038ae37b,0x012ac852,0x03a0b0fe,0x0097c2bb,0x00a017d2,0x01eb8b2a},{0x0120b962,0x0005fb42,0x0353b6fd,0x0061f8ce,0x007a1463,0x01560a64,0x00e0a792,0x01907c92,0x013a6622,0x007b47f1}} +}; diff --git a/src/ext/ed25519/donna/ed25519-donna-64bit-sse2.h b/src/ext/ed25519/donna/ed25519-donna-64bit-sse2.h new file mode 100644 index 0000000..ca08651 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-64bit-sse2.h @@ -0,0 +1,436 @@ +#if defined(ED25519_GCC_64BIT_SSE_CHOOSE) + +#define HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS + +DONNA_NOINLINE static void +ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) { + int64_t breg = (int64_t)b; + uint64_t sign = (uint64_t)breg >> 63; + uint64_t mask = ~(sign - 1); + uint64_t u = (breg + mask) ^ mask; + + __asm__ __volatile__ ( + /* ysubx+xaddy+t2d */ + "movq %0, %%rax ;\n" + "movd %%rax, %%xmm14 ;\n" + "pshufd $0x00, %%xmm14, %%xmm14 ;\n" + "pxor %%xmm0, %%xmm0 ;\n" + "pxor %%xmm1, %%xmm1 ;\n" + "pxor %%xmm2, %%xmm2 ;\n" + "pxor %%xmm3, %%xmm3 ;\n" + "pxor %%xmm4, %%xmm4 ;\n" + "pxor %%xmm5, %%xmm5 ;\n" + + /* 0 */ + "movq $0, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movq $1, %%rax ;\n" + "movd %%rax, %%xmm6 ;\n" + "pxor %%xmm7, %%xmm7 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm6, %%xmm2 ;\n" + "por %%xmm7, %%xmm3 ;\n" + + /* 1 */ + "movq $1, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 0(%1), %%xmm6 ;\n" + "movdqa 16(%1), %%xmm7 ;\n" + "movdqa 32(%1), %%xmm8 ;\n" + "movdqa 48(%1), %%xmm9 ;\n" + "movdqa 64(%1), %%xmm10 ;\n" + "movdqa 80(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 2 */ + "movq $2, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 96(%1), %%xmm6 ;\n" + "movdqa 112(%1), %%xmm7 ;\n" + "movdqa 128(%1), %%xmm8 ;\n" + "movdqa 144(%1), %%xmm9 ;\n" + "movdqa 160(%1), %%xmm10 ;\n" + "movdqa 176(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 3 */ + "movq $3, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 192(%1), %%xmm6 ;\n" + "movdqa 208(%1), %%xmm7 ;\n" + "movdqa 224(%1), %%xmm8 ;\n" + "movdqa 240(%1), %%xmm9 ;\n" + "movdqa 256(%1), %%xmm10 ;\n" + "movdqa 272(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 4 */ + "movq $4, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 288(%1), %%xmm6 ;\n" + "movdqa 304(%1), %%xmm7 ;\n" + "movdqa 320(%1), %%xmm8 ;\n" + "movdqa 336(%1), %%xmm9 ;\n" + "movdqa 352(%1), %%xmm10 ;\n" + "movdqa 368(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 5 */ + "movq $5, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 384(%1), %%xmm6 ;\n" + "movdqa 400(%1), %%xmm7 ;\n" + "movdqa 416(%1), %%xmm8 ;\n" + "movdqa 432(%1), %%xmm9 ;\n" + "movdqa 448(%1), %%xmm10 ;\n" + "movdqa 464(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 6 */ + "movq $6, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 480(%1), %%xmm6 ;\n" + "movdqa 496(%1), %%xmm7 ;\n" + "movdqa 512(%1), %%xmm8 ;\n" + "movdqa 528(%1), %%xmm9 ;\n" + "movdqa 544(%1), %%xmm10 ;\n" + "movdqa 560(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 7 */ + "movq $7, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 576(%1), %%xmm6 ;\n" + "movdqa 592(%1), %%xmm7 ;\n" + "movdqa 608(%1), %%xmm8 ;\n" + "movdqa 624(%1), %%xmm9 ;\n" + "movdqa 640(%1), %%xmm10 ;\n" + "movdqa 656(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 8 */ + "movq $8, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 672(%1), %%xmm6 ;\n" + "movdqa 688(%1), %%xmm7 ;\n" + "movdqa 704(%1), %%xmm8 ;\n" + "movdqa 720(%1), %%xmm9 ;\n" + "movdqa 736(%1), %%xmm10 ;\n" + "movdqa 752(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* conditionally swap ysubx and xaddy */ + "movq %3, %%rax ;\n" + "xorq $1, %%rax ;\n" + "movd %%rax, %%xmm14 ;\n" + "pxor %%xmm15, %%xmm15 ;\n" + "pshufd $0x00, %%xmm14, %%xmm14 ;\n" + "pxor %%xmm0, %%xmm2 ;\n" + "pxor %%xmm1, %%xmm3 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa %%xmm2, %%xmm6 ;\n" + "movdqa %%xmm3, %%xmm7 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pxor %%xmm6, %%xmm0 ;\n" + "pxor %%xmm7, %%xmm1 ;\n" + "pxor %%xmm0, %%xmm2 ;\n" + "pxor %%xmm1, %%xmm3 ;\n" + + /* store ysubx */ + "xorq %%rax, %%rax ;\n" + "movd %%xmm0, %%rcx ;\n" + "movd %%xmm0, %%r8 ;\n" + "movd %%xmm1, %%rsi ;\n" + "pshufd $0xee, %%xmm0, %%xmm0 ;\n" + "pshufd $0xee, %%xmm1, %%xmm1 ;\n" + "movd %%xmm0, %%rdx ;\n" + "movd %%xmm1, %%rdi ;\n" + "shrdq $51, %%rdx, %%r8 ;\n" + "shrdq $38, %%rsi, %%rdx ;\n" + "shrdq $25, %%rdi, %%rsi ;\n" + "shrq $12, %%rdi ;\n" + "movq %%rcx, %%r9 ;\n" + "movq %%r8, %%r10 ;\n" + "movq %%rdx, %%r11 ;\n" + "movq %%rsi, %%r12 ;\n" + "movq %%rdi, %%r13 ;\n" + "shrq $26, %%r9 ;\n" + "shrq $26, %%r10 ;\n" + "shrq $26, %%r11 ;\n" + "shrq $26, %%r12 ;\n" + "shrq $26, %%r13 ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "andl $0x1ffffff, %%r9d ;\n" + "andl $0x3ffffff, %%r8d ;\n" + "andl $0x1ffffff, %%r10d ;\n" + "andl $0x3ffffff, %%edx ;\n" + "andl $0x1ffffff, %%r11d ;\n" + "andl $0x3ffffff, %%esi ;\n" + "andl $0x1ffffff, %%r12d ;\n" + "andl $0x3ffffff, %%edi ;\n" + "andl $0x1ffffff, %%r13d ;\n" + "movl %%ecx, 0(%2) ;\n" + "movl %%r9d, 4(%2) ;\n" + "movl %%r8d, 8(%2) ;\n" + "movl %%r10d, 12(%2) ;\n" + "movl %%edx, 16(%2) ;\n" + "movl %%r11d, 20(%2) ;\n" + "movl %%esi, 24(%2) ;\n" + "movl %%r12d, 28(%2) ;\n" + "movl %%edi, 32(%2) ;\n" + "movl %%r13d, 36(%2) ;\n" + "movq %%rax, 40(%2) ;\n" + + /* store xaddy */ + "movd %%xmm2, %%rcx ;\n" + "movd %%xmm2, %%r8 ;\n" + "movd %%xmm3, %%rsi ;\n" + "pshufd $0xee, %%xmm2, %%xmm2 ;\n" + "pshufd $0xee, %%xmm3, %%xmm3 ;\n" + "movd %%xmm2, %%rdx ;\n" + "movd %%xmm3, %%rdi ;\n" + "shrdq $51, %%rdx, %%r8 ;\n" + "shrdq $38, %%rsi, %%rdx ;\n" + "shrdq $25, %%rdi, %%rsi ;\n" + "shrq $12, %%rdi ;\n" + "movq %%rcx, %%r9 ;\n" + "movq %%r8, %%r10 ;\n" + "movq %%rdx, %%r11 ;\n" + "movq %%rsi, %%r12 ;\n" + "movq %%rdi, %%r13 ;\n" + "shrq $26, %%r9 ;\n" + "shrq $26, %%r10 ;\n" + "shrq $26, %%r11 ;\n" + "shrq $26, %%r12 ;\n" + "shrq $26, %%r13 ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "andl $0x1ffffff, %%r9d ;\n" + "andl $0x3ffffff, %%r8d ;\n" + "andl $0x1ffffff, %%r10d ;\n" + "andl $0x3ffffff, %%edx ;\n" + "andl $0x1ffffff, %%r11d ;\n" + "andl $0x3ffffff, %%esi ;\n" + "andl $0x1ffffff, %%r12d ;\n" + "andl $0x3ffffff, %%edi ;\n" + "andl $0x1ffffff, %%r13d ;\n" + "movl %%ecx, 48(%2) ;\n" + "movl %%r9d, 52(%2) ;\n" + "movl %%r8d, 56(%2) ;\n" + "movl %%r10d, 60(%2) ;\n" + "movl %%edx, 64(%2) ;\n" + "movl %%r11d, 68(%2) ;\n" + "movl %%esi, 72(%2) ;\n" + "movl %%r12d, 76(%2) ;\n" + "movl %%edi, 80(%2) ;\n" + "movl %%r13d, 84(%2) ;\n" + "movq %%rax, 88(%2) ;\n" + + /* extract t2d */ + "xorq %%rax, %%rax ;\n" + "movd %%xmm4, %%rcx ;\n" + "movd %%xmm4, %%r8 ;\n" + "movd %%xmm5, %%rsi ;\n" + "pshufd $0xee, %%xmm4, %%xmm4 ;\n" + "pshufd $0xee, %%xmm5, %%xmm5 ;\n" + "movd %%xmm4, %%rdx ;\n" + "movd %%xmm5, %%rdi ;\n" + "shrdq $51, %%rdx, %%r8 ;\n" + "shrdq $38, %%rsi, %%rdx ;\n" + "shrdq $25, %%rdi, %%rsi ;\n" + "shrq $12, %%rdi ;\n" + "movq %%rcx, %%r9 ;\n" + "movq %%r8, %%r10 ;\n" + "movq %%rdx, %%r11 ;\n" + "movq %%rsi, %%r12 ;\n" + "movq %%rdi, %%r13 ;\n" + "shrq $26, %%r9 ;\n" + "shrq $26, %%r10 ;\n" + "shrq $26, %%r11 ;\n" + "shrq $26, %%r12 ;\n" + "shrq $26, %%r13 ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "andl $0x1ffffff, %%r9d ;\n" + "andl $0x3ffffff, %%r8d ;\n" + "andl $0x1ffffff, %%r10d ;\n" + "andl $0x3ffffff, %%edx ;\n" + "andl $0x1ffffff, %%r11d ;\n" + "andl $0x3ffffff, %%esi ;\n" + "andl $0x1ffffff, %%r12d ;\n" + "andl $0x3ffffff, %%edi ;\n" + "andl $0x1ffffff, %%r13d ;\n" + "movd %%ecx, %%xmm0 ;\n" + "movd %%r9d, %%xmm4 ;\n" + "movd %%r8d, %%xmm8 ;\n" + "movd %%r10d, %%xmm3 ;\n" + "movd %%edx, %%xmm1 ;\n" + "movd %%r11d, %%xmm5 ;\n" + "movd %%esi, %%xmm6 ;\n" + "movd %%r12d, %%xmm7 ;\n" + "movd %%edi, %%xmm2 ;\n" + "movd %%r13d, %%xmm9 ;\n" + "punpckldq %%xmm4, %%xmm0 ;\n" + "punpckldq %%xmm3, %%xmm8 ;\n" + "punpckldq %%xmm5, %%xmm1 ;\n" + "punpckldq %%xmm7, %%xmm6 ;\n" + "punpckldq %%xmm9, %%xmm2 ;\n" + "punpcklqdq %%xmm8, %%xmm0 ;\n" + "punpcklqdq %%xmm6, %%xmm1 ;\n" + + /* set up 2p in to 3/4 */ + "movl $0x7ffffda, %%ecx ;\n" + "movl $0x3fffffe, %%edx ;\n" + "movl $0x7fffffe, %%eax ;\n" + "movd %%ecx, %%xmm3 ;\n" + "movd %%edx, %%xmm5 ;\n" + "movd %%eax, %%xmm4 ;\n" + "punpckldq %%xmm5, %%xmm3 ;\n" + "punpckldq %%xmm5, %%xmm4 ;\n" + "punpcklqdq %%xmm4, %%xmm3 ;\n" + "movdqa %%xmm4, %%xmm5 ;\n" + "punpcklqdq %%xmm4, %%xmm4 ;\n" + + /* subtract and conditionally move */ + "movl %3, %%ecx ;\n" + "sub $1, %%ecx ;\n" + "movd %%ecx, %%xmm6 ;\n" + "pshufd $0x00, %%xmm6, %%xmm6 ;\n" + "movdqa %%xmm6, %%xmm7 ;\n" + "psubd %%xmm0, %%xmm3 ;\n" + "psubd %%xmm1, %%xmm4 ;\n" + "psubd %%xmm2, %%xmm5 ;\n" + "pand %%xmm6, %%xmm0 ;\n" + "pand %%xmm6, %%xmm1 ;\n" + "pand %%xmm6, %%xmm2 ;\n" + "pandn %%xmm3, %%xmm6 ;\n" + "movdqa %%xmm7, %%xmm3 ;\n" + "pandn %%xmm4, %%xmm7 ;\n" + "pandn %%xmm5, %%xmm3 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm3, %%xmm2 ;\n" + + /* store t2d */ + "movdqa %%xmm0, 96(%2) ;\n" + "movdqa %%xmm1, 112(%2) ;\n" + "movdqa %%xmm2, 128(%2) ;\n" + : + : "m"(u), "r"(&table[pos * 8]), "r"(t), "m"(sign) /* %0 = u, %1 = table, %2 = t, %3 = sign */ + : + "%rax", "%rcx", "%rdx", "%rdi", "%rsi", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", + "%xmm0", "%xmm1", "%xmm2", "%xmm3", "%xmm4", "%xmm5", "%xmm6", "%xmm7", "%xmm8", "%xmm9", "%xmm10", "%xmm11", "%xmm14", "%xmm14", + "cc", "memory" + ); +} + +#endif /* defined(ED25519_GCC_64BIT_SSE_CHOOSE) */ + diff --git a/src/ext/ed25519/donna/ed25519-donna-64bit-tables.h b/src/ext/ed25519/donna/ed25519-donna-64bit-tables.h new file mode 100644 index 0000000..4a6ff9e --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-64bit-tables.h @@ -0,0 +1,53 @@ +static const ge25519 ge25519_basepoint = { + {0x00062d608f25d51a,0x000412a4b4f6592a,0x00075b7171a4b31d,0x0001ff60527118fe,0x000216936d3cd6e5}, + {0x0006666666666658,0x0004cccccccccccc,0x0001999999999999,0x0003333333333333,0x0006666666666666}, + {0x0000000000000001,0x0000000000000000,0x0000000000000000,0x0000000000000000,0x0000000000000000}, + {0x00068ab3a5b7dda3,0x00000eea2a5eadbb,0x0002af8df483c27e,0x000332b375274732,0x00067875f0fd78b7} +}; + +static const bignum25519 ge25519_ecd = { + 0x00034dca135978a3,0x0001a8283b156ebd,0x0005e7a26001c029,0x000739c663a03cbb,0x00052036cee2b6ff +}; + +static const bignum25519 ge25519_ec2d = { + 0x00069b9426b2f159,0x00035050762add7a,0x0003cf44c0038052,0x0006738cc7407977,0x0002406d9dc56dff +}; + +static const bignum25519 ge25519_sqrtneg1 = { + 0x00061b274a0ea0b0,0x0000d5a5fc8f189d,0x0007ef5e9cbd0c60,0x00078595a6804c9e,0x0002b8324804fc1d +}; + +static const ge25519_niels ge25519_niels_sliding_multiples[32] = { + {{0x00003905d740913e,0x0000ba2817d673a2,0x00023e2827f4e67c,0x000133d2e0c21a34,0x00044fd2f9298f81},{0x000493c6f58c3b85,0x0000df7181c325f7,0x0000f50b0b3e4cb7,0x0005329385a44c32,0x00007cf9d3a33d4b},{0x00011205877aaa68,0x000479955893d579,0x00050d66309b67a0,0x0002d42d0dbee5ee,0x0006f117b689f0c6}}, + {{0x00011fe8a4fcd265,0x0007bcb8374faacc,0x00052f5af4ef4d4f,0x0005314098f98d10,0x0002ab91587555bd},{0x0005b0a84cee9730,0x00061d10c97155e4,0x0004059cc8096a10,0x00047a608da8014f,0x0007a164e1b9a80f},{0x0006933f0dd0d889,0x00044386bb4c4295,0x0003cb6d3162508c,0x00026368b872a2c6,0x0005a2826af12b9b}}, + {{0x000182c3a447d6ba,0x00022964e536eff2,0x000192821f540053,0x0002f9f19e788e5c,0x000154a7e73eb1b5},{0x0002bc4408a5bb33,0x000078ebdda05442,0x0002ffb112354123,0x000375ee8df5862d,0x0002945ccf146e20},{0x0003dbf1812a8285,0x0000fa17ba3f9797,0x0006f69cb49c3820,0x00034d5a0db3858d,0x00043aabe696b3bb}}, + {{0x00072c9aaa3221b1,0x000267774474f74d,0x000064b0e9b28085,0x0003f04ef53b27c9,0x0001d6edd5d2e531},{0x00025cd0944ea3bf,0x00075673b81a4d63,0x000150b925d1c0d4,0x00013f38d9294114,0x000461bea69283c9},{0x00036dc801b8b3a2,0x0000e0a7d4935e30,0x0001deb7cecc0d7d,0x000053a94e20dd2c,0x0007a9fbb1c6a0f9}}, + {{0x0006217e039d8064,0x0006dea408337e6d,0x00057ac112628206,0x000647cb65e30473,0x00049c05a51fadc9},{0x0006678aa6a8632f,0x0005ea3788d8b365,0x00021bd6d6994279,0x0007ace75919e4e3,0x00034b9ed338add7},{0x0004e8bf9045af1b,0x000514e33a45e0d6,0x0007533c5b8bfe0f,0x000583557b7e14c9,0x00073c172021b008}}, + {{0x00075b0249864348,0x00052ee11070262b,0x000237ae54fb5acd,0x0003bfd1d03aaab5,0x00018ab598029d5c},{0x000700848a802ade,0x0001e04605c4e5f7,0x0005c0d01b9767fb,0x0007d7889f42388b,0x0004275aae2546d8},{0x00032cc5fd6089e9,0x000426505c949b05,0x00046a18880c7ad2,0x0004a4221888ccda,0x0003dc65522b53df}}, + {{0x0007013b327fbf93,0x0001336eeded6a0d,0x0002b565a2bbf3af,0x000253ce89591955,0x0000267882d17602},{0x0000c222a2007f6d,0x000356b79bdb77ee,0x00041ee81efe12ce,0x000120a9bd07097d,0x000234fd7eec346f},{0x0000a119732ea378,0x00063bf1ba8e2a6c,0x00069f94cc90df9a,0x000431d1779bfc48,0x000497ba6fdaa097}}, + {{0x0003cd86468ccf0b,0x00048553221ac081,0x0006c9464b4e0a6e,0x00075fba84180403,0x00043b5cd4218d05},{0x0006cc0313cfeaa0,0x0001a313848da499,0x0007cb534219230a,0x00039596dedefd60,0x00061e22917f12de},{0x0002762f9bd0b516,0x0001c6e7fbddcbb3,0x00075909c3ace2bd,0x00042101972d3ec9,0x000511d61210ae4d}}, + {{0x000386484420de87,0x0002d6b25db68102,0x000650b4962873c0,0x0004081cfd271394,0x00071a7fe6fe2482},{0x000676ef950e9d81,0x0001b81ae089f258,0x00063c4922951883,0x0002f1d54d9b3237,0x0006d325924ddb85},{0x000182b8a5c8c854,0x00073fcbe5406d8e,0x0005de3430cff451,0x000554b967ac8c41,0x0004746c4b6559ee}}, + {{0x000546c864741147,0x0003a1df99092690,0x0001ca8cc9f4d6bb,0x00036b7fc9cd3b03,0x000219663497db5e},{0x00077b3c6dc69a2b,0x0004edf13ec2fa6e,0x0004e85ad77beac8,0x0007dba2b28e7bda,0x0005c9a51de34fe9},{0x0000f1cf79f10e67,0x00043ccb0a2b7ea2,0x00005089dfff776a,0x0001dd84e1d38b88,0x0004804503c60822}}, + {{0x000021d23a36d175,0x0004fd3373c6476d,0x00020e291eeed02a,0x00062f2ecf2e7210,0x000771e098858de4},{0x00049ed02ca37fc7,0x000474c2b5957884,0x0005b8388e816683,0x0004b6c454b76be4,0x000553398a516506},{0x0002f5d278451edf,0x000730b133997342,0x0006965420eb6975,0x000308a3bfa516cf,0x0005a5ed1d68ff5a}}, + {{0x0005e0c558527359,0x0003395b73afd75c,0x000072afa4e4b970,0x00062214329e0f6d,0x000019b60135fefd},{0x0005122afe150e83,0x0004afc966bb0232,0x0001c478833c8268,0x00017839c3fc148f,0x00044acb897d8bf9},{0x000068145e134b83,0x0001e4860982c3cc,0x000068fb5f13d799,0x0007c9283744547e,0x000150c49fde6ad2}}, + {{0x0001863c9cdca868,0x0003770e295a1709,0x0000d85a3720fd13,0x0005e0ff1f71ab06,0x00078a6d7791e05f},{0x0003f29509471138,0x000729eeb4ca31cf,0x00069c22b575bfbc,0x0004910857bce212,0x0006b2b5a075bb99},{0x0007704b47a0b976,0x0002ae82e91aab17,0x00050bd6429806cd,0x00068055158fd8ea,0x000725c7ffc4ad55}}, + {{0x00002bf71cd098c0,0x00049dabcc6cd230,0x00040a6533f905b2,0x000573efac2eb8a4,0x0004cd54625f855f},{0x00026715d1cf99b2,0x0002205441a69c88,0x000448427dcd4b54,0x0001d191e88abdc5,0x000794cc9277cb1f},{0x0006c426c2ac5053,0x0005a65ece4b095e,0x0000c44086f26bb6,0x0007429568197885,0x0007008357b6fcc8}}, + {{0x00039fbb82584a34,0x00047a568f257a03,0x00014d88091ead91,0x0002145b18b1ce24,0x00013a92a3669d6d},{0x0000672738773f01,0x000752bf799f6171,0x0006b4a6dae33323,0x0007b54696ead1dc,0x00006ef7e9851ad0},{0x0003771cc0577de5,0x0003ca06bb8b9952,0x00000b81c5d50390,0x00043512340780ec,0x0003c296ddf8a2af}}, + {{0x00034d2ebb1f2541,0x0000e815b723ff9d,0x000286b416e25443,0x0000bdfe38d1bee8,0x0000a892c7007477},{0x000515f9d914a713,0x00073191ff2255d5,0x00054f5cc2a4bdef,0x0003dd57fc118bcf,0x0007a99d393490c7},{0x0002ed2436bda3e8,0x00002afd00f291ea,0x0000be7381dea321,0x0003e952d4b2b193,0x000286762d28302f}}, + {{0x00058e2bce2ef5bd,0x00068ce8f78c6f8a,0x0006ee26e39261b2,0x00033d0aa50bcf9d,0x0007686f2a3d6f17},{0x000036093ce35b25,0x0003b64d7552e9cf,0x00071ee0fe0b8460,0x00069d0660c969e5,0x00032f1da046a9d9},{0x000512a66d597c6a,0x0000609a70a57551,0x000026c08a3c464c,0x0004531fc8ee39e1,0x000561305f8a9ad2}}, + {{0x0002cc28e7b0c0d5,0x00077b60eb8a6ce4,0x0004042985c277a6,0x000636657b46d3eb,0x000030a1aef2c57c},{0x0004978dec92aed1,0x000069adae7ca201,0x00011ee923290f55,0x00069641898d916c,0x00000aaec53e35d4},{0x0001f773003ad2aa,0x000005642cc10f76,0x00003b48f82cfca6,0x0002403c10ee4329,0x00020be9c1c24065}}, + {{0x0000e44ae2025e60,0x0005f97b9727041c,0x0005683472c0ecec,0x000188882eb1ce7c,0x00069764c545067e},{0x000387d8249673a6,0x0005bea8dc927c2a,0x0005bd8ed5650ef0,0x0000ef0e3fcd40e1,0x000750ab3361f0ac},{0x00023283a2f81037,0x000477aff97e23d1,0x0000b8958dbcbb68,0x0000205b97e8add6,0x00054f96b3fb7075}}, + {{0x0005afc616b11ecd,0x00039f4aec8f22ef,0x0003b39e1625d92e,0x0005f85bd4508873,0x00078e6839fbe85d},{0x0005f20429669279,0x00008fafae4941f5,0x00015d83c4eb7688,0x0001cf379eca4146,0x0003d7fe9c52bb75},{0x00032df737b8856b,0x0000608342f14e06,0x0003967889d74175,0x0001211907fba550,0x00070f268f350088}}, + {{0x0004112070dcf355,0x0007dcff9c22e464,0x00054ada60e03325,0x00025cd98eef769a,0x000404e56c039b8c},{0x00064583b1805f47,0x00022c1baf832cd0,0x000132c01bd4d717,0x0004ecf4c3a75b8f,0x0007c0d345cfad88},{0x00071f4b8c78338a,0x00062cfc16bc2b23,0x00017cf51280d9aa,0x0003bbae5e20a95a,0x00020d754762aaec}}, + {{0x0004feb135b9f543,0x00063bd192ad93ae,0x00044e2ea612cdf7,0x000670f4991583ab,0x00038b8ada8790b4},{0x0007c36fc73bb758,0x0004a6c797734bd1,0x0000ef248ab3950e,0x00063154c9a53ec8,0x0002b8f1e46f3cee},{0x00004a9cdf51f95d,0x0005d963fbd596b8,0x00022d9b68ace54a,0x0004a98e8836c599,0x000049aeb32ceba1}}, + {{0x00067d3c63dcfe7e,0x000112f0adc81aee,0x00053df04c827165,0x0002fe5b33b430f0,0x00051c665e0c8d62},{0x00007d0b75fc7931,0x00016f4ce4ba754a,0x0005ace4c03fbe49,0x00027e0ec12a159c,0x000795ee17530f67},{0x00025b0a52ecbd81,0x0005dc0695fce4a9,0x0003b928c575047d,0x00023bf3512686e5,0x0006cd19bf49dc54}}, + {{0x0007619052179ca3,0x0000c16593f0afd0,0x000265c4795c7428,0x00031c40515d5442,0x0007520f3db40b2e},{0x0006612165afc386,0x0001171aa36203ff,0x0002642ea820a8aa,0x0001f3bb7b313f10,0x0005e01b3a7429e4},{0x00050be3d39357a1,0x0003ab33d294a7b6,0x0004c479ba59edb3,0x0004c30d184d326f,0x00071092c9ccef3c}}, + {{0x0000523f0364918c,0x000687f56d638a7b,0x00020796928ad013,0x0005d38405a54f33,0x0000ea15b03d0257},{0x0003d8ac74051dcf,0x00010ab6f543d0ad,0x0005d0f3ac0fda90,0x0005ef1d2573e5e4,0x0004173a5bb7137a},{0x00056e31f0f9218a,0x0005635f88e102f8,0x0002cbc5d969a5b8,0x000533fbc98b347a,0x0005fc565614a4e3}}, + {{0x0006570dc46d7ae5,0x00018a9f1b91e26d,0x000436b6183f42ab,0x000550acaa4f8198,0x00062711c414c454},{0x0002e1e67790988e,0x0001e38b9ae44912,0x000648fbb4075654,0x00028df1d840cd72,0x0003214c7409d466},{0x0001827406651770,0x0004d144f286c265,0x00017488f0ee9281,0x00019e6cdb5c760c,0x0005bea94073ecb8}}, + {{0x0005bf0912c89be4,0x00062fadcaf38c83,0x00025ec196b3ce2c,0x00077655ff4f017b,0x0003aacd5c148f61},{0x0000ce63f343d2f8,0x0001e0a87d1e368e,0x000045edbc019eea,0x0006979aed28d0d1,0x0004ad0785944f1b},{0x00063b34c3318301,0x0000e0e62d04d0b1,0x000676a233726701,0x00029e9a042d9769,0x0003aff0cb1d9028}}, + {{0x0005c7eb3a20405e,0x0005fdb5aad930f8,0x0004a757e63b8c47,0x00028e9492972456,0x000110e7e86f4cd2},{0x0006430bf4c53505,0x000264c3e4507244,0x00074c9f19a39270,0x00073f84f799bc47,0x0002ccf9f732bd99},{0x0000d89ed603f5e4,0x00051e1604018af8,0x0000b8eedc4a2218,0x00051ba98b9384d0,0x00005c557e0b9693}}, + {{0x0001ce311fc97e6f,0x0006023f3fb5db1f,0x0007b49775e8fc98,0x0003ad70adbf5045,0x0006e154c178fe98},{0x0006bbb089c20eb0,0x0006df41fb0b9eee,0x00051087ed87e16f,0x000102db5c9fa731,0x000289fef0841861},{0x00016336fed69abf,0x0004f066b929f9ec,0x0004e9ff9e6c5b93,0x00018c89bc4bb2ba,0x0006afbf642a95ca}}, + {{0x0000de0c62f5d2c1,0x00049601cf734fb5,0x0006b5c38263f0f6,0x0004623ef5b56d06,0x0000db4b851b9503},{0x00055070f913a8cc,0x000765619eac2bbc,0x0003ab5225f47459,0x00076ced14ab5b48,0x00012c093cedb801},{0x00047f9308b8190f,0x000414235c621f82,0x00031f5ff41a5a76,0x0006736773aab96d,0x00033aa8799c6635}}, + {{0x0007f51ebd085cf2,0x00012cfa67e3f5e1,0x0001800cf1e3d46a,0x00054337615ff0a8,0x000233c6f29e8e21},{0x0000f588fc156cb1,0x000363414da4f069,0x0007296ad9b68aea,0x0004d3711316ae43,0x000212cd0c1c8d58},{0x0004d5107f18c781,0x00064a4fd3a51a5e,0x0004f4cd0448bb37,0x000671d38543151e,0x0001db7778911914}}, + {{0x000352397c6bc26f,0x00018a7aa0227bbe,0x0005e68cc1ea5f8b,0x0006fe3e3a7a1d5f,0x00031ad97ad26e2a},{0x00014769dd701ab6,0x00028339f1b4b667,0x0004ab214b8ae37b,0x00025f0aefa0b0fe,0x0007ae2ca8a017d2},{0x000017ed0920b962,0x000187e33b53b6fd,0x00055829907a1463,0x000641f248e0a792,0x0001ed1fc53a6622}} +}; diff --git a/src/ext/ed25519/donna/ed25519-donna-64bit-x86-32bit.h b/src/ext/ed25519/donna/ed25519-donna-64bit-x86-32bit.h new file mode 100644 index 0000000..1ce109c --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-64bit-x86-32bit.h @@ -0,0 +1,435 @@ +#if defined(ED25519_GCC_64BIT_32BIT_CHOOSE) + +#define HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS + +DONNA_NOINLINE static void +ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) { + int64_t breg = (int64_t)b; + uint64_t sign = (uint64_t)breg >> 63; + uint64_t mask = ~(sign - 1); + uint64_t u = (breg + mask) ^ mask; + + __asm__ __volatile__ ( + /* ysubx+xaddy+t2d */ + "movq %0, %%rax ;\n" + "movd %%rax, %%xmm14 ;\n" + "pshufd $0x00, %%xmm14, %%xmm14 ;\n" + "pxor %%xmm0, %%xmm0 ;\n" + "pxor %%xmm1, %%xmm1 ;\n" + "pxor %%xmm2, %%xmm2 ;\n" + "pxor %%xmm3, %%xmm3 ;\n" + "pxor %%xmm4, %%xmm4 ;\n" + "pxor %%xmm5, %%xmm5 ;\n" + + /* 0 */ + "movq $0, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movq $1, %%rax ;\n" + "movd %%rax, %%xmm6 ;\n" + "pxor %%xmm7, %%xmm7 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm6, %%xmm2 ;\n" + "por %%xmm7, %%xmm3 ;\n" + + /* 1 */ + "movq $1, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 0(%1), %%xmm6 ;\n" + "movdqa 16(%1), %%xmm7 ;\n" + "movdqa 32(%1), %%xmm8 ;\n" + "movdqa 48(%1), %%xmm9 ;\n" + "movdqa 64(%1), %%xmm10 ;\n" + "movdqa 80(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 2 */ + "movq $2, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 96(%1), %%xmm6 ;\n" + "movdqa 112(%1), %%xmm7 ;\n" + "movdqa 128(%1), %%xmm8 ;\n" + "movdqa 144(%1), %%xmm9 ;\n" + "movdqa 160(%1), %%xmm10 ;\n" + "movdqa 176(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 3 */ + "movq $3, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 192(%1), %%xmm6 ;\n" + "movdqa 208(%1), %%xmm7 ;\n" + "movdqa 224(%1), %%xmm8 ;\n" + "movdqa 240(%1), %%xmm9 ;\n" + "movdqa 256(%1), %%xmm10 ;\n" + "movdqa 272(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 4 */ + "movq $4, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 288(%1), %%xmm6 ;\n" + "movdqa 304(%1), %%xmm7 ;\n" + "movdqa 320(%1), %%xmm8 ;\n" + "movdqa 336(%1), %%xmm9 ;\n" + "movdqa 352(%1), %%xmm10 ;\n" + "movdqa 368(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 5 */ + "movq $5, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 384(%1), %%xmm6 ;\n" + "movdqa 400(%1), %%xmm7 ;\n" + "movdqa 416(%1), %%xmm8 ;\n" + "movdqa 432(%1), %%xmm9 ;\n" + "movdqa 448(%1), %%xmm10 ;\n" + "movdqa 464(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 6 */ + "movq $6, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 480(%1), %%xmm6 ;\n" + "movdqa 496(%1), %%xmm7 ;\n" + "movdqa 512(%1), %%xmm8 ;\n" + "movdqa 528(%1), %%xmm9 ;\n" + "movdqa 544(%1), %%xmm10 ;\n" + "movdqa 560(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 7 */ + "movq $7, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 576(%1), %%xmm6 ;\n" + "movdqa 592(%1), %%xmm7 ;\n" + "movdqa 608(%1), %%xmm8 ;\n" + "movdqa 624(%1), %%xmm9 ;\n" + "movdqa 640(%1), %%xmm10 ;\n" + "movdqa 656(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 8 */ + "movq $8, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 672(%1), %%xmm6 ;\n" + "movdqa 688(%1), %%xmm7 ;\n" + "movdqa 704(%1), %%xmm8 ;\n" + "movdqa 720(%1), %%xmm9 ;\n" + "movdqa 736(%1), %%xmm10 ;\n" + "movdqa 752(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* conditionally swap ysubx and xaddy */ + "movq %3, %%rax ;\n" + "xorq $1, %%rax ;\n" + "movd %%rax, %%xmm14 ;\n" + "pxor %%xmm15, %%xmm15 ;\n" + "pshufd $0x00, %%xmm14, %%xmm14 ;\n" + "pxor %%xmm0, %%xmm2 ;\n" + "pxor %%xmm1, %%xmm3 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa %%xmm2, %%xmm6 ;\n" + "movdqa %%xmm3, %%xmm7 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pxor %%xmm6, %%xmm0 ;\n" + "pxor %%xmm7, %%xmm1 ;\n" + "pxor %%xmm0, %%xmm2 ;\n" + "pxor %%xmm1, %%xmm3 ;\n" + + /* store ysubx */ + "xorq %%rax, %%rax ;\n" + "movd %%xmm0, %%rcx ;\n" + "movd %%xmm0, %%r8 ;\n" + "movd %%xmm1, %%rsi ;\n" + "pshufd $0xee, %%xmm0, %%xmm0 ;\n" + "pshufd $0xee, %%xmm1, %%xmm1 ;\n" + "movd %%xmm0, %%rdx ;\n" + "movd %%xmm1, %%rdi ;\n" + "shrdq $51, %%rdx, %%r8 ;\n" + "shrdq $38, %%rsi, %%rdx ;\n" + "shrdq $25, %%rdi, %%rsi ;\n" + "shrq $12, %%rdi ;\n" + "movq %%rcx, %%r9 ;\n" + "movq %%r8, %%r10 ;\n" + "movq %%rdx, %%r11 ;\n" + "movq %%rsi, %%r12 ;\n" + "movq %%rdi, %%r13 ;\n" + "shrq $26, %%r9 ;\n" + "shrq $26, %%r10 ;\n" + "shrq $26, %%r11 ;\n" + "shrq $26, %%r12 ;\n" + "shrq $26, %%r13 ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "andl $0x1ffffff, %%r9d ;\n" + "andl $0x3ffffff, %%r8d ;\n" + "andl $0x1ffffff, %%r10d ;\n" + "andl $0x3ffffff, %%edx ;\n" + "andl $0x1ffffff, %%r11d ;\n" + "andl $0x3ffffff, %%esi ;\n" + "andl $0x1ffffff, %%r12d ;\n" + "andl $0x3ffffff, %%edi ;\n" + "andl $0x1ffffff, %%r13d ;\n" + "movl %%ecx, 0(%2) ;\n" + "movl %%r9d, 4(%2) ;\n" + "movl %%r8d, 8(%2) ;\n" + "movl %%r10d, 12(%2) ;\n" + "movl %%edx, 16(%2) ;\n" + "movl %%r11d, 20(%2) ;\n" + "movl %%esi, 24(%2) ;\n" + "movl %%r12d, 28(%2) ;\n" + "movl %%edi, 32(%2) ;\n" + "movl %%r13d, 36(%2) ;\n" + + /* store xaddy */ + "movd %%xmm2, %%rcx ;\n" + "movd %%xmm2, %%r8 ;\n" + "movd %%xmm3, %%rsi ;\n" + "pshufd $0xee, %%xmm2, %%xmm2 ;\n" + "pshufd $0xee, %%xmm3, %%xmm3 ;\n" + "movd %%xmm2, %%rdx ;\n" + "movd %%xmm3, %%rdi ;\n" + "shrdq $51, %%rdx, %%r8 ;\n" + "shrdq $38, %%rsi, %%rdx ;\n" + "shrdq $25, %%rdi, %%rsi ;\n" + "shrq $12, %%rdi ;\n" + "movq %%rcx, %%r9 ;\n" + "movq %%r8, %%r10 ;\n" + "movq %%rdx, %%r11 ;\n" + "movq %%rsi, %%r12 ;\n" + "movq %%rdi, %%r13 ;\n" + "shrq $26, %%r9 ;\n" + "shrq $26, %%r10 ;\n" + "shrq $26, %%r11 ;\n" + "shrq $26, %%r12 ;\n" + "shrq $26, %%r13 ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "andl $0x1ffffff, %%r9d ;\n" + "andl $0x3ffffff, %%r8d ;\n" + "andl $0x1ffffff, %%r10d ;\n" + "andl $0x3ffffff, %%edx ;\n" + "andl $0x1ffffff, %%r11d ;\n" + "andl $0x3ffffff, %%esi ;\n" + "andl $0x1ffffff, %%r12d ;\n" + "andl $0x3ffffff, %%edi ;\n" + "andl $0x1ffffff, %%r13d ;\n" + "movl %%ecx, 40(%2) ;\n" + "movl %%r9d, 44(%2) ;\n" + "movl %%r8d, 48(%2) ;\n" + "movl %%r10d, 52(%2) ;\n" + "movl %%edx, 56(%2) ;\n" + "movl %%r11d, 60(%2) ;\n" + "movl %%esi, 64(%2) ;\n" + "movl %%r12d, 68(%2) ;\n" + "movl %%edi, 72(%2) ;\n" + "movl %%r13d, 76(%2) ;\n" + + /* extract t2d */ + "xorq %%rax, %%rax ;\n" + "movd %%xmm4, %%rcx ;\n" + "movd %%xmm4, %%r8 ;\n" + "movd %%xmm5, %%rsi ;\n" + "pshufd $0xee, %%xmm4, %%xmm4 ;\n" + "pshufd $0xee, %%xmm5, %%xmm5 ;\n" + "movd %%xmm4, %%rdx ;\n" + "movd %%xmm5, %%rdi ;\n" + "shrdq $51, %%rdx, %%r8 ;\n" + "shrdq $38, %%rsi, %%rdx ;\n" + "shrdq $25, %%rdi, %%rsi ;\n" + "shrq $12, %%rdi ;\n" + "movq %%rcx, %%r9 ;\n" + "movq %%r8, %%r10 ;\n" + "movq %%rdx, %%r11 ;\n" + "movq %%rsi, %%r12 ;\n" + "movq %%rdi, %%r13 ;\n" + "shrq $26, %%r9 ;\n" + "shrq $26, %%r10 ;\n" + "shrq $26, %%r11 ;\n" + "shrq $26, %%r12 ;\n" + "shrq $26, %%r13 ;\n" + "andl $0x3ffffff, %%ecx ;\n" + "andl $0x1ffffff, %%r9d ;\n" + "andl $0x3ffffff, %%r8d ;\n" + "andl $0x1ffffff, %%r10d ;\n" + "andl $0x3ffffff, %%edx ;\n" + "andl $0x1ffffff, %%r11d ;\n" + "andl $0x3ffffff, %%esi ;\n" + "andl $0x1ffffff, %%r12d ;\n" + "andl $0x3ffffff, %%edi ;\n" + "andl $0x1ffffff, %%r13d ;\n" + "movd %%ecx, %%xmm0 ;\n" + "movd %%r9d, %%xmm4 ;\n" + "movd %%r8d, %%xmm8 ;\n" + "movd %%r10d, %%xmm3 ;\n" + "movd %%edx, %%xmm1 ;\n" + "movd %%r11d, %%xmm5 ;\n" + "movd %%esi, %%xmm6 ;\n" + "movd %%r12d, %%xmm7 ;\n" + "movd %%edi, %%xmm2 ;\n" + "movd %%r13d, %%xmm9 ;\n" + "punpckldq %%xmm4, %%xmm0 ;\n" + "punpckldq %%xmm3, %%xmm8 ;\n" + "punpckldq %%xmm5, %%xmm1 ;\n" + "punpckldq %%xmm7, %%xmm6 ;\n" + "punpckldq %%xmm9, %%xmm2 ;\n" + "punpcklqdq %%xmm8, %%xmm0 ;\n" + "punpcklqdq %%xmm6, %%xmm1 ;\n" + + /* set up 2p in to 3/4 */ + "movl $0x7ffffda, %%ecx ;\n" + "movl $0x3fffffe, %%edx ;\n" + "movl $0x7fffffe, %%eax ;\n" + "movd %%ecx, %%xmm3 ;\n" + "movd %%edx, %%xmm5 ;\n" + "movd %%eax, %%xmm4 ;\n" + "punpckldq %%xmm5, %%xmm3 ;\n" + "punpckldq %%xmm5, %%xmm4 ;\n" + "punpcklqdq %%xmm4, %%xmm3 ;\n" + "movdqa %%xmm4, %%xmm5 ;\n" + "punpcklqdq %%xmm4, %%xmm4 ;\n" + + /* subtract and conditionally move */ + "movl %3, %%ecx ;\n" + "sub $1, %%ecx ;\n" + "movd %%ecx, %%xmm6 ;\n" + "pshufd $0x00, %%xmm6, %%xmm6 ;\n" + "movdqa %%xmm6, %%xmm7 ;\n" + "psubd %%xmm0, %%xmm3 ;\n" + "psubd %%xmm1, %%xmm4 ;\n" + "psubd %%xmm2, %%xmm5 ;\n" + "pand %%xmm6, %%xmm0 ;\n" + "pand %%xmm6, %%xmm1 ;\n" + "pand %%xmm6, %%xmm2 ;\n" + "pandn %%xmm3, %%xmm6 ;\n" + "movdqa %%xmm7, %%xmm3 ;\n" + "pandn %%xmm4, %%xmm7 ;\n" + "pandn %%xmm5, %%xmm3 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm3, %%xmm2 ;\n" + + /* store t2d */ + "movdqa %%xmm0, 80(%2) ;\n" + "movdqa %%xmm1, 96(%2) ;\n" + "movd %%xmm2, %%rax ;\n" + "movq %%rax, 112(%2) ;\n" + : + : "m"(u), "r"(&table[pos * 8]), "r"(t), "m"(sign) /* %0 = u, %1 = table, %2 = t, %3 = sign */ + : + "%rax", "%rcx", "%rdx", "%rdi", "%rsi", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", + "%xmm0", "%xmm1", "%xmm2", "%xmm3", "%xmm4", "%xmm5", "%xmm6", "%xmm7", "%xmm8", "%xmm9", "%xmm10", "%xmm11", "%xmm14", "%xmm14", + "cc", "memory" + ); +} + +#endif /* defined(ED25519_GCC_64BIT_32BIT_CHOOSE) */ + diff --git a/src/ext/ed25519/donna/ed25519-donna-64bit-x86.h b/src/ext/ed25519/donna/ed25519-donna-64bit-x86.h new file mode 100644 index 0000000..30bd472 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-64bit-x86.h @@ -0,0 +1,351 @@ +#if defined(ED25519_GCC_64BIT_X86_CHOOSE) + +#define HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS + +DONNA_NOINLINE static void +ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) { + int64_t breg = (int64_t)b; + uint64_t sign = (uint64_t)breg >> 63; + uint64_t mask = ~(sign - 1); + uint64_t u = (breg + mask) ^ mask; + + __asm__ __volatile__ ( + /* ysubx+xaddy+t2d */ + "movq %0, %%rax ;\n" + "movd %%rax, %%xmm14 ;\n" + "pshufd $0x00, %%xmm14, %%xmm14 ;\n" + "pxor %%xmm0, %%xmm0 ;\n" + "pxor %%xmm1, %%xmm1 ;\n" + "pxor %%xmm2, %%xmm2 ;\n" + "pxor %%xmm3, %%xmm3 ;\n" + "pxor %%xmm4, %%xmm4 ;\n" + "pxor %%xmm5, %%xmm5 ;\n" + + /* 0 */ + "movq $0, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movq $1, %%rax ;\n" + "movd %%rax, %%xmm6 ;\n" + "pxor %%xmm7, %%xmm7 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm6, %%xmm2 ;\n" + "por %%xmm7, %%xmm3 ;\n" + + /* 1 */ + "movq $1, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 0(%1), %%xmm6 ;\n" + "movdqa 16(%1), %%xmm7 ;\n" + "movdqa 32(%1), %%xmm8 ;\n" + "movdqa 48(%1), %%xmm9 ;\n" + "movdqa 64(%1), %%xmm10 ;\n" + "movdqa 80(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 2 */ + "movq $2, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 96(%1), %%xmm6 ;\n" + "movdqa 112(%1), %%xmm7 ;\n" + "movdqa 128(%1), %%xmm8 ;\n" + "movdqa 144(%1), %%xmm9 ;\n" + "movdqa 160(%1), %%xmm10 ;\n" + "movdqa 176(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 3 */ + "movq $3, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 192(%1), %%xmm6 ;\n" + "movdqa 208(%1), %%xmm7 ;\n" + "movdqa 224(%1), %%xmm8 ;\n" + "movdqa 240(%1), %%xmm9 ;\n" + "movdqa 256(%1), %%xmm10 ;\n" + "movdqa 272(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 4 */ + "movq $4, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 288(%1), %%xmm6 ;\n" + "movdqa 304(%1), %%xmm7 ;\n" + "movdqa 320(%1), %%xmm8 ;\n" + "movdqa 336(%1), %%xmm9 ;\n" + "movdqa 352(%1), %%xmm10 ;\n" + "movdqa 368(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 5 */ + "movq $5, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 384(%1), %%xmm6 ;\n" + "movdqa 400(%1), %%xmm7 ;\n" + "movdqa 416(%1), %%xmm8 ;\n" + "movdqa 432(%1), %%xmm9 ;\n" + "movdqa 448(%1), %%xmm10 ;\n" + "movdqa 464(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 6 */ + "movq $6, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 480(%1), %%xmm6 ;\n" + "movdqa 496(%1), %%xmm7 ;\n" + "movdqa 512(%1), %%xmm8 ;\n" + "movdqa 528(%1), %%xmm9 ;\n" + "movdqa 544(%1), %%xmm10 ;\n" + "movdqa 560(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 7 */ + "movq $7, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 576(%1), %%xmm6 ;\n" + "movdqa 592(%1), %%xmm7 ;\n" + "movdqa 608(%1), %%xmm8 ;\n" + "movdqa 624(%1), %%xmm9 ;\n" + "movdqa 640(%1), %%xmm10 ;\n" + "movdqa 656(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* 8 */ + "movq $8, %%rax ;\n" + "movd %%rax, %%xmm15 ;\n" + "pshufd $0x00, %%xmm15, %%xmm15 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa 672(%1), %%xmm6 ;\n" + "movdqa 688(%1), %%xmm7 ;\n" + "movdqa 704(%1), %%xmm8 ;\n" + "movdqa 720(%1), %%xmm9 ;\n" + "movdqa 736(%1), %%xmm10 ;\n" + "movdqa 752(%1), %%xmm11 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pand %%xmm15, %%xmm8 ;\n" + "pand %%xmm15, %%xmm9 ;\n" + "pand %%xmm15, %%xmm10 ;\n" + "pand %%xmm15, %%xmm11 ;\n" + "por %%xmm6, %%xmm0 ;\n" + "por %%xmm7, %%xmm1 ;\n" + "por %%xmm8, %%xmm2 ;\n" + "por %%xmm9, %%xmm3 ;\n" + "por %%xmm10, %%xmm4 ;\n" + "por %%xmm11, %%xmm5 ;\n" + + /* conditionally swap ysubx and xaddy */ + "movq %3, %%rax ;\n" + "xorq $1, %%rax ;\n" + "movd %%rax, %%xmm14 ;\n" + "pxor %%xmm15, %%xmm15 ;\n" + "pshufd $0x00, %%xmm14, %%xmm14 ;\n" + "pxor %%xmm0, %%xmm2 ;\n" + "pxor %%xmm1, %%xmm3 ;\n" + "pcmpeqd %%xmm14, %%xmm15 ;\n" + "movdqa %%xmm2, %%xmm6 ;\n" + "movdqa %%xmm3, %%xmm7 ;\n" + "pand %%xmm15, %%xmm6 ;\n" + "pand %%xmm15, %%xmm7 ;\n" + "pxor %%xmm6, %%xmm0 ;\n" + "pxor %%xmm7, %%xmm1 ;\n" + "pxor %%xmm0, %%xmm2 ;\n" + "pxor %%xmm1, %%xmm3 ;\n" + + /* store ysubx */ + "movq $0x7ffffffffffff, %%rax ;\n" + "movd %%xmm0, %%rcx ;\n" + "movd %%xmm0, %%r8 ;\n" + "movd %%xmm1, %%rsi ;\n" + "pshufd $0xee, %%xmm0, %%xmm0 ;\n" + "pshufd $0xee, %%xmm1, %%xmm1 ;\n" + "movd %%xmm0, %%rdx ;\n" + "movd %%xmm1, %%rdi ;\n" + "shrdq $51, %%rdx, %%r8 ;\n" + "shrdq $38, %%rsi, %%rdx ;\n" + "shrdq $25, %%rdi, %%rsi ;\n" + "shrq $12, %%rdi ;\n" + "andq %%rax, %%rcx ;\n" + "andq %%rax, %%r8 ;\n" + "andq %%rax, %%rdx ;\n" + "andq %%rax, %%rsi ;\n" + "andq %%rax, %%rdi ;\n" + "movq %%rcx, 0(%2) ;\n" + "movq %%r8, 8(%2) ;\n" + "movq %%rdx, 16(%2) ;\n" + "movq %%rsi, 24(%2) ;\n" + "movq %%rdi, 32(%2) ;\n" + + /* store xaddy */ + "movq $0x7ffffffffffff, %%rax ;\n" + "movd %%xmm2, %%rcx ;\n" + "movd %%xmm2, %%r8 ;\n" + "movd %%xmm3, %%rsi ;\n" + "pshufd $0xee, %%xmm2, %%xmm2 ;\n" + "pshufd $0xee, %%xmm3, %%xmm3 ;\n" + "movd %%xmm2, %%rdx ;\n" + "movd %%xmm3, %%rdi ;\n" + "shrdq $51, %%rdx, %%r8 ;\n" + "shrdq $38, %%rsi, %%rdx ;\n" + "shrdq $25, %%rdi, %%rsi ;\n" + "shrq $12, %%rdi ;\n" + "andq %%rax, %%rcx ;\n" + "andq %%rax, %%r8 ;\n" + "andq %%rax, %%rdx ;\n" + "andq %%rax, %%rsi ;\n" + "andq %%rax, %%rdi ;\n" + "movq %%rcx, 40(%2) ;\n" + "movq %%r8, 48(%2) ;\n" + "movq %%rdx, 56(%2) ;\n" + "movq %%rsi, 64(%2) ;\n" + "movq %%rdi, 72(%2) ;\n" + + /* extract t2d */ + "movq $0x7ffffffffffff, %%rax ;\n" + "movd %%xmm4, %%rcx ;\n" + "movd %%xmm4, %%r8 ;\n" + "movd %%xmm5, %%rsi ;\n" + "pshufd $0xee, %%xmm4, %%xmm4 ;\n" + "pshufd $0xee, %%xmm5, %%xmm5 ;\n" + "movd %%xmm4, %%rdx ;\n" + "movd %%xmm5, %%rdi ;\n" + "shrdq $51, %%rdx, %%r8 ;\n" + "shrdq $38, %%rsi, %%rdx ;\n" + "shrdq $25, %%rdi, %%rsi ;\n" + "shrq $12, %%rdi ;\n" + "andq %%rax, %%rcx ;\n" + "andq %%rax, %%r8 ;\n" + "andq %%rax, %%rdx ;\n" + "andq %%rax, %%rsi ;\n" + "andq %%rax, %%rdi ;\n" + + /* conditionally negate t2d */ + "movq %3, %%rax ;\n" + "movq $0xfffffffffffda, %%r9 ;\n" + "movq $0xffffffffffffe, %%r10 ;\n" + "movq %%r10, %%r11 ;\n" + "movq %%r10, %%r12 ;\n" + "movq %%r10, %%r13 ;\n" + "subq %%rcx, %%r9 ;\n" + "subq %%r8, %%r10 ;\n" + "subq %%rdx, %%r11 ;\n" + "subq %%rsi, %%r12 ;\n" + "subq %%rdi, %%r13 ;\n" + "cmpq $1, %%rax ;\n" + "cmove %%r9, %%rcx ;\n" + "cmove %%r10, %%r8 ;\n" + "cmove %%r11, %%rdx ;\n" + "cmove %%r12, %%rsi ;\n" + "cmove %%r13, %%rdi ;\n" + + /* store t2d */ + "movq %%rcx, 80(%2) ;\n" + "movq %%r8, 88(%2) ;\n" + "movq %%rdx, 96(%2) ;\n" + "movq %%rsi, 104(%2) ;\n" + "movq %%rdi, 112(%2) ;\n" + : + : "m"(u), "r"(&table[pos * 8]), "r"(t), "m"(sign) /* %0 = u, %1 = table, %2 = t, %3 = sign */ + : + "%rax", "%rcx", "%rdx", "%rdi", "%rsi", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", + "%xmm0", "%xmm1", "%xmm2", "%xmm3", "%xmm4", "%xmm5", "%xmm6", "%xmm7", "%xmm8", "%xmm9", "%xmm10", "%xmm11", "%xmm14", "%xmm14", + "cc", "memory" + ); +} + +#endif /* defined(ED25519_GCC_64BIT_X86_CHOOSE) */ + diff --git a/src/ext/ed25519/donna/ed25519-donna-basepoint-table.h b/src/ext/ed25519/donna/ed25519-donna-basepoint-table.h new file mode 100644 index 0000000..41dcd52 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-basepoint-table.h @@ -0,0 +1,259 @@ +/* multiples of the base point in packed {ysubx, xaddy, t2d} form */ +static const uint8_t ALIGN(16) ge25519_niels_base_multiples[256][96] = { + {0x3e,0x91,0x40,0xd7,0x05,0x39,0x10,0x9d,0xb3,0xbe,0x40,0xd1,0x05,0x9f,0x39,0xfd,0x09,0x8a,0x8f,0x68,0x34,0x84,0xc1,0xa5,0x67,0x12,0xf8,0x98,0x92,0x2f,0xfd,0x44,0x85,0x3b,0x8c,0xf5,0xc6,0x93,0xbc,0x2f,0x19,0x0e,0x8c,0xfb,0xc6,0x2d,0x93,0xcf,0xc2,0x42,0x3d,0x64,0x98,0x48,0x0b,0x27,0x65,0xba,0xd4,0x33,0x3a,0x9d,0xcf,0x07,0x59,0xbb,0x6f,0x4b,0x67,0x15,0xbd,0xdb,0xea,0xa5,0xa2,0xee,0x00,0x3f,0xe1,0x41,0xfa,0xc6,0x57,0xc9,0x1c,0x9d,0xd4,0xcd,0xca,0xec,0x16,0xaf,0x1f,0xbe,0x0e,0x4f}, + {0xa8,0xd5,0xb4,0x42,0x60,0xa5,0x99,0x8a,0xf6,0xac,0x60,0x4e,0x0c,0x81,0x2b,0x8f,0xaa,0x37,0x6e,0xb1,0x6b,0x23,0x9e,0xe0,0x55,0x25,0xc9,0x69,0xa6,0x95,0xb5,0x6b,0xd7,0x71,0x3c,0x93,0xfc,0xe7,0x24,0x92,0xb5,0xf5,0x0f,0x7a,0x96,0x9d,0x46,0x9f,0x02,0x07,0xd6,0xe1,0x65,0x9a,0xa6,0x5a,0x2e,0x2e,0x7d,0xa8,0x3f,0x06,0x0c,0x59,0x02,0x68,0xd3,0xda,0xaa,0x7e,0x34,0x6e,0x05,0x48,0xee,0x83,0x93,0x59,0xf3,0xba,0x26,0x68,0x07,0xe6,0x10,0xbe,0xca,0x3b,0xb8,0xd1,0x5e,0x16,0x0a,0x4f,0x31,0x49}, + {0x65,0xd2,0xfc,0xa4,0xe8,0x1f,0x61,0x56,0x7d,0xba,0xc1,0xe5,0xfd,0x53,0xd3,0x3b,0xbd,0xd6,0x4b,0x21,0x1a,0xf3,0x31,0x81,0x62,0xda,0x5b,0x55,0x87,0x15,0xb9,0x2a,0x30,0x97,0xee,0x4c,0xa8,0xb0,0x25,0xaf,0x8a,0x4b,0x86,0xe8,0x30,0x84,0x5a,0x02,0x32,0x67,0x01,0x9f,0x02,0x50,0x1b,0xc1,0xf4,0xf8,0x80,0x9a,0x1b,0x4e,0x16,0x7a,0x34,0x48,0x67,0xf1,0xf4,0x11,0xf2,0x9b,0x95,0xf8,0x2d,0xf6,0x17,0x6b,0x4e,0xb8,0x4e,0x2a,0x72,0x5b,0x07,0x6f,0xde,0xd7,0x21,0x2a,0xbb,0x63,0xb9,0x04,0x9a,0x54}, + {0xbf,0x18,0x68,0x05,0x0a,0x05,0xfe,0x95,0xa9,0xfa,0x60,0x56,0x71,0x89,0x7e,0x32,0x73,0x50,0xa0,0x06,0xcd,0xe3,0xe8,0xc3,0x9a,0xa4,0x45,0x74,0x4c,0x3f,0x93,0x27,0x9f,0x09,0xfc,0x8e,0xb9,0x51,0x73,0x28,0x38,0x25,0xfd,0x7d,0xf4,0xc6,0x65,0x67,0x65,0x92,0x0a,0xfb,0x3d,0x8d,0x34,0xca,0x27,0x87,0xe5,0x21,0x03,0x91,0x0e,0x68,0xb0,0x26,0x14,0xe5,0xec,0x45,0x1e,0xbf,0x94,0x0f,0xba,0x6d,0x3d,0xc6,0x2b,0xe3,0xc0,0x52,0xf8,0x8c,0xd5,0x74,0x29,0xe4,0x18,0x4c,0xe6,0xb0,0xb1,0x79,0xf0,0x44}, + {0xba,0xd6,0x47,0xa4,0xc3,0x82,0x91,0x7f,0xb7,0x29,0x27,0x4b,0xd1,0x14,0x00,0xd5,0x87,0xa0,0x64,0xb8,0x1c,0xf1,0x3c,0xe3,0xf3,0x55,0x1b,0xeb,0x73,0x7e,0x4a,0x15,0x33,0xbb,0xa5,0x08,0x44,0xbc,0x12,0xa2,0x02,0xed,0x5e,0xc7,0xc3,0x48,0x50,0x8d,0x44,0xec,0xbf,0x5a,0x0c,0xeb,0x1b,0xdd,0xeb,0x06,0xe2,0x46,0xf1,0xcc,0x45,0x29,0xb3,0x03,0xd0,0xe7,0x79,0xa1,0x32,0xc8,0x7e,0x4d,0x12,0x00,0x0a,0x9d,0x72,0x5f,0xf3,0x8f,0x6d,0x0e,0xa1,0xd4,0xc1,0x62,0x98,0x7a,0xb2,0x38,0x59,0xac,0xb8,0x68}, + {0xa4,0x8c,0x7d,0x7b,0xb6,0x06,0x98,0x49,0x39,0x27,0xd2,0x27,0x84,0xe2,0x5b,0x57,0xb9,0x53,0x45,0x20,0xe7,0x5c,0x08,0xbb,0x84,0x78,0x41,0xae,0x41,0x4c,0xb6,0x38,0x31,0x71,0x15,0x77,0xeb,0xee,0x0c,0x3a,0x88,0xaf,0xc8,0x00,0x89,0x15,0x27,0x9b,0x36,0xa7,0x59,0xda,0x68,0xb6,0x65,0x80,0xbd,0x38,0xcc,0xa2,0xb6,0x7b,0xe5,0x51,0xa4,0xe3,0x9d,0x68,0x91,0xad,0x9d,0x8f,0x37,0x91,0xfb,0xf8,0x28,0x24,0x5f,0x17,0x88,0xb9,0xcf,0x9f,0x32,0xb5,0x0a,0x05,0x9f,0xc0,0x54,0x13,0xa2,0xdf,0x65,0x78}, + {0xb1,0x21,0x32,0xaa,0x9a,0x2c,0x6f,0xba,0xa7,0x23,0xba,0x3b,0x53,0x21,0xa0,0x6c,0x3a,0x2c,0x19,0x92,0x4f,0x76,0xea,0x9d,0xe0,0x17,0x53,0x2e,0x5d,0xdd,0x6e,0x1d,0xbf,0xa3,0x4e,0x94,0xd0,0x5c,0x1a,0x6b,0xd2,0xc0,0x9d,0xb3,0x3a,0x35,0x70,0x74,0x49,0x2e,0x54,0x28,0x82,0x52,0xb2,0x71,0x7e,0x92,0x3c,0x28,0x69,0xea,0x1b,0x46,0x36,0xda,0x0f,0xab,0xac,0x8a,0x7a,0x21,0xc8,0x49,0x35,0x3d,0x54,0xc6,0x28,0xa5,0x68,0x75,0xab,0x13,0x8b,0x5b,0xd0,0x37,0x37,0xbc,0x2c,0x3a,0x62,0xef,0x3c,0x23}, + {0xd9,0x34,0x92,0xf3,0xed,0x5d,0xa7,0xe2,0xf9,0x58,0xb5,0xe1,0x80,0x76,0x3d,0x96,0xfb,0x23,0x3c,0x6e,0xac,0x41,0x27,0x2c,0xc3,0x01,0x0e,0x32,0xa1,0x24,0x90,0x3a,0x8f,0x3e,0xdd,0x04,0x66,0x59,0xb7,0x59,0x2c,0x70,0x88,0xe2,0x77,0x03,0xb3,0x6c,0x23,0xc3,0xd9,0x5e,0x66,0x9c,0x33,0xb1,0x2f,0xe5,0xbc,0x61,0x60,0xe7,0x15,0x09,0x7e,0xa3,0x34,0xa8,0x35,0xe8,0x7d,0xdf,0xea,0x57,0x98,0x68,0xda,0x9c,0xe1,0x8b,0x26,0xb3,0x67,0x71,0x36,0x85,0x11,0x2c,0xc2,0xd5,0xef,0xdb,0xd9,0xb3,0x9e,0x58}, + {0x5e,0x51,0xaa,0x49,0x54,0x63,0x5b,0xed,0x3a,0x82,0xc6,0x0b,0x9f,0xc4,0x65,0xa8,0xc4,0xd1,0x42,0x5b,0xe9,0x1f,0x0c,0x85,0xb9,0x15,0xd3,0x03,0x6f,0x6d,0xd7,0x30,0x1d,0x9c,0x2f,0x63,0x0e,0xdd,0xcc,0x2e,0x15,0x31,0x89,0x76,0x96,0xb6,0xd0,0x51,0x58,0x7a,0x63,0xa8,0x6b,0xb7,0xdf,0x52,0x39,0xef,0x0e,0xa0,0x49,0x7d,0xd3,0x6d,0xc7,0xe4,0x06,0x21,0x17,0x44,0x44,0x6c,0x69,0x7f,0x8d,0x92,0x80,0xd6,0x53,0xfb,0x26,0x3f,0x4d,0x69,0xa4,0x9e,0x73,0xb4,0xb0,0x4b,0x86,0x2e,0x11,0x97,0xc6,0x10}, + {0xde,0x5f,0xbe,0x7d,0x27,0xc4,0x93,0x64,0xa2,0x7e,0xad,0x19,0xad,0x4f,0x5d,0x26,0x90,0x45,0x30,0x46,0xc8,0xdf,0x00,0x0e,0x09,0xfe,0x66,0xed,0xab,0x1c,0xe6,0x25,0x05,0xc8,0x58,0x83,0xa0,0x2a,0xa6,0x0c,0x47,0x42,0x20,0x7a,0xe3,0x4a,0x3d,0x6a,0xdc,0xed,0x11,0x3b,0xa6,0xd3,0x64,0x74,0xef,0x06,0x08,0x55,0xaf,0x9b,0xbf,0x03,0x04,0x66,0x58,0xcc,0x28,0xe1,0x13,0x3f,0x7e,0x74,0x59,0xb4,0xec,0x73,0x58,0x6f,0xf5,0x68,0x12,0xcc,0xed,0x3d,0xb6,0xa0,0x2c,0xe2,0x86,0x45,0x63,0x78,0x6d,0x56}, + {0x34,0x08,0xc1,0x9c,0x9f,0xa4,0x37,0x16,0x51,0xc4,0x9b,0xa8,0xd5,0x56,0x8e,0xbc,0xdb,0xd2,0x7f,0x7f,0x0f,0xec,0xb5,0x1c,0xd9,0x35,0xcc,0x5e,0xca,0x5b,0x97,0x33,0xd0,0x2f,0x5a,0xc6,0x85,0x42,0x05,0xa1,0xc3,0x67,0x16,0xf3,0x2a,0x11,0x64,0x6c,0x58,0xee,0x1a,0x73,0x40,0xe2,0x0a,0x68,0x2a,0xb2,0x93,0x47,0xf3,0xa5,0xfb,0x14,0xd4,0xf7,0x85,0x69,0x16,0x46,0xd7,0x3c,0x57,0x00,0xc8,0xc9,0x84,0x5e,0x3e,0x59,0x1e,0x13,0x61,0x7b,0xb6,0xf2,0xc3,0x2f,0x6c,0x52,0xfc,0x83,0xea,0x9c,0x82,0x14}, + {0xc2,0x95,0xdd,0x97,0x84,0x7b,0x43,0xff,0xa7,0xb5,0x4e,0xaa,0x30,0x4e,0x74,0x6c,0x8b,0xe8,0x85,0x3c,0x61,0x5d,0x0c,0x9e,0x73,0x81,0x75,0x5f,0x1e,0xc7,0xd9,0x2f,0xb8,0xec,0x71,0x4e,0x2f,0x0b,0xe7,0x21,0xe3,0x77,0xa4,0x40,0xb9,0xdd,0x56,0xe6,0x80,0x4f,0x1d,0xce,0xce,0x56,0x65,0xbf,0x7e,0x7b,0x5d,0x53,0xc4,0x3b,0xfc,0x05,0xdd,0xde,0xaf,0x52,0xae,0xb3,0xb8,0x24,0xcf,0x30,0x3b,0xed,0x8c,0x63,0x95,0x34,0x95,0x81,0xbe,0xa9,0x83,0xbc,0xa4,0x33,0x04,0x1f,0x65,0x5c,0x47,0x67,0x37,0x37}, + {0xd9,0xad,0xd1,0x40,0xfd,0x99,0xba,0x2f,0x27,0xd0,0xf4,0x96,0x6f,0x16,0x07,0xb3,0xae,0x3b,0xf0,0x15,0x52,0xf0,0x63,0x43,0x99,0xf9,0x18,0x3b,0x6c,0xa5,0xbe,0x1f,0x90,0x65,0x24,0x14,0xcb,0x95,0x40,0x63,0x35,0x55,0xc1,0x16,0x40,0x14,0x12,0xef,0x60,0xbc,0x10,0x89,0x0c,0x14,0x38,0x9e,0x8c,0x7c,0x90,0x30,0x57,0x90,0xf5,0x6b,0x8a,0x5b,0x41,0xe1,0xf1,0x78,0xa7,0x0f,0x7e,0xa7,0xc3,0xba,0xf7,0x9f,0x40,0x06,0x50,0x9a,0xa2,0x9a,0xb8,0xd7,0x52,0x6f,0x56,0x5a,0x63,0x7a,0xf6,0x1c,0x52,0x02}, + 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{0x2e,0x34,0xc5,0x49,0xaf,0x92,0xbc,0x1a,0xd0,0xfa,0xe6,0xb2,0x11,0xd8,0xee,0xff,0x29,0x4e,0xc8,0xfc,0x8d,0x8c,0xa2,0xef,0x43,0xc5,0x4c,0xa4,0x18,0xdf,0xb5,0x11,0xfc,0x75,0xa9,0x42,0x8a,0xbb,0x7b,0xbf,0x58,0xa3,0xad,0x96,0x77,0x39,0x5c,0x8c,0x48,0xaa,0xed,0xcd,0x6f,0xc7,0x7f,0xe2,0xa6,0x20,0xbc,0xf6,0xd7,0x5f,0x73,0x19,0x66,0x42,0xc8,0x42,0xd0,0x90,0xab,0xe3,0x7e,0x54,0x19,0x7f,0x0f,0x8e,0x84,0xeb,0xb9,0x97,0xa4,0x65,0xd0,0xa1,0x03,0x25,0x5f,0x89,0xdf,0x91,0x11,0x91,0xef,0x0f} +}; diff --git a/src/ext/ed25519/donna/ed25519-donna-batchverify.h b/src/ext/ed25519/donna/ed25519-donna-batchverify.h new file mode 100644 index 0000000..43c4923 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-batchverify.h @@ -0,0 +1,275 @@ +/* + Ed25519 batch verification +*/ + +#define max_batch_size 64 +#define heap_batch_size ((max_batch_size * 2) + 1) + +/* which limb is the 128th bit in? */ +static const size_t limb128bits = (128 + bignum256modm_bits_per_limb - 1) / bignum256modm_bits_per_limb; + +typedef size_t heap_index_t; + +typedef struct batch_heap_t { + unsigned char r[heap_batch_size][16]; /* 128 bit random values */ + ge25519 points[heap_batch_size]; + bignum256modm scalars[heap_batch_size]; + heap_index_t heap[heap_batch_size]; + size_t size; +} batch_heap; + +/* swap two values in the heap */ +static void +heap_swap(heap_index_t *heap, size_t a, size_t b) { + heap_index_t temp; + temp = heap[a]; + heap[a] = heap[b]; + heap[b] = temp; +} + +/* add the scalar at the end of the list to the heap */ +static void +heap_insert_next(batch_heap *heap) { + size_t node = heap->size, parent; + heap_index_t *pheap = heap->heap; + bignum256modm *scalars = heap->scalars; + + /* insert at the bottom */ + pheap[node] = (heap_index_t)node; + + /* sift node up to its sorted spot */ + parent = (node - 1) / 2; + while (node && lt256_modm_batch(scalars[pheap[parent]], scalars[pheap[node]], bignum256modm_limb_size - 1)) { + heap_swap(pheap, parent, node); + node = parent; + parent = (node - 1) / 2; + } + heap->size++; +} + +/* update the heap when the root element is updated */ +static void +heap_updated_root(batch_heap *heap, size_t limbsize) { + size_t node, parent, childr, childl; + heap_index_t *pheap = heap->heap; + bignum256modm *scalars = heap->scalars; + + /* sift root to the bottom */ + parent = 0; + node = 1; + childl = 1; + childr = 2; + while ((childr < heap->size)) { + node = lt256_modm_batch(scalars[pheap[childl]], scalars[pheap[childr]], limbsize) ? childr : childl; + heap_swap(pheap, parent, node); + parent = node; + childl = (parent * 2) + 1; + childr = childl + 1; + } + + /* sift root back up to its sorted spot */ + parent = (node - 1) / 2; + while (node && lte256_modm_batch(scalars[pheap[parent]], scalars[pheap[node]], limbsize)) { + heap_swap(pheap, parent, node); + node = parent; + parent = (node - 1) / 2; + } +} + +/* build the heap with count elements, count must be >= 3 */ +static void +heap_build(batch_heap *heap, size_t count) { + heap->heap[0] = 0; + heap->size = 0; + while (heap->size < count) + heap_insert_next(heap); +} + +/* extend the heap to contain new_count elements */ +static void +heap_extend(batch_heap *heap, size_t new_count) { + while (heap->size < new_count) + heap_insert_next(heap); +} + +/* get the top 2 elements of the heap */ +static void +heap_get_top2(batch_heap *heap, heap_index_t *max1, heap_index_t *max2, size_t limbsize) { + heap_index_t h0 = heap->heap[0], h1 = heap->heap[1], h2 = heap->heap[2]; + if (lt256_modm_batch(heap->scalars[h1], heap->scalars[h2], limbsize)) + h1 = h2; + *max1 = h0; + *max2 = h1; +} + +/* */ +static void +ge25519_multi_scalarmult_vartime_final(ge25519 *r, ge25519 *point, bignum256modm scalar) { + const bignum256modm_element_t topbit = ((bignum256modm_element_t)1 << (bignum256modm_bits_per_limb - 1)); + size_t limb = limb128bits; + bignum256modm_element_t flag; + + if (isone256_modm_batch(scalar)) { + /* this will happen most of the time after bos-carter */ + *r = *point; + return; + } else if (iszero256_modm_batch(scalar)) { + /* this will only happen if all scalars == 0 */ + memset(r, 0, sizeof(*r)); + r->y[0] = 1; + r->z[0] = 1; + return; + } + + *r = *point; + + /* find the limb where first bit is set */ + while (!scalar[limb]) + limb--; + + /* find the first bit */ + flag = topbit; + while ((scalar[limb] & flag) == 0) + flag >>= 1; + + /* exponentiate */ + for (;;) { + ge25519_double(r, r); + if (scalar[limb] & flag) + ge25519_add(r, r, point); + + flag >>= 1; + if (!flag) { + if (!limb--) + break; + flag = topbit; + } + } +} + +/* count must be >= 5 */ +static void +ge25519_multi_scalarmult_vartime(ge25519 *r, batch_heap *heap, size_t count) { + heap_index_t max1, max2; + + /* start with the full limb size */ + size_t limbsize = bignum256modm_limb_size - 1; + + /* whether the heap has been extended to include the 128 bit scalars */ + int extended = 0; + + /* grab an odd number of scalars to build the heap, unknown limb sizes */ + heap_build(heap, ((count + 1) / 2) | 1); + + for (;;) { + heap_get_top2(heap, &max1, &max2, limbsize); + + /* only one scalar remaining, we're done */ + if (iszero256_modm_batch(heap->scalars[max2])) + break; + + /* exhausted another limb? */ + if (!heap->scalars[max1][limbsize]) + limbsize -= 1; + + /* can we extend to the 128 bit scalars? */ + if (!extended && isatmost128bits256_modm_batch(heap->scalars[max1])) { + heap_extend(heap, count); + heap_get_top2(heap, &max1, &max2, limbsize); + extended = 1; + } + + sub256_modm_batch(heap->scalars[max1], heap->scalars[max1], heap->scalars[max2], limbsize); + ge25519_add(&heap->points[max2], &heap->points[max2], &heap->points[max1]); + heap_updated_root(heap, limbsize); + } + + ge25519_multi_scalarmult_vartime_final(r, &heap->points[max1], heap->scalars[max1]); +} + +/* not actually used for anything other than testing */ +unsigned char batch_point_buffer[3][32]; + +static int +ge25519_is_neutral_vartime(const ge25519 *p) { + static const unsigned char zero[32] = {0}; + unsigned char point_buffer[3][32]; + curve25519_contract(point_buffer[0], p->x); + curve25519_contract(point_buffer[1], p->y); + curve25519_contract(point_buffer[2], p->z); + memcpy(batch_point_buffer[1], point_buffer[1], 32); + return (memcmp(point_buffer[0], zero, 32) == 0) && (memcmp(point_buffer[1], point_buffer[2], 32) == 0); +} + +int +ED25519_FN(ed25519_sign_open_batch) (const unsigned char **m, size_t *mlen, const unsigned char **pk, const unsigned char **RS, size_t num, int *valid) { + batch_heap ALIGN(16) batch; + ge25519 ALIGN(16) p; + bignum256modm *r_scalars; + size_t i, batchsize; + unsigned char hram[64]; + int ret = 0; + + for (i = 0; i < num; i++) + valid[i] = 1; + + while (num > 3) { + batchsize = (num > max_batch_size) ? max_batch_size : num; + + /* generate r (scalars[batchsize+1]..scalars[2*batchsize] */ + ED25519_FN(ed25519_randombytes_unsafe) (batch.r, batchsize * 16); + r_scalars = &batch.scalars[batchsize + 1]; + for (i = 0; i < batchsize; i++) + expand256_modm(r_scalars[i], batch.r[i], 16); + + /* compute scalars[0] = ((r1s1 + r2s2 + ...)) */ + for (i = 0; i < batchsize; i++) { + expand256_modm(batch.scalars[i], RS[i] + 32, 32); + mul256_modm(batch.scalars[i], batch.scalars[i], r_scalars[i]); + } + for (i = 1; i < batchsize; i++) + add256_modm(batch.scalars[0], batch.scalars[0], batch.scalars[i]); + + /* compute scalars[1]..scalars[batchsize] as r[i]*H(R[i],A[i],m[i]) */ + for (i = 0; i < batchsize; i++) { + ed25519_hram(hram, RS[i], pk[i], m[i], mlen[i]); + expand256_modm(batch.scalars[i+1], hram, 64); + mul256_modm(batch.scalars[i+1], batch.scalars[i+1], r_scalars[i]); + } + + /* compute points */ + batch.points[0] = ge25519_basepoint; + for (i = 0; i < batchsize; i++) + if (!ge25519_unpack_negative_vartime(&batch.points[i+1], pk[i])) + goto fallback; + for (i = 0; i < batchsize; i++) + if (!ge25519_unpack_negative_vartime(&batch.points[batchsize+i+1], RS[i])) + goto fallback; + + ge25519_multi_scalarmult_vartime(&p, &batch, (batchsize * 2) + 1); + if (!ge25519_is_neutral_vartime(&p)) { + ret |= 2; + + fallback: + for (i = 0; i < batchsize; i++) { + valid[i] = ED25519_FN(ed25519_sign_open) (m[i], mlen[i], pk[i], RS[i]) ? 0 : 1; + ret |= (valid[i] ^ 1); + } + } + + m += batchsize; + mlen += batchsize; + pk += batchsize; + RS += batchsize; + num -= batchsize; + valid += batchsize; + } + + for (i = 0; i < num; i++) { + valid[i] = ED25519_FN(ed25519_sign_open) (m[i], mlen[i], pk[i], RS[i]) ? 0 : 1; + ret |= (valid[i] ^ 1); + } + + return ret; +} + diff --git a/src/ext/ed25519/donna/ed25519-donna-impl-base.h b/src/ext/ed25519/donna/ed25519-donna-impl-base.h new file mode 100644 index 0000000..48913ed --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-impl-base.h @@ -0,0 +1,364 @@ +/* + conversions +*/ + +DONNA_INLINE static void +ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) { + curve25519_mul(r->x, p->x, p->t); + curve25519_mul(r->y, p->y, p->z); + curve25519_mul(r->z, p->z, p->t); +} + +DONNA_INLINE static void +ge25519_p1p1_to_full(ge25519 *r, const ge25519_p1p1 *p) { + curve25519_mul(r->x, p->x, p->t); + curve25519_mul(r->y, p->y, p->z); + curve25519_mul(r->z, p->z, p->t); + curve25519_mul(r->t, p->x, p->y); +} + +static void +ge25519_full_to_pniels(ge25519_pniels *p, const ge25519 *r) { + curve25519_sub(p->ysubx, r->y, r->x); + curve25519_add(p->xaddy, r->y, r->x); + curve25519_copy(p->z, r->z); + curve25519_mul(p->t2d, r->t, ge25519_ec2d); +} + +/* + adding & doubling +*/ + +static void +ge25519_add_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519 *q) { + bignum25519 a,b,c,d,t,u; + + curve25519_sub(a, p->y, p->x); + curve25519_add(b, p->y, p->x); + curve25519_sub(t, q->y, q->x); + curve25519_add(u, q->y, q->x); + curve25519_mul(a, a, t); + curve25519_mul(b, b, u); + curve25519_mul(c, p->t, q->t); + curve25519_mul(c, c, ge25519_ec2d); + curve25519_mul(d, p->z, q->z); + curve25519_add(d, d, d); + curve25519_sub(r->x, b, a); + curve25519_add(r->y, b, a); + curve25519_add_after_basic(r->z, d, c); + curve25519_sub_after_basic(r->t, d, c); +} + + +static void +ge25519_double_p1p1(ge25519_p1p1 *r, const ge25519 *p) { + bignum25519 a,b,c; + + curve25519_square(a, p->x); + curve25519_square(b, p->y); + curve25519_square(c, p->z); + curve25519_add_reduce(c, c, c); + curve25519_add(r->x, p->x, p->y); + curve25519_square(r->x, r->x); + curve25519_add(r->y, b, a); + curve25519_sub(r->z, b, a); + curve25519_sub_after_basic(r->x, r->x, r->y); + curve25519_sub_after_basic(r->t, c, r->z); +} + +static void +ge25519_nielsadd2_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_niels *q, unsigned char signbit) { + const bignum25519 *qb = (const bignum25519 *)q; + bignum25519 *rb = (bignum25519 *)r; + bignum25519 a,b,c; + + curve25519_sub(a, p->y, p->x); + curve25519_add(b, p->y, p->x); + curve25519_mul(a, a, qb[signbit]); /* x for +, y for - */ + curve25519_mul(r->x, b, qb[signbit^1]); /* y for +, x for - */ + curve25519_add(r->y, r->x, a); + curve25519_sub(r->x, r->x, a); + curve25519_mul(c, p->t, q->t2d); + curve25519_add_reduce(r->t, p->z, p->z); + curve25519_copy(r->z, r->t); + curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */ + curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */ +} + +static void +ge25519_pnielsadd_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_pniels *q, unsigned char signbit) { + const bignum25519 *qb = (const bignum25519 *)q; + bignum25519 *rb = (bignum25519 *)r; + bignum25519 a,b,c; + + curve25519_sub(a, p->y, p->x); + curve25519_add(b, p->y, p->x); + curve25519_mul(a, a, qb[signbit]); /* ysubx for +, xaddy for - */ + curve25519_mul(r->x, b, qb[signbit^1]); /* xaddy for +, ysubx for - */ + curve25519_add(r->y, r->x, a); + curve25519_sub(r->x, r->x, a); + curve25519_mul(c, p->t, q->t2d); + curve25519_mul(r->t, p->z, q->z); + curve25519_add_reduce(r->t, r->t, r->t); + curve25519_copy(r->z, r->t); + curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */ + curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */ +} + +static void +ge25519_double_partial(ge25519 *r, const ge25519 *p) { + ge25519_p1p1 t; + ge25519_double_p1p1(&t, p); + ge25519_p1p1_to_partial(r, &t); +} + +static void +ge25519_double(ge25519 *r, const ge25519 *p) { + ge25519_p1p1 t; + ge25519_double_p1p1(&t, p); + ge25519_p1p1_to_full(r, &t); +} + +static void +ge25519_add(ge25519 *r, const ge25519 *p, const ge25519 *q) { + ge25519_p1p1 t; + ge25519_add_p1p1(&t, p, q); + ge25519_p1p1_to_full(r, &t); +} + +static void +ge25519_nielsadd2(ge25519 *r, const ge25519_niels *q) { + bignum25519 a,b,c,e,f,g,h; + + curve25519_sub(a, r->y, r->x); + curve25519_add(b, r->y, r->x); + curve25519_mul(a, a, q->ysubx); + curve25519_mul(e, b, q->xaddy); + curve25519_add(h, e, a); + curve25519_sub(e, e, a); + curve25519_mul(c, r->t, q->t2d); + curve25519_add(f, r->z, r->z); + curve25519_add_after_basic(g, f, c); + curve25519_sub_after_basic(f, f, c); + curve25519_mul(r->x, e, f); + curve25519_mul(r->y, h, g); + curve25519_mul(r->z, g, f); + curve25519_mul(r->t, e, h); +} + +static void +ge25519_pnielsadd(ge25519_pniels *r, const ge25519 *p, const ge25519_pniels *q) { + bignum25519 a,b,c,x,y,z,t; + + curve25519_sub(a, p->y, p->x); + curve25519_add(b, p->y, p->x); + curve25519_mul(a, a, q->ysubx); + curve25519_mul(x, b, q->xaddy); + curve25519_add(y, x, a); + curve25519_sub(x, x, a); + curve25519_mul(c, p->t, q->t2d); + curve25519_mul(t, p->z, q->z); + curve25519_add(t, t, t); + curve25519_add_after_basic(z, t, c); + curve25519_sub_after_basic(t, t, c); + curve25519_mul(r->xaddy, x, t); + curve25519_mul(r->ysubx, y, z); + curve25519_mul(r->z, z, t); + curve25519_mul(r->t2d, x, y); + curve25519_copy(y, r->ysubx); + curve25519_sub(r->ysubx, r->ysubx, r->xaddy); + curve25519_add(r->xaddy, r->xaddy, y); + curve25519_mul(r->t2d, r->t2d, ge25519_ec2d); +} + + +/* + pack & unpack +*/ + +static void +ge25519_pack(unsigned char r[32], const ge25519 *p) { + bignum25519 tx, ty, zi; + unsigned char parity[32]; + curve25519_recip(zi, p->z); + curve25519_mul(tx, p->x, zi); + curve25519_mul(ty, p->y, zi); + curve25519_contract(r, ty); + curve25519_contract(parity, tx); + r[31] ^= ((parity[0] & 1) << 7); +} + +static int +ge25519_unpack_negative_vartime(ge25519 *r, const unsigned char p[32]) { + static const unsigned char zero[32] = {0}; + static const bignum25519 one = {1}; + unsigned char parity = p[31] >> 7; + unsigned char check[32]; + bignum25519 t, root, num, den, d3; + + curve25519_expand(r->y, p); + curve25519_copy(r->z, one); + curve25519_square(num, r->y); /* x = y^2 */ + curve25519_mul(den, num, ge25519_ecd); /* den = dy^2 */ + curve25519_sub_reduce(num, num, r->z); /* x = y^1 - 1 */ + curve25519_add(den, den, r->z); /* den = dy^2 + 1 */ + + /* Computation of sqrt(num/den) */ + /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */ + curve25519_square(t, den); + curve25519_mul(d3, t, den); + curve25519_square(r->x, d3); + curve25519_mul(r->x, r->x, den); + curve25519_mul(r->x, r->x, num); + curve25519_pow_two252m3(r->x, r->x); + + /* 2. computation of r->x = num * den^3 * (num*den^7)^((p-5)/8) */ + curve25519_mul(r->x, r->x, d3); + curve25519_mul(r->x, r->x, num); + + /* 3. Check if either of the roots works: */ + curve25519_square(t, r->x); + curve25519_mul(t, t, den); + curve25519_sub_reduce(root, t, num); + curve25519_contract(check, root); + if (!ed25519_verify(check, zero, 32)) { + curve25519_add_reduce(t, t, num); + curve25519_contract(check, t); + if (!ed25519_verify(check, zero, 32)) + return 0; + curve25519_mul(r->x, r->x, ge25519_sqrtneg1); + } + + curve25519_contract(check, r->x); + if ((check[0] & 1) == parity) { + curve25519_copy(t, r->x); + curve25519_neg(r->x, t); + } + curve25519_mul(r->t, r->x, r->y); + return 1; +} + + +/* + scalarmults +*/ + +#define S1_SWINDOWSIZE 5 +#define S1_TABLE_SIZE (1<<(S1_SWINDOWSIZE-2)) +#define S2_SWINDOWSIZE 7 +#define S2_TABLE_SIZE (1<<(S2_SWINDOWSIZE-2)) + +/* computes [s1]p1 + [s2]basepoint */ +static void +ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const bignum256modm s1, const bignum256modm s2) { + signed char slide1[256], slide2[256]; + ge25519_pniels pre1[S1_TABLE_SIZE]; + ge25519 d1; + ge25519_p1p1 t; + int32_t i; + + contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE); + contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE); + + ge25519_double(&d1, p1); + ge25519_full_to_pniels(pre1, p1); + for (i = 0; i < S1_TABLE_SIZE - 1; i++) + ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]); + + /* set neutral */ + memset(r, 0, sizeof(ge25519)); + r->y[0] = 1; + r->z[0] = 1; + + i = 255; + while ((i >= 0) && !(slide1[i] | slide2[i])) + i--; + + for (; i >= 0; i--) { + ge25519_double_p1p1(&t, r); + + if (slide1[i]) { + ge25519_p1p1_to_full(r, &t); + ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (unsigned char)slide1[i] >> 7); + } + + if (slide2[i]) { + ge25519_p1p1_to_full(r, &t); + ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (unsigned char)slide2[i] >> 7); + } + + ge25519_p1p1_to_partial(r, &t); + } +} + + + +#if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS) + +static uint32_t +ge25519_windowb_equal(uint32_t b, uint32_t c) { + return ((b ^ c) - 1) >> 31; +} + +static void +ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) { + bignum25519 neg; + uint32_t sign = (uint32_t)((unsigned char)b >> 7); + uint32_t mask = ~(sign - 1); + uint32_t u = (b + mask) ^ mask; + uint32_t i; + + /* ysubx, xaddy, t2d in packed form. initialize to ysubx = 1, xaddy = 1, t2d = 0 */ + uint8_t packed[96] = {0}; + packed[0] = 1; + packed[32] = 1; + + for (i = 0; i < 8; i++) + curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1)); + + /* expand in to t */ + curve25519_expand(t->ysubx, packed + 0); + curve25519_expand(t->xaddy, packed + 32); + curve25519_expand(t->t2d , packed + 64); + + /* adjust for sign */ + curve25519_swap_conditional(t->ysubx, t->xaddy, sign); + curve25519_neg(neg, t->t2d); + curve25519_swap_conditional(t->t2d, neg, sign); +} + +#endif /* HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS */ + + +/* computes [s]basepoint */ +static void +ge25519_scalarmult_base_niels(ge25519 *r, const uint8_t basepoint_table[256][96], const bignum256modm s) { + signed char b[64]; + uint32_t i; + ge25519_niels t; + + contract256_window4_modm(b, s); + + ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]); + curve25519_sub_reduce(r->x, t.xaddy, t.ysubx); + curve25519_add_reduce(r->y, t.xaddy, t.ysubx); + memset(r->z, 0, sizeof(bignum25519)); + curve25519_copy(r->t, t.t2d); + r->z[0] = 2; + for (i = 3; i < 64; i += 2) { + ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]); + ge25519_nielsadd2(r, &t); + } + ge25519_double_partial(r, r); + ge25519_double_partial(r, r); + ge25519_double_partial(r, r); + ge25519_double(r, r); + ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]); + curve25519_mul(t.t2d, t.t2d, ge25519_ecd); + ge25519_nielsadd2(r, &t); + for(i = 2; i < 64; i += 2) { + ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]); + ge25519_nielsadd2(r, &t); + } +} + diff --git a/src/ext/ed25519/donna/ed25519-donna-impl-sse2.h b/src/ext/ed25519/donna/ed25519-donna-impl-sse2.h new file mode 100644 index 0000000..5fe3416 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-impl-sse2.h @@ -0,0 +1,390 @@ +/* + conversions +*/ + +static void +ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) { + packed64bignum25519 ALIGN(16) xz, tt, xzout; + curve25519_mul(r->y, p->y, p->z); + curve25519_tangle64(xz, p->x, p->z); + curve25519_tangleone64(tt, p->t); + curve25519_mul_packed64(xzout, xz, tt); + curve25519_untangle64(r->x, r->z, xzout); +} + +static void +ge25519_p1p1_to_full(ge25519 *r, const ge25519_p1p1 *p) { + packed64bignum25519 ALIGN(16) zy, xt, xx, zz, ty; + curve25519_tangle64(ty, p->t, p->y); + curve25519_tangleone64(xx, p->x); + curve25519_mul_packed64(xt, xx, ty); + curve25519_untangle64(r->x, r->t, xt); + curve25519_tangleone64(zz, p->z); + curve25519_mul_packed64(zy, zz, ty); + curve25519_untangle64(r->z, r->y, zy); +} + +static void +ge25519_full_to_pniels(ge25519_pniels *p, const ge25519 *r) { + curve25519_sub(p->ysubx, r->y, r->x); + curve25519_add(p->xaddy, r->x, r->y); + curve25519_copy(p->z, r->z); + curve25519_mul(p->t2d, r->t, ge25519_ec2d); +} + +/* + adding & doubling +*/ + +static void +ge25519_add_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519 *q) { + bignum25519 ALIGN(16) a,b,c,d; + packed32bignum25519 ALIGN(16) xx, yy, yypxx, yymxx, bd, ac, bdmac, bdpac; + packed64bignum25519 ALIGN(16) at, bu, atbu, ptz, qtz, cd; + + curve25519_tangle32(yy, p->y, q->y); + curve25519_tangle32(xx, p->x, q->x); + curve25519_add_packed32(yypxx, yy, xx); + curve25519_sub_packed32(yymxx, yy, xx); + curve25519_tangle64_from32(at, bu, yymxx, yypxx); + curve25519_mul_packed64(atbu, at, bu); + curve25519_untangle64(a, b, atbu); + curve25519_tangle64(ptz, p->t, p->z); + curve25519_tangle64(qtz, q->t, q->z); + curve25519_mul_packed64(cd, ptz, qtz); + curve25519_untangle64(c, d, cd); + curve25519_mul(c, c, ge25519_ec2d); + curve25519_add_reduce(d, d, d); + /* reduce, so no after_basic is needed later */ + curve25519_tangle32(bd, b, d); + curve25519_tangle32(ac, a, c); + curve25519_sub_packed32(bdmac, bd, ac); + curve25519_add_packed32(bdpac, bd, ac); + curve25519_untangle32(r->x, r->t, bdmac); + curve25519_untangle32(r->y, r->z, bdpac); +} + + +static void +ge25519_double_p1p1(ge25519_p1p1 *r, const ge25519 *p) { + bignum25519 ALIGN(16) a,b,c,x; + packed64bignum25519 ALIGN(16) xy, zx, ab, cx; + packed32bignum25519 ALIGN(16) xc, yz, xt, yc, ac, bc; + + curve25519_add(x, p->x, p->y); + curve25519_tangle64(xy, p->x, p->y); + curve25519_square_packed64(ab, xy); + curve25519_untangle64(a, b, ab); + curve25519_tangle64(zx, p->z, x); + curve25519_square_packed64(cx, zx); + curve25519_untangle64(c, x, cx); + curve25519_tangle32(bc, b, c); + curve25519_tangle32(ac, a, c); + curve25519_add_reduce_packed32(yc, bc, ac); + curve25519_untangle32(r->y, c, yc); + curve25519_sub(r->z, b, a); + curve25519_tangle32(yz, r->y, r->z); + curve25519_tangle32(xc, x, c); + curve25519_sub_after_basic_packed32(xt, xc, yz); + curve25519_untangle32(r->x, r->t, xt); +} + +static void +ge25519_nielsadd2_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_niels *q, unsigned char signbit) { + const bignum25519 *qb = (const bignum25519 *)q; + bignum25519 *rb = (bignum25519 *)r; + bignum25519 ALIGN(16) a,b,c; + packed64bignum25519 ALIGN(16) ab, yx, aybx; + packed32bignum25519 ALIGN(16) bd, ac, bdac; + + curve25519_sub(a, p->y, p->x); + curve25519_add(b, p->y, p->x); + curve25519_tangle64(ab, a, b); + curve25519_tangle64(yx, qb[signbit], qb[signbit^1]); + curve25519_mul_packed64(aybx, ab, yx); + curve25519_untangle64(a, b, aybx); + curve25519_add(r->y, b, a); + curve25519_add_reduce(r->t, p->z, p->z); + curve25519_mul(c, p->t, q->t2d); + curve25519_copy(r->z, r->t); + curve25519_add(rb[2+signbit], rb[2+signbit], c); + curve25519_tangle32(bd, b, rb[2+(signbit^1)]); + curve25519_tangle32(ac, a, c); + curve25519_sub_packed32(bdac, bd, ac); + curve25519_untangle32(r->x, rb[2+(signbit^1)], bdac); +} + +static void +ge25519_pnielsadd_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_pniels *q, unsigned char signbit) { + const bignum25519 *qb = (const bignum25519 *)q; + bignum25519 *rb = (bignum25519 *)r; + bignum25519 ALIGN(16) a,b,c; + packed64bignum25519 ALIGN(16) ab, yx, aybx, zt, zt2d, tc; + packed32bignum25519 ALIGN(16) bd, ac, bdac; + + curve25519_sub(a, p->y, p->x); + curve25519_add(b, p->y, p->x); + curve25519_tangle64(ab, a, b); + curve25519_tangle64(yx, qb[signbit], qb[signbit^1]); + curve25519_mul_packed64(aybx, ab, yx); + curve25519_untangle64(a, b, aybx); + curve25519_add(r->y, b, a); + curve25519_tangle64(zt, p->z, p->t); + curve25519_tangle64(zt2d, q->z, q->t2d); + curve25519_mul_packed64(tc, zt, zt2d); + curve25519_untangle64(r->t, c, tc); + curve25519_add_reduce(r->t, r->t, r->t); + curve25519_copy(r->z, r->t); + curve25519_add(rb[2+signbit], rb[2+signbit], c); + curve25519_tangle32(bd, b, rb[2+(signbit^1)]); + curve25519_tangle32(ac, a, c); + curve25519_sub_packed32(bdac, bd, ac); + curve25519_untangle32(r->x, rb[2+(signbit^1)], bdac); +} + +static void +ge25519_double(ge25519 *r, const ge25519 *p) { + ge25519_p1p1 ALIGN(16) t; + ge25519_double_p1p1(&t, p); + ge25519_p1p1_to_full(r, &t); +} + +static void +ge25519_add(ge25519 *r, const ge25519 *p, const ge25519 *q) { + ge25519_p1p1 ALIGN(16) t; + ge25519_add_p1p1(&t, p, q); + ge25519_p1p1_to_full(r, &t); +} + +static void +ge25519_double_partial(ge25519 *r, const ge25519 *p) { + ge25519_p1p1 ALIGN(16) t; + ge25519_double_p1p1(&t, p); + ge25519_p1p1_to_partial(r, &t); +} + +static void +ge25519_nielsadd2(ge25519 *r, const ge25519_niels *q) { + packed64bignum25519 ALIGN(16) ab, yx, aybx, eg, ff, hh, xz, ty; + packed32bignum25519 ALIGN(16) bd, ac, bdac; + bignum25519 ALIGN(16) a,b,c,d,e,f,g,h; + + curve25519_sub(a, r->y, r->x); + curve25519_add(b, r->y, r->x); + curve25519_tangle64(ab, a, b); + curve25519_tangle64(yx, q->ysubx, q->xaddy); + curve25519_mul_packed64(aybx, ab, yx); + curve25519_untangle64(a, b, aybx); + curve25519_add(h, b, a); + curve25519_add_reduce(d, r->z, r->z); + curve25519_mul(c, r->t, q->t2d); + curve25519_add(g, d, c); /* d is reduced, so no need for after_basic */ + curve25519_tangle32(bd, b, d); + curve25519_tangle32(ac, a, c); + curve25519_sub_packed32(bdac, bd, ac); /* d is reduced, so no need for after_basic */ + curve25519_untangle32(e, f, bdac); + curve25519_tangle64(eg, e, g); + curve25519_tangleone64(ff, f); + curve25519_mul_packed64(xz, eg, ff); + curve25519_untangle64(r->x, r->z, xz); + curve25519_tangleone64(hh, h); + curve25519_mul_packed64(ty, eg, hh); + curve25519_untangle64(r->t, r->y, ty); +} + +static void +ge25519_pnielsadd(ge25519_pniels *r, const ge25519 *p, const ge25519_pniels *q) { + ge25519_p1p1 ALIGN(16) t; + ge25519 ALIGN(16) f; + ge25519_pnielsadd_p1p1(&t, p, q, 0); + ge25519_p1p1_to_full(&f, &t); + ge25519_full_to_pniels(r, &f); +} + +/* + pack & unpack +*/ + +static void +ge25519_pack(unsigned char r[32], const ge25519 *p) { + bignum25519 ALIGN(16) tx, ty, zi; + unsigned char parity[32]; + curve25519_recip(zi, p->z); + curve25519_mul(tx, p->x, zi); + curve25519_mul(ty, p->y, zi); + curve25519_contract(r, ty); + curve25519_contract(parity, tx); + r[31] ^= ((parity[0] & 1) << 7); +} + + +static int +ge25519_unpack_negative_vartime(ge25519 *r, const unsigned char p[32]) { + static const bignum25519 ALIGN(16) one = {1}; + static const unsigned char zero[32] = {0}; + unsigned char parity = p[31] >> 7; + unsigned char check[32]; + bignum25519 ALIGN(16) t, root, num, den, d3; + + curve25519_expand(r->y, p); + curve25519_copy(r->z, one); + curve25519_square_times(num, r->y, 1); /* x = y^2 */ + curve25519_mul(den, num, ge25519_ecd); /* den = dy^2 */ + curve25519_sub_reduce(num, num, r->z); /* x = y^2 - 1 */ + curve25519_add(den, den, r->z); /* den = dy^2 + 1 */ + + /* Computation of sqrt(num/den) */ + /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */ + curve25519_square_times(t, den, 1); + curve25519_mul(d3, t, den); + curve25519_square_times(r->x, d3, 1); + curve25519_mul(r->x, r->x, den); + curve25519_mul(r->x, r->x, num); + curve25519_pow_two252m3(r->x, r->x); + + /* 2. computation of r->x = t * num * den^3 */ + curve25519_mul(r->x, r->x, d3); + curve25519_mul(r->x, r->x, num); + + /* 3. Check if either of the roots works: */ + curve25519_square_times(t, r->x, 1); + curve25519_mul(t, t, den); + curve25519_copy(root, t); + curve25519_sub_reduce(root, root, num); + curve25519_contract(check, root); + if (!ed25519_verify(check, zero, 32)) { + curve25519_add_reduce(t, t, num); + curve25519_contract(check, t); + if (!ed25519_verify(check, zero, 32)) + return 0; + curve25519_mul(r->x, r->x, ge25519_sqrtneg1); + } + + curve25519_contract(check, r->x); + if ((check[0] & 1) == parity) { + curve25519_copy(t, r->x); + curve25519_neg(r->x, t); + } + curve25519_mul(r->t, r->x, r->y); + return 1; +} + + + +/* + scalarmults +*/ + +#define S1_SWINDOWSIZE 5 +#define S1_TABLE_SIZE (1<<(S1_SWINDOWSIZE-2)) +#define S2_SWINDOWSIZE 7 +#define S2_TABLE_SIZE (1<<(S2_SWINDOWSIZE-2)) + +static void +ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const bignum256modm s1, const bignum256modm s2) { + signed char slide1[256], slide2[256]; + ge25519_pniels ALIGN(16) pre1[S1_TABLE_SIZE]; + ge25519 ALIGN(16) d1; + ge25519_p1p1 ALIGN(16) t; + int32_t i; + + contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE); + contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE); + + ge25519_double(&d1, p1); + ge25519_full_to_pniels(pre1, p1); + for (i = 0; i < S1_TABLE_SIZE - 1; i++) + ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]); + + /* set neutral */ + memset(r, 0, sizeof(ge25519)); + r->y[0] = 1; + r->z[0] = 1; + + i = 255; + while ((i >= 0) && !(slide1[i] | slide2[i])) + i--; + + for (; i >= 0; i--) { + ge25519_double_p1p1(&t, r); + + if (slide1[i]) { + ge25519_p1p1_to_full(r, &t); + ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (unsigned char)slide1[i] >> 7); + } + + if (slide2[i]) { + ge25519_p1p1_to_full(r, &t); + ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (unsigned char)slide2[i] >> 7); + } + + ge25519_p1p1_to_partial(r, &t); + } +} + +#if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS) + +static uint32_t +ge25519_windowb_equal(uint32_t b, uint32_t c) { + return ((b ^ c) - 1) >> 31; +} + +static void +ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) { + bignum25519 ALIGN(16) neg; + uint32_t sign = (uint32_t)((unsigned char)b >> 7); + uint32_t mask = ~(sign - 1); + uint32_t u = (b + mask) ^ mask; + uint32_t i; + + /* ysubx, xaddy, t2d in packed form. initialize to ysubx = 1, xaddy = 1, t2d = 0 */ + uint8_t ALIGN(16) packed[96] = {0}; + packed[0] = 1; + packed[32] = 1; + + for (i = 0; i < 8; i++) + curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1)); + + /* expand in to t */ + curve25519_expand(t->ysubx, packed + 0); + curve25519_expand(t->xaddy, packed + 32); + curve25519_expand(t->t2d , packed + 64); + + /* adjust for sign */ + curve25519_swap_conditional(t->ysubx, t->xaddy, sign); + curve25519_neg(neg, t->t2d); + curve25519_swap_conditional(t->t2d, neg, sign); +} + +#endif /* HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS */ + +static void +ge25519_scalarmult_base_niels(ge25519 *r, const uint8_t table[256][96], const bignum256modm s) { + signed char b[64]; + uint32_t i; + ge25519_niels ALIGN(16) t; + + contract256_window4_modm(b, s); + + ge25519_scalarmult_base_choose_niels(&t, table, 0, b[1]); + curve25519_sub_reduce(r->x, t.xaddy, t.ysubx); + curve25519_add_reduce(r->y, t.xaddy, t.ysubx); + memset(r->z, 0, sizeof(bignum25519)); + r->z[0] = 2; + curve25519_copy(r->t, t.t2d); + for (i = 3; i < 64; i += 2) { + ge25519_scalarmult_base_choose_niels(&t, table, i / 2, b[i]); + ge25519_nielsadd2(r, &t); + } + ge25519_double_partial(r, r); + ge25519_double_partial(r, r); + ge25519_double_partial(r, r); + ge25519_double(r, r); + ge25519_scalarmult_base_choose_niels(&t, table, 0, b[0]); + curve25519_mul(t.t2d, t.t2d, ge25519_ecd); + ge25519_nielsadd2(r, &t); + for(i = 2; i < 64; i += 2) { + ge25519_scalarmult_base_choose_niels(&t, table, i / 2, b[i]); + ge25519_nielsadd2(r, &t); + } +} diff --git a/src/ext/ed25519/donna/ed25519-donna-portable-identify.h b/src/ext/ed25519/donna/ed25519-donna-portable-identify.h new file mode 100644 index 0000000..26a264c --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-portable-identify.h @@ -0,0 +1,103 @@ +/* os */ +#if defined(_WIN32) || defined(_WIN64) || defined(__TOS_WIN__) || defined(__WINDOWS__) + #define OS_WINDOWS +#elif defined(sun) || defined(__sun) || defined(__SVR4) || defined(__svr4__) + #define OS_SOLARIS +#else + #include <sys/param.h> /* need this to define BSD */ + #define OS_NIX + #if defined(__linux__) + #define OS_LINUX + #elif defined(BSD) + #define OS_BSD + #if defined(MACOS_X) || (defined(__APPLE__) & defined(__MACH__)) + #define OS_OSX + #elif defined(macintosh) || defined(Macintosh) + #define OS_MAC + #elif defined(__OpenBSD__) + #define OS_OPENBSD + #endif + #endif +#endif + + +/* compiler */ +#if defined(_MSC_VER) + #define COMPILER_MSVC +#endif +#if defined(__ICC) + #define COMPILER_INTEL +#endif +#if defined(__GNUC__) + #if (__GNUC__ >= 3) + #define COMPILER_GCC ((__GNUC__ * 10000) + (__GNUC_MINOR__ * 100) + (__GNUC_PATCHLEVEL__)) + #else + #define COMPILER_GCC ((__GNUC__ * 10000) + (__GNUC_MINOR__ * 100) ) + #endif +#endif +#if defined(__PATHCC__) + #define COMPILER_PATHCC +#endif +#if defined(__clang__) + #define COMPILER_CLANG ((__clang_major__ * 10000) + (__clang_minor__ * 100) + (__clang_patchlevel__)) +#endif + + + +/* cpu */ +#if defined(__amd64__) || defined(__amd64) || defined(__x86_64__ ) || defined(_M_X64) + #define CPU_X86_64 +#elif defined(__i586__) || defined(__i686__) || (defined(_M_IX86) && (_M_IX86 >= 500)) + #define CPU_X86 500 +#elif defined(__i486__) || (defined(_M_IX86) && (_M_IX86 >= 400)) + #define CPU_X86 400 +#elif defined(__i386__) || (defined(_M_IX86) && (_M_IX86 >= 300)) || defined(__X86__) || defined(_X86_) || defined(__I86__) + #define CPU_X86 300 +#elif defined(__ia64__) || defined(_IA64) || defined(__IA64__) || defined(_M_IA64) || defined(__ia64) + #define CPU_IA64 +#endif + +#if defined(__sparc__) || defined(__sparc) || defined(__sparcv9) + #define CPU_SPARC + #if defined(__sparcv9) + #define CPU_SPARC64 + #endif +#endif + +#if defined(powerpc) || defined(__PPC__) || defined(__ppc__) || defined(_ARCH_PPC) || defined(__powerpc__) || defined(__powerpc) || defined(POWERPC) || defined(_M_PPC) + #define CPU_PPC + #if defined(_ARCH_PWR7) + #define CPU_POWER7 + #elif defined(__64BIT__) + #define CPU_PPC64 + #else + #define CPU_PPC32 + #endif +#endif + +#if defined(__hppa__) || defined(__hppa) + #define CPU_HPPA +#endif + +#if defined(__alpha__) || defined(__alpha) || defined(_M_ALPHA) + #define CPU_ALPHA +#endif + +/* 64 bit cpu */ +#if defined(CPU_X86_64) || defined(CPU_IA64) || defined(CPU_SPARC64) || defined(__64BIT__) || defined(__LP64__) || defined(_LP64) || (defined(_MIPS_SZLONG) && (_MIPS_SZLONG == 64)) + #define CPU_64BITS +#endif + +#if defined(COMPILER_MSVC) + typedef signed char int8_t; + typedef unsigned char uint8_t; + typedef signed short int16_t; + typedef unsigned short uint16_t; + typedef signed int int32_t; + typedef unsigned int uint32_t; + typedef signed __int64 int64_t; + typedef unsigned __int64 uint64_t; +#else + #include <stdint.h> +#endif + diff --git a/src/ext/ed25519/donna/ed25519-donna-portable.h b/src/ext/ed25519/donna/ed25519-donna-portable.h new file mode 100644 index 0000000..0a0f7fc --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna-portable.h @@ -0,0 +1,135 @@ +#include "ed25519-donna-portable-identify.h" + +#define mul32x32_64(a,b) (((uint64_t)(a))*(b)) + +/* platform */ +#if defined(COMPILER_MSVC) + #include <intrin.h> + #if !defined(_DEBUG) + #undef mul32x32_64 + #define mul32x32_64(a,b) __emulu(a,b) + #endif + #undef inline + #define inline __forceinline + #define DONNA_INLINE __forceinline + #define DONNA_NOINLINE __declspec(noinline) + #define ALIGN(x) __declspec(align(x)) + #define ROTL32(a,b) _rotl(a,b) + #define ROTR32(a,b) _rotr(a,b) +#else + #include <sys/param.h> + #define DONNA_INLINE inline __attribute__((always_inline)) + #define DONNA_NOINLINE __attribute__((noinline)) + #define ALIGN(x) __attribute__((aligned(x))) + #define ROTL32(a,b) (((a) << (b)) | ((a) >> (32 - b))) + #define ROTR32(a,b) (((a) >> (b)) | ((a) << (32 - b))) +#endif + +/* uint128_t */ +#if defined(CPU_64BITS) && !defined(ED25519_FORCE_32BIT) + #if defined(COMPILER_CLANG) && (COMPILER_CLANG >= 30100) + #define HAVE_NATIVE_UINT128 + typedef unsigned __int128 uint128_t; + #elif defined(COMPILER_MSVC) + #define HAVE_UINT128 + typedef struct uint128_t { + uint64_t lo, hi; + } uint128_t; + #define mul64x64_128(out,a,b) out.lo = _umul128(a,b,&out.hi); + #define shr128_pair(out,hi,lo,shift) out = __shiftright128(lo, hi, shift); + #define shl128_pair(out,hi,lo,shift) out = __shiftleft128(lo, hi, shift); + #define shr128(out,in,shift) shr128_pair(out, in.hi, in.lo, shift) + #define shl128(out,in,shift) shl128_pair(out, in.hi, in.lo, shift) + #define add128(a,b) { uint64_t p = a.lo; a.lo += b.lo; a.hi += b.hi + (a.lo < p); } + #define add128_64(a,b) { uint64_t p = a.lo; a.lo += b; a.hi += (a.lo < p); } + #define lo128(a) (a.lo) + #define hi128(a) (a.hi) + #elif defined(COMPILER_GCC) && !defined(HAVE_NATIVE_UINT128) + #if defined(__SIZEOF_INT128__) + #define HAVE_NATIVE_UINT128 + typedef unsigned __int128 uint128_t; + #elif (COMPILER_GCC >= 40400) + #define HAVE_NATIVE_UINT128 + typedef unsigned uint128_t __attribute__((mode(TI))); + #elif defined(CPU_X86_64) + #define HAVE_UINT128 + typedef struct uint128_t { + uint64_t lo, hi; + } uint128_t; + #define mul64x64_128(out,a,b) __asm__ ("mulq %3" : "=a" (out.lo), "=d" (out.hi) : "a" (a), "rm" (b)); + #define shr128_pair(out,hi,lo,shift) __asm__ ("shrdq %2,%1,%0" : "+r" (lo) : "r" (hi), "J" (shift)); out = lo; + #define shl128_pair(out,hi,lo,shift) __asm__ ("shldq %2,%1,%0" : "+r" (hi) : "r" (lo), "J" (shift)); out = hi; + #define shr128(out,in,shift) shr128_pair(out,in.hi, in.lo, shift) + #define shl128(out,in,shift) shl128_pair(out,in.hi, in.lo, shift) + #define add128(a,b) __asm__ ("addq %4,%2; adcq %5,%3" : "=r" (a.hi), "=r" (a.lo) : "1" (a.lo), "0" (a.hi), "rm" (b.lo), "rm" (b.hi) : "cc"); + #define add128_64(a,b) __asm__ ("addq %4,%2; adcq $0,%3" : "=r" (a.hi), "=r" (a.lo) : "1" (a.lo), "0" (a.hi), "rm" (b) : "cc"); + #define lo128(a) (a.lo) + #define hi128(a) (a.hi) + #endif + #endif + + #if defined(HAVE_NATIVE_UINT128) + #define HAVE_UINT128 + #define mul64x64_128(out,a,b) out = (uint128_t)a * b; + #define shr128_pair(out,hi,lo,shift) out = (uint64_t)((((uint128_t)hi << 64) | lo) >> (shift)); + #define shl128_pair(out,hi,lo,shift) out = (uint64_t)(((((uint128_t)hi << 64) | lo) << (shift)) >> 64); + #define shr128(out,in,shift) out = (uint64_t)(in >> (shift)); + #define shl128(out,in,shift) out = (uint64_t)((in << shift) >> 64); + #define add128(a,b) a += b; + #define add128_64(a,b) a += (uint64_t)b; + #define lo128(a) ((uint64_t)a) + #define hi128(a) ((uint64_t)(a >> 64)) + #endif + + #if !defined(HAVE_UINT128) + #error Need a uint128_t implementation! + #endif +#endif + +/* endian */ +#if !defined(ED25519_OPENSSLRNG) +static inline void U32TO8_LE(unsigned char *p, const uint32_t v) { + p[0] = (unsigned char)(v ); + p[1] = (unsigned char)(v >> 8); + p[2] = (unsigned char)(v >> 16); + p[3] = (unsigned char)(v >> 24); +} +#endif + +#if !defined(HAVE_UINT128) +static inline uint32_t U8TO32_LE(const unsigned char *p) { + return + (((uint32_t)(p[0]) ) | + ((uint32_t)(p[1]) << 8) | + ((uint32_t)(p[2]) << 16) | + ((uint32_t)(p[3]) << 24)); +} +#else +static inline uint64_t U8TO64_LE(const unsigned char *p) { + return + (((uint64_t)(p[0]) ) | + ((uint64_t)(p[1]) << 8) | + ((uint64_t)(p[2]) << 16) | + ((uint64_t)(p[3]) << 24) | + ((uint64_t)(p[4]) << 32) | + ((uint64_t)(p[5]) << 40) | + ((uint64_t)(p[6]) << 48) | + ((uint64_t)(p[7]) << 56)); +} + +static inline void U64TO8_LE(unsigned char *p, const uint64_t v) { + p[0] = (unsigned char)(v ); + p[1] = (unsigned char)(v >> 8); + p[2] = (unsigned char)(v >> 16); + p[3] = (unsigned char)(v >> 24); + p[4] = (unsigned char)(v >> 32); + p[5] = (unsigned char)(v >> 40); + p[6] = (unsigned char)(v >> 48); + p[7] = (unsigned char)(v >> 56); +} +#endif + +#include <stdlib.h> +#include <string.h> + + diff --git a/src/ext/ed25519/donna/ed25519-donna.h b/src/ext/ed25519/donna/ed25519-donna.h new file mode 100644 index 0000000..de1120f --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-donna.h @@ -0,0 +1,115 @@ +/* + Public domain by Andrew M. liquidsun@gmail.com + Modified from the amd64-51-30k implementation by + Daniel J. Bernstein + Niels Duif + Tanja Lange + Peter Schwabe + Bo-Yin Yang +*/ + + +#include "ed25519-donna-portable.h" + +#if defined(ED25519_SSE2) +#else + #if defined(HAVE_UINT128) && !defined(ED25519_FORCE_32BIT) + #define ED25519_64BIT + #else + #define ED25519_32BIT + #endif +#endif + +#if !defined(ED25519_NO_INLINE_ASM) + /* detect extra features first so un-needed functions can be disabled throughout */ + #if defined(ED25519_SSE2) + #if defined(COMPILER_GCC) && defined(CPU_X86) + #define ED25519_GCC_32BIT_SSE_CHOOSE + #elif defined(COMPILER_GCC) && defined(CPU_X86_64) + #define ED25519_GCC_64BIT_SSE_CHOOSE + #endif + #else + #if defined(CPU_X86_64) + #if defined(COMPILER_GCC) + #if defined(ED25519_64BIT) + #define ED25519_GCC_64BIT_X86_CHOOSE + #else + #define ED25519_GCC_64BIT_32BIT_CHOOSE + #endif + #endif + #endif + #endif +#endif + +#if defined(ED25519_SSE2) + #include "curve25519-donna-sse2.h" +#elif defined(ED25519_64BIT) + #include "curve25519-donna-64bit.h" +#else + #include "curve25519-donna-32bit.h" +#endif + +#include "curve25519-donna-helpers.h" + +/* separate uint128 check for 64 bit sse2 */ +#if defined(HAVE_UINT128) && !defined(ED25519_FORCE_32BIT) + #include "modm-donna-64bit.h" +#else + #include "modm-donna-32bit.h" +#endif + +typedef unsigned char hash_512bits[64]; + +/* + Timing safe memory compare +*/ +static int +ed25519_verify(const unsigned char *x, const unsigned char *y, size_t len) { + size_t differentbits = 0; + while (len--) + differentbits |= (*x++ ^ *y++); + return (int) (1 & ((differentbits - 1) >> 8)); +} + + +/* + * Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2 + * with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555 + * Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960); + */ + +typedef struct ge25519_t { + bignum25519 x, y, z, t; +} ge25519; + +typedef struct ge25519_p1p1_t { + bignum25519 x, y, z, t; +} ge25519_p1p1; + +typedef struct ge25519_niels_t { + bignum25519 ysubx, xaddy, t2d; +} ge25519_niels; + +typedef struct ge25519_pniels_t { + bignum25519 ysubx, xaddy, z, t2d; +} ge25519_pniels; + +#include "ed25519-donna-basepoint-table.h" + +#if defined(ED25519_64BIT) + #include "ed25519-donna-64bit-tables.h" + #include "ed25519-donna-64bit-x86.h" +#else + #include "ed25519-donna-32bit-tables.h" + #include "ed25519-donna-64bit-x86-32bit.h" +#endif + + +#if defined(ED25519_SSE2) + #include "ed25519-donna-32bit-sse2.h" + #include "ed25519-donna-64bit-sse2.h" + #include "ed25519-donna-impl-sse2.h" +#else + #include "ed25519-donna-impl-base.h" +#endif + diff --git a/src/ext/ed25519/donna/ed25519-hash-custom.h b/src/ext/ed25519/donna/ed25519-hash-custom.h new file mode 100644 index 0000000..7dc2491 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-hash-custom.h @@ -0,0 +1,11 @@ +/* + a custom hash must have a 512bit digest and implement: + + struct ed25519_hash_context; + + void ed25519_hash_init(ed25519_hash_context *ctx); + void ed25519_hash_update(ed25519_hash_context *ctx, const uint8_t *in, size_t inlen); + void ed25519_hash_final(ed25519_hash_context *ctx, uint8_t *hash); + void ed25519_hash(uint8_t *hash, const uint8_t *in, size_t inlen); +*/ + diff --git a/src/ext/ed25519/donna/ed25519-hash.h b/src/ext/ed25519/donna/ed25519-hash.h new file mode 100644 index 0000000..6ba8f52 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-hash.h @@ -0,0 +1,219 @@ +#if defined(ED25519_REFHASH) + +/* reference/slow SHA-512. really, do not use this */ + +#define HASH_BLOCK_SIZE 128 +#define HASH_DIGEST_SIZE 64 + +typedef struct sha512_state_t { + uint64_t H[8]; + uint64_t T[2]; + uint32_t leftover; + uint8_t buffer[HASH_BLOCK_SIZE]; +} sha512_state; + +typedef sha512_state ed25519_hash_context; + +static const uint64_t sha512_constants[80] = { + 0x428a2f98d728ae22ull, 0x7137449123ef65cdull, 0xb5c0fbcfec4d3b2full, 0xe9b5dba58189dbbcull, + 0x3956c25bf348b538ull, 0x59f111f1b605d019ull, 0x923f82a4af194f9bull, 0xab1c5ed5da6d8118ull, + 0xd807aa98a3030242ull, 0x12835b0145706fbeull, 0x243185be4ee4b28cull, 0x550c7dc3d5ffb4e2ull, + 0x72be5d74f27b896full, 0x80deb1fe3b1696b1ull, 0x9bdc06a725c71235ull, 0xc19bf174cf692694ull, + 0xe49b69c19ef14ad2ull, 0xefbe4786384f25e3ull, 0x0fc19dc68b8cd5b5ull, 0x240ca1cc77ac9c65ull, + 0x2de92c6f592b0275ull, 0x4a7484aa6ea6e483ull, 0x5cb0a9dcbd41fbd4ull, 0x76f988da831153b5ull, + 0x983e5152ee66dfabull, 0xa831c66d2db43210ull, 0xb00327c898fb213full, 0xbf597fc7beef0ee4ull, + 0xc6e00bf33da88fc2ull, 0xd5a79147930aa725ull, 0x06ca6351e003826full, 0x142929670a0e6e70ull, + 0x27b70a8546d22ffcull, 0x2e1b21385c26c926ull, 0x4d2c6dfc5ac42aedull, 0x53380d139d95b3dfull, + 0x650a73548baf63deull, 0x766a0abb3c77b2a8ull, 0x81c2c92e47edaee6ull, 0x92722c851482353bull, + 0xa2bfe8a14cf10364ull, 0xa81a664bbc423001ull, 0xc24b8b70d0f89791ull, 0xc76c51a30654be30ull, + 0xd192e819d6ef5218ull, 0xd69906245565a910ull, 0xf40e35855771202aull, 0x106aa07032bbd1b8ull, + 0x19a4c116b8d2d0c8ull, 0x1e376c085141ab53ull, 0x2748774cdf8eeb99ull, 0x34b0bcb5e19b48a8ull, + 0x391c0cb3c5c95a63ull, 0x4ed8aa4ae3418acbull, 0x5b9cca4f7763e373ull, 0x682e6ff3d6b2b8a3ull, + 0x748f82ee5defb2fcull, 0x78a5636f43172f60ull, 0x84c87814a1f0ab72ull, 0x8cc702081a6439ecull, + 0x90befffa23631e28ull, 0xa4506cebde82bde9ull, 0xbef9a3f7b2c67915ull, 0xc67178f2e372532bull, + 0xca273eceea26619cull, 0xd186b8c721c0c207ull, 0xeada7dd6cde0eb1eull, 0xf57d4f7fee6ed178ull, + 0x06f067aa72176fbaull, 0x0a637dc5a2c898a6ull, 0x113f9804bef90daeull, 0x1b710b35131c471bull, + 0x28db77f523047d84ull, 0x32caab7b40c72493ull, 0x3c9ebe0a15c9bebcull, 0x431d67c49c100d4cull, + 0x4cc5d4becb3e42b6ull, 0x597f299cfc657e2aull, 0x5fcb6fab3ad6faecull, 0x6c44198c4a475817ull +}; + +static uint64_t +sha512_ROTR64(uint64_t x, int k) { + return (x >> k) | (x << (64 - k)); +} + +static uint64_t +sha512_LOAD64_BE(const uint8_t *p) { + return + ((uint64_t)p[0] << 56) | + ((uint64_t)p[1] << 48) | + ((uint64_t)p[2] << 40) | + ((uint64_t)p[3] << 32) | + ((uint64_t)p[4] << 24) | + ((uint64_t)p[5] << 16) | + ((uint64_t)p[6] << 8) | + ((uint64_t)p[7] ); +} + +static void +sha512_STORE64_BE(uint8_t *p, uint64_t v) { + p[0] = (uint8_t)(v >> 56); + p[1] = (uint8_t)(v >> 48); + p[2] = (uint8_t)(v >> 40); + p[3] = (uint8_t)(v >> 32); + p[4] = (uint8_t)(v >> 24); + p[5] = (uint8_t)(v >> 16); + p[6] = (uint8_t)(v >> 8); + p[7] = (uint8_t)(v ); +} + +#define Ch(x,y,z) (z ^ (x & (y ^ z))) +#define Maj(x,y,z) (((x | y) & z) | (x & y)) +#define S0(x) (sha512_ROTR64(x, 28) ^ sha512_ROTR64(x, 34) ^ sha512_ROTR64(x, 39)) +#define S1(x) (sha512_ROTR64(x, 14) ^ sha512_ROTR64(x, 18) ^ sha512_ROTR64(x, 41)) +#define G0(x) (sha512_ROTR64(x, 1) ^ sha512_ROTR64(x, 8) ^ (x >> 7)) +#define G1(x) (sha512_ROTR64(x, 19) ^ sha512_ROTR64(x, 61) ^ (x >> 6)) +#define W0(in,i) (sha512_LOAD64_BE(&in[i * 8])) +#define W1(i) (G1(w[i - 2]) + w[i - 7] + G0(w[i - 15]) + w[i - 16]) +#define STEP(i) \ + t1 = S0(r[0]) + Maj(r[0], r[1], r[2]); \ + t0 = r[7] + S1(r[4]) + Ch(r[4], r[5], r[6]) + sha512_constants[i] + w[i]; \ + r[7] = r[6]; \ + r[6] = r[5]; \ + r[5] = r[4]; \ + r[4] = r[3] + t0; \ + r[3] = r[2]; \ + r[2] = r[1]; \ + r[1] = r[0]; \ + r[0] = t0 + t1; + +static void +sha512_blocks(sha512_state *S, const uint8_t *in, size_t blocks) { + uint64_t r[8], w[80], t0, t1; + size_t i; + + for (i = 0; i < 8; i++) r[i] = S->H[i]; + + while (blocks--) { + for (i = 0; i < 16; i++) { w[i] = W0(in, i); } + for (i = 16; i < 80; i++) { w[i] = W1(i); } + for (i = 0; i < 80; i++) { STEP(i); } + for (i = 0; i < 8; i++) { r[i] += S->H[i]; S->H[i] = r[i]; } + S->T[0] += HASH_BLOCK_SIZE * 8; + S->T[1] += (!S->T[0]) ? 1 : 0; + in += HASH_BLOCK_SIZE; + } +} + +static void +ed25519_hash_init(sha512_state *S) { + S->H[0] = 0x6a09e667f3bcc908ull; + S->H[1] = 0xbb67ae8584caa73bull; + S->H[2] = 0x3c6ef372fe94f82bull; + S->H[3] = 0xa54ff53a5f1d36f1ull; + S->H[4] = 0x510e527fade682d1ull; + S->H[5] = 0x9b05688c2b3e6c1full; + S->H[6] = 0x1f83d9abfb41bd6bull; + S->H[7] = 0x5be0cd19137e2179ull; + S->T[0] = 0; + S->T[1] = 0; + S->leftover = 0; +} + +static void +ed25519_hash_update(sha512_state *S, const uint8_t *in, size_t inlen) { + size_t blocks, want; + + /* handle the previous data */ + if (S->leftover) { + want = (HASH_BLOCK_SIZE - S->leftover); + want = (want < inlen) ? want : inlen; + memcpy(S->buffer + S->leftover, in, want); + S->leftover += (uint32_t)want; + if (S->leftover < HASH_BLOCK_SIZE) + return; + in += want; + inlen -= want; + sha512_blocks(S, S->buffer, 1); + } + + /* handle the current data */ + blocks = (inlen & ~(HASH_BLOCK_SIZE - 1)); + S->leftover = (uint32_t)(inlen - blocks); + if (blocks) { + sha512_blocks(S, in, blocks / HASH_BLOCK_SIZE); + in += blocks; + } + + /* handle leftover data */ + if (S->leftover) + memcpy(S->buffer, in, S->leftover); +} + +static void +ed25519_hash_final(sha512_state *S, uint8_t *hash) { + uint64_t t0 = S->T[0] + (S->leftover * 8), t1 = S->T[1]; + + S->buffer[S->leftover] = 0x80; + if (S->leftover <= 111) { + memset(S->buffer + S->leftover + 1, 0, 111 - S->leftover); + } else { + memset(S->buffer + S->leftover + 1, 0, 127 - S->leftover); + sha512_blocks(S, S->buffer, 1); + memset(S->buffer, 0, 112); + } + + sha512_STORE64_BE(S->buffer + 112, t1); + sha512_STORE64_BE(S->buffer + 120, t0); + sha512_blocks(S, S->buffer, 1); + + sha512_STORE64_BE(&hash[ 0], S->H[0]); + sha512_STORE64_BE(&hash[ 8], S->H[1]); + sha512_STORE64_BE(&hash[16], S->H[2]); + sha512_STORE64_BE(&hash[24], S->H[3]); + sha512_STORE64_BE(&hash[32], S->H[4]); + sha512_STORE64_BE(&hash[40], S->H[5]); + sha512_STORE64_BE(&hash[48], S->H[6]); + sha512_STORE64_BE(&hash[56], S->H[7]); +} + +static void +ed25519_hash(uint8_t *hash, const uint8_t *in, size_t inlen) { + ed25519_hash_context ctx; + ed25519_hash_init(&ctx); + ed25519_hash_update(&ctx, in, inlen); + ed25519_hash_final(&ctx, hash); +} + +#elif defined(ED25519_CUSTOMHASH) + +#include "ed25519-hash-custom.h" + +#else + +#include <openssl/sha.h> + +typedef SHA512_CTX ed25519_hash_context; + +static void +ed25519_hash_init(ed25519_hash_context *ctx) { + SHA512_Init(ctx); +} + +static void +ed25519_hash_update(ed25519_hash_context *ctx, const uint8_t *in, size_t inlen) { + SHA512_Update(ctx, in, inlen); +} + +static void +ed25519_hash_final(ed25519_hash_context *ctx, uint8_t *hash) { + SHA512_Final(hash, ctx); +} + +static void +ed25519_hash(uint8_t *hash, const uint8_t *in, size_t inlen) { + SHA512(in, inlen, hash); +} + +#endif + diff --git a/src/ext/ed25519/donna/ed25519-randombytes-custom.h b/src/ext/ed25519/donna/ed25519-randombytes-custom.h new file mode 100644 index 0000000..9f51063 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-randombytes-custom.h @@ -0,0 +1,8 @@ +/* + a custom randombytes must implement: + + void ED25519_FN(ed25519_randombytes_unsafe) (void *p, size_t len); + + ed25519_randombytes_unsafe is used by the batch verification function + to create random scalars +*/ diff --git a/src/ext/ed25519/donna/ed25519-randombytes.h b/src/ext/ed25519/donna/ed25519-randombytes.h new file mode 100644 index 0000000..1dc6290 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519-randombytes.h @@ -0,0 +1,91 @@ +#if defined(ED25519_TEST) +/* + ISAAC+ "variant", the paper is not clear on operator precedence and other + things. This is the "first in, first out" option! + + Not threadsafe or securely initialized, only for deterministic testing +*/ +typedef struct isaacp_state_t { + uint32_t state[256]; + unsigned char buffer[1024]; + uint32_t a, b, c; + size_t left; +} isaacp_state; + +#define isaacp_step(offset, mix) \ + x = mm[i + offset]; \ + a = (a ^ (mix)) + (mm[(i + offset + 128) & 0xff]); \ + y = (a ^ b) + mm[(x >> 2) & 0xff]; \ + mm[i + offset] = y; \ + b = (x + a) ^ mm[(y >> 10) & 0xff]; \ + U32TO8_LE(out + (i + offset) * 4, b); + +static void +isaacp_mix(isaacp_state *st) { + uint32_t i, x, y; + uint32_t a = st->a, b = st->b, c = st->c; + uint32_t *mm = st->state; + unsigned char *out = st->buffer; + + c = c + 1; + b = b + c; + + for (i = 0; i < 256; i += 4) { + isaacp_step(0, ROTL32(a,13)) + isaacp_step(1, ROTR32(a, 6)) + isaacp_step(2, ROTL32(a, 2)) + isaacp_step(3, ROTR32(a,16)) + } + + st->a = a; + st->b = b; + st->c = c; + st->left = 1024; +} + +static void +isaacp_random(isaacp_state *st, void *p, size_t len) { + size_t use; + unsigned char *c = (unsigned char *)p; + while (len) { + use = (len > st->left) ? st->left : len; + memcpy(c, st->buffer + (sizeof(st->buffer) - st->left), use); + + st->left -= use; + c += use; + len -= use; + + if (!st->left) + isaacp_mix(st); + } +} + +void +ED25519_FN(ed25519_randombytes_unsafe) (void *p, size_t len) { + static int initialized = 0; + static isaacp_state rng; + + if (!initialized) { + memset(&rng, 0, sizeof(rng)); + isaacp_mix(&rng); + isaacp_mix(&rng); + initialized = 1; + } + + isaacp_random(&rng, p, len); +} +#elif defined(ED25519_CUSTOMRANDOM) + +#include "ed25519-randombytes-custom.h" + +#else + +#include <openssl/rand.h> + +void +ED25519_FN(ed25519_randombytes_unsafe) (void *p, size_t len) { + + RAND_bytes(p, (int) len); + +} +#endif diff --git a/src/ext/ed25519/donna/ed25519.c b/src/ext/ed25519/donna/ed25519.c new file mode 100644 index 0000000..58a755b --- /dev/null +++ b/src/ext/ed25519/donna/ed25519.c @@ -0,0 +1,150 @@ +/* + Public domain by Andrew M. liquidsun@gmail.com + + Ed25519 reference implementation using Ed25519-donna +*/ + + +/* define ED25519_SUFFIX to have it appended to the end of each public function */ +#if !defined(ED25519_SUFFIX) +#define ED25519_SUFFIX +#endif + +#define ED25519_FN3(fn,suffix) fn##suffix +#define ED25519_FN2(fn,suffix) ED25519_FN3(fn,suffix) +#define ED25519_FN(fn) ED25519_FN2(fn,ED25519_SUFFIX) + +#include "ed25519-donna.h" +#include "ed25519.h" +#include "ed25519-randombytes.h" +#include "ed25519-hash.h" + +/* + Generates a (extsk[0..31]) and aExt (extsk[32..63]) +*/ + +DONNA_INLINE static void +ed25519_extsk(hash_512bits extsk, const ed25519_secret_key sk) { + ed25519_hash(extsk, sk, 32); + extsk[0] &= 248; + extsk[31] &= 127; + extsk[31] |= 64; +} + +static void +ed25519_hram(hash_512bits hram, const ed25519_signature RS, const ed25519_public_key pk, const unsigned char *m, size_t mlen) { + ed25519_hash_context ctx; + ed25519_hash_init(&ctx); + ed25519_hash_update(&ctx, RS, 32); + ed25519_hash_update(&ctx, pk, 32); + ed25519_hash_update(&ctx, m, mlen); + ed25519_hash_final(&ctx, hram); +} + +void +ED25519_FN(ed25519_publickey) (const ed25519_secret_key sk, ed25519_public_key pk) { + bignum256modm a; + ge25519 ALIGN(16) A; + hash_512bits extsk; + + /* A = aB */ + ed25519_extsk(extsk, sk); + expand256_modm(a, extsk, 32); + ge25519_scalarmult_base_niels(&A, ge25519_niels_base_multiples, a); + ge25519_pack(pk, &A); +} + + +void +ED25519_FN(ed25519_sign) (const unsigned char *m, size_t mlen, const ed25519_secret_key sk, const ed25519_public_key pk, ed25519_signature RS) { + ed25519_hash_context ctx; + bignum256modm r, S, a; + ge25519 ALIGN(16) R; + hash_512bits extsk, hashr, hram; + + ed25519_extsk(extsk, sk); + + /* r = H(aExt[32..64], m) */ + ed25519_hash_init(&ctx); + ed25519_hash_update(&ctx, extsk + 32, 32); + ed25519_hash_update(&ctx, m, mlen); + ed25519_hash_final(&ctx, hashr); + expand256_modm(r, hashr, 64); + + /* R = rB */ + ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r); + ge25519_pack(RS, &R); + + /* S = H(R,A,m).. */ + ed25519_hram(hram, RS, pk, m, mlen); + expand256_modm(S, hram, 64); + + /* S = H(R,A,m)a */ + expand256_modm(a, extsk, 32); + mul256_modm(S, S, a); + + /* S = (r + H(R,A,m)a) */ + add256_modm(S, S, r); + + /* S = (r + H(R,A,m)a) mod L */ + contract256_modm(RS + 32, S); +} + +int +ED25519_FN(ed25519_sign_open) (const unsigned char *m, size_t mlen, const ed25519_public_key pk, const ed25519_signature RS) { + ge25519 ALIGN(16) R, A; + hash_512bits hash; + bignum256modm hram, S; + unsigned char checkR[32]; + + if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk)) + return -1; + + /* hram = H(R,A,m) */ + ed25519_hram(hash, RS, pk, m, mlen); + expand256_modm(hram, hash, 64); + + /* S */ + expand256_modm(S, RS + 32, 32); + + /* SB - H(R,A,m)A */ + ge25519_double_scalarmult_vartime(&R, &A, hram, S); + ge25519_pack(checkR, &R); + + /* check that R = SB - H(R,A,m)A */ + return ed25519_verify(RS, checkR, 32) ? 0 : -1; +} + +#include "ed25519-donna-batchverify.h" + +/* + Fast Curve25519 basepoint scalar multiplication +*/ + +void +ED25519_FN(curved25519_scalarmult_basepoint) (curved25519_key pk, const curved25519_key e) { + curved25519_key ec; + bignum256modm s; + bignum25519 ALIGN(16) yplusz, zminusy; + ge25519 ALIGN(16) p; + size_t i; + + /* clamp */ + for (i = 0; i < 32; i++) ec[i] = e[i]; + ec[0] &= 248; + ec[31] &= 127; + ec[31] |= 64; + + expand_raw256_modm(s, ec); + + /* scalar * basepoint */ + ge25519_scalarmult_base_niels(&p, ge25519_niels_base_multiples, s); + + /* u = (y + z) / (z - y) */ + curve25519_add(yplusz, p.y, p.z); + curve25519_sub(zminusy, p.z, p.y); + curve25519_recip(zminusy, zminusy); + curve25519_mul(yplusz, yplusz, zminusy); + curve25519_contract(pk, yplusz); +} + diff --git a/src/ext/ed25519/donna/ed25519.h b/src/ext/ed25519/donna/ed25519.h new file mode 100644 index 0000000..dc86675 --- /dev/null +++ b/src/ext/ed25519/donna/ed25519.h @@ -0,0 +1,30 @@ +#ifndef ED25519_H +#define ED25519_H + +#include <stdlib.h> + +#if defined(__cplusplus) +extern "C" { +#endif + +typedef unsigned char ed25519_signature[64]; +typedef unsigned char ed25519_public_key[32]; +typedef unsigned char ed25519_secret_key[32]; + +typedef unsigned char curved25519_key[32]; + +void ed25519_publickey(const ed25519_secret_key sk, ed25519_public_key pk); +int ed25519_sign_open(const unsigned char *m, size_t mlen, const ed25519_public_key pk, const ed25519_signature RS); +void ed25519_sign(const unsigned char *m, size_t mlen, const ed25519_secret_key sk, const ed25519_public_key pk, ed25519_signature RS); + +int ed25519_sign_open_batch(const unsigned char **m, size_t *mlen, const unsigned char **pk, const unsigned char **RS, size_t num, int *valid); + +void ed25519_randombytes_unsafe(void *out, size_t count); + +void curved25519_scalarmult_basepoint(curved25519_key pk, const curved25519_key e); + +#if defined(__cplusplus) +} +#endif + +#endif // ED25519_H diff --git a/src/ext/ed25519/donna/fuzz/README.md b/src/ext/ed25519/donna/fuzz/README.md new file mode 100644 index 0000000..306ddfe --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/README.md @@ -0,0 +1,173 @@ +This code fuzzes ed25519-donna (and optionally ed25519-donna-sse2) against the ref10 implementations of +[curve25519](https://github.com/floodyberry/supercop/tree/master/crypto_scalarmult/curve2...) and +[ed25519](https://github.com/floodyberry/supercop/tree/master/crypto_sign/ed25519/ref1...). + +Curve25519 tests that generating a public key from a secret key + +# Building + +## *nix + PHP + +`php build-nix.php (required parameters) (optional parameters)` + +Required parameters: + +* `--function=[curve25519,ed25519]` +* `--bits=[32,64]` + +Optional parameters: + +* `--with-sse2` + + Also fuzz against ed25519-donna-sse2 +* `--with-openssl` + + Build with OpenSSL's SHA-512. + + Default: Reference SHA-512 implementation (slow!) + +* `--compiler=[gcc,clang,icc]` + + Default: gcc + +* `--no-asm` + + Do not use platform specific assembler + + +example: + + php build-nix.php --bits=64 --function=ed25519 --with-sse2 --compiler=icc + +## Windows + +Create a project with access to the ed25519 files. + +If you are not using OpenSSL, add the `ED25519_REFHASH` define to the projects +"Properties/Preprocessor/Preprocessor Definitions" option + +Add the following files to the project: + +* `fuzz/curve25519-ref10.c` +* `fuzz/ed25519-ref10.c` +* `fuzz/ed25519-donna.c` +* `fuzz/ed25519-donna-sse2.c` (optional) +* `fuzz-[curve25519/ed25519].c` (depending on which you want to fuzz) + +If you are also fuzzing against ed25519-donna-sse2, add the `ED25519_SSE2` define for `fuzz-[curve25519/ed25519].c` under +its "Properties/Preprocessor/Preprocessor Definitions" option. + +# Running + +If everything agrees, the program will only output occasional status dots (every 0x1000 passes) +and a 64bit progress count (every 0x20000 passes): + + fuzzing: ref10 curved25519 curved25519-sse2 + + ................................ [0000000000020000] + ................................ [0000000000040000] + ................................ [0000000000060000] + ................................ [0000000000080000] + ................................ [00000000000a0000] + ................................ [00000000000c0000] + +If any of the implementations do not agree with the ref10 implementation, the program will dump +the random data that was used, the data generated by the ref10 implementation, and diffs of the +ed25519-donna data against the ref10 data. + +## Example errors + +These are example error dumps (with intentionally introduced errors). + +### Ed25519 + +Random data: + +* sk, or Secret Key +* m, or Message + +Generated data: + +* pk, or Public Key +* sig, or Signature +* valid, or if the signature of the message is valid with the public key + +Dump: + + sk: + 0x3b,0xb7,0x17,0x7a,0x66,0xdc,0xb7,0x9a,0x90,0x25,0x07,0x99,0x96,0xf3,0x92,0xef, + 0x78,0xf8,0xad,0x6c,0x35,0x87,0x81,0x67,0x03,0xe6,0x95,0xba,0x06,0x18,0x7c,0x9c, + + m: + 0x7c,0x8d,0x3d,0xe1,0x92,0xee,0x7a,0xb8,0x4d,0xc9,0xfb,0x02,0x34,0x1e,0x5a,0x91, + 0xee,0x01,0xa6,0xb8,0xab,0x37,0x3f,0x3d,0x6d,0xa2,0x47,0xe3,0x27,0x93,0x7c,0xb7, + 0x77,0x07,0xb6,0x88,0x41,0x22,0xf3,0x3f,0xce,0xcb,0x6b,0x3e,0x2b,0x23,0x68,0x7f, + 0x5b,0xb9,0xda,0x04,0xbb,0xae,0x42,0x50,0xf5,0xe9,0xc5,0x11,0xbd,0x52,0x76,0x98, + 0xf1,0x87,0x09,0xb9,0x89,0x0a,0x52,0x69,0x01,0xce,0xe0,0x4a,0xa6,0x46,0x5a,0xe1, + 0x63,0x14,0xe0,0x81,0x52,0xec,0xcd,0xcf,0x70,0x54,0x7d,0xa3,0x49,0x8b,0xf0,0x89, + 0x70,0x07,0x12,0x2a,0xd9,0xaa,0x16,0x01,0xb2,0x16,0x3a,0xbb,0xfc,0xfa,0x13,0x5b, + 0x69,0x83,0x92,0x70,0x95,0x76,0xa0,0x8e,0x16,0x79,0xcc,0xaa,0xb5,0x7c,0xf8,0x7a, + + ref10: + pk: + 0x71,0xb0,0x5e,0x62,0x1b,0xe3,0xe7,0x36,0x91,0x8b,0xc0,0x13,0x36,0x0c,0xc9,0x04, + 0x16,0xf5,0xff,0x48,0x0c,0x83,0x6b,0x88,0x53,0xa2,0xc6,0x0f,0xf7,0xac,0x42,0x04, + + sig: + 0x3e,0x05,0xc5,0x37,0x16,0x0b,0x29,0x30,0x89,0xa3,0xe7,0x83,0x08,0x16,0xdd,0x96, + 0x02,0xfa,0x0d,0x44,0x2c,0x43,0xaa,0x80,0x93,0x04,0x58,0x22,0x09,0xbf,0x11,0xa5, + 0xcc,0xa5,0x3c,0x9f,0xa0,0xa4,0x64,0x5a,0x4a,0xdb,0x20,0xfb,0xc7,0x9b,0xfd,0x3f, + 0x08,0xae,0xc4,0x3c,0x1e,0xd8,0xb6,0xb4,0xd2,0x6d,0x80,0x92,0xcb,0x71,0xf3,0x02, + + valid: yes + + ed25519-donna: + pk diff: + ____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,____, + ____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,____, + + sig diff: + 0x2c,0xb9,0x25,0x14,0xd0,0x94,0xeb,0xfe,0x46,0x02,0xc2,0xe8,0xa3,0xeb,0xbf,0xb5, + 0x72,0x84,0xbf,0xc1,0x8a,0x32,0x30,0x99,0xf7,0x58,0xfe,0x06,0xa8,0xdc,0xdc,0xab, + 0xb5,0x57,0x03,0x33,0x87,0xce,0x54,0x55,0x6a,0x69,0x8a,0xc4,0xb7,0x2a,0xed,0x97, + 0xb4,0x68,0xe7,0x52,0x7a,0x07,0x55,0x3b,0xa2,0x94,0xd6,0x5e,0xa1,0x61,0x80,0x08, + + valid: no + +In this case, the generated public key matches, but the generated signature is completely +different and does not validate. + +### Curve25519 + +Random data: + +* sk, or Secret Key + +Generated data: + +* pk, or Public Key + +Dump: + + sk: + 0x44,0xec,0x0b,0x0e,0xa2,0x0e,0x9c,0x5b,0x8c,0xce,0x7b,0x1d,0x68,0xae,0x0f,0x9e, + 0x81,0xe2,0x04,0x76,0xda,0x87,0xa4,0x9e,0xc9,0x4f,0x3b,0xf9,0xc3,0x89,0x63,0x70, + + + ref10: + 0x24,0x55,0x55,0xc0,0xf9,0x80,0xaf,0x02,0x43,0xee,0x8c,0x7f,0xc1,0xad,0x90,0x95, + 0x57,0x91,0x14,0x2e,0xf2,0x14,0x22,0x80,0xdd,0x4e,0x3c,0x85,0x71,0x84,0x8c,0x62, + + + curved25519 diff: + 0x12,0xd1,0x61,0x2b,0x16,0xb3,0xd8,0x29,0xf8,0xa3,0xba,0x70,0x4e,0x49,0x4f,0x43, + 0xa1,0x3c,0x6b,0x42,0x11,0x61,0xcc,0x30,0x87,0x73,0x46,0xfb,0x85,0xc7,0x9a,0x35, + + + curved25519-sse2 diff: + ____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,____, + ____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,____, + + +In this case, curved25519 is totally wrong, while curved25519-sse2 matches the reference +implementation. \ No newline at end of file diff --git a/src/ext/ed25519/donna/fuzz/build-nix.php b/src/ext/ed25519/donna/fuzz/build-nix.php new file mode 100644 index 0000000..c69144e --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/build-nix.php @@ -0,0 +1,134 @@ +<?php + function echoln($str) { + echo $str; + echo "\n"; + } + + function usage($reason) { + echoln("Usage: php build-nix.php [flags]"); + echoln("Flags in parantheses are optional"); + echoln(""); + echoln(" --bits=[32,64]"); + echoln(" --function=[curve25519,ed25519]"); + echoln(" (--compiler=[*gcc,clang,icc]) which compiler to use, gcc is default"); + echoln(" (--with-openssl) use openssl for SHA512"); + echoln(" (--with-sse2) additionally fuzz against SSE2"); + echoln(" (--no-asm) don't use platform specific asm"); + echoln(""); + if ($reason) + echoln($reason); + } + + function cleanup() { + system("rm -f *.o"); + } + + function runcmd($desc, $cmd) { + echoln($desc); + + $ret = 0; + system($cmd, $ret); + if ($ret) { + cleanup(); + exit; + } + } + + class argument { + var $set, $value; + } + + class multiargument extends argument { + function multiargument($flag, $legal_values) { + global $argc, $argv; + + $this->set = false; + + $map = array(); + foreach($legal_values as $value) + $map[$value] = true; + + for ($i = 1; $i < $argc; $i++) { + if (!preg_match("!--".$flag."=(.*)!", $argv[$i], $m)) + continue; + if (isset($map[$m[1]])) { + $this->value = $m[1]; + $this->set = true; + return; + } else { + usage("{$m[1]} is not a valid parameter to --{$flag}!"); + exit(1); + } + } + } + } + + class flag extends argument { + function flag($flag) { + global $argc, $argv; + + $this->set = false; + + $flag = "--{$flag}"; + for ($i = 1; $i < $argc; $i++) { + if ($argv[$i] !== $flag) + continue; + $this->value = true; + $this->set = true; + return; + } + } + } + + $bits = new multiargument("bits", array("32", "64")); + $function = new multiargument("function", array("curve25519", "ed25519")); + $compiler = new multiargument("compiler", array("gcc", "clang", "icc")); + $with_sse2 = new flag("with-sse2"); + $with_openssl = new flag("with-openssl"); + $no_asm = new flag("no-asm"); + + $err = ""; + if (!$bits->set) + $err .= "--bits not set\n"; + if (!$function->set) + $err .= "--function not set\n"; + + if ($err !== "") { + usage($err); + exit; + } + + $compile = ($compiler->set) ? $compiler->value : "gcc"; + $link = ""; + $flags = "-O3 -m{$bits->value}"; + $ret = 0; + + if ($with_openssl->set) $link .= " -lssl -lcrypto"; + if (!$with_openssl->set) $flags .= " -DED25519_REFHASH -DED25519_TEST"; + if ($no_asm->set) $flags .= " -DED25519_NO_INLINE_ASM"; + + if ($function->value === "curve25519") { + runcmd("building ref10..", "{$compile} {$flags} curve25519-ref10.c -c -o curve25519-ref10.o"); + runcmd("building ed25519..", "{$compile} {$flags} ed25519-donna.c -c -o ed25519.o"); + if ($with_sse2->set) { + runcmd("building ed25519-sse2..", "{$compile} {$flags} ed25519-donna-sse2.c -c -o ed25519-sse2.o -msse2"); + $flags .= " -DED25519_SSE2"; + $link .= " ed25519-sse2.o"; + } + runcmd("linking..", "{$compile} {$flags} {$link} fuzz-curve25519.c ed25519.o curve25519-ref10.o -o fuzz-curve25519"); + echoln("fuzz-curve25519 built."); + } else if ($function->value === "ed25519") { + runcmd("building ref10..", "{$compile} {$flags} ed25519-ref10.c -c -o ed25519-ref10.o"); + runcmd("building ed25519..", "{$compile} {$flags} ed25519-donna.c -c -o ed25519.o"); + if ($with_sse2->set) { + runcmd("building ed25519-sse2..", "{$compile} {$flags} ed25519-donna-sse2.c -c -o ed25519-sse2.o -msse2"); + $flags .= " -DED25519_SSE2"; + $link .= " ed25519-sse2.o"; + } + runcmd("linking..", "{$compile} {$flags} {$link} fuzz-ed25519.c ed25519.o ed25519-ref10.o -o fuzz-ed25519"); + echoln("fuzz-ed25519 built."); + } + + + cleanup(); +?> diff --git a/src/ext/ed25519/donna/fuzz/curve25519-ref10.c b/src/ext/ed25519/donna/fuzz/curve25519-ref10.c new file mode 100644 index 0000000..efefce6 --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/curve25519-ref10.c @@ -0,0 +1,1272 @@ +#include <stdint.h> + +typedef int32_t crypto_int32; +typedef int64_t crypto_int64; +typedef uint64_t crypto_uint64; + +typedef crypto_int32 fe[10]; + +/* +h = 0 +*/ + +void fe_0(fe h) +{ + h[0] = 0; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; + h[5] = 0; + h[6] = 0; + h[7] = 0; + h[8] = 0; + h[9] = 0; +} + +/* +h = 1 +*/ + +void fe_1(fe h) +{ + h[0] = 1; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; + h[5] = 0; + h[6] = 0; + h[7] = 0; + h[8] = 0; + h[9] = 0; +} + +/* +h = f + g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +void fe_add(fe h,fe f,fe g) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 g0 = g[0]; + crypto_int32 g1 = g[1]; + crypto_int32 g2 = g[2]; + crypto_int32 g3 = g[3]; + crypto_int32 g4 = g[4]; + crypto_int32 g5 = g[5]; + crypto_int32 g6 = g[6]; + crypto_int32 g7 = g[7]; + crypto_int32 g8 = g[8]; + crypto_int32 g9 = g[9]; + crypto_int32 h0 = f0 + g0; + crypto_int32 h1 = f1 + g1; + crypto_int32 h2 = f2 + g2; + crypto_int32 h3 = f3 + g3; + crypto_int32 h4 = f4 + g4; + crypto_int32 h5 = f5 + g5; + crypto_int32 h6 = f6 + g6; + crypto_int32 h7 = f7 + g7; + crypto_int32 h8 = f8 + g8; + crypto_int32 h9 = f9 + g9; + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* +h = f +*/ + +void fe_copy(fe h,fe f) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + h[0] = f0; + h[1] = f1; + h[2] = f2; + h[3] = f3; + h[4] = f4; + h[5] = f5; + h[6] = f6; + h[7] = f7; + h[8] = f8; + h[9] = f9; +} + + +/* +Replace (f,g) with (g,f) if b == 1; +replace (f,g) with (f,g) if b == 0. + +Preconditions: b in {0,1}. +*/ + +void fe_cswap(fe f,fe g,unsigned int b) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 g0 = g[0]; + crypto_int32 g1 = g[1]; + crypto_int32 g2 = g[2]; + crypto_int32 g3 = g[3]; + crypto_int32 g4 = g[4]; + crypto_int32 g5 = g[5]; + crypto_int32 g6 = g[6]; + crypto_int32 g7 = g[7]; + crypto_int32 g8 = g[8]; + crypto_int32 g9 = g[9]; + crypto_int32 x0 = f0 ^ g0; + crypto_int32 x1 = f1 ^ g1; + crypto_int32 x2 = f2 ^ g2; + crypto_int32 x3 = f3 ^ g3; + crypto_int32 x4 = f4 ^ g4; + crypto_int32 x5 = f5 ^ g5; + crypto_int32 x6 = f6 ^ g6; + crypto_int32 x7 = f7 ^ g7; + crypto_int32 x8 = f8 ^ g8; + crypto_int32 x9 = f9 ^ g9; + b = -b; + x0 &= b; + x1 &= b; + x2 &= b; + x3 &= b; + x4 &= b; + x5 &= b; + x6 &= b; + x7 &= b; + x8 &= b; + x9 &= b; + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; + f[5] = f5 ^ x5; + f[6] = f6 ^ x6; + f[7] = f7 ^ x7; + f[8] = f8 ^ x8; + f[9] = f9 ^ x9; + g[0] = g0 ^ x0; + g[1] = g1 ^ x1; + g[2] = g2 ^ x2; + g[3] = g3 ^ x3; + g[4] = g4 ^ x4; + g[5] = g5 ^ x5; + g[6] = g6 ^ x6; + g[7] = g7 ^ x7; + g[8] = g8 ^ x8; + g[9] = g9 ^ x9; +} + +static crypto_uint64 load_3(const unsigned char *in) +{ + crypto_uint64 result; + result = (crypto_uint64) in[0]; + result |= ((crypto_uint64) in[1]) << 8; + result |= ((crypto_uint64) in[2]) << 16; + return result; +} + +static crypto_uint64 load_4(const unsigned char *in) +{ + crypto_uint64 result; + result = (crypto_uint64) in[0]; + result |= ((crypto_uint64) in[1]) << 8; + result |= ((crypto_uint64) in[2]) << 16; + result |= ((crypto_uint64) in[3]) << 24; + return result; +} + +void fe_frombytes(fe h,const unsigned char *s) +{ + crypto_int64 h0 = load_4(s); + crypto_int64 h1 = load_3(s + 4) << 6; + crypto_int64 h2 = load_3(s + 7) << 5; + crypto_int64 h3 = load_3(s + 10) << 3; + crypto_int64 h4 = load_3(s + 13) << 2; + crypto_int64 h5 = load_4(s + 16); + crypto_int64 h6 = load_3(s + 20) << 7; + crypto_int64 h7 = load_3(s + 23) << 5; + crypto_int64 h8 = load_3(s + 26) << 4; + crypto_int64 h9 = load_3(s + 29) << 2; + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + + carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + + +/* +h = f * g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + +Postconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +*/ + +/* +Notes on implementation strategy: + +Using schoolbook multiplication. +Karatsuba would save a little in some cost models. + +Most multiplications by 2 and 19 are 32-bit precomputations; +cheaper than 64-bit postcomputations. + +There is one remaining multiplication by 19 in the carry chain; +one *19 precomputation can be merged into this, +but the resulting data flow is considerably less clean. + +There are 12 carries below. +10 of them are 2-way parallelizable and vectorizable. +Can get away with 11 carries, but then data flow is much deeper. + +With tighter constraints on inputs can squeeze carries into int32. +*/ + +void fe_mul(fe h,fe f,fe g) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 g0 = g[0]; + crypto_int32 g1 = g[1]; + crypto_int32 g2 = g[2]; + crypto_int32 g3 = g[3]; + crypto_int32 g4 = g[4]; + crypto_int32 g5 = g[5]; + crypto_int32 g6 = g[6]; + crypto_int32 g7 = g[7]; + crypto_int32 g8 = g[8]; + crypto_int32 g9 = g[9]; + crypto_int32 g1_19 = 19 * g1; /* 1.4*2^29 */ + crypto_int32 g2_19 = 19 * g2; /* 1.4*2^30; still ok */ + crypto_int32 g3_19 = 19 * g3; + crypto_int32 g4_19 = 19 * g4; + crypto_int32 g5_19 = 19 * g5; + crypto_int32 g6_19 = 19 * g6; + crypto_int32 g7_19 = 19 * g7; + crypto_int32 g8_19 = 19 * g8; + crypto_int32 g9_19 = 19 * g9; + crypto_int32 f1_2 = 2 * f1; + crypto_int32 f3_2 = 2 * f3; + crypto_int32 f5_2 = 2 * f5; + crypto_int32 f7_2 = 2 * f7; + crypto_int32 f9_2 = 2 * f9; + crypto_int64 f0g0 = f0 * (crypto_int64) g0; + crypto_int64 f0g1 = f0 * (crypto_int64) g1; + crypto_int64 f0g2 = f0 * (crypto_int64) g2; + crypto_int64 f0g3 = f0 * (crypto_int64) g3; + crypto_int64 f0g4 = f0 * (crypto_int64) g4; + crypto_int64 f0g5 = f0 * (crypto_int64) g5; + crypto_int64 f0g6 = f0 * (crypto_int64) g6; + crypto_int64 f0g7 = f0 * (crypto_int64) g7; + crypto_int64 f0g8 = f0 * (crypto_int64) g8; + crypto_int64 f0g9 = f0 * (crypto_int64) g9; + crypto_int64 f1g0 = f1 * (crypto_int64) g0; + crypto_int64 f1g1_2 = f1_2 * (crypto_int64) g1; + crypto_int64 f1g2 = f1 * (crypto_int64) g2; + crypto_int64 f1g3_2 = f1_2 * (crypto_int64) g3; + crypto_int64 f1g4 = f1 * (crypto_int64) g4; + crypto_int64 f1g5_2 = f1_2 * (crypto_int64) g5; + crypto_int64 f1g6 = f1 * (crypto_int64) g6; + crypto_int64 f1g7_2 = f1_2 * (crypto_int64) g7; + crypto_int64 f1g8 = f1 * (crypto_int64) g8; + crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19; + crypto_int64 f2g0 = f2 * (crypto_int64) g0; + crypto_int64 f2g1 = f2 * (crypto_int64) g1; + crypto_int64 f2g2 = f2 * (crypto_int64) g2; + crypto_int64 f2g3 = f2 * (crypto_int64) g3; + crypto_int64 f2g4 = f2 * (crypto_int64) g4; + crypto_int64 f2g5 = f2 * (crypto_int64) g5; + crypto_int64 f2g6 = f2 * (crypto_int64) g6; + crypto_int64 f2g7 = f2 * (crypto_int64) g7; + crypto_int64 f2g8_19 = f2 * (crypto_int64) g8_19; + crypto_int64 f2g9_19 = f2 * (crypto_int64) g9_19; + crypto_int64 f3g0 = f3 * (crypto_int64) g0; + crypto_int64 f3g1_2 = f3_2 * (crypto_int64) g1; + crypto_int64 f3g2 = f3 * (crypto_int64) g2; + crypto_int64 f3g3_2 = f3_2 * (crypto_int64) g3; + crypto_int64 f3g4 = f3 * (crypto_int64) g4; + crypto_int64 f3g5_2 = f3_2 * (crypto_int64) g5; + crypto_int64 f3g6 = f3 * (crypto_int64) g6; + crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19; + crypto_int64 f3g8_19 = f3 * (crypto_int64) g8_19; + crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19; + crypto_int64 f4g0 = f4 * (crypto_int64) g0; + crypto_int64 f4g1 = f4 * (crypto_int64) g1; + crypto_int64 f4g2 = f4 * (crypto_int64) g2; + crypto_int64 f4g3 = f4 * (crypto_int64) g3; + crypto_int64 f4g4 = f4 * (crypto_int64) g4; + crypto_int64 f4g5 = f4 * (crypto_int64) g5; + crypto_int64 f4g6_19 = f4 * (crypto_int64) g6_19; + crypto_int64 f4g7_19 = f4 * (crypto_int64) g7_19; + crypto_int64 f4g8_19 = f4 * (crypto_int64) g8_19; + crypto_int64 f4g9_19 = f4 * (crypto_int64) g9_19; + crypto_int64 f5g0 = f5 * (crypto_int64) g0; + crypto_int64 f5g1_2 = f5_2 * (crypto_int64) g1; + crypto_int64 f5g2 = f5 * (crypto_int64) g2; + crypto_int64 f5g3_2 = f5_2 * (crypto_int64) g3; + crypto_int64 f5g4 = f5 * (crypto_int64) g4; + crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19; + crypto_int64 f5g6_19 = f5 * (crypto_int64) g6_19; + crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19; + crypto_int64 f5g8_19 = f5 * (crypto_int64) g8_19; + crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19; + crypto_int64 f6g0 = f6 * (crypto_int64) g0; + crypto_int64 f6g1 = f6 * (crypto_int64) g1; + crypto_int64 f6g2 = f6 * (crypto_int64) g2; + crypto_int64 f6g3 = f6 * (crypto_int64) g3; + crypto_int64 f6g4_19 = f6 * (crypto_int64) g4_19; + crypto_int64 f6g5_19 = f6 * (crypto_int64) g5_19; + crypto_int64 f6g6_19 = f6 * (crypto_int64) g6_19; + crypto_int64 f6g7_19 = f6 * (crypto_int64) g7_19; + crypto_int64 f6g8_19 = f6 * (crypto_int64) g8_19; + crypto_int64 f6g9_19 = f6 * (crypto_int64) g9_19; + crypto_int64 f7g0 = f7 * (crypto_int64) g0; + crypto_int64 f7g1_2 = f7_2 * (crypto_int64) g1; + crypto_int64 f7g2 = f7 * (crypto_int64) g2; + crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19; + crypto_int64 f7g4_19 = f7 * (crypto_int64) g4_19; + crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19; + crypto_int64 f7g6_19 = f7 * (crypto_int64) g6_19; + crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19; + crypto_int64 f7g8_19 = f7 * (crypto_int64) g8_19; + crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19; + crypto_int64 f8g0 = f8 * (crypto_int64) g0; + crypto_int64 f8g1 = f8 * (crypto_int64) g1; + crypto_int64 f8g2_19 = f8 * (crypto_int64) g2_19; + crypto_int64 f8g3_19 = f8 * (crypto_int64) g3_19; + crypto_int64 f8g4_19 = f8 * (crypto_int64) g4_19; + crypto_int64 f8g5_19 = f8 * (crypto_int64) g5_19; + crypto_int64 f8g6_19 = f8 * (crypto_int64) g6_19; + crypto_int64 f8g7_19 = f8 * (crypto_int64) g7_19; + crypto_int64 f8g8_19 = f8 * (crypto_int64) g8_19; + crypto_int64 f8g9_19 = f8 * (crypto_int64) g9_19; + crypto_int64 f9g0 = f9 * (crypto_int64) g0; + crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19; + crypto_int64 f9g2_19 = f9 * (crypto_int64) g2_19; + crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19; + crypto_int64 f9g4_19 = f9 * (crypto_int64) g4_19; + crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19; + crypto_int64 f9g6_19 = f9 * (crypto_int64) g6_19; + crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19; + crypto_int64 f9g8_19 = f9 * (crypto_int64) g8_19; + crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19; + crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; + crypto_int64 h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; + crypto_int64 h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; + crypto_int64 h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; + crypto_int64 h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; + crypto_int64 h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; + crypto_int64 h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; + crypto_int64 h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; + crypto_int64 h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; + crypto_int64 h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + + /* + |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38)) + i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8 + |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19)) + i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9 + */ + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.51*2^58 */ + /* |h5| <= 1.51*2^58 */ + + carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.21*2^59 */ + /* |h6| <= 1.21*2^59 */ + + carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.51*2^58 */ + /* |h7| <= 1.51*2^58 */ + + carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.52*2^33 */ + /* |h8| <= 1.52*2^33 */ + + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.51*2^58 */ + + carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.8*2^37 */ + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* +h = f * 121666 +Can overlap h with f. + +Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + +Postconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +*/ + +void fe_mul121666(fe h,fe f) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int64 h0 = f0 * (crypto_int64) 121666; + crypto_int64 h1 = f1 * (crypto_int64) 121666; + crypto_int64 h2 = f2 * (crypto_int64) 121666; + crypto_int64 h3 = f3 * (crypto_int64) 121666; + crypto_int64 h4 = f4 * (crypto_int64) 121666; + crypto_int64 h5 = f5 * (crypto_int64) 121666; + crypto_int64 h6 = f6 * (crypto_int64) 121666; + crypto_int64 h7 = f7 * (crypto_int64) 121666; + crypto_int64 h8 = f8 * (crypto_int64) 121666; + crypto_int64 h9 = f9 * (crypto_int64) 121666; + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + + carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* +h = f * f +Can overlap h with f. + +Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + +Postconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +*/ + +/* +See fe_mul.c for discussion of implementation strategy. +*/ + +void fe_sq(fe h,fe f) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 f0_2 = 2 * f0; + crypto_int32 f1_2 = 2 * f1; + crypto_int32 f2_2 = 2 * f2; + crypto_int32 f3_2 = 2 * f3; + crypto_int32 f4_2 = 2 * f4; + crypto_int32 f5_2 = 2 * f5; + crypto_int32 f6_2 = 2 * f6; + crypto_int32 f7_2 = 2 * f7; + crypto_int32 f5_38 = 38 * f5; /* 1.31*2^30 */ + crypto_int32 f6_19 = 19 * f6; /* 1.31*2^30 */ + crypto_int32 f7_38 = 38 * f7; /* 1.31*2^30 */ + crypto_int32 f8_19 = 19 * f8; /* 1.31*2^30 */ + crypto_int32 f9_38 = 38 * f9; /* 1.31*2^30 */ + crypto_int64 f0f0 = f0 * (crypto_int64) f0; + crypto_int64 f0f1_2 = f0_2 * (crypto_int64) f1; + crypto_int64 f0f2_2 = f0_2 * (crypto_int64) f2; + crypto_int64 f0f3_2 = f0_2 * (crypto_int64) f3; + crypto_int64 f0f4_2 = f0_2 * (crypto_int64) f4; + crypto_int64 f0f5_2 = f0_2 * (crypto_int64) f5; + crypto_int64 f0f6_2 = f0_2 * (crypto_int64) f6; + crypto_int64 f0f7_2 = f0_2 * (crypto_int64) f7; + crypto_int64 f0f8_2 = f0_2 * (crypto_int64) f8; + crypto_int64 f0f9_2 = f0_2 * (crypto_int64) f9; + crypto_int64 f1f1_2 = f1_2 * (crypto_int64) f1; + crypto_int64 f1f2_2 = f1_2 * (crypto_int64) f2; + crypto_int64 f1f3_4 = f1_2 * (crypto_int64) f3_2; + crypto_int64 f1f4_2 = f1_2 * (crypto_int64) f4; + crypto_int64 f1f5_4 = f1_2 * (crypto_int64) f5_2; + crypto_int64 f1f6_2 = f1_2 * (crypto_int64) f6; + crypto_int64 f1f7_4 = f1_2 * (crypto_int64) f7_2; + crypto_int64 f1f8_2 = f1_2 * (crypto_int64) f8; + crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38; + crypto_int64 f2f2 = f2 * (crypto_int64) f2; + crypto_int64 f2f3_2 = f2_2 * (crypto_int64) f3; + crypto_int64 f2f4_2 = f2_2 * (crypto_int64) f4; + crypto_int64 f2f5_2 = f2_2 * (crypto_int64) f5; + crypto_int64 f2f6_2 = f2_2 * (crypto_int64) f6; + crypto_int64 f2f7_2 = f2_2 * (crypto_int64) f7; + crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19; + crypto_int64 f2f9_38 = f2 * (crypto_int64) f9_38; + crypto_int64 f3f3_2 = f3_2 * (crypto_int64) f3; + crypto_int64 f3f4_2 = f3_2 * (crypto_int64) f4; + crypto_int64 f3f5_4 = f3_2 * (crypto_int64) f5_2; + crypto_int64 f3f6_2 = f3_2 * (crypto_int64) f6; + crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38; + crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19; + crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38; + crypto_int64 f4f4 = f4 * (crypto_int64) f4; + crypto_int64 f4f5_2 = f4_2 * (crypto_int64) f5; + crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19; + crypto_int64 f4f7_38 = f4 * (crypto_int64) f7_38; + crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19; + crypto_int64 f4f9_38 = f4 * (crypto_int64) f9_38; + crypto_int64 f5f5_38 = f5 * (crypto_int64) f5_38; + crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19; + crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38; + crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19; + crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38; + crypto_int64 f6f6_19 = f6 * (crypto_int64) f6_19; + crypto_int64 f6f7_38 = f6 * (crypto_int64) f7_38; + crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19; + crypto_int64 f6f9_38 = f6 * (crypto_int64) f9_38; + crypto_int64 f7f7_38 = f7 * (crypto_int64) f7_38; + crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19; + crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38; + crypto_int64 f8f8_19 = f8 * (crypto_int64) f8_19; + crypto_int64 f8f9_38 = f8 * (crypto_int64) f9_38; + crypto_int64 f9f9_38 = f9 * (crypto_int64) f9_38; + crypto_int64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + + carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + + carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + + carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* +h = f - g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +void fe_sub(fe h,fe f,fe g) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 g0 = g[0]; + crypto_int32 g1 = g[1]; + crypto_int32 g2 = g[2]; + crypto_int32 g3 = g[3]; + crypto_int32 g4 = g[4]; + crypto_int32 g5 = g[5]; + crypto_int32 g6 = g[6]; + crypto_int32 g7 = g[7]; + crypto_int32 g8 = g[8]; + crypto_int32 g9 = g[9]; + crypto_int32 h0 = f0 - g0; + crypto_int32 h1 = f1 - g1; + crypto_int32 h2 = f2 - g2; + crypto_int32 h3 = f3 - g3; + crypto_int32 h4 = f4 - g4; + crypto_int32 h5 = f5 - g5; + crypto_int32 h6 = f6 - g6; + crypto_int32 h7 = f7 - g7; + crypto_int32 h8 = f8 - g8; + crypto_int32 h9 = f9 - g9; + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* +Preconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Write p=2^255-19; q=floor(h/p). +Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). + +Proof: + Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. + Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4. + + Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). + Then 0<y<1. + + Write r=h-pq. + Have 0<=r<=p-1=2^255-20. + Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. + + Write x=r+19(2^-255)r+y. + Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. + + Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) + so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. +*/ + +void fe_tobytes(unsigned char *s,fe h) +{ + crypto_int32 h0 = h[0]; + crypto_int32 h1 = h[1]; + crypto_int32 h2 = h[2]; + crypto_int32 h3 = h[3]; + crypto_int32 h4 = h[4]; + crypto_int32 h5 = h[5]; + crypto_int32 h6 = h[6]; + crypto_int32 h7 = h[7]; + crypto_int32 h8 = h[8]; + crypto_int32 h9 = h[9]; + crypto_int32 q; + crypto_int32 carry0; + crypto_int32 carry1; + crypto_int32 carry2; + crypto_int32 carry3; + crypto_int32 carry4; + crypto_int32 carry5; + crypto_int32 carry6; + crypto_int32 carry7; + crypto_int32 carry8; + crypto_int32 carry9; + + q = (19 * h9 + (((crypto_int32) 1) << 24)) >> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + + carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26; + carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25; + carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26; + carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25; + carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26; + carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25; + carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26; + carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25; + carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26; + carry9 = h9 >> 25; h9 -= carry9 << 25; + /* h10 = carry9 */ + + /* + Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + Have h0+...+2^230 h9 between 0 and 2^255-1; + evidently 2^255 h10-2^255 q = 0. + Goal: Output h0+...+2^230 h9. + */ + + s[0] = h0 >> 0; + s[1] = h0 >> 8; + s[2] = h0 >> 16; + s[3] = (h0 >> 24) | (h1 << 2); + s[4] = h1 >> 6; + s[5] = h1 >> 14; + s[6] = (h1 >> 22) | (h2 << 3); + s[7] = h2 >> 5; + s[8] = h2 >> 13; + s[9] = (h2 >> 21) | (h3 << 5); + s[10] = h3 >> 3; + s[11] = h3 >> 11; + s[12] = (h3 >> 19) | (h4 << 6); + s[13] = h4 >> 2; + s[14] = h4 >> 10; + s[15] = h4 >> 18; + s[16] = h5 >> 0; + s[17] = h5 >> 8; + s[18] = h5 >> 16; + s[19] = (h5 >> 24) | (h6 << 1); + s[20] = h6 >> 7; + s[21] = h6 >> 15; + s[22] = (h6 >> 23) | (h7 << 3); + s[23] = h7 >> 5; + s[24] = h7 >> 13; + s[25] = (h7 >> 21) | (h8 << 4); + s[26] = h8 >> 4; + s[27] = h8 >> 12; + s[28] = (h8 >> 20) | (h9 << 6); + s[29] = h9 >> 2; + s[30] = h9 >> 10; + s[31] = h9 >> 18; +} + +void fe_invert(fe out,fe z) +{ + fe t0; + fe t1; + fe t2; + fe t3; + int i; + + +/* qhasm: fe z1 */ + +/* qhasm: fe z2 */ + +/* qhasm: fe z8 */ + +/* qhasm: fe z9 */ + +/* qhasm: fe z11 */ + +/* qhasm: fe z22 */ + +/* qhasm: fe z_5_0 */ + +/* qhasm: fe z_10_5 */ + +/* qhasm: fe z_10_0 */ + +/* qhasm: fe z_20_10 */ + +/* qhasm: fe z_20_0 */ + +/* qhasm: fe z_40_20 */ + +/* qhasm: fe z_40_0 */ + +/* qhasm: fe z_50_10 */ + +/* qhasm: fe z_50_0 */ + +/* qhasm: fe z_100_50 */ + +/* qhasm: fe z_100_0 */ + +/* qhasm: fe z_200_100 */ + +/* qhasm: fe z_200_0 */ + +/* qhasm: fe z_250_50 */ + +/* qhasm: fe z_250_0 */ + +/* qhasm: fe z_255_5 */ + +/* qhasm: fe z_255_21 */ + +/* qhasm: enter pow225521 */ + +/* qhasm: z2 = z1^2^1 */ +/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */ +/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */ +fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0); + +/* qhasm: z8 = z2^2^2 */ +/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */ +/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */ +fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1); + +/* qhasm: z9 = z1*z8 */ +/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */ +/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */ +fe_mul(t1,z,t1); + +/* qhasm: z11 = z2*z9 */ +/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */ +/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */ +fe_mul(t0,t0,t1); + +/* qhasm: z22 = z11^2^1 */ +/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */ +/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */ +fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2); + +/* qhasm: z_5_0 = z9*z22 */ +/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */ +/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */ +fe_mul(t1,t1,t2); + +/* qhasm: z_10_5 = z_5_0^2^5 */ +/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */ +/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */ +fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2); + +/* qhasm: z_10_0 = z_10_5*z_5_0 */ +/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */ +/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */ +fe_mul(t1,t2,t1); + +/* qhasm: z_20_10 = z_10_0^2^10 */ +/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */ +/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */ +fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2); + +/* qhasm: z_20_0 = z_20_10*z_10_0 */ +/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */ +/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */ +fe_mul(t2,t2,t1); + +/* qhasm: z_40_20 = z_20_0^2^20 */ +/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */ +/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */ +fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3); + +/* qhasm: z_40_0 = z_40_20*z_20_0 */ +/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */ +/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */ +fe_mul(t2,t3,t2); + +/* qhasm: z_50_10 = z_40_0^2^10 */ +/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */ +/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */ +fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2); + +/* qhasm: z_50_0 = z_50_10*z_10_0 */ +/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */ +/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */ +fe_mul(t1,t2,t1); + +/* qhasm: z_100_50 = z_50_0^2^50 */ +/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */ +/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */ +fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2); + +/* qhasm: z_100_0 = z_100_50*z_50_0 */ +/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */ +/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */ +fe_mul(t2,t2,t1); + +/* qhasm: z_200_100 = z_100_0^2^100 */ +/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */ +/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */ +fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3); + +/* qhasm: z_200_0 = z_200_100*z_100_0 */ +/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */ +/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */ +fe_mul(t2,t3,t2); + +/* qhasm: z_250_50 = z_200_0^2^50 */ +/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */ +/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */ +fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2); + +/* qhasm: z_250_0 = z_250_50*z_50_0 */ +/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */ +/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */ +fe_mul(t1,t2,t1); + +/* qhasm: z_255_5 = z_250_0^2^5 */ +/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */ +/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */ +fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1); + +/* qhasm: z_255_21 = z_255_5*z11 */ +/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */ +/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */ +fe_mul(out,t1,t0); + +/* qhasm: return */ + + return; +} + + +int crypto_scalarmult_ref10(unsigned char *q, + const unsigned char *n, + const unsigned char *p) +{ + unsigned char e[32]; + unsigned int i; + fe x1; + fe x2; + fe z2; + fe x3; + fe z3; + fe tmp0; + fe tmp1; + int pos; + unsigned int swap; + unsigned int b; + + for (i = 0;i < 32;++i) e[i] = n[i]; + e[0] &= 248; + e[31] &= 127; + e[31] |= 64; + fe_frombytes(x1,p); + fe_1(x2); + fe_0(z2); + fe_copy(x3,x1); + fe_1(z3); + + swap = 0; + for (pos = 254;pos >= 0;--pos) { + b = e[pos / 8] >> (pos & 7); + b &= 1; + swap ^= b; + fe_cswap(x2,x3,swap); + fe_cswap(z2,z3,swap); + swap = b; +/* qhasm: fe X2 */ + +/* qhasm: fe Z2 */ + +/* qhasm: fe X3 */ + +/* qhasm: fe Z3 */ + +/* qhasm: fe X4 */ + +/* qhasm: fe Z4 */ + +/* qhasm: fe X5 */ + +/* qhasm: fe Z5 */ + +/* qhasm: fe A */ + +/* qhasm: fe B */ + +/* qhasm: fe C */ + +/* qhasm: fe D */ + +/* qhasm: fe E */ + +/* qhasm: fe AA */ + +/* qhasm: fe BB */ + +/* qhasm: fe DA */ + +/* qhasm: fe CB */ + +/* qhasm: fe t0 */ + +/* qhasm: fe t1 */ + +/* qhasm: fe t2 */ + +/* qhasm: fe t3 */ + +/* qhasm: fe t4 */ + +/* qhasm: enter ladder */ + +/* qhasm: D = X3-Z3 */ +/* asm 1: fe_sub(>D=fe#5,<X3=fe#3,<Z3=fe#4); */ +/* asm 2: fe_sub(>D=tmp0,<X3=x3,<Z3=z3); */ +fe_sub(tmp0,x3,z3); + +/* qhasm: B = X2-Z2 */ +/* asm 1: fe_sub(>B=fe#6,<X2=fe#1,<Z2=fe#2); */ +/* asm 2: fe_sub(>B=tmp1,<X2=x2,<Z2=z2); */ +fe_sub(tmp1,x2,z2); + +/* qhasm: A = X2+Z2 */ +/* asm 1: fe_add(>A=fe#1,<X2=fe#1,<Z2=fe#2); */ +/* asm 2: fe_add(>A=x2,<X2=x2,<Z2=z2); */ +fe_add(x2,x2,z2); + +/* qhasm: C = X3+Z3 */ +/* asm 1: fe_add(>C=fe#2,<X3=fe#3,<Z3=fe#4); */ +/* asm 2: fe_add(>C=z2,<X3=x3,<Z3=z3); */ +fe_add(z2,x3,z3); + +/* qhasm: DA = D*A */ +/* asm 1: fe_mul(>DA=fe#4,<D=fe#5,<A=fe#1); */ +/* asm 2: fe_mul(>DA=z3,<D=tmp0,<A=x2); */ +fe_mul(z3,tmp0,x2); + +/* qhasm: CB = C*B */ +/* asm 1: fe_mul(>CB=fe#2,<C=fe#2,<B=fe#6); */ +/* asm 2: fe_mul(>CB=z2,<C=z2,<B=tmp1); */ +fe_mul(z2,z2,tmp1); + +/* qhasm: BB = B^2 */ +/* asm 1: fe_sq(>BB=fe#5,<B=fe#6); */ +/* asm 2: fe_sq(>BB=tmp0,<B=tmp1); */ +fe_sq(tmp0,tmp1); + +/* qhasm: AA = A^2 */ +/* asm 1: fe_sq(>AA=fe#6,<A=fe#1); */ +/* asm 2: fe_sq(>AA=tmp1,<A=x2); */ +fe_sq(tmp1,x2); + +/* qhasm: t0 = DA+CB */ +/* asm 1: fe_add(>t0=fe#3,<DA=fe#4,<CB=fe#2); */ +/* asm 2: fe_add(>t0=x3,<DA=z3,<CB=z2); */ +fe_add(x3,z3,z2); + +/* qhasm: assign x3 to t0 */ + +/* qhasm: t1 = DA-CB */ +/* asm 1: fe_sub(>t1=fe#2,<DA=fe#4,<CB=fe#2); */ +/* asm 2: fe_sub(>t1=z2,<DA=z3,<CB=z2); */ +fe_sub(z2,z3,z2); + +/* qhasm: X4 = AA*BB */ +/* asm 1: fe_mul(>X4=fe#1,<AA=fe#6,<BB=fe#5); */ +/* asm 2: fe_mul(>X4=x2,<AA=tmp1,<BB=tmp0); */ +fe_mul(x2,tmp1,tmp0); + +/* qhasm: E = AA-BB */ +/* asm 1: fe_sub(>E=fe#6,<AA=fe#6,<BB=fe#5); */ +/* asm 2: fe_sub(>E=tmp1,<AA=tmp1,<BB=tmp0); */ +fe_sub(tmp1,tmp1,tmp0); + +/* qhasm: t2 = t1^2 */ +/* asm 1: fe_sq(>t2=fe#2,<t1=fe#2); */ +/* asm 2: fe_sq(>t2=z2,<t1=z2); */ +fe_sq(z2,z2); + +/* qhasm: t3 = a24*E */ +/* asm 1: fe_mul121666(>t3=fe#4,<E=fe#6); */ +/* asm 2: fe_mul121666(>t3=z3,<E=tmp1); */ +fe_mul121666(z3,tmp1); + +/* qhasm: X5 = t0^2 */ +/* asm 1: fe_sq(>X5=fe#3,<t0=fe#3); */ +/* asm 2: fe_sq(>X5=x3,<t0=x3); */ +fe_sq(x3,x3); + +/* qhasm: t4 = BB+t3 */ +/* asm 1: fe_add(>t4=fe#5,<BB=fe#5,<t3=fe#4); */ +/* asm 2: fe_add(>t4=tmp0,<BB=tmp0,<t3=z3); */ +fe_add(tmp0,tmp0,z3); + +/* qhasm: Z5 = X1*t2 */ +/* asm 1: fe_mul(>Z5=fe#4,x1,<t2=fe#2); */ +/* asm 2: fe_mul(>Z5=z3,x1,<t2=z2); */ +fe_mul(z3,x1,z2); + +/* qhasm: Z4 = E*t4 */ +/* asm 1: fe_mul(>Z4=fe#2,<E=fe#6,<t4=fe#5); */ +/* asm 2: fe_mul(>Z4=z2,<E=tmp1,<t4=tmp0); */ +fe_mul(z2,tmp1,tmp0); + +/* qhasm: return */ + } + fe_cswap(x2,x3,swap); + fe_cswap(z2,z3,swap); + + fe_invert(z2,z2); + fe_mul(x2,x2,z2); + fe_tobytes(q,x2); + return 0; +} + +static const unsigned char basepoint[32] = {9}; + +int crypto_scalarmult_base_ref10(unsigned char *q,const unsigned char *n) +{ + return crypto_scalarmult_ref10(q,n,basepoint); +} + diff --git a/src/ext/ed25519/donna/fuzz/curve25519-ref10.h b/src/ext/ed25519/donna/fuzz/curve25519-ref10.h new file mode 100644 index 0000000..fc005b5 --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/curve25519-ref10.h @@ -0,0 +1,8 @@ +#ifndef CURVE25519_REF10_H +#define CURVE25519_REF10_H + +int crypto_scalarmult_base_ref10(unsigned char *q,const unsigned char *n); +int crypto_scalarmult_ref10(unsigned char *q, const unsigned char *n, const unsigned char *p); + +#endif /* CURVE25519_REF10_H */ + diff --git a/src/ext/ed25519/donna/fuzz/ed25519-donna-sse2.c b/src/ext/ed25519/donna/fuzz/ed25519-donna-sse2.c new file mode 100644 index 0000000..ba47b1e --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/ed25519-donna-sse2.c @@ -0,0 +1,3 @@ +#define ED25519_SUFFIX _sse2 +#define ED25519_SSE2 +#include "../ed25519.c" diff --git a/src/ext/ed25519/donna/fuzz/ed25519-donna.c b/src/ext/ed25519/donna/fuzz/ed25519-donna.c new file mode 100644 index 0000000..45d03b6 --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/ed25519-donna.c @@ -0,0 +1 @@ +#include "../ed25519.c" diff --git a/src/ext/ed25519/donna/fuzz/ed25519-donna.h b/src/ext/ed25519/donna/fuzz/ed25519-donna.h new file mode 100644 index 0000000..7cd72e3 --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/ed25519-donna.h @@ -0,0 +1,34 @@ +#ifndef ED25519_H +#define ED25519_H + +#include <stdlib.h> + +typedef unsigned char ed25519_signature[64]; +typedef unsigned char ed25519_public_key[32]; +typedef unsigned char ed25519_secret_key[32]; + +typedef unsigned char curved25519_key[32]; + +void ed25519_publickey(const ed25519_secret_key sk, ed25519_public_key pk); +int ed25519_sign_open(const unsigned char *m, size_t mlen, const ed25519_public_key pk, const ed25519_signature RS); +void ed25519_sign(const unsigned char *m, size_t mlen, const ed25519_secret_key sk, const ed25519_public_key pk, ed25519_signature RS); + +int ed25519_sign_open_batch(const unsigned char **m, size_t *mlen, const unsigned char **pk, const unsigned char **RS, size_t num, int *valid); + +void ed25519_randombytes_unsafe(void *out, size_t count); + +void curved25519_scalarmult_basepoint(curved25519_key pk, const curved25519_key e); + +#if defined(ED25519_SSE2) +void ed25519_publickey_sse2(const ed25519_secret_key sk, ed25519_public_key pk); +int ed25519_sign_open_sse2(const unsigned char *m, size_t mlen, const ed25519_public_key pk, const ed25519_signature RS); +void ed25519_sign_sse2(const unsigned char *m, size_t mlen, const ed25519_secret_key sk, const ed25519_public_key pk, ed25519_signature RS); + +int ed25519_sign_open_batch_sse2(const unsigned char **m, size_t *mlen, const unsigned char **pk, const unsigned char **RS, size_t num, int *valid); + +void ed25519_randombytes_unsafe_sse2(void *out, size_t count); + +void curved25519_scalarmult_basepoint_sse2(curved25519_key pk, const curved25519_key e); +#endif + +#endif // ED25519_H diff --git a/src/ext/ed25519/donna/fuzz/ed25519-ref10.c b/src/ext/ed25519/donna/fuzz/ed25519-ref10.c new file mode 100644 index 0000000..a8e802d --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/ed25519-ref10.c @@ -0,0 +1,4647 @@ +#include <stdint.h> +#include <stddef.h> +#include <string.h> + +static int crypto_verify_32(const unsigned char *x,const unsigned char *y) +{ + unsigned int differentbits = 0; +#define F(i) differentbits |= x[i] ^ y[i]; + F(0) + F(1) + F(2) + F(3) + F(4) + F(5) + F(6) + F(7) + F(8) + F(9) + F(10) + F(11) + F(12) + F(13) + F(14) + F(15) + F(16) + F(17) + F(18) + F(19) + F(20) + F(21) + F(22) + F(23) + F(24) + F(25) + F(26) + F(27) + F(28) + F(29) + F(30) + F(31) + return (1 & ((differentbits - 1) >> 8)) - 1; +} + +#if defined(ED25519_REFHASH) + +/* reference/slow SHA-512. really, do not use this */ + +#define HASH_BLOCK_SIZE 128 +#define HASH_DIGEST_SIZE 64 + +typedef struct sha512_state_t { + uint64_t H[8]; + uint64_t T[2]; + uint32_t leftover; + uint8_t buffer[HASH_BLOCK_SIZE]; +} sha512_state; + +typedef sha512_state ed25519_hash_context; + +static const uint64_t sha512_constants[80] = { + 0x428a2f98d728ae22ull, 0x7137449123ef65cdull, 0xb5c0fbcfec4d3b2full, 0xe9b5dba58189dbbcull, + 0x3956c25bf348b538ull, 0x59f111f1b605d019ull, 0x923f82a4af194f9bull, 0xab1c5ed5da6d8118ull, + 0xd807aa98a3030242ull, 0x12835b0145706fbeull, 0x243185be4ee4b28cull, 0x550c7dc3d5ffb4e2ull, + 0x72be5d74f27b896full, 0x80deb1fe3b1696b1ull, 0x9bdc06a725c71235ull, 0xc19bf174cf692694ull, + 0xe49b69c19ef14ad2ull, 0xefbe4786384f25e3ull, 0x0fc19dc68b8cd5b5ull, 0x240ca1cc77ac9c65ull, + 0x2de92c6f592b0275ull, 0x4a7484aa6ea6e483ull, 0x5cb0a9dcbd41fbd4ull, 0x76f988da831153b5ull, + 0x983e5152ee66dfabull, 0xa831c66d2db43210ull, 0xb00327c898fb213full, 0xbf597fc7beef0ee4ull, + 0xc6e00bf33da88fc2ull, 0xd5a79147930aa725ull, 0x06ca6351e003826full, 0x142929670a0e6e70ull, + 0x27b70a8546d22ffcull, 0x2e1b21385c26c926ull, 0x4d2c6dfc5ac42aedull, 0x53380d139d95b3dfull, + 0x650a73548baf63deull, 0x766a0abb3c77b2a8ull, 0x81c2c92e47edaee6ull, 0x92722c851482353bull, + 0xa2bfe8a14cf10364ull, 0xa81a664bbc423001ull, 0xc24b8b70d0f89791ull, 0xc76c51a30654be30ull, + 0xd192e819d6ef5218ull, 0xd69906245565a910ull, 0xf40e35855771202aull, 0x106aa07032bbd1b8ull, + 0x19a4c116b8d2d0c8ull, 0x1e376c085141ab53ull, 0x2748774cdf8eeb99ull, 0x34b0bcb5e19b48a8ull, + 0x391c0cb3c5c95a63ull, 0x4ed8aa4ae3418acbull, 0x5b9cca4f7763e373ull, 0x682e6ff3d6b2b8a3ull, + 0x748f82ee5defb2fcull, 0x78a5636f43172f60ull, 0x84c87814a1f0ab72ull, 0x8cc702081a6439ecull, + 0x90befffa23631e28ull, 0xa4506cebde82bde9ull, 0xbef9a3f7b2c67915ull, 0xc67178f2e372532bull, + 0xca273eceea26619cull, 0xd186b8c721c0c207ull, 0xeada7dd6cde0eb1eull, 0xf57d4f7fee6ed178ull, + 0x06f067aa72176fbaull, 0x0a637dc5a2c898a6ull, 0x113f9804bef90daeull, 0x1b710b35131c471bull, + 0x28db77f523047d84ull, 0x32caab7b40c72493ull, 0x3c9ebe0a15c9bebcull, 0x431d67c49c100d4cull, + 0x4cc5d4becb3e42b6ull, 0x597f299cfc657e2aull, 0x5fcb6fab3ad6faecull, 0x6c44198c4a475817ull +}; + +static uint64_t +sha512_ROTR64(uint64_t x, int k) { + return (x >> k) | (x << (64 - k)); +} + +static uint64_t +sha512_LOAD64_BE(const uint8_t *p) { + return + ((uint64_t)p[0] << 56) | + ((uint64_t)p[1] << 48) | + ((uint64_t)p[2] << 40) | + ((uint64_t)p[3] << 32) | + ((uint64_t)p[4] << 24) | + ((uint64_t)p[5] << 16) | + ((uint64_t)p[6] << 8) | + ((uint64_t)p[7] ); +} + +static void +sha512_STORE64_BE(uint8_t *p, uint64_t v) { + p[0] = (uint8_t)(v >> 56); + p[1] = (uint8_t)(v >> 48); + p[2] = (uint8_t)(v >> 40); + p[3] = (uint8_t)(v >> 32); + p[4] = (uint8_t)(v >> 24); + p[5] = (uint8_t)(v >> 16); + p[6] = (uint8_t)(v >> 8); + p[7] = (uint8_t)(v ); +} + +#define Ch(x,y,z) (z ^ (x & (y ^ z))) +#define Maj(x,y,z) (((x | y) & z) | (x & y)) +#define S0(x) (sha512_ROTR64(x, 28) ^ sha512_ROTR64(x, 34) ^ sha512_ROTR64(x, 39)) +#define S1(x) (sha512_ROTR64(x, 14) ^ sha512_ROTR64(x, 18) ^ sha512_ROTR64(x, 41)) +#define G0(x) (sha512_ROTR64(x, 1) ^ sha512_ROTR64(x, 8) ^ (x >> 7)) +#define G1(x) (sha512_ROTR64(x, 19) ^ sha512_ROTR64(x, 61) ^ (x >> 6)) +#define W0(in,i) (sha512_LOAD64_BE(&in[i * 8])) +#define W1(i) (G1(w[i - 2]) + w[i - 7] + G0(w[i - 15]) + w[i - 16]) +#define STEP(i) \ + t1 = S0(r[0]) + Maj(r[0], r[1], r[2]); \ + t0 = r[7] + S1(r[4]) + Ch(r[4], r[5], r[6]) + sha512_constants[i] + w[i]; \ + r[7] = r[6]; \ + r[6] = r[5]; \ + r[5] = r[4]; \ + r[4] = r[3] + t0; \ + r[3] = r[2]; \ + r[2] = r[1]; \ + r[1] = r[0]; \ + r[0] = t0 + t1; + +static void +sha512_blocks(sha512_state *S, const uint8_t *in, size_t blocks) { + uint64_t r[8], w[80], t0, t1; + size_t i; + + for (i = 0; i < 8; i++) r[i] = S->H[i]; + + while (blocks--) { + for (i = 0; i < 16; i++) { w[i] = W0(in, i); } + for (i = 16; i < 80; i++) { w[i] = W1(i); } + for (i = 0; i < 80; i++) { STEP(i); } + for (i = 0; i < 8; i++) { r[i] += S->H[i]; S->H[i] = r[i]; } + S->T[0] += HASH_BLOCK_SIZE * 8; + S->T[1] += (!S->T[0]) ? 1 : 0; + in += HASH_BLOCK_SIZE; + } +} + +static void +ed25519_hash_init(sha512_state *S) { + S->H[0] = 0x6a09e667f3bcc908ull; + S->H[1] = 0xbb67ae8584caa73bull; + S->H[2] = 0x3c6ef372fe94f82bull; + S->H[3] = 0xa54ff53a5f1d36f1ull; + S->H[4] = 0x510e527fade682d1ull; + S->H[5] = 0x9b05688c2b3e6c1full; + S->H[6] = 0x1f83d9abfb41bd6bull; + S->H[7] = 0x5be0cd19137e2179ull; + S->T[0] = 0; + S->T[1] = 0; + S->leftover = 0; +} + +static void +ed25519_hash_update(sha512_state *S, const uint8_t *in, size_t inlen) { + size_t blocks, want; + + /* handle the previous data */ + if (S->leftover) { + want = (HASH_BLOCK_SIZE - S->leftover); + want = (want < inlen) ? want : inlen; + memcpy(S->buffer + S->leftover, in, want); + S->leftover += (uint32_t)want; + if (S->leftover < HASH_BLOCK_SIZE) + return; + in += want; + inlen -= want; + sha512_blocks(S, S->buffer, 1); + } + + /* handle the current data */ + blocks = (inlen & ~(HASH_BLOCK_SIZE - 1)); + S->leftover = (uint32_t)(inlen - blocks); + if (blocks) { + sha512_blocks(S, in, blocks / HASH_BLOCK_SIZE); + in += blocks; + } + + /* handle leftover data */ + if (S->leftover) + memcpy(S->buffer, in, S->leftover); +} + +static void +ed25519_hash_final(sha512_state *S, uint8_t *hash) { + uint64_t t0 = S->T[0] + (S->leftover * 8), t1 = S->T[1]; + + S->buffer[S->leftover] = 0x80; + if (S->leftover <= 111) { + memset(S->buffer + S->leftover + 1, 0, 111 - S->leftover); + } else { + memset(S->buffer + S->leftover + 1, 0, 127 - S->leftover); + sha512_blocks(S, S->buffer, 1); + memset(S->buffer, 0, 112); + } + + sha512_STORE64_BE(S->buffer + 112, t1); + sha512_STORE64_BE(S->buffer + 120, t0); + sha512_blocks(S, S->buffer, 1); + + sha512_STORE64_BE(&hash[ 0], S->H[0]); + sha512_STORE64_BE(&hash[ 8], S->H[1]); + sha512_STORE64_BE(&hash[16], S->H[2]); + sha512_STORE64_BE(&hash[24], S->H[3]); + sha512_STORE64_BE(&hash[32], S->H[4]); + sha512_STORE64_BE(&hash[40], S->H[5]); + sha512_STORE64_BE(&hash[48], S->H[6]); + sha512_STORE64_BE(&hash[56], S->H[7]); +} + +static void +crypto_hash_sha512(unsigned char *hash, const unsigned char *in, size_t inlen) { + ed25519_hash_context ctx; + ed25519_hash_init(&ctx); + ed25519_hash_update(&ctx, in, inlen); + ed25519_hash_final(&ctx, hash); +} + +#else + +#include <openssl/sha.h> + +static void +crypto_hash_sha512(unsigned char *hash, const unsigned char *in, size_t inlen) { + SHA512(in, inlen, hash); +} + +#endif + + + + +typedef int32_t crypto_int32; +typedef uint32_t crypto_uint32; +typedef int64_t crypto_int64; +typedef uint64_t crypto_uint64; + +typedef crypto_int32 fe[10]; + +/* +h = 0 +*/ + +static void fe_0(fe h) +{ + h[0] = 0; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; + h[5] = 0; + h[6] = 0; + h[7] = 0; + h[8] = 0; + h[9] = 0; +} + +/* +h = 1 +*/ + +static void fe_1(fe h) +{ + h[0] = 1; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; + h[5] = 0; + h[6] = 0; + h[7] = 0; + h[8] = 0; + h[9] = 0; +} + +/* +h = f + g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +static void fe_add(fe h,const fe f,const fe g) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 g0 = g[0]; + crypto_int32 g1 = g[1]; + crypto_int32 g2 = g[2]; + crypto_int32 g3 = g[3]; + crypto_int32 g4 = g[4]; + crypto_int32 g5 = g[5]; + crypto_int32 g6 = g[6]; + crypto_int32 g7 = g[7]; + crypto_int32 g8 = g[8]; + crypto_int32 g9 = g[9]; + crypto_int32 h0 = f0 + g0; + crypto_int32 h1 = f1 + g1; + crypto_int32 h2 = f2 + g2; + crypto_int32 h3 = f3 + g3; + crypto_int32 h4 = f4 + g4; + crypto_int32 h5 = f5 + g5; + crypto_int32 h6 = f6 + g6; + crypto_int32 h7 = f7 + g7; + crypto_int32 h8 = f8 + g8; + crypto_int32 h9 = f9 + g9; + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + + +/* +Replace (f,g) with (g,g) if b == 1; +replace (f,g) with (f,g) if b == 0. + +Preconditions: b in {0,1}. +*/ + +static void fe_cmov(fe f,const fe g,unsigned int b) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 g0 = g[0]; + crypto_int32 g1 = g[1]; + crypto_int32 g2 = g[2]; + crypto_int32 g3 = g[3]; + crypto_int32 g4 = g[4]; + crypto_int32 g5 = g[5]; + crypto_int32 g6 = g[6]; + crypto_int32 g7 = g[7]; + crypto_int32 g8 = g[8]; + crypto_int32 g9 = g[9]; + crypto_int32 x0 = f0 ^ g0; + crypto_int32 x1 = f1 ^ g1; + crypto_int32 x2 = f2 ^ g2; + crypto_int32 x3 = f3 ^ g3; + crypto_int32 x4 = f4 ^ g4; + crypto_int32 x5 = f5 ^ g5; + crypto_int32 x6 = f6 ^ g6; + crypto_int32 x7 = f7 ^ g7; + crypto_int32 x8 = f8 ^ g8; + crypto_int32 x9 = f9 ^ g9; + b = -b; + x0 &= b; + x1 &= b; + x2 &= b; + x3 &= b; + x4 &= b; + x5 &= b; + x6 &= b; + x7 &= b; + x8 &= b; + x9 &= b; + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; + f[5] = f5 ^ x5; + f[6] = f6 ^ x6; + f[7] = f7 ^ x7; + f[8] = f8 ^ x8; + f[9] = f9 ^ x9; +} + + +/* +h = f +*/ + +static void fe_copy(fe h,const fe f) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + h[0] = f0; + h[1] = f1; + h[2] = f2; + h[3] = f3; + h[4] = f4; + h[5] = f5; + h[6] = f6; + h[7] = f7; + h[8] = f8; + h[9] = f9; +} + + +static crypto_uint64 load_3(const unsigned char *in) +{ + crypto_uint64 result; + result = (crypto_uint64) in[0]; + result |= ((crypto_uint64) in[1]) << 8; + result |= ((crypto_uint64) in[2]) << 16; + return result; +} + +static crypto_uint64 load_4(const unsigned char *in) +{ + crypto_uint64 result; + result = (crypto_uint64) in[0]; + result |= ((crypto_uint64) in[1]) << 8; + result |= ((crypto_uint64) in[2]) << 16; + result |= ((crypto_uint64) in[3]) << 24; + return result; +} + +/* +Ignores top bit of h. +*/ + +static void fe_frombytes(fe h,const unsigned char *s) +{ + crypto_int64 h0 = load_4(s); + crypto_int64 h1 = load_3(s + 4) << 6; + crypto_int64 h2 = load_3(s + 7) << 5; + crypto_int64 h3 = load_3(s + 10) << 3; + crypto_int64 h4 = load_3(s + 13) << 2; + crypto_int64 h5 = load_4(s + 16); + crypto_int64 h6 = load_3(s + 20) << 7; + crypto_int64 h7 = load_3(s + 23) << 5; + crypto_int64 h8 = load_3(s + 26) << 4; + crypto_int64 h9 = (load_3(s + 29) & 8388607) << 2; + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + + carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* +Preconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + +Write p=2^255-19; q=floor(h/p). +Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). + +Proof: + Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. + Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. + + Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). + Then 0<y<1. + + Write r=h-pq. + Have 0<=r<=p-1=2^255-20. + Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. + + Write x=r+19(2^-255)r+y. + Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. + + Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) + so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. +*/ + +static void fe_tobytes(unsigned char *s,const fe h) +{ + crypto_int32 h0 = h[0]; + crypto_int32 h1 = h[1]; + crypto_int32 h2 = h[2]; + crypto_int32 h3 = h[3]; + crypto_int32 h4 = h[4]; + crypto_int32 h5 = h[5]; + crypto_int32 h6 = h[6]; + crypto_int32 h7 = h[7]; + crypto_int32 h8 = h[8]; + crypto_int32 h9 = h[9]; + crypto_int32 q; + crypto_int32 carry0; + crypto_int32 carry1; + crypto_int32 carry2; + crypto_int32 carry3; + crypto_int32 carry4; + crypto_int32 carry5; + crypto_int32 carry6; + crypto_int32 carry7; + crypto_int32 carry8; + crypto_int32 carry9; + + q = (19 * h9 + (((crypto_int32) 1) << 24)) >> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + + carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26; + carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25; + carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26; + carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25; + carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26; + carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25; + carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26; + carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25; + carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26; + carry9 = h9 >> 25; h9 -= carry9 << 25; + /* h10 = carry9 */ + + /* + Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + Have h0+...+2^230 h9 between 0 and 2^255-1; + evidently 2^255 h10-2^255 q = 0. + Goal: Output h0+...+2^230 h9. + */ + + s[0] = h0 >> 0; + s[1] = h0 >> 8; + s[2] = h0 >> 16; + s[3] = (h0 >> 24) | (h1 << 2); + s[4] = h1 >> 6; + s[5] = h1 >> 14; + s[6] = (h1 >> 22) | (h2 << 3); + s[7] = h2 >> 5; + s[8] = h2 >> 13; + s[9] = (h2 >> 21) | (h3 << 5); + s[10] = h3 >> 3; + s[11] = h3 >> 11; + s[12] = (h3 >> 19) | (h4 << 6); + s[13] = h4 >> 2; + s[14] = h4 >> 10; + s[15] = h4 >> 18; + s[16] = h5 >> 0; + s[17] = h5 >> 8; + s[18] = h5 >> 16; + s[19] = (h5 >> 24) | (h6 << 1); + s[20] = h6 >> 7; + s[21] = h6 >> 15; + s[22] = (h6 >> 23) | (h7 << 3); + s[23] = h7 >> 5; + s[24] = h7 >> 13; + s[25] = (h7 >> 21) | (h8 << 4); + s[26] = h8 >> 4; + s[27] = h8 >> 12; + s[28] = (h8 >> 20) | (h9 << 6); + s[29] = h9 >> 2; + s[30] = h9 >> 10; + s[31] = h9 >> 18; +} + + +/* +h = f - g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +static void fe_sub(fe h,const fe f,const fe g) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 g0 = g[0]; + crypto_int32 g1 = g[1]; + crypto_int32 g2 = g[2]; + crypto_int32 g3 = g[3]; + crypto_int32 g4 = g[4]; + crypto_int32 g5 = g[5]; + crypto_int32 g6 = g[6]; + crypto_int32 g7 = g[7]; + crypto_int32 g8 = g[8]; + crypto_int32 g9 = g[9]; + crypto_int32 h0 = f0 - g0; + crypto_int32 h1 = f1 - g1; + crypto_int32 h2 = f2 - g2; + crypto_int32 h3 = f3 - g3; + crypto_int32 h4 = f4 - g4; + crypto_int32 h5 = f5 - g5; + crypto_int32 h6 = f6 - g6; + crypto_int32 h7 = f7 - g7; + crypto_int32 h8 = f8 - g8; + crypto_int32 h9 = f9 - g9; + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + + +/* +h = f * f +Can overlap h with f. + +Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + +Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. +*/ + +/* +See fe_mul.c for discussion of implementation strategy. +*/ + +static void fe_sq(fe h,const fe f) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 f0_2 = 2 * f0; + crypto_int32 f1_2 = 2 * f1; + crypto_int32 f2_2 = 2 * f2; + crypto_int32 f3_2 = 2 * f3; + crypto_int32 f4_2 = 2 * f4; + crypto_int32 f5_2 = 2 * f5; + crypto_int32 f6_2 = 2 * f6; + crypto_int32 f7_2 = 2 * f7; + crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */ + crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */ + crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */ + crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */ + crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */ + crypto_int64 f0f0 = f0 * (crypto_int64) f0; + crypto_int64 f0f1_2 = f0_2 * (crypto_int64) f1; + crypto_int64 f0f2_2 = f0_2 * (crypto_int64) f2; + crypto_int64 f0f3_2 = f0_2 * (crypto_int64) f3; + crypto_int64 f0f4_2 = f0_2 * (crypto_int64) f4; + crypto_int64 f0f5_2 = f0_2 * (crypto_int64) f5; + crypto_int64 f0f6_2 = f0_2 * (crypto_int64) f6; + crypto_int64 f0f7_2 = f0_2 * (crypto_int64) f7; + crypto_int64 f0f8_2 = f0_2 * (crypto_int64) f8; + crypto_int64 f0f9_2 = f0_2 * (crypto_int64) f9; + crypto_int64 f1f1_2 = f1_2 * (crypto_int64) f1; + crypto_int64 f1f2_2 = f1_2 * (crypto_int64) f2; + crypto_int64 f1f3_4 = f1_2 * (crypto_int64) f3_2; + crypto_int64 f1f4_2 = f1_2 * (crypto_int64) f4; + crypto_int64 f1f5_4 = f1_2 * (crypto_int64) f5_2; + crypto_int64 f1f6_2 = f1_2 * (crypto_int64) f6; + crypto_int64 f1f7_4 = f1_2 * (crypto_int64) f7_2; + crypto_int64 f1f8_2 = f1_2 * (crypto_int64) f8; + crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38; + crypto_int64 f2f2 = f2 * (crypto_int64) f2; + crypto_int64 f2f3_2 = f2_2 * (crypto_int64) f3; + crypto_int64 f2f4_2 = f2_2 * (crypto_int64) f4; + crypto_int64 f2f5_2 = f2_2 * (crypto_int64) f5; + crypto_int64 f2f6_2 = f2_2 * (crypto_int64) f6; + crypto_int64 f2f7_2 = f2_2 * (crypto_int64) f7; + crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19; + crypto_int64 f2f9_38 = f2 * (crypto_int64) f9_38; + crypto_int64 f3f3_2 = f3_2 * (crypto_int64) f3; + crypto_int64 f3f4_2 = f3_2 * (crypto_int64) f4; + crypto_int64 f3f5_4 = f3_2 * (crypto_int64) f5_2; + crypto_int64 f3f6_2 = f3_2 * (crypto_int64) f6; + crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38; + crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19; + crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38; + crypto_int64 f4f4 = f4 * (crypto_int64) f4; + crypto_int64 f4f5_2 = f4_2 * (crypto_int64) f5; + crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19; + crypto_int64 f4f7_38 = f4 * (crypto_int64) f7_38; + crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19; + crypto_int64 f4f9_38 = f4 * (crypto_int64) f9_38; + crypto_int64 f5f5_38 = f5 * (crypto_int64) f5_38; + crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19; + crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38; + crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19; + crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38; + crypto_int64 f6f6_19 = f6 * (crypto_int64) f6_19; + crypto_int64 f6f7_38 = f6 * (crypto_int64) f7_38; + crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19; + crypto_int64 f6f9_38 = f6 * (crypto_int64) f9_38; + crypto_int64 f7f7_38 = f7 * (crypto_int64) f7_38; + crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19; + crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38; + crypto_int64 f8f8_19 = f8 * (crypto_int64) f8_19; + crypto_int64 f8f9_38 = f8 * (crypto_int64) f9_38; + crypto_int64 f9f9_38 = f9 * (crypto_int64) f9_38; + crypto_int64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + + carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + + carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + + carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* +h = 2 * f * f +Can overlap h with f. + +Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + +Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. +*/ + +/* +See fe_mul.c for discussion of implementation strategy. +*/ + +static void fe_sq2(fe h,const fe f) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 f0_2 = 2 * f0; + crypto_int32 f1_2 = 2 * f1; + crypto_int32 f2_2 = 2 * f2; + crypto_int32 f3_2 = 2 * f3; + crypto_int32 f4_2 = 2 * f4; + crypto_int32 f5_2 = 2 * f5; + crypto_int32 f6_2 = 2 * f6; + crypto_int32 f7_2 = 2 * f7; + crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */ + crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */ + crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */ + crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */ + crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */ + crypto_int64 f0f0 = f0 * (crypto_int64) f0; + crypto_int64 f0f1_2 = f0_2 * (crypto_int64) f1; + crypto_int64 f0f2_2 = f0_2 * (crypto_int64) f2; + crypto_int64 f0f3_2 = f0_2 * (crypto_int64) f3; + crypto_int64 f0f4_2 = f0_2 * (crypto_int64) f4; + crypto_int64 f0f5_2 = f0_2 * (crypto_int64) f5; + crypto_int64 f0f6_2 = f0_2 * (crypto_int64) f6; + crypto_int64 f0f7_2 = f0_2 * (crypto_int64) f7; + crypto_int64 f0f8_2 = f0_2 * (crypto_int64) f8; + crypto_int64 f0f9_2 = f0_2 * (crypto_int64) f9; + crypto_int64 f1f1_2 = f1_2 * (crypto_int64) f1; + crypto_int64 f1f2_2 = f1_2 * (crypto_int64) f2; + crypto_int64 f1f3_4 = f1_2 * (crypto_int64) f3_2; + crypto_int64 f1f4_2 = f1_2 * (crypto_int64) f4; + crypto_int64 f1f5_4 = f1_2 * (crypto_int64) f5_2; + crypto_int64 f1f6_2 = f1_2 * (crypto_int64) f6; + crypto_int64 f1f7_4 = f1_2 * (crypto_int64) f7_2; + crypto_int64 f1f8_2 = f1_2 * (crypto_int64) f8; + crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38; + crypto_int64 f2f2 = f2 * (crypto_int64) f2; + crypto_int64 f2f3_2 = f2_2 * (crypto_int64) f3; + crypto_int64 f2f4_2 = f2_2 * (crypto_int64) f4; + crypto_int64 f2f5_2 = f2_2 * (crypto_int64) f5; + crypto_int64 f2f6_2 = f2_2 * (crypto_int64) f6; + crypto_int64 f2f7_2 = f2_2 * (crypto_int64) f7; + crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19; + crypto_int64 f2f9_38 = f2 * (crypto_int64) f9_38; + crypto_int64 f3f3_2 = f3_2 * (crypto_int64) f3; + crypto_int64 f3f4_2 = f3_2 * (crypto_int64) f4; + crypto_int64 f3f5_4 = f3_2 * (crypto_int64) f5_2; + crypto_int64 f3f6_2 = f3_2 * (crypto_int64) f6; + crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38; + crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19; + crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38; + crypto_int64 f4f4 = f4 * (crypto_int64) f4; + crypto_int64 f4f5_2 = f4_2 * (crypto_int64) f5; + crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19; + crypto_int64 f4f7_38 = f4 * (crypto_int64) f7_38; + crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19; + crypto_int64 f4f9_38 = f4 * (crypto_int64) f9_38; + crypto_int64 f5f5_38 = f5 * (crypto_int64) f5_38; + crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19; + crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38; + crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19; + crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38; + crypto_int64 f6f6_19 = f6 * (crypto_int64) f6_19; + crypto_int64 f6f7_38 = f6 * (crypto_int64) f7_38; + crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19; + crypto_int64 f6f9_38 = f6 * (crypto_int64) f9_38; + crypto_int64 f7f7_38 = f7 * (crypto_int64) f7_38; + crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19; + crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38; + crypto_int64 f8f8_19 = f8 * (crypto_int64) f8_19; + crypto_int64 f8f9_38 = f8 * (crypto_int64) f9_38; + crypto_int64 f9f9_38 = f9 * (crypto_int64) f9_38; + crypto_int64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + + carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + + carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + + carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* +h = f * g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + +Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. +*/ + +/* +Notes on implementation strategy: + +Using schoolbook multiplication. +Karatsuba would save a little in some cost models. + +Most multiplications by 2 and 19 are 32-bit precomputations; +cheaper than 64-bit postcomputations. + +There is one remaining multiplication by 19 in the carry chain; +one *19 precomputation can be merged into this, +but the resulting data flow is considerably less clean. + +There are 12 carries below. +10 of them are 2-way parallelizable and vectorizable. +Can get away with 11 carries, but then data flow is much deeper. + +With tighter constraints on inputs can squeeze carries into int32. +*/ + +static void fe_mul(fe h,const fe f,const fe g) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 g0 = g[0]; + crypto_int32 g1 = g[1]; + crypto_int32 g2 = g[2]; + crypto_int32 g3 = g[3]; + crypto_int32 g4 = g[4]; + crypto_int32 g5 = g[5]; + crypto_int32 g6 = g[6]; + crypto_int32 g7 = g[7]; + crypto_int32 g8 = g[8]; + crypto_int32 g9 = g[9]; + crypto_int32 g1_19 = 19 * g1; /* 1.959375*2^29 */ + crypto_int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ + crypto_int32 g3_19 = 19 * g3; + crypto_int32 g4_19 = 19 * g4; + crypto_int32 g5_19 = 19 * g5; + crypto_int32 g6_19 = 19 * g6; + crypto_int32 g7_19 = 19 * g7; + crypto_int32 g8_19 = 19 * g8; + crypto_int32 g9_19 = 19 * g9; + crypto_int32 f1_2 = 2 * f1; + crypto_int32 f3_2 = 2 * f3; + crypto_int32 f5_2 = 2 * f5; + crypto_int32 f7_2 = 2 * f7; + crypto_int32 f9_2 = 2 * f9; + crypto_int64 f0g0 = f0 * (crypto_int64) g0; + crypto_int64 f0g1 = f0 * (crypto_int64) g1; + crypto_int64 f0g2 = f0 * (crypto_int64) g2; + crypto_int64 f0g3 = f0 * (crypto_int64) g3; + crypto_int64 f0g4 = f0 * (crypto_int64) g4; + crypto_int64 f0g5 = f0 * (crypto_int64) g5; + crypto_int64 f0g6 = f0 * (crypto_int64) g6; + crypto_int64 f0g7 = f0 * (crypto_int64) g7; + crypto_int64 f0g8 = f0 * (crypto_int64) g8; + crypto_int64 f0g9 = f0 * (crypto_int64) g9; + crypto_int64 f1g0 = f1 * (crypto_int64) g0; + crypto_int64 f1g1_2 = f1_2 * (crypto_int64) g1; + crypto_int64 f1g2 = f1 * (crypto_int64) g2; + crypto_int64 f1g3_2 = f1_2 * (crypto_int64) g3; + crypto_int64 f1g4 = f1 * (crypto_int64) g4; + crypto_int64 f1g5_2 = f1_2 * (crypto_int64) g5; + crypto_int64 f1g6 = f1 * (crypto_int64) g6; + crypto_int64 f1g7_2 = f1_2 * (crypto_int64) g7; + crypto_int64 f1g8 = f1 * (crypto_int64) g8; + crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19; + crypto_int64 f2g0 = f2 * (crypto_int64) g0; + crypto_int64 f2g1 = f2 * (crypto_int64) g1; + crypto_int64 f2g2 = f2 * (crypto_int64) g2; + crypto_int64 f2g3 = f2 * (crypto_int64) g3; + crypto_int64 f2g4 = f2 * (crypto_int64) g4; + crypto_int64 f2g5 = f2 * (crypto_int64) g5; + crypto_int64 f2g6 = f2 * (crypto_int64) g6; + crypto_int64 f2g7 = f2 * (crypto_int64) g7; + crypto_int64 f2g8_19 = f2 * (crypto_int64) g8_19; + crypto_int64 f2g9_19 = f2 * (crypto_int64) g9_19; + crypto_int64 f3g0 = f3 * (crypto_int64) g0; + crypto_int64 f3g1_2 = f3_2 * (crypto_int64) g1; + crypto_int64 f3g2 = f3 * (crypto_int64) g2; + crypto_int64 f3g3_2 = f3_2 * (crypto_int64) g3; + crypto_int64 f3g4 = f3 * (crypto_int64) g4; + crypto_int64 f3g5_2 = f3_2 * (crypto_int64) g5; + crypto_int64 f3g6 = f3 * (crypto_int64) g6; + crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19; + crypto_int64 f3g8_19 = f3 * (crypto_int64) g8_19; + crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19; + crypto_int64 f4g0 = f4 * (crypto_int64) g0; + crypto_int64 f4g1 = f4 * (crypto_int64) g1; + crypto_int64 f4g2 = f4 * (crypto_int64) g2; + crypto_int64 f4g3 = f4 * (crypto_int64) g3; + crypto_int64 f4g4 = f4 * (crypto_int64) g4; + crypto_int64 f4g5 = f4 * (crypto_int64) g5; + crypto_int64 f4g6_19 = f4 * (crypto_int64) g6_19; + crypto_int64 f4g7_19 = f4 * (crypto_int64) g7_19; + crypto_int64 f4g8_19 = f4 * (crypto_int64) g8_19; + crypto_int64 f4g9_19 = f4 * (crypto_int64) g9_19; + crypto_int64 f5g0 = f5 * (crypto_int64) g0; + crypto_int64 f5g1_2 = f5_2 * (crypto_int64) g1; + crypto_int64 f5g2 = f5 * (crypto_int64) g2; + crypto_int64 f5g3_2 = f5_2 * (crypto_int64) g3; + crypto_int64 f5g4 = f5 * (crypto_int64) g4; + crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19; + crypto_int64 f5g6_19 = f5 * (crypto_int64) g6_19; + crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19; + crypto_int64 f5g8_19 = f5 * (crypto_int64) g8_19; + crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19; + crypto_int64 f6g0 = f6 * (crypto_int64) g0; + crypto_int64 f6g1 = f6 * (crypto_int64) g1; + crypto_int64 f6g2 = f6 * (crypto_int64) g2; + crypto_int64 f6g3 = f6 * (crypto_int64) g3; + crypto_int64 f6g4_19 = f6 * (crypto_int64) g4_19; + crypto_int64 f6g5_19 = f6 * (crypto_int64) g5_19; + crypto_int64 f6g6_19 = f6 * (crypto_int64) g6_19; + crypto_int64 f6g7_19 = f6 * (crypto_int64) g7_19; + crypto_int64 f6g8_19 = f6 * (crypto_int64) g8_19; + crypto_int64 f6g9_19 = f6 * (crypto_int64) g9_19; + crypto_int64 f7g0 = f7 * (crypto_int64) g0; + crypto_int64 f7g1_2 = f7_2 * (crypto_int64) g1; + crypto_int64 f7g2 = f7 * (crypto_int64) g2; + crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19; + crypto_int64 f7g4_19 = f7 * (crypto_int64) g4_19; + crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19; + crypto_int64 f7g6_19 = f7 * (crypto_int64) g6_19; + crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19; + crypto_int64 f7g8_19 = f7 * (crypto_int64) g8_19; + crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19; + crypto_int64 f8g0 = f8 * (crypto_int64) g0; + crypto_int64 f8g1 = f8 * (crypto_int64) g1; + crypto_int64 f8g2_19 = f8 * (crypto_int64) g2_19; + crypto_int64 f8g3_19 = f8 * (crypto_int64) g3_19; + crypto_int64 f8g4_19 = f8 * (crypto_int64) g4_19; + crypto_int64 f8g5_19 = f8 * (crypto_int64) g5_19; + crypto_int64 f8g6_19 = f8 * (crypto_int64) g6_19; + crypto_int64 f8g7_19 = f8 * (crypto_int64) g7_19; + crypto_int64 f8g8_19 = f8 * (crypto_int64) g8_19; + crypto_int64 f8g9_19 = f8 * (crypto_int64) g9_19; + crypto_int64 f9g0 = f9 * (crypto_int64) g0; + crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19; + crypto_int64 f9g2_19 = f9 * (crypto_int64) g2_19; + crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19; + crypto_int64 f9g4_19 = f9 * (crypto_int64) g4_19; + crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19; + crypto_int64 f9g6_19 = f9 * (crypto_int64) g6_19; + crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19; + crypto_int64 f9g8_19 = f9 * (crypto_int64) g8_19; + crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19; + crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; + crypto_int64 h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; + crypto_int64 h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; + crypto_int64 h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; + crypto_int64 h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; + crypto_int64 h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; + crypto_int64 h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; + crypto_int64 h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; + crypto_int64 h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; + crypto_int64 h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + + /* + |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) + i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 + |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) + i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 + */ + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + /* |h6| <= 1.41*2^60 */ + + carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + /* |h7| <= 1.71*2^59 */ + + carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + /* |h8| <= 1.41*2^60 */ + + carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.71*2^59 */ + + carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + + +/* +return 1 if f is in {1,3,5,...,q-2} +return 0 if f is in {0,2,4,...,q-1} + +Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +static int fe_isnegative(const fe f) +{ + unsigned char s[32]; + fe_tobytes(s,f); + return s[0] & 1; +} + + +/* +return 1 if f == 0 +return 0 if f != 0 + +Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +static const unsigned char zero[32] = {0}; + +static int fe_isnonzero(const fe f) +{ + unsigned char s[32]; + fe_tobytes(s,f); + return crypto_verify_32(s,zero); +} + +/* +h = -f + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +*/ + +static void fe_neg(fe h,const fe f) +{ + crypto_int32 f0 = f[0]; + crypto_int32 f1 = f[1]; + crypto_int32 f2 = f[2]; + crypto_int32 f3 = f[3]; + crypto_int32 f4 = f[4]; + crypto_int32 f5 = f[5]; + crypto_int32 f6 = f[6]; + crypto_int32 f7 = f[7]; + crypto_int32 f8 = f[8]; + crypto_int32 f9 = f[9]; + crypto_int32 h0 = -f0; + crypto_int32 h1 = -f1; + crypto_int32 h2 = -f2; + crypto_int32 h3 = -f3; + crypto_int32 h4 = -f4; + crypto_int32 h5 = -f5; + crypto_int32 h6 = -f6; + crypto_int32 h7 = -f7; + crypto_int32 h8 = -f8; + crypto_int32 h9 = -f9; + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +static void fe_invert(fe out,const fe z) +{ + fe t0; + fe t1; + fe t2; + fe t3; + int i; + + +/* qhasm: fe z1 */ + +/* qhasm: fe z2 */ + +/* qhasm: fe z8 */ + +/* qhasm: fe z9 */ + +/* qhasm: fe z11 */ + +/* qhasm: fe z22 */ + +/* qhasm: fe z_5_0 */ + +/* qhasm: fe z_10_5 */ + +/* qhasm: fe z_10_0 */ + +/* qhasm: fe z_20_10 */ + +/* qhasm: fe z_20_0 */ + +/* qhasm: fe z_40_20 */ + +/* qhasm: fe z_40_0 */ + +/* qhasm: fe z_50_10 */ + +/* qhasm: fe z_50_0 */ + +/* qhasm: fe z_100_50 */ + +/* qhasm: fe z_100_0 */ + +/* qhasm: fe z_200_100 */ + +/* qhasm: fe z_200_0 */ + +/* qhasm: fe z_250_50 */ + +/* qhasm: fe z_250_0 */ + +/* qhasm: fe z_255_5 */ + +/* qhasm: fe z_255_21 */ + +/* qhasm: enter pow225521 */ + +/* qhasm: z2 = z1^2^1 */ +/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */ +/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */ +fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0); + +/* qhasm: z8 = z2^2^2 */ +/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */ +/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */ +fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1); + +/* qhasm: z9 = z1*z8 */ +/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */ +/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */ +fe_mul(t1,z,t1); + +/* qhasm: z11 = z2*z9 */ +/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */ +/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */ +fe_mul(t0,t0,t1); + +/* qhasm: z22 = z11^2^1 */ +/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */ +/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */ +fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2); + +/* qhasm: z_5_0 = z9*z22 */ +/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */ +/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */ +fe_mul(t1,t1,t2); + +/* qhasm: z_10_5 = z_5_0^2^5 */ +/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */ +/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */ +fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2); + +/* qhasm: z_10_0 = z_10_5*z_5_0 */ +/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */ +/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */ +fe_mul(t1,t2,t1); + +/* qhasm: z_20_10 = z_10_0^2^10 */ +/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */ +/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */ +fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2); + +/* qhasm: z_20_0 = z_20_10*z_10_0 */ +/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */ +/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */ +fe_mul(t2,t2,t1); + +/* qhasm: z_40_20 = z_20_0^2^20 */ +/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */ +/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */ +fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3); + +/* qhasm: z_40_0 = z_40_20*z_20_0 */ +/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */ +/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */ +fe_mul(t2,t3,t2); + +/* qhasm: z_50_10 = z_40_0^2^10 */ +/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */ +/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */ +fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2); + +/* qhasm: z_50_0 = z_50_10*z_10_0 */ +/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */ +/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */ +fe_mul(t1,t2,t1); + +/* qhasm: z_100_50 = z_50_0^2^50 */ +/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */ +/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */ +fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2); + +/* qhasm: z_100_0 = z_100_50*z_50_0 */ +/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */ +/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */ +fe_mul(t2,t2,t1); + +/* qhasm: z_200_100 = z_100_0^2^100 */ +/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */ +/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */ +fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3); + +/* qhasm: z_200_0 = z_200_100*z_100_0 */ +/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */ +/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */ +fe_mul(t2,t3,t2); + +/* qhasm: z_250_50 = z_200_0^2^50 */ +/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */ +/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */ +fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2); + +/* qhasm: z_250_0 = z_250_50*z_50_0 */ +/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */ +/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */ +fe_mul(t1,t2,t1); + +/* qhasm: z_255_5 = z_250_0^2^5 */ +/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */ +/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */ +fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1); + +/* qhasm: z_255_21 = z_255_5*z11 */ +/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */ +/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */ +fe_mul(out,t1,t0); + +/* qhasm: return */ + + return; +} + + +static void fe_pow22523(fe out,const fe z) +{ + fe t0; + fe t1; + fe t2; + int i; + + +/* qhasm: fe z1 */ + +/* qhasm: fe z2 */ + +/* qhasm: fe z8 */ + +/* qhasm: fe z9 */ + +/* qhasm: fe z11 */ + +/* qhasm: fe z22 */ + +/* qhasm: fe z_5_0 */ + +/* qhasm: fe z_10_5 */ + +/* qhasm: fe z_10_0 */ + +/* qhasm: fe z_20_10 */ + +/* qhasm: fe z_20_0 */ + +/* qhasm: fe z_40_20 */ + +/* qhasm: fe z_40_0 */ + +/* qhasm: fe z_50_10 */ + +/* qhasm: fe z_50_0 */ + +/* qhasm: fe z_100_50 */ + +/* qhasm: fe z_100_0 */ + +/* qhasm: fe z_200_100 */ + +/* qhasm: fe z_200_0 */ + +/* qhasm: fe z_250_50 */ + +/* qhasm: fe z_250_0 */ + +/* qhasm: fe z_252_2 */ + +/* qhasm: fe z_252_3 */ + +/* qhasm: enter pow22523 */ + +/* qhasm: z2 = z1^2^1 */ +/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */ +/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */ +fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0); + +/* qhasm: z8 = z2^2^2 */ +/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */ +/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */ +fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1); + +/* qhasm: z9 = z1*z8 */ +/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */ +/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */ +fe_mul(t1,z,t1); + +/* qhasm: z11 = z2*z9 */ +/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */ +/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */ +fe_mul(t0,t0,t1); + +/* qhasm: z22 = z11^2^1 */ +/* asm 1: fe_sq(>z22=fe#1,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#1,>z22=fe#1); */ +/* asm 2: fe_sq(>z22=t0,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t0,>z22=t0); */ +fe_sq(t0,t0); for (i = 1;i < 1;++i) fe_sq(t0,t0); + +/* qhasm: z_5_0 = z9*z22 */ +/* asm 1: fe_mul(>z_5_0=fe#1,<z9=fe#2,<z22=fe#1); */ +/* asm 2: fe_mul(>z_5_0=t0,<z9=t1,<z22=t0); */ +fe_mul(t0,t1,t0); + +/* qhasm: z_10_5 = z_5_0^2^5 */ +/* asm 1: fe_sq(>z_10_5=fe#2,<z_5_0=fe#1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#2,>z_10_5=fe#2); */ +/* asm 2: fe_sq(>z_10_5=t1,<z_5_0=t0); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t1,>z_10_5=t1); */ +fe_sq(t1,t0); for (i = 1;i < 5;++i) fe_sq(t1,t1); + +/* qhasm: z_10_0 = z_10_5*z_5_0 */ +/* asm 1: fe_mul(>z_10_0=fe#1,<z_10_5=fe#2,<z_5_0=fe#1); */ +/* asm 2: fe_mul(>z_10_0=t0,<z_10_5=t1,<z_5_0=t0); */ +fe_mul(t0,t1,t0); + +/* qhasm: z_20_10 = z_10_0^2^10 */ +/* asm 1: fe_sq(>z_20_10=fe#2,<z_10_0=fe#1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#2,>z_20_10=fe#2); */ +/* asm 2: fe_sq(>z_20_10=t1,<z_10_0=t0); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t1,>z_20_10=t1); */ +fe_sq(t1,t0); for (i = 1;i < 10;++i) fe_sq(t1,t1); + +/* qhasm: z_20_0 = z_20_10*z_10_0 */ +/* asm 1: fe_mul(>z_20_0=fe#2,<z_20_10=fe#2,<z_10_0=fe#1); */ +/* asm 2: fe_mul(>z_20_0=t1,<z_20_10=t1,<z_10_0=t0); */ +fe_mul(t1,t1,t0); + +/* qhasm: z_40_20 = z_20_0^2^20 */ +/* asm 1: fe_sq(>z_40_20=fe#3,<z_20_0=fe#2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#3,>z_40_20=fe#3); */ +/* asm 2: fe_sq(>z_40_20=t2,<z_20_0=t1); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t2,>z_40_20=t2); */ +fe_sq(t2,t1); for (i = 1;i < 20;++i) fe_sq(t2,t2); + +/* qhasm: z_40_0 = z_40_20*z_20_0 */ +/* asm 1: fe_mul(>z_40_0=fe#2,<z_40_20=fe#3,<z_20_0=fe#2); */ +/* asm 2: fe_mul(>z_40_0=t1,<z_40_20=t2,<z_20_0=t1); */ +fe_mul(t1,t2,t1); + +/* qhasm: z_50_10 = z_40_0^2^10 */ +/* asm 1: fe_sq(>z_50_10=fe#2,<z_40_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#2,>z_50_10=fe#2); */ +/* asm 2: fe_sq(>z_50_10=t1,<z_40_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t1,>z_50_10=t1); */ +fe_sq(t1,t1); for (i = 1;i < 10;++i) fe_sq(t1,t1); + +/* qhasm: z_50_0 = z_50_10*z_10_0 */ +/* asm 1: fe_mul(>z_50_0=fe#1,<z_50_10=fe#2,<z_10_0=fe#1); */ +/* asm 2: fe_mul(>z_50_0=t0,<z_50_10=t1,<z_10_0=t0); */ +fe_mul(t0,t1,t0); + +/* qhasm: z_100_50 = z_50_0^2^50 */ +/* asm 1: fe_sq(>z_100_50=fe#2,<z_50_0=fe#1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#2,>z_100_50=fe#2); */ +/* asm 2: fe_sq(>z_100_50=t1,<z_50_0=t0); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t1,>z_100_50=t1); */ +fe_sq(t1,t0); for (i = 1;i < 50;++i) fe_sq(t1,t1); + +/* qhasm: z_100_0 = z_100_50*z_50_0 */ +/* asm 1: fe_mul(>z_100_0=fe#2,<z_100_50=fe#2,<z_50_0=fe#1); */ +/* asm 2: fe_mul(>z_100_0=t1,<z_100_50=t1,<z_50_0=t0); */ +fe_mul(t1,t1,t0); + +/* qhasm: z_200_100 = z_100_0^2^100 */ +/* asm 1: fe_sq(>z_200_100=fe#3,<z_100_0=fe#2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#3,>z_200_100=fe#3); */ +/* asm 2: fe_sq(>z_200_100=t2,<z_100_0=t1); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t2,>z_200_100=t2); */ +fe_sq(t2,t1); for (i = 1;i < 100;++i) fe_sq(t2,t2); + +/* qhasm: z_200_0 = z_200_100*z_100_0 */ +/* asm 1: fe_mul(>z_200_0=fe#2,<z_200_100=fe#3,<z_100_0=fe#2); */ +/* asm 2: fe_mul(>z_200_0=t1,<z_200_100=t2,<z_100_0=t1); */ +fe_mul(t1,t2,t1); + +/* qhasm: z_250_50 = z_200_0^2^50 */ +/* asm 1: fe_sq(>z_250_50=fe#2,<z_200_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#2,>z_250_50=fe#2); */ +/* asm 2: fe_sq(>z_250_50=t1,<z_200_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t1,>z_250_50=t1); */ +fe_sq(t1,t1); for (i = 1;i < 50;++i) fe_sq(t1,t1); + +/* qhasm: z_250_0 = z_250_50*z_50_0 */ +/* asm 1: fe_mul(>z_250_0=fe#1,<z_250_50=fe#2,<z_50_0=fe#1); */ +/* asm 2: fe_mul(>z_250_0=t0,<z_250_50=t1,<z_50_0=t0); */ +fe_mul(t0,t1,t0); + +/* qhasm: z_252_2 = z_250_0^2^2 */ +/* asm 1: fe_sq(>z_252_2=fe#1,<z_250_0=fe#1); for (i = 1;i < 2;++i) fe_sq(>z_252_2=fe#1,>z_252_2=fe#1); */ +/* asm 2: fe_sq(>z_252_2=t0,<z_250_0=t0); for (i = 1;i < 2;++i) fe_sq(>z_252_2=t0,>z_252_2=t0); */ +fe_sq(t0,t0); for (i = 1;i < 2;++i) fe_sq(t0,t0); + +/* qhasm: z_252_3 = z_252_2*z1 */ +/* asm 1: fe_mul(>z_252_3=fe#12,<z_252_2=fe#1,<z1=fe#11); */ +/* asm 2: fe_mul(>z_252_3=out,<z_252_2=t0,<z1=z); */ +fe_mul(out,t0,z); + +/* qhasm: return */ + + + return; +} + + +/* +ge means group element. + +Here the group is the set of pairs (x,y) of field elements (see fe.h) +satisfying -x^2 + y^2 = 1 + d x^2y^2 +where d = -121665/121666. + +Representations: + ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z + ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT + ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T + ge_precomp (Duif): (y+x,y-x,2dxy) +*/ + +typedef struct { + fe X; + fe Y; + fe Z; +} ge_p2; + +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p3; + +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p1p1; + +typedef struct { + fe yplusx; + fe yminusx; + fe xy2d; +} ge_precomp; + +typedef struct { + fe YplusX; + fe YminusX; + fe Z; + fe T2d; +} ge_cached; + +static const fe d = { +-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116 +} ; + +static const fe sqrtm1 = { +-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482 +} ; + +static const fe d2 = { +-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199 +} ; + +static ge_precomp Bi[8] = { + { + { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 }, + { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 }, + { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 }, + }, + { + { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 }, + { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 }, + { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 }, + }, + { + { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 }, + { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 }, + { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 }, + }, + { + { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 }, + { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 }, + { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 }, + }, + { + { -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 }, + { -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 }, + { 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 }, + }, + { + { -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 }, + { 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 }, + { 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 }, + }, + { + { -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 }, + { -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 }, + { -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 }, + }, + { + { -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 }, + { -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 }, + { -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 }, + }, +} ; + + +/* base[i][j] = (j+1)*256^i*B */ +static ge_precomp base[32][8] = { +{ + { + { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 }, + { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 }, + { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 }, + }, + { + { -12815894,-12976347,-21581243,11784320,-25355658,-2750717,-11717903,-3814571,-358445,-10211303 }, + { -21703237,6903825,27185491,6451973,-29577724,-9554005,-15616551,11189268,-26829678,-5319081 }, + { 26966642,11152617,32442495,15396054,14353839,-12752335,-3128826,-9541118,-15472047,-4166697 }, + }, + { + { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 }, + { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 }, + { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 }, + }, + { + { -17036878,13921892,10945806,-6033431,27105052,-16084379,-28926210,15006023,3284568,-6276540 }, + { 23599295,-8306047,-11193664,-7687416,13236774,10506355,7464579,9656445,13059162,10374397 }, + { 7798556,16710257,3033922,2874086,28997861,2835604,32406664,-3839045,-641708,-101325 }, + }, + { + { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 }, + { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 }, + { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 }, + }, + { + { -15371964,-12862754,32573250,4720197,-26436522,5875511,-19188627,-15224819,-9818940,-12085777 }, + { -8549212,109983,15149363,2178705,22900618,4543417,3044240,-15689887,1762328,14866737 }, + { -18199695,-15951423,-10473290,1707278,-17185920,3916101,-28236412,3959421,27914454,4383652 }, + }, + { + { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 }, + { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 }, + { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 }, + }, + { + { 14499471,-2729599,-33191113,-4254652,28494862,14271267,30290735,10876454,-33154098,2381726 }, + { -7195431,-2655363,-14730155,462251,-27724326,3941372,-6236617,3696005,-32300832,15351955 }, + { 27431194,8222322,16448760,-3907995,-18707002,11938355,-32961401,-2970515,29551813,10109425 }, + }, +}, +{ + { + { -13657040,-13155431,-31283750,11777098,21447386,6519384,-2378284,-1627556,10092783,-4764171 }, + { 27939166,14210322,4677035,16277044,-22964462,-12398139,-32508754,12005538,-17810127,12803510 }, + { 17228999,-15661624,-1233527,300140,-1224870,-11714777,30364213,-9038194,18016357,4397660 }, + }, + { + { -10958843,-7690207,4776341,-14954238,27850028,-15602212,-26619106,14544525,-17477504,982639 }, + { 29253598,15796703,-2863982,-9908884,10057023,3163536,7332899,-4120128,-21047696,9934963 }, + { 5793303,16271923,-24131614,-10116404,29188560,1206517,-14747930,4559895,-30123922,-10897950 }, + }, + { + { -27643952,-11493006,16282657,-11036493,28414021,-15012264,24191034,4541697,-13338309,5500568 }, + { 12650548,-1497113,9052871,11355358,-17680037,-8400164,-17430592,12264343,10874051,13524335 }, + { 25556948,-3045990,714651,2510400,23394682,-10415330,33119038,5080568,-22528059,5376628 }, + }, + { + { -26088264,-4011052,-17013699,-3537628,-6726793,1920897,-22321305,-9447443,4535768,1569007 }, + { -2255422,14606630,-21692440,-8039818,28430649,8775819,-30494562,3044290,31848280,12543772 }, + { -22028579,2943893,-31857513,6777306,13784462,-4292203,-27377195,-2062731,7718482,14474653 }, + }, + { + { 2385315,2454213,-22631320,46603,-4437935,-15680415,656965,-7236665,24316168,-5253567 }, + { 13741529,10911568,-33233417,-8603737,-20177830,-1033297,33040651,-13424532,-20729456,8321686 }, + { 21060490,-2212744,15712757,-4336099,1639040,10656336,23845965,-11874838,-9984458,608372 }, + }, + { + { -13672732,-15087586,-10889693,-7557059,-6036909,11305547,1123968,-6780577,27229399,23887 }, + { -23244140,-294205,-11744728,14712571,-29465699,-2029617,12797024,-6440308,-1633405,16678954 }, + { -29500620,4770662,-16054387,14001338,7830047,9564805,-1508144,-4795045,-17169265,4904953 }, + }, + { + { 24059557,14617003,19037157,-15039908,19766093,-14906429,5169211,16191880,2128236,-4326833 }, + { -16981152,4124966,-8540610,-10653797,30336522,-14105247,-29806336,916033,-6882542,-2986532 }, + { -22630907,12419372,-7134229,-7473371,-16478904,16739175,285431,2763829,15736322,4143876 }, + }, + { + { 2379352,11839345,-4110402,-5988665,11274298,794957,212801,-14594663,23527084,-16458268 }, + { 33431127,-11130478,-17838966,-15626900,8909499,8376530,-32625340,4087881,-15188911,-14416214 }, + { 1767683,7197987,-13205226,-2022635,-13091350,448826,5799055,4357868,-4774191,-16323038 }, + }, +}, +{ + { + { 6721966,13833823,-23523388,-1551314,26354293,-11863321,23365147,-3949732,7390890,2759800 }, + { 4409041,2052381,23373853,10530217,7676779,-12885954,21302353,-4264057,1244380,-12919645 }, + { -4421239,7169619,4982368,-2957590,30256825,-2777540,14086413,9208236,15886429,16489664 }, + }, + { + { 1996075,10375649,14346367,13311202,-6874135,-16438411,-13693198,398369,-30606455,-712933 }, + { -25307465,9795880,-2777414,14878809,-33531835,14780363,13348553,12076947,-30836462,5113182 }, + { -17770784,11797796,31950843,13929123,-25888302,12288344,-30341101,-7336386,13847711,5387222 }, + }, + { + { -18582163,-3416217,17824843,-2340966,22744343,-10442611,8763061,3617786,-19600662,10370991 }, + { 20246567,-14369378,22358229,-543712,18507283,-10413996,14554437,-8746092,32232924,16763880 }, + { 9648505,10094563,26416693,14745928,-30374318,-6472621,11094161,15689506,3140038,-16510092 }, + }, + { + { -16160072,5472695,31895588,4744994,8823515,10365685,-27224800,9448613,-28774454,366295 }, + { 19153450,11523972,-11096490,-6503142,-24647631,5420647,28344573,8041113,719605,11671788 }, + { 8678025,2694440,-6808014,2517372,4964326,11152271,-15432916,-15266516,27000813,-10195553 }, + }, + { + { -15157904,7134312,8639287,-2814877,-7235688,10421742,564065,5336097,6750977,-14521026 }, + { 11836410,-3979488,26297894,16080799,23455045,15735944,1695823,-8819122,8169720,16220347 }, + { -18115838,8653647,17578566,-6092619,-8025777,-16012763,-11144307,-2627664,-5990708,-14166033 }, + }, + { + { -23308498,-10968312,15213228,-10081214,-30853605,-11050004,27884329,2847284,2655861,1738395 }, + { -27537433,-14253021,-25336301,-8002780,-9370762,8129821,21651608,-3239336,-19087449,-11005278 }, + { 1533110,3437855,23735889,459276,29970501,11335377,26030092,5821408,10478196,8544890 }, + }, + { + { 32173121,-16129311,24896207,3921497,22579056,-3410854,19270449,12217473,17789017,-3395995 }, + { -30552961,-2228401,-15578829,-10147201,13243889,517024,15479401,-3853233,30460520,1052596 }, + { -11614875,13323618,32618793,8175907,-15230173,12596687,27491595,-4612359,3179268,-9478891 }, + }, + { + { 31947069,-14366651,-4640583,-15339921,-15125977,-6039709,-14756777,-16411740,19072640,-9511060 }, + { 11685058,11822410,3158003,-13952594,33402194,-4165066,5977896,-5215017,473099,5040608 }, + { -20290863,8198642,-27410132,11602123,1290375,-2799760,28326862,1721092,-19558642,-3131606 }, + }, +}, +{ + { + { 7881532,10687937,7578723,7738378,-18951012,-2553952,21820786,8076149,-27868496,11538389 }, + { -19935666,3899861,18283497,-6801568,-15728660,-11249211,8754525,7446702,-5676054,5797016 }, + { -11295600,-3793569,-15782110,-7964573,12708869,-8456199,2014099,-9050574,-2369172,-5877341 }, + }, + { + { -22472376,-11568741,-27682020,1146375,18956691,16640559,1192730,-3714199,15123619,10811505 }, + { 14352098,-3419715,-18942044,10822655,32750596,4699007,-70363,15776356,-28886779,-11974553 }, + { -28241164,-8072475,-4978962,-5315317,29416931,1847569,-20654173,-16484855,4714547,-9600655 }, + }, + { + { 15200332,8368572,19679101,15970074,-31872674,1959451,24611599,-4543832,-11745876,12340220 }, + { 12876937,-10480056,33134381,6590940,-6307776,14872440,9613953,8241152,15370987,9608631 }, + { -4143277,-12014408,8446281,-391603,4407738,13629032,-7724868,15866074,-28210621,-8814099 }, + }, + { + { 26660628,-15677655,8393734,358047,-7401291,992988,-23904233,858697,20571223,8420556 }, + { 14620715,13067227,-15447274,8264467,14106269,15080814,33531827,12516406,-21574435,-12476749 }, + { 236881,10476226,57258,-14677024,6472998,2466984,17258519,7256740,8791136,15069930 }, + }, + { + { 1276410,-9371918,22949635,-16322807,-23493039,-5702186,14711875,4874229,-30663140,-2331391 }, + { 5855666,4990204,-13711848,7294284,-7804282,1924647,-1423175,-7912378,-33069337,9234253 }, + { 20590503,-9018988,31529744,-7352666,-2706834,10650548,31559055,-11609587,18979186,13396066 }, + }, + { + { 24474287,4968103,22267082,4407354,24063882,-8325180,-18816887,13594782,33514650,7021958 }, + { -11566906,-6565505,-21365085,15928892,-26158305,4315421,-25948728,-3916677,-21480480,12868082 }, + { -28635013,13504661,19988037,-2132761,21078225,6443208,-21446107,2244500,-12455797,-8089383 }, + }, + { + { -30595528,13793479,-5852820,319136,-25723172,-6263899,33086546,8957937,-15233648,5540521 }, + { -11630176,-11503902,-8119500,-7643073,2620056,1022908,-23710744,-1568984,-16128528,-14962807 }, + { 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*r,const ge_p1p1 *p) +{ + fe_mul(r->X,p->X,p->T); + fe_mul(r->Y,p->Y,p->Z); + fe_mul(r->Z,p->Z,p->T); + fe_mul(r->T,p->X,p->Y); +} + +/* +r = p +*/ + +static void ge_p3_to_p2(ge_p2 *r,const ge_p3 *p) +{ + fe_copy(r->X,p->X); + fe_copy(r->Y,p->Y); + fe_copy(r->Z,p->Z); +} + + +/* +r = 2 * p +*/ + +static void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p) +{ + fe t0; +/* qhasm: enter ge_p2_dbl */ + +/* qhasm: fe X1 */ + +/* qhasm: fe Y1 */ + +/* qhasm: fe Z1 */ + +/* qhasm: fe A */ + +/* qhasm: fe AA */ + +/* qhasm: fe XX */ + +/* qhasm: fe YY */ + +/* qhasm: fe B */ + +/* qhasm: fe X3 */ + +/* qhasm: fe Y3 */ + +/* qhasm: fe Z3 */ + +/* qhasm: fe T3 */ + +/* qhasm: XX=X1^2 */ +/* asm 1: fe_sq(>XX=fe#1,<X1=fe#11); */ +/* asm 2: fe_sq(>XX=r->X,<X1=p->X); */ +fe_sq(r->X,p->X); + +/* qhasm: YY=Y1^2 */ +/* asm 1: fe_sq(>YY=fe#3,<Y1=fe#12); */ +/* asm 2: fe_sq(>YY=r->Z,<Y1=p->Y); */ +fe_sq(r->Z,p->Y); + +/* qhasm: B=2*Z1^2 */ +/* asm 1: fe_sq2(>B=fe#4,<Z1=fe#13); */ +/* asm 2: fe_sq2(>B=r->T,<Z1=p->Z); */ +fe_sq2(r->T,p->Z); + +/* qhasm: A=X1+Y1 */ +/* asm 1: fe_add(>A=fe#2,<X1=fe#11,<Y1=fe#12); */ +/* asm 2: fe_add(>A=r->Y,<X1=p->X,<Y1=p->Y); */ +fe_add(r->Y,p->X,p->Y); + +/* qhasm: AA=A^2 */ +/* asm 1: fe_sq(>AA=fe#5,<A=fe#2); */ +/* asm 2: fe_sq(>AA=t0,<A=r->Y); */ +fe_sq(t0,r->Y); + +/* qhasm: Y3=YY+XX */ +/* asm 1: fe_add(>Y3=fe#2,<YY=fe#3,<XX=fe#1); */ +/* asm 2: fe_add(>Y3=r->Y,<YY=r->Z,<XX=r->X); */ +fe_add(r->Y,r->Z,r->X); + +/* qhasm: Z3=YY-XX */ +/* asm 1: fe_sub(>Z3=fe#3,<YY=fe#3,<XX=fe#1); */ +/* asm 2: fe_sub(>Z3=r->Z,<YY=r->Z,<XX=r->X); */ +fe_sub(r->Z,r->Z,r->X); + +/* qhasm: X3=AA-Y3 */ +/* asm 1: fe_sub(>X3=fe#1,<AA=fe#5,<Y3=fe#2); */ +/* asm 2: fe_sub(>X3=r->X,<AA=t0,<Y3=r->Y); */ +fe_sub(r->X,t0,r->Y); + +/* qhasm: T3=B-Z3 */ +/* asm 1: fe_sub(>T3=fe#4,<B=fe#4,<Z3=fe#3); */ +/* asm 2: fe_sub(>T3=r->T,<B=r->T,<Z3=r->Z); */ +fe_sub(r->T,r->T,r->Z); + +/* qhasm: return */ +} + + +/* +r = 2 * p +*/ + +static void ge_p3_dbl(ge_p1p1 *r,const ge_p3 *p) +{ + ge_p2 q; + ge_p3_to_p2(&q,p); + ge_p2_dbl(r,&q); +} + + +/* +r = p +*/ + +static void ge_p3_to_cached(ge_cached *r,const ge_p3 *p) +{ + fe_add(r->YplusX,p->Y,p->X); + fe_sub(r->YminusX,p->Y,p->X); + fe_copy(r->Z,p->Z); + fe_mul(r->T2d,p->T,d2); +} + +/* +r = p + q +*/ + +static void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) +{ + fe t0; +/* qhasm: enter ge_add */ + +/* qhasm: fe X1 */ + +/* qhasm: fe Y1 */ + +/* qhasm: fe Z1 */ + +/* qhasm: fe Z2 */ + +/* qhasm: fe T1 */ + +/* qhasm: fe ZZ */ + +/* qhasm: fe YpX2 */ + +/* qhasm: fe YmX2 */ + +/* qhasm: fe T2d2 */ + +/* qhasm: fe X3 */ + +/* qhasm: fe Y3 */ + +/* qhasm: fe Z3 */ + +/* qhasm: fe T3 */ + +/* qhasm: fe YpX1 */ + +/* qhasm: fe YmX1 */ + +/* qhasm: fe A */ + +/* qhasm: fe B */ + +/* qhasm: fe C */ + +/* qhasm: fe D */ + +/* qhasm: YpX1 = Y1+X1 */ +/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */ +/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */ +fe_add(r->X,p->Y,p->X); + +/* qhasm: YmX1 = Y1-X1 */ +/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */ +/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */ +fe_sub(r->Y,p->Y,p->X); + +/* qhasm: A = YpX1*YpX2 */ +/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YpX2=fe#15); */ +/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YpX2=q->YplusX); */ +fe_mul(r->Z,r->X,q->YplusX); + +/* qhasm: B = YmX1*YmX2 */ +/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YmX2=fe#16); */ +/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YmX2=q->YminusX); */ +fe_mul(r->Y,r->Y,q->YminusX); + +/* qhasm: C = T2d2*T1 */ +/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */ +/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */ +fe_mul(r->T,q->T2d,p->T); + +/* qhasm: ZZ = Z1*Z2 */ +/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */ +/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */ +fe_mul(r->X,p->Z,q->Z); + +/* qhasm: D = 2*ZZ */ +/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */ +/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */ +fe_add(t0,r->X,r->X); + +/* qhasm: X3 = A-B */ +/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */ +/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */ +fe_sub(r->X,r->Z,r->Y); + +/* qhasm: Y3 = A+B */ +/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */ +/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */ +fe_add(r->Y,r->Z,r->Y); + +/* qhasm: Z3 = D+C */ +/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */ +/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */ +fe_add(r->Z,t0,r->T); + +/* qhasm: T3 = D-C */ +/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */ +/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */ +fe_sub(r->T,t0,r->T); + +/* qhasm: return */ +} + + +/* +r = p - q +*/ + +static void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) +{ + fe t0; +/* qhasm: enter ge_sub */ + +/* qhasm: fe X1 */ + +/* qhasm: fe Y1 */ + +/* qhasm: fe Z1 */ + +/* qhasm: fe Z2 */ + +/* qhasm: fe T1 */ + +/* qhasm: fe ZZ */ + +/* qhasm: fe YpX2 */ + +/* qhasm: fe YmX2 */ + +/* qhasm: fe T2d2 */ + +/* qhasm: fe X3 */ + +/* qhasm: fe Y3 */ + +/* qhasm: fe Z3 */ + +/* qhasm: fe T3 */ + +/* qhasm: fe YpX1 */ + +/* qhasm: fe YmX1 */ + +/* qhasm: fe A */ + +/* qhasm: fe B */ + +/* qhasm: fe C */ + +/* qhasm: fe D */ + +/* qhasm: YpX1 = Y1+X1 */ +/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */ +/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */ +fe_add(r->X,p->Y,p->X); + +/* qhasm: YmX1 = Y1-X1 */ +/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */ +/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */ +fe_sub(r->Y,p->Y,p->X); + +/* qhasm: A = YpX1*YmX2 */ +/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YmX2=fe#16); */ +/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YmX2=q->YminusX); */ +fe_mul(r->Z,r->X,q->YminusX); + +/* qhasm: B = YmX1*YpX2 */ +/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YpX2=fe#15); */ +/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YpX2=q->YplusX); */ +fe_mul(r->Y,r->Y,q->YplusX); + +/* qhasm: C = T2d2*T1 */ +/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */ +/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */ +fe_mul(r->T,q->T2d,p->T); + +/* qhasm: ZZ = Z1*Z2 */ +/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */ +/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */ +fe_mul(r->X,p->Z,q->Z); + +/* qhasm: D = 2*ZZ */ +/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */ +/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */ +fe_add(t0,r->X,r->X); + +/* qhasm: X3 = A-B */ +/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */ +/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */ +fe_sub(r->X,r->Z,r->Y); + +/* qhasm: Y3 = A+B */ +/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */ +/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */ +fe_add(r->Y,r->Z,r->Y); + +/* qhasm: Z3 = D-C */ +/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */ +/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */ +fe_sub(r->Z,t0,r->T); + +/* qhasm: T3 = D+C */ +/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */ +/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */ +fe_add(r->T,t0,r->T); + +/* qhasm: return */ +} + + +/* +r = p + q +*/ + +static void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) +{ + fe t0; +/* qhasm: enter ge_madd */ + +/* qhasm: fe X1 */ + +/* qhasm: fe Y1 */ + +/* qhasm: fe Z1 */ + +/* qhasm: fe T1 */ + +/* qhasm: fe ypx2 */ + +/* qhasm: fe ymx2 */ + +/* qhasm: fe xy2d2 */ + +/* qhasm: fe X3 */ + +/* qhasm: fe Y3 */ + +/* qhasm: fe Z3 */ + +/* qhasm: fe T3 */ + +/* qhasm: fe YpX1 */ + +/* qhasm: fe YmX1 */ + +/* qhasm: fe A */ + +/* qhasm: fe B */ + +/* qhasm: fe C */ + +/* qhasm: fe D */ + +/* qhasm: YpX1 = Y1+X1 */ +/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */ +/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */ +fe_add(r->X,p->Y,p->X); + +/* qhasm: YmX1 = Y1-X1 */ +/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */ +/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */ +fe_sub(r->Y,p->Y,p->X); + +/* qhasm: A = YpX1*ypx2 */ +/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ypx2=fe#15); */ +/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ypx2=q->yplusx); */ +fe_mul(r->Z,r->X,q->yplusx); + +/* qhasm: B = YmX1*ymx2 */ +/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ymx2=fe#16); */ +/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ymx2=q->yminusx); */ +fe_mul(r->Y,r->Y,q->yminusx); + +/* qhasm: C = xy2d2*T1 */ +/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */ +/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */ +fe_mul(r->T,q->xy2d,p->T); + +/* qhasm: D = 2*Z1 */ +/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */ +/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */ +fe_add(t0,p->Z,p->Z); + +/* qhasm: X3 = A-B */ +/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */ +/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */ +fe_sub(r->X,r->Z,r->Y); + +/* qhasm: Y3 = A+B */ +/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */ +/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */ +fe_add(r->Y,r->Z,r->Y); + +/* qhasm: Z3 = D+C */ +/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */ +/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */ +fe_add(r->Z,t0,r->T); + +/* qhasm: T3 = D-C */ +/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */ +/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */ +fe_sub(r->T,t0,r->T); + +/* qhasm: return */ +} + + +/* +r = p - q +*/ + +static void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) +{ + fe t0; +/* qhasm: enter ge_msub */ + +/* qhasm: fe X1 */ + +/* qhasm: fe Y1 */ + +/* qhasm: fe Z1 */ + +/* qhasm: fe T1 */ + +/* qhasm: fe ypx2 */ + +/* qhasm: fe ymx2 */ + +/* qhasm: fe xy2d2 */ + +/* qhasm: fe X3 */ + +/* qhasm: fe Y3 */ + +/* qhasm: fe Z3 */ + +/* qhasm: fe T3 */ + +/* qhasm: fe YpX1 */ + +/* qhasm: fe YmX1 */ + +/* qhasm: fe A */ + +/* qhasm: fe B */ + +/* qhasm: fe C */ + +/* qhasm: fe D */ + +/* qhasm: YpX1 = Y1+X1 */ +/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */ +/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */ +fe_add(r->X,p->Y,p->X); + +/* qhasm: YmX1 = Y1-X1 */ +/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */ +/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */ +fe_sub(r->Y,p->Y,p->X); + +/* qhasm: A = YpX1*ymx2 */ +/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ymx2=fe#16); */ +/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ymx2=q->yminusx); */ +fe_mul(r->Z,r->X,q->yminusx); + +/* qhasm: B = YmX1*ypx2 */ +/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ypx2=fe#15); */ +/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ypx2=q->yplusx); */ +fe_mul(r->Y,r->Y,q->yplusx); + +/* qhasm: C = xy2d2*T1 */ +/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */ +/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */ +fe_mul(r->T,q->xy2d,p->T); + +/* qhasm: D = 2*Z1 */ +/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */ +/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */ +fe_add(t0,p->Z,p->Z); + +/* qhasm: X3 = A-B */ +/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */ +/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */ +fe_sub(r->X,r->Z,r->Y); + +/* qhasm: Y3 = A+B */ +/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */ +/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */ +fe_add(r->Y,r->Z,r->Y); + +/* qhasm: Z3 = D-C */ +/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */ +/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */ +fe_sub(r->Z,t0,r->T); + +/* qhasm: T3 = D+C */ +/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */ +/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */ +fe_add(r->T,t0,r->T); + +/* qhasm: return */ +} + + +static void ge_p3_tobytes(unsigned char *s,const ge_p3 *h) +{ + fe recip; + fe x; + fe y; + + fe_invert(recip,h->Z); + fe_mul(x,h->X,recip); + fe_mul(y,h->Y,recip); + fe_tobytes(s,y); + s[31] ^= fe_isnegative(x) << 7; +} + +static void ge_tobytes(unsigned char *s,const ge_p2 *h) +{ + fe recip; + fe x; + fe y; + + fe_invert(recip,h->Z); + fe_mul(x,h->X,recip); + fe_mul(y,h->Y,recip); + fe_tobytes(s,y); + s[31] ^= fe_isnegative(x) << 7; +} + +static int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s) +{ + fe u; + fe v; + fe v3; + fe vxx; + fe check; + + fe_frombytes(h->Y,s); + fe_1(h->Z); + fe_sq(u,h->Y); + fe_mul(v,u,d); + fe_sub(u,u,h->Z); /* u = y^2-1 */ + fe_add(v,v,h->Z); /* v = dy^2+1 */ + + fe_sq(v3,v); + fe_mul(v3,v3,v); /* v3 = v^3 */ + fe_sq(h->X,v3); + fe_mul(h->X,h->X,v); + fe_mul(h->X,h->X,u); /* x = uv^7 */ + + fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */ + fe_mul(h->X,h->X,v3); + fe_mul(h->X,h->X,u); /* x = uv^3(uv^7)^((q-5)/8) */ + + fe_sq(vxx,h->X); + fe_mul(vxx,vxx,v); + fe_sub(check,vxx,u); /* vx^2-u */ + if (fe_isnonzero(check)) { + fe_add(check,vxx,u); /* vx^2+u */ + if (fe_isnonzero(check)) return -1; + fe_mul(h->X,h->X,sqrtm1); + } + + if (fe_isnegative(h->X) == (s[31] >> 7)) + fe_neg(h->X,h->X); + + fe_mul(h->T,h->X,h->Y); + return 0; +} + + +static void slide(signed char *r,const unsigned char *a) +{ + int i; + int b; + int k; + + for (i = 0;i < 256;++i) + r[i] = 1 & (a[i >> 3] >> (i & 7)); + + for (i = 0;i < 256;++i) + if (r[i]) { + for (b = 1;b <= 6 && i + b < 256;++b) { + if (r[i + b]) { + if (r[i] + (r[i + b] << b) <= 15) { + r[i] += r[i + b] << b; r[i + b] = 0; + } else if (r[i] - (r[i + b] << b) >= -15) { + r[i] -= r[i + b] << b; + for (k = i + b;k < 256;++k) { + if (!r[k]) { + r[k] = 1; + break; + } + r[k] = 0; + } + } else + break; + } + } + } + +} + + +/* +r = a * A + b * B +where a = a[0]+256*a[1]+...+256^31 a[31]. +and b = b[0]+256*b[1]+...+256^31 b[31]. +B is the Ed25519 base point (x,4/5) with x positive. +*/ + +static void ge_double_scalarmult_vartime(ge_p2 *r,const unsigned char *a,const ge_p3 *A,const unsigned char *b) +{ + signed char aslide[256]; + signed char bslide[256]; + ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ + ge_p1p1 t; + ge_p3 u; + ge_p3 A2; + int i; + + slide(aslide,a); + slide(bslide,b); + + ge_p3_to_cached(&Ai[0],A); + ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t); + ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u); + ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u); + ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u); + ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u); + ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u); + ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u); + ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u); + + ge_p2_0(r); + + for (i = 255;i >= 0;--i) { + if (aslide[i] || bslide[i]) break; + } + + for (;i >= 0;--i) { + ge_p2_dbl(&t,r); + + if (aslide[i] > 0) { + ge_p1p1_to_p3(&u,&t); + ge_add(&t,&u,&Ai[aslide[i]/2]); + } else if (aslide[i] < 0) { + ge_p1p1_to_p3(&u,&t); + ge_sub(&t,&u,&Ai[(-aslide[i])/2]); + } + + if (bslide[i] > 0) { + ge_p1p1_to_p3(&u,&t); + ge_madd(&t,&u,&Bi[bslide[i]/2]); + } else if (bslide[i] < 0) { + ge_p1p1_to_p3(&u,&t); + ge_msub(&t,&u,&Bi[(-bslide[i])/2]); + } + + ge_p1p1_to_p2(r,&t); + } +} + +static unsigned char equal(signed char b,signed char c) +{ + unsigned char ub = b; + unsigned char uc = c; + unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ + crypto_uint32 y = x; /* 0: yes; 1..255: no */ + y -= 1; /* 4294967295: yes; 0..254: no */ + y >>= 31; /* 1: yes; 0: no */ + return y; +} + +static unsigned char negative(signed char b) +{ + unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ + x >>= 63; /* 1: yes; 0: no */ + return x; +} + +static void cmov(ge_precomp *t,ge_precomp *u,unsigned char b) +{ + fe_cmov(t->yplusx,u->yplusx,b); + fe_cmov(t->yminusx,u->yminusx,b); + fe_cmov(t->xy2d,u->xy2d,b); +} + + + +static void select(ge_precomp *t,int pos,signed char b) +{ + ge_precomp minust; + unsigned char bnegative = negative(b); + unsigned char babs = b - (((-bnegative) & b) << 1); + + ge_precomp_0(t); + cmov(t,&base[pos][0],equal(babs,1)); + cmov(t,&base[pos][1],equal(babs,2)); + cmov(t,&base[pos][2],equal(babs,3)); + cmov(t,&base[pos][3],equal(babs,4)); + cmov(t,&base[pos][4],equal(babs,5)); + cmov(t,&base[pos][5],equal(babs,6)); + cmov(t,&base[pos][6],equal(babs,7)); + cmov(t,&base[pos][7],equal(babs,8)); + fe_copy(minust.yplusx,t->yminusx); + fe_copy(minust.yminusx,t->yplusx); + fe_neg(minust.xy2d,t->xy2d); + cmov(t,&minust,bnegative); +} + +/* +h = a * B +where a = a[0]+256*a[1]+...+256^31 a[31] +B is the Ed25519 base point (x,4/5) with x positive. + +Preconditions: + a[31] <= 127 +*/ + +static void ge_scalarmult_base(ge_p3 *h,const unsigned char *a) +{ + signed char e[64]; + signed char carry; + ge_p1p1 r; + ge_p2 s; + ge_precomp t; + int i; + + for (i = 0;i < 32;++i) { + e[2 * i + 0] = (a[i] >> 0) & 15; + e[2 * i + 1] = (a[i] >> 4) & 15; + } + /* each e[i] is between 0 and 15 */ + /* e[63] is between 0 and 7 */ + + carry = 0; + for (i = 0;i < 63;++i) { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry << 4; + } + e[63] += carry; + /* each e[i] is between -8 and 8 */ + + ge_p3_0(h); + for (i = 1;i < 64;i += 2) { + select(&t,i / 2,e[i]); + ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); + } + + ge_p3_dbl(&r,h); ge_p1p1_to_p2(&s,&r); + ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); + ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); + ge_p2_dbl(&r,&s); ge_p1p1_to_p3(h,&r); + + for (i = 0;i < 64;i += 2) { + select(&t,i / 2,e[i]); + ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); + } +} + +/* +Input: + s[0]+256*s[1]+...+256^63*s[63] = s + +Output: + s[0]+256*s[1]+...+256^31*s[31] = s mod l + where l = 2^252 + 27742317777372353535851937790883648493. + Overwrites s in place. +*/ + +static void sc_reduce(unsigned char *s) +{ + crypto_int64 s0 = 2097151 & load_3(s); + crypto_int64 s1 = 2097151 & (load_4(s + 2) >> 5); + crypto_int64 s2 = 2097151 & (load_3(s + 5) >> 2); + crypto_int64 s3 = 2097151 & (load_4(s + 7) >> 7); + crypto_int64 s4 = 2097151 & (load_4(s + 10) >> 4); + crypto_int64 s5 = 2097151 & (load_3(s + 13) >> 1); + crypto_int64 s6 = 2097151 & (load_4(s + 15) >> 6); + crypto_int64 s7 = 2097151 & (load_3(s + 18) >> 3); + crypto_int64 s8 = 2097151 & load_3(s + 21); + crypto_int64 s9 = 2097151 & (load_4(s + 23) >> 5); + crypto_int64 s10 = 2097151 & (load_3(s + 26) >> 2); + crypto_int64 s11 = 2097151 & (load_4(s + 28) >> 7); + crypto_int64 s12 = 2097151 & (load_4(s + 31) >> 4); + crypto_int64 s13 = 2097151 & (load_3(s + 34) >> 1); + crypto_int64 s14 = 2097151 & (load_4(s + 36) >> 6); + crypto_int64 s15 = 2097151 & (load_3(s + 39) >> 3); + crypto_int64 s16 = 2097151 & load_3(s + 42); + crypto_int64 s17 = 2097151 & (load_4(s + 44) >> 5); + crypto_int64 s18 = 2097151 & (load_3(s + 47) >> 2); + crypto_int64 s19 = 2097151 & (load_4(s + 49) >> 7); + crypto_int64 s20 = 2097151 & (load_4(s + 52) >> 4); + crypto_int64 s21 = 2097151 & (load_3(s + 55) >> 1); + crypto_int64 s22 = 2097151 & (load_4(s + 57) >> 6); + crypto_int64 s23 = (load_4(s + 60) >> 3); + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + crypto_int64 carry10; + crypto_int64 carry11; + crypto_int64 carry12; + crypto_int64 carry13; + crypto_int64 carry14; + crypto_int64 carry15; + crypto_int64 carry16; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + s23 = 0; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + s22 = 0; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + s21 = 0; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + s20 = 0; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + s19 = 0; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + s18 = 0; + + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + s17 = 0; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + s16 = 0; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + s15 = 0; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + s14 = 0; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + s13 = 0; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 << 5); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 << 2); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 << 7); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 << 4); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 << 1); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 << 6); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 << 3); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 << 5); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 << 2); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 << 7); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +/* +Input: + a[0]+256*a[1]+...+256^31*a[31] = a + b[0]+256*b[1]+...+256^31*b[31] = b + c[0]+256*c[1]+...+256^31*c[31] = c + +Output: + s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l + where l = 2^252 + 27742317777372353535851937790883648493. +*/ + +static void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,const unsigned char *c) +{ + crypto_int64 a0 = 2097151 & load_3(a); + crypto_int64 a1 = 2097151 & (load_4(a + 2) >> 5); + crypto_int64 a2 = 2097151 & (load_3(a + 5) >> 2); + crypto_int64 a3 = 2097151 & (load_4(a + 7) >> 7); + crypto_int64 a4 = 2097151 & (load_4(a + 10) >> 4); + crypto_int64 a5 = 2097151 & (load_3(a + 13) >> 1); + crypto_int64 a6 = 2097151 & (load_4(a + 15) >> 6); + crypto_int64 a7 = 2097151 & (load_3(a + 18) >> 3); + crypto_int64 a8 = 2097151 & load_3(a + 21); + crypto_int64 a9 = 2097151 & (load_4(a + 23) >> 5); + crypto_int64 a10 = 2097151 & (load_3(a + 26) >> 2); + crypto_int64 a11 = (load_4(a + 28) >> 7); + crypto_int64 b0 = 2097151 & load_3(b); + crypto_int64 b1 = 2097151 & (load_4(b + 2) >> 5); + crypto_int64 b2 = 2097151 & (load_3(b + 5) >> 2); + crypto_int64 b3 = 2097151 & (load_4(b + 7) >> 7); + crypto_int64 b4 = 2097151 & (load_4(b + 10) >> 4); + crypto_int64 b5 = 2097151 & (load_3(b + 13) >> 1); + crypto_int64 b6 = 2097151 & (load_4(b + 15) >> 6); + crypto_int64 b7 = 2097151 & (load_3(b + 18) >> 3); + crypto_int64 b8 = 2097151 & load_3(b + 21); + crypto_int64 b9 = 2097151 & (load_4(b + 23) >> 5); + crypto_int64 b10 = 2097151 & (load_3(b + 26) >> 2); + crypto_int64 b11 = (load_4(b + 28) >> 7); + crypto_int64 c0 = 2097151 & load_3(c); + crypto_int64 c1 = 2097151 & (load_4(c + 2) >> 5); + crypto_int64 c2 = 2097151 & (load_3(c + 5) >> 2); + crypto_int64 c3 = 2097151 & (load_4(c + 7) >> 7); + crypto_int64 c4 = 2097151 & (load_4(c + 10) >> 4); + crypto_int64 c5 = 2097151 & (load_3(c + 13) >> 1); + crypto_int64 c6 = 2097151 & (load_4(c + 15) >> 6); + crypto_int64 c7 = 2097151 & (load_3(c + 18) >> 3); + crypto_int64 c8 = 2097151 & load_3(c + 21); + crypto_int64 c9 = 2097151 & (load_4(c + 23) >> 5); + crypto_int64 c10 = 2097151 & (load_3(c + 26) >> 2); + crypto_int64 c11 = (load_4(c + 28) >> 7); + crypto_int64 s0; + crypto_int64 s1; + crypto_int64 s2; + crypto_int64 s3; + crypto_int64 s4; + crypto_int64 s5; + crypto_int64 s6; + crypto_int64 s7; + crypto_int64 s8; + crypto_int64 s9; + crypto_int64 s10; + crypto_int64 s11; + crypto_int64 s12; + crypto_int64 s13; + crypto_int64 s14; + crypto_int64 s15; + crypto_int64 s16; + crypto_int64 s17; + crypto_int64 s18; + crypto_int64 s19; + crypto_int64 s20; + crypto_int64 s21; + crypto_int64 s22; + crypto_int64 s23; + crypto_int64 carry0; + crypto_int64 carry1; + crypto_int64 carry2; + crypto_int64 carry3; + crypto_int64 carry4; + crypto_int64 carry5; + crypto_int64 carry6; + crypto_int64 carry7; + crypto_int64 carry8; + crypto_int64 carry9; + crypto_int64 carry10; + crypto_int64 carry11; + crypto_int64 carry12; + crypto_int64 carry13; + crypto_int64 carry14; + crypto_int64 carry15; + crypto_int64 carry16; + crypto_int64 carry17; + crypto_int64 carry18; + crypto_int64 carry19; + crypto_int64 carry20; + crypto_int64 carry21; + crypto_int64 carry22; + + s0 = c0 + a0*b0; + s1 = c1 + a0*b1 + a1*b0; + s2 = c2 + a0*b2 + a1*b1 + a2*b0; + s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0; + s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0; + s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0; + s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0; + s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0; + s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0; + s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0; + s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0; + s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0; + s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1; + s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2; + s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3; + s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4; + s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5; + s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6; + s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7; + s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8; + s20 = a9*b11 + a10*b10 + a11*b9; + s21 = a10*b11 + a11*b10; + s22 = a11*b11; + s23 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21; + carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21; + carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21; + carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21; + carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + s23 = 0; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + s22 = 0; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + s21 = 0; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + s20 = 0; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + s19 = 0; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + s18 = 0; + + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + s17 = 0; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + s16 = 0; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + s15 = 0; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + s14 = 0; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + s13 = 0; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 << 5); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 << 2); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 << 7); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 << 4); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 << 1); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 << 6); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 << 3); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 << 5); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 << 2); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 << 7); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +/* +int crypto_sign_keypair(unsigned char *pk,unsigned char *sk) +{ + unsigned char h[64]; + ge_p3 A; + int i; + + randombytes(sk,32); + crypto_hash_sha512(h,sk,32); + h[0] &= 248; + h[31] &= 63; + h[31] |= 64; + + ge_scalarmult_base(&A,h); + ge_p3_tobytes(pk,&A); + + for (i = 0;i < 32;++i) sk[32 + i] = pk[i]; + return 0; +} +*/ + +int crypto_sign_pk_ref10(unsigned char *pk,unsigned char *sk) +{ + unsigned char h[64]; + ge_p3 A; + int i; + + crypto_hash_sha512(h,sk,32); + h[0] &= 248; + h[31] &= 63; + h[31] |= 64; + + ge_scalarmult_base(&A,h); + ge_p3_tobytes(pk,&A); + + for (i = 0;i < 32;++i) sk[32 + i] = pk[i]; + return 0; +} + +int crypto_sign_ref10( + unsigned char *sm,unsigned long long *smlen, + const unsigned char *m,unsigned long long mlen, + const unsigned char *sk +) +{ + unsigned char az[64]; + unsigned char r[64]; + unsigned char hram[64]; + ge_p3 R; + unsigned long long i; + + crypto_hash_sha512(az,sk,32); + az[0] &= 248; + az[31] &= 63; + az[31] |= 64; + + *smlen = mlen + 64; + for (i = 0;i < mlen;++i) sm[64 + i] = m[i]; + for (i = 0;i < 32;++i) sm[32 + i] = az[32 + i]; + crypto_hash_sha512(r,sm + 32,mlen + 32); + for (i = 0;i < 32;++i) sm[32 + i] = sk[32 + i]; + + sc_reduce(r); + ge_scalarmult_base(&R,r); + ge_p3_tobytes(sm,&R); + + crypto_hash_sha512(hram,sm,mlen + 64); + sc_reduce(hram); + sc_muladd(sm + 32,hram,az,r); + + return 0; +} + +int crypto_sign_open_ref10( + unsigned char *m,unsigned long long *mlen, + const unsigned char *sm,unsigned long long smlen, + const unsigned char *pk +) +{ + unsigned char h[64]; + unsigned char checkr[32]; + ge_p3 A; + ge_p2 R; + unsigned long long i; + + *mlen = -1; + if (smlen < 64) return -1; + if (sm[63] & 224) return -1; + if (ge_frombytes_negate_vartime(&A,pk) != 0) return -1; + + for (i = 0;i < smlen;++i) m[i] = sm[i]; + for (i = 0;i < 32;++i) m[32 + i] = pk[i]; + crypto_hash_sha512(h,m,smlen); + sc_reduce(h); + + ge_double_scalarmult_vartime(&R,h,&A,sm + 32); + ge_tobytes(checkr,&R); + if (crypto_verify_32(checkr,sm) != 0) { + for (i = 0;i < smlen;++i) m[i] = 0; + return -1; + } + + for (i = 0;i < smlen - 64;++i) m[i] = sm[64 + i]; + for (i = smlen - 64;i < smlen;++i) m[i] = 0; + *mlen = smlen - 64; + return 0; +} + diff --git a/src/ext/ed25519/donna/fuzz/ed25519-ref10.h b/src/ext/ed25519/donna/fuzz/ed25519-ref10.h new file mode 100644 index 0000000..c8a0f69 --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/ed25519-ref10.h @@ -0,0 +1,9 @@ +#ifndef ED25519_REF10_H +#define ED25519_REF10_H + +int crypto_sign_pk_ref10(unsigned char *pk,unsigned char *sk); +int crypto_sign_ref10(unsigned char *sm,unsigned long long *smlen,const unsigned char *m,unsigned long long mlen,const unsigned char *sk); +int crypto_sign_open_ref10(unsigned char *m,unsigned long long *mlen,const unsigned char *sm,unsigned long long smlen,const unsigned char *pk); + +#endif /* ED25519_REF10_H */ + diff --git a/src/ext/ed25519/donna/fuzz/fuzz-curve25519.c b/src/ext/ed25519/donna/fuzz/fuzz-curve25519.c new file mode 100644 index 0000000..4301701 --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/fuzz-curve25519.c @@ -0,0 +1,172 @@ +#if defined(_WIN32) + #include <windows.h> + #include <wincrypt.h> + typedef unsigned int uint32_t; + typedef unsigned __int64 uint64_t; +#else + #include <stdint.h> +#endif + +#include <string.h> +#include <stdio.h> + +#include "ed25519-donna.h" +#include "curve25519-ref10.h" + +static void +print_diff(const char *desc, const unsigned char *a, const unsigned char *b, size_t len) { + size_t p = 0; + unsigned char diff; + printf("%s diff:\n", desc); + while (len--) { + diff = *a++ ^ *b++; + if (!diff) + printf("____,"); + else + printf("0x%02x,", diff); + if ((++p & 15) == 0) + printf("\n"); + } + printf("\n\n"); +} + +static void +print_bytes(const char *desc, const unsigned char *bytes, size_t len) { + size_t p = 0; + printf("%s:\n", desc); + while (len--) { + printf("0x%02x,", *bytes++); + if ((++p & 15) == 0) + printf("\n"); + } + printf("\n\n"); +} + + +/* chacha20/12 prng */ +void +prng(unsigned char *out, size_t bytes) { + static uint32_t state[16]; + static int init = 0; + uint32_t x[16], t; + size_t i; + + if (!init) { + #if defined(_WIN32) + HCRYPTPROV csp; + if (!CryptAcquireContext(&csp, 0, 0, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) { + printf("CryptAcquireContext failed\n"); + exit(1); + } + if (!CryptGenRandom(csp, (DWORD)sizeof(state), (BYTE*)state)) { + printf("CryptGenRandom failed\n"); + exit(1); + } + CryptReleaseContext(csp, 0); + #else + FILE *f = NULL; + f = fopen("/dev/urandom", "rb"); + if (!f) { + printf("failed to open /dev/urandom\n"); + exit(1); + } + if (fread(state, sizeof(state), 1, f) != 1) { + printf("read error on /dev/urandom\n"); + exit(1); + } + #endif + init = 1; + } + + while (bytes) { + for (i = 0; i < 16; i++) x[i] = state[i]; + + #define rotl32(x,k) ((x << k) | (x >> (32 - k))) + #define quarter(a,b,c,d) \ + x[a] += x[b]; t = x[d]^x[a]; x[d] = rotl32(t,16); \ + x[c] += x[d]; t = x[b]^x[c]; x[b] = rotl32(t,12); \ + x[a] += x[b]; t = x[d]^x[a]; x[d] = rotl32(t, 8); \ + x[c] += x[d]; t = x[b]^x[c]; x[b] = rotl32(t, 7); + + for (i = 0; i < 12; i += 2) { + quarter( 0, 4, 8,12) + quarter( 1, 5, 9,13) + quarter( 2, 6,10,14) + quarter( 3, 7,11,15) + quarter( 0, 5,10,15) + quarter( 1, 6,11,12) + quarter( 2, 7, 8,13) + quarter( 3, 4, 9,14) + }; + + if (bytes <= 64) { + memcpy(out, x, bytes); + bytes = 0; + } else { + memcpy(out, x, 64); + bytes -= 64; + out += 64; + } + + /* don't need a nonce, so last 4 words are the counter. 2^136 bytes can be generated */ + if (!++state[12]) if (!++state[13]) if (!++state[14]) ++state[15]; + } +} + + + +int main() { + const size_t skmax = 1024; + static unsigned char sk[1024][32]; + unsigned char pk[3][32]; + unsigned char *skp; + size_t ski, pki, i; + uint64_t ctr; + + printf("fuzzing: "); + printf(" ref10"); + printf(" curved25519"); +#if defined(ED25519_SSE2) + printf(" curved25519-sse2"); +#endif + printf("\n\n"); + + for (ctr = 0, ski = skmax;;ctr++) { + if (ski == skmax) { + prng((unsigned char *)sk, sizeof(sk)); + ski = 0; + } + skp = sk[ski++]; + + pki = 0; + crypto_scalarmult_base_ref10(pk[pki++], skp); + curved25519_scalarmult_basepoint(pk[pki++], skp); + #if defined(ED25519_SSE2) + curved25519_scalarmult_basepoint_sse2(pk[pki++], skp); + #endif + + for (i = 1; i < pki; i++) { + if (memcmp(pk[0], pk[i], 32) != 0) { + printf("\n\n"); + print_bytes("sk", skp, 32); + print_bytes("ref10", pk[0], 32); + print_diff("curved25519", pk[0], pk[1], 32); + #if defined(ED25519_SSE2) + print_diff("curved25519-sse2", pk[0], pk[2], 32); + #endif + exit(1); + } + } + + if (ctr && (ctr % 0x1000 == 0)) { + printf("."); + if ((ctr % 0x20000) == 0) { + printf(" ["); + for (i = 0; i < 8; i++) + printf("%02x", (unsigned char)(ctr >> ((7 - i) * 8))); + printf("]\n"); + } + } + } +} + diff --git a/src/ext/ed25519/donna/fuzz/fuzz-ed25519.c b/src/ext/ed25519/donna/fuzz/fuzz-ed25519.c new file mode 100644 index 0000000..b242e8e --- /dev/null +++ b/src/ext/ed25519/donna/fuzz/fuzz-ed25519.c @@ -0,0 +1,219 @@ +#if defined(_WIN32) + #include <windows.h> + #include <wincrypt.h> + typedef unsigned int uint32_t; +#else + #include <stdint.h> +#endif + +#include <string.h> +#include <stdio.h> + +#include "ed25519-donna.h" +#include "ed25519-ref10.h" + +static void +print_diff(const char *desc, const unsigned char *a, const unsigned char *b, size_t len) { + size_t p = 0; + unsigned char diff; + printf("%s diff:\n", desc); + while (len--) { + diff = *a++ ^ *b++; + if (!diff) + printf("____,"); + else + printf("0x%02x,", diff); + if ((++p & 15) == 0) + printf("\n"); + } + printf("\n"); +} + +static void +print_bytes(const char *desc, const unsigned char *bytes, size_t len) { + size_t p = 0; + printf("%s:\n", desc); + while (len--) { + printf("0x%02x,", *bytes++); + if ((++p & 15) == 0) + printf("\n"); + } + printf("\n"); +} + + +/* chacha20/12 prng */ +void +prng(unsigned char *out, size_t bytes) { + static uint32_t state[16]; + static int init = 0; + uint32_t x[16], t; + size_t i; + + if (!init) { + #if defined(_WIN32) + HCRYPTPROV csp = NULL; + if (!CryptAcquireContext(&csp, 0, 0, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) { + printf("CryptAcquireContext failed\n"); + exit(1); + } + if (!CryptGenRandom(csp, (DWORD)sizeof(state), (BYTE*)state)) { + printf("CryptGenRandom failed\n"); + exit(1); + } + CryptReleaseContext(csp, 0); + #else + FILE *f = NULL; + f = fopen("/dev/urandom", "rb"); + if (!f) { + printf("failed to open /dev/urandom\n"); + exit(1); + } + if (fread(state, sizeof(state), 1, f) != 1) { + printf("read error on /dev/urandom\n"); + exit(1); + } + #endif + init = 1; + } + + while (bytes) { + for (i = 0; i < 16; i++) x[i] = state[i]; + + #define rotl32(x,k) ((x << k) | (x >> (32 - k))) + #define quarter(a,b,c,d) \ + x[a] += x[b]; t = x[d]^x[a]; x[d] = rotl32(t,16); \ + x[c] += x[d]; t = x[b]^x[c]; x[b] = rotl32(t,12); \ + x[a] += x[b]; t = x[d]^x[a]; x[d] = rotl32(t, 8); \ + x[c] += x[d]; t = x[b]^x[c]; x[b] = rotl32(t, 7); + + for (i = 0; i < 12; i += 2) { + quarter( 0, 4, 8,12) + quarter( 1, 5, 9,13) + quarter( 2, 6,10,14) + quarter( 3, 7,11,15) + quarter( 0, 5,10,15) + quarter( 1, 6,11,12) + quarter( 2, 7, 8,13) + quarter( 3, 4, 9,14) + }; + + if (bytes <= 64) { + memcpy(out, x, bytes); + bytes = 0; + } else { + memcpy(out, x, 64); + bytes -= 64; + out += 64; + } + + /* don't need a nonce, so last 4 words are the counter. 2^136 bytes can be generated */ + if (!++state[12]) if (!++state[13]) if (!++state[14]) ++state[15]; + } +} + +typedef struct random_data_t { + unsigned char sk[32]; + unsigned char m[128]; +} random_data; + +typedef struct generated_data_t { + unsigned char pk[32]; + unsigned char sig[64]; + int valid; +} generated_data; + +static void +print_generated(const char *desc, generated_data *g) { + printf("%s:\n", desc); + print_bytes("pk", g->pk, 32); + print_bytes("sig", g->sig, 64); + printf("valid: %s\n\n", g->valid ? "no" : "yes"); +} + +static void +print_generated_diff(const char *desc, const generated_data *base, generated_data *g) { + printf("%s:\n", desc); + print_diff("pk", base->pk, g->pk, 32); + print_diff("sig", base->sig, g->sig, 64); + printf("valid: %s\n\n", (base->valid == g->valid) ? "___" : (g->valid ? "no" : "yes")); +} + +int main() { + const size_t rndmax = 128; + static random_data rnd[128]; + static generated_data gen[3]; + random_data *r; + generated_data *g; + unsigned long long dummylen; + unsigned char dummysk[64]; + unsigned char dummymsg[2][128+64]; + size_t rndi, geni, i, j; + uint64_t ctr; + + printf("fuzzing: "); + printf(" ref10"); + printf(" ed25519-donna"); +#if defined(ED25519_SSE2) + printf(" ed25519-donna-sse2"); +#endif + printf("\n\n"); + + for (ctr = 0, rndi = rndmax;;ctr++) { + if (rndi == rndmax) { + prng((unsigned char *)rnd, sizeof(rnd)); + rndi = 0; + } + r = &rnd[rndi++]; + + /* ref10, lots of horrible gymnastics to work around the wonky api */ + geni = 0; + g = &gen[geni++]; + memcpy(dummysk, r->sk, 32); /* pk is appended to the sk, need to copy the sk to a larger buffer */ + crypto_sign_pk_ref10(dummysk + 32, dummysk); + memcpy(g->pk, dummysk + 32, 32); + crypto_sign_ref10(dummymsg[0], &dummylen, r->m, 128, dummysk); + memcpy(g->sig, dummymsg[0], 64); /* sig is placed in front of the signed message */ + g->valid = crypto_sign_open_ref10(dummymsg[1], &dummylen, dummymsg[0], 128 + 64, g->pk); + + /* ed25519-donna */ + g = &gen[geni++]; + ed25519_publickey(r->sk, g->pk); + ed25519_sign(r->m, 128, r->sk, g->pk, g->sig); + g->valid = ed25519_sign_open(r->m, 128, g->pk, g->sig); + + #if defined(ED25519_SSE2) + /* ed25519-donna-sse2 */ + g = &gen[geni++]; + ed25519_publickey_sse2(r->sk, g->pk); + ed25519_sign_sse2(r->m, 128, r->sk, g->pk, g->sig); + g->valid = ed25519_sign_open_sse2(r->m, 128, g->pk, g->sig); + #endif + + /* compare implementations 1..geni against the reference */ + for (i = 1; i < geni; i++) { + if (memcmp(&gen[0], &gen[i], sizeof(generated_data)) != 0) { + printf("\n\n"); + print_bytes("sk", r->sk, 32); + print_bytes("m", r->m, 128); + print_generated("ref10", &gen[0]); + print_generated_diff("ed25519-donna", &gen[0], &gen[1]); + #if defined(ED25519_SSE2) + print_generated_diff("ed25519-donna-sse2", &gen[0], &gen[2]); + #endif + exit(1); + } + } + + /* print out status */ + if (ctr && (ctr % 0x1000 == 0)) { + printf("."); + if ((ctr % 0x20000) == 0) { + printf(" ["); + for (i = 0; i < 8; i++) + printf("%02x", (unsigned char)(ctr >> ((7 - i) * 8))); + printf("]\n"); + } + } + } +} \ No newline at end of file diff --git a/src/ext/ed25519/donna/modm-donna-32bit.h b/src/ext/ed25519/donna/modm-donna-32bit.h new file mode 100644 index 0000000..dfd76be --- /dev/null +++ b/src/ext/ed25519/donna/modm-donna-32bit.h @@ -0,0 +1,469 @@ +/* + Public domain by Andrew M. liquidsun@gmail.com +*/ + + +/* + Arithmetic modulo the group order n = 2^252 + 27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989 + + k = 32 + b = 1 << 8 = 256 + m = 2^252 + 27742317777372353535851937790883648493 = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed + mu = floor( b^(k*2) / m ) = 0xfffffffffffffffffffffffffffffffeb2106215d086329a7ed9ce5a30a2c131b +*/ + +#define bignum256modm_bits_per_limb 30 +#define bignum256modm_limb_size 9 + +typedef uint32_t bignum256modm_element_t; +typedef bignum256modm_element_t bignum256modm[9]; + +static const bignum256modm modm_m = { + 0x1cf5d3ed, 0x20498c69, 0x2f79cd65, 0x37be77a8, + 0x00000014, 0x00000000, 0x00000000, 0x00000000, + 0x00001000 +}; + +static const bignum256modm modm_mu = { + 0x0a2c131b, 0x3673968c, 0x06329a7e, 0x01885742, + 0x3fffeb21, 0x3fffffff, 0x3fffffff, 0x3fffffff, + 0x000fffff +}; + +static bignum256modm_element_t +lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) { + return (a - b) >> 31; +} + +/* see HAC, Alg. 14.42 Step 4 */ +static void +reduce256_modm(bignum256modm r) { + bignum256modm t; + bignum256modm_element_t b = 0, pb, mask; + + /* t = r - m */ + pb = 0; + pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 30)); pb = b; + pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 30)); pb = b; + pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 30)); pb = b; + pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 30)); pb = b; + pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 30)); pb = b; + pb += modm_m[5]; b = lt_modm(r[5], pb); t[5] = (r[5] - pb + (b << 30)); pb = b; + pb += modm_m[6]; b = lt_modm(r[6], pb); t[6] = (r[6] - pb + (b << 30)); pb = b; + pb += modm_m[7]; b = lt_modm(r[7], pb); t[7] = (r[7] - pb + (b << 30)); pb = b; + pb += modm_m[8]; b = lt_modm(r[8], pb); t[8] = (r[8] - pb + (b << 16)); + + /* keep r if r was smaller than m */ + mask = b - 1; + r[0] ^= mask & (r[0] ^ t[0]); + r[1] ^= mask & (r[1] ^ t[1]); + r[2] ^= mask & (r[2] ^ t[2]); + r[3] ^= mask & (r[3] ^ t[3]); + r[4] ^= mask & (r[4] ^ t[4]); + r[5] ^= mask & (r[5] ^ t[5]); + r[6] ^= mask & (r[6] ^ t[6]); + r[7] ^= mask & (r[7] ^ t[7]); + r[8] ^= mask & (r[8] ^ t[8]); +} + +/* + Barrett reduction, see HAC, Alg. 14.42 + + Instead of passing in x, pre-process in to q1 and r1 for efficiency +*/ +static void +barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) { + bignum256modm q3, r2; + uint64_t c; + bignum256modm_element_t f, b, pb; + + /* q1 = x >> 248 = 264 bits = 9 30 bit elements + q2 = mu * q1 + q3 = (q2 / 256(32+1)) = q2 / (2^8)^(32+1) = q2 >> 264 */ + c = mul32x32_64(modm_mu[0], q1[7]) + mul32x32_64(modm_mu[1], q1[6]) + mul32x32_64(modm_mu[2], q1[5]) + mul32x32_64(modm_mu[3], q1[4]) + mul32x32_64(modm_mu[4], q1[3]) + mul32x32_64(modm_mu[5], q1[2]) + mul32x32_64(modm_mu[6], q1[1]) + mul32x32_64(modm_mu[7], q1[0]); + c >>= 30; + c += mul32x32_64(modm_mu[0], q1[8]) + mul32x32_64(modm_mu[1], q1[7]) + mul32x32_64(modm_mu[2], q1[6]) + mul32x32_64(modm_mu[3], q1[5]) + mul32x32_64(modm_mu[4], q1[4]) + mul32x32_64(modm_mu[5], q1[3]) + mul32x32_64(modm_mu[6], q1[2]) + mul32x32_64(modm_mu[7], q1[1]) + mul32x32_64(modm_mu[8], q1[0]); + f = (bignum256modm_element_t)c; q3[0] = (f >> 24) & 0x3f; c >>= 30; + c += mul32x32_64(modm_mu[1], q1[8]) + mul32x32_64(modm_mu[2], q1[7]) + mul32x32_64(modm_mu[3], q1[6]) + mul32x32_64(modm_mu[4], q1[5]) + mul32x32_64(modm_mu[5], q1[4]) + mul32x32_64(modm_mu[6], q1[3]) + mul32x32_64(modm_mu[7], q1[2]) + mul32x32_64(modm_mu[8], q1[1]); + f = (bignum256modm_element_t)c; q3[0] |= (f << 6) & 0x3fffffff; q3[1] = (f >> 24) & 0x3f; c >>= 30; + c += mul32x32_64(modm_mu[2], q1[8]) + mul32x32_64(modm_mu[3], q1[7]) + mul32x32_64(modm_mu[4], q1[6]) + mul32x32_64(modm_mu[5], q1[5]) + mul32x32_64(modm_mu[6], q1[4]) + mul32x32_64(modm_mu[7], q1[3]) + mul32x32_64(modm_mu[8], q1[2]); + f = (bignum256modm_element_t)c; q3[1] |= (f << 6) & 0x3fffffff; q3[2] = (f >> 24) & 0x3f; c >>= 30; + c += mul32x32_64(modm_mu[3], q1[8]) + mul32x32_64(modm_mu[4], q1[7]) + mul32x32_64(modm_mu[5], q1[6]) + mul32x32_64(modm_mu[6], q1[5]) + mul32x32_64(modm_mu[7], q1[4]) + mul32x32_64(modm_mu[8], q1[3]); + f = (bignum256modm_element_t)c; q3[2] |= (f << 6) & 0x3fffffff; q3[3] = (f >> 24) & 0x3f; c >>= 30; + c += mul32x32_64(modm_mu[4], q1[8]) + mul32x32_64(modm_mu[5], q1[7]) + mul32x32_64(modm_mu[6], q1[6]) + mul32x32_64(modm_mu[7], q1[5]) + mul32x32_64(modm_mu[8], q1[4]); + f = (bignum256modm_element_t)c; q3[3] |= (f << 6) & 0x3fffffff; q3[4] = (f >> 24) & 0x3f; c >>= 30; + c += mul32x32_64(modm_mu[5], q1[8]) + mul32x32_64(modm_mu[6], q1[7]) + mul32x32_64(modm_mu[7], q1[6]) + mul32x32_64(modm_mu[8], q1[5]); + f = (bignum256modm_element_t)c; q3[4] |= (f << 6) & 0x3fffffff; q3[5] = (f >> 24) & 0x3f; c >>= 30; + c += mul32x32_64(modm_mu[6], q1[8]) + mul32x32_64(modm_mu[7], q1[7]) + mul32x32_64(modm_mu[8], q1[6]); + f = (bignum256modm_element_t)c; q3[5] |= (f << 6) & 0x3fffffff; q3[6] = (f >> 24) & 0x3f; c >>= 30; + c += mul32x32_64(modm_mu[7], q1[8]) + mul32x32_64(modm_mu[8], q1[7]); + f = (bignum256modm_element_t)c; q3[6] |= (f << 6) & 0x3fffffff; q3[7] = (f >> 24) & 0x3f; c >>= 30; + c += mul32x32_64(modm_mu[8], q1[8]); + f = (bignum256modm_element_t)c; q3[7] |= (f << 6) & 0x3fffffff; q3[8] = (bignum256modm_element_t)(c >> 24); + + /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) + r2 = (q3 * m) mod (256^(32+1)) = (q3 * m) & ((1 << 264) - 1) */ + c = mul32x32_64(modm_m[0], q3[0]); + r2[0] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30; + c += mul32x32_64(modm_m[0], q3[1]) + mul32x32_64(modm_m[1], q3[0]); + r2[1] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30; + c += mul32x32_64(modm_m[0], q3[2]) + mul32x32_64(modm_m[1], q3[1]) + mul32x32_64(modm_m[2], q3[0]); + r2[2] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30; + c += mul32x32_64(modm_m[0], q3[3]) + mul32x32_64(modm_m[1], q3[2]) + mul32x32_64(modm_m[2], q3[1]) + mul32x32_64(modm_m[3], q3[0]); + r2[3] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30; + c += mul32x32_64(modm_m[0], q3[4]) + mul32x32_64(modm_m[1], q3[3]) + mul32x32_64(modm_m[2], q3[2]) + mul32x32_64(modm_m[3], q3[1]) + mul32x32_64(modm_m[4], q3[0]); + r2[4] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30; + c += mul32x32_64(modm_m[0], q3[5]) + mul32x32_64(modm_m[1], q3[4]) + mul32x32_64(modm_m[2], q3[3]) + mul32x32_64(modm_m[3], q3[2]) + mul32x32_64(modm_m[4], q3[1]) + mul32x32_64(modm_m[5], q3[0]); + r2[5] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30; + c += mul32x32_64(modm_m[0], q3[6]) + mul32x32_64(modm_m[1], q3[5]) + mul32x32_64(modm_m[2], q3[4]) + mul32x32_64(modm_m[3], q3[3]) + mul32x32_64(modm_m[4], q3[2]) + mul32x32_64(modm_m[5], q3[1]) + mul32x32_64(modm_m[6], q3[0]); + r2[6] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30; + c += mul32x32_64(modm_m[0], q3[7]) + mul32x32_64(modm_m[1], q3[6]) + mul32x32_64(modm_m[2], q3[5]) + mul32x32_64(modm_m[3], q3[4]) + mul32x32_64(modm_m[4], q3[3]) + mul32x32_64(modm_m[5], q3[2]) + mul32x32_64(modm_m[6], q3[1]) + mul32x32_64(modm_m[7], q3[0]); + r2[7] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30; + c += mul32x32_64(modm_m[0], q3[8]) + mul32x32_64(modm_m[1], q3[7]) + mul32x32_64(modm_m[2], q3[6]) + mul32x32_64(modm_m[3], q3[5]) + mul32x32_64(modm_m[4], q3[4]) + mul32x32_64(modm_m[5], q3[3]) + mul32x32_64(modm_m[6], q3[2]) + mul32x32_64(modm_m[7], q3[1]) + mul32x32_64(modm_m[8], q3[0]); + r2[8] = (bignum256modm_element_t)(c & 0xffffff); + + /* r = r1 - r2 + if (r < 0) r += (1 << 264) */ + pb = 0; + pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 30)); pb = b; + pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 30)); pb = b; + pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 30)); pb = b; + pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 30)); pb = b; + pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 30)); pb = b; + pb += r2[5]; b = lt_modm(r1[5], pb); r[5] = (r1[5] - pb + (b << 30)); pb = b; + pb += r2[6]; b = lt_modm(r1[6], pb); r[6] = (r1[6] - pb + (b << 30)); pb = b; + pb += r2[7]; b = lt_modm(r1[7], pb); r[7] = (r1[7] - pb + (b << 30)); pb = b; + pb += r2[8]; b = lt_modm(r1[8], pb); r[8] = (r1[8] - pb + (b << 24)); + + reduce256_modm(r); + reduce256_modm(r); +} + +/* addition modulo m */ +static void +add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) { + bignum256modm_element_t c; + + c = x[0] + y[0]; r[0] = c & 0x3fffffff; c >>= 30; + c += x[1] + y[1]; r[1] = c & 0x3fffffff; c >>= 30; + c += x[2] + y[2]; r[2] = c & 0x3fffffff; c >>= 30; + c += x[3] + y[3]; r[3] = c & 0x3fffffff; c >>= 30; + c += x[4] + y[4]; r[4] = c & 0x3fffffff; c >>= 30; + c += x[5] + y[5]; r[5] = c & 0x3fffffff; c >>= 30; + c += x[6] + y[6]; r[6] = c & 0x3fffffff; c >>= 30; + c += x[7] + y[7]; r[7] = c & 0x3fffffff; c >>= 30; + c += x[8] + y[8]; r[8] = c; + + reduce256_modm(r); +} + +/* multiplication modulo m */ +static void +mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) { + bignum256modm r1, q1; + uint64_t c; + bignum256modm_element_t f; + + /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) + q1 = x >> 248 = 264 bits = 9 30 bit elements */ + c = mul32x32_64(x[0], y[0]); + f = (bignum256modm_element_t)c; r1[0] = (f & 0x3fffffff); c >>= 30; + c += mul32x32_64(x[0], y[1]) + mul32x32_64(x[1], y[0]); + f = (bignum256modm_element_t)c; r1[1] = (f & 0x3fffffff); c >>= 30; + c += mul32x32_64(x[0], y[2]) + mul32x32_64(x[1], y[1]) + mul32x32_64(x[2], y[0]); + f = (bignum256modm_element_t)c; r1[2] = (f & 0x3fffffff); c >>= 30; + c += mul32x32_64(x[0], y[3]) + mul32x32_64(x[1], y[2]) + mul32x32_64(x[2], y[1]) + mul32x32_64(x[3], y[0]); + f = (bignum256modm_element_t)c; r1[3] = (f & 0x3fffffff); c >>= 30; + c += mul32x32_64(x[0], y[4]) + mul32x32_64(x[1], y[3]) + mul32x32_64(x[2], y[2]) + mul32x32_64(x[3], y[1]) + mul32x32_64(x[4], y[0]); + f = (bignum256modm_element_t)c; r1[4] = (f & 0x3fffffff); c >>= 30; + c += mul32x32_64(x[0], y[5]) + mul32x32_64(x[1], y[4]) + mul32x32_64(x[2], y[3]) + mul32x32_64(x[3], y[2]) + mul32x32_64(x[4], y[1]) + mul32x32_64(x[5], y[0]); + f = (bignum256modm_element_t)c; r1[5] = (f & 0x3fffffff); c >>= 30; + c += mul32x32_64(x[0], y[6]) + mul32x32_64(x[1], y[5]) + mul32x32_64(x[2], y[4]) + mul32x32_64(x[3], y[3]) + mul32x32_64(x[4], y[2]) + mul32x32_64(x[5], y[1]) + mul32x32_64(x[6], y[0]); + f = (bignum256modm_element_t)c; r1[6] = (f & 0x3fffffff); c >>= 30; + c += mul32x32_64(x[0], y[7]) + mul32x32_64(x[1], y[6]) + mul32x32_64(x[2], y[5]) + mul32x32_64(x[3], y[4]) + mul32x32_64(x[4], y[3]) + mul32x32_64(x[5], y[2]) + mul32x32_64(x[6], y[1]) + mul32x32_64(x[7], y[0]); + f = (bignum256modm_element_t)c; r1[7] = (f & 0x3fffffff); c >>= 30; + c += mul32x32_64(x[0], y[8]) + mul32x32_64(x[1], y[7]) + mul32x32_64(x[2], y[6]) + mul32x32_64(x[3], y[5]) + mul32x32_64(x[4], y[4]) + mul32x32_64(x[5], y[3]) + mul32x32_64(x[6], y[2]) + mul32x32_64(x[7], y[1]) + mul32x32_64(x[8], y[0]); + f = (bignum256modm_element_t)c; r1[8] = (f & 0x00ffffff); q1[0] = (f >> 8) & 0x3fffff; c >>= 30; + c += mul32x32_64(x[1], y[8]) + mul32x32_64(x[2], y[7]) + mul32x32_64(x[3], y[6]) + mul32x32_64(x[4], y[5]) + mul32x32_64(x[5], y[4]) + mul32x32_64(x[6], y[3]) + mul32x32_64(x[7], y[2]) + mul32x32_64(x[8], y[1]); + f = (bignum256modm_element_t)c; q1[0] = (q1[0] | (f << 22)) & 0x3fffffff; q1[1] = (f >> 8) & 0x3fffff; c >>= 30; + c += mul32x32_64(x[2], y[8]) + mul32x32_64(x[3], y[7]) + mul32x32_64(x[4], y[6]) + mul32x32_64(x[5], y[5]) + mul32x32_64(x[6], y[4]) + mul32x32_64(x[7], y[3]) + mul32x32_64(x[8], y[2]); + f = (bignum256modm_element_t)c; q1[1] = (q1[1] | (f << 22)) & 0x3fffffff; q1[2] = (f >> 8) & 0x3fffff; c >>= 30; + c += mul32x32_64(x[3], y[8]) + mul32x32_64(x[4], y[7]) + mul32x32_64(x[5], y[6]) + mul32x32_64(x[6], y[5]) + mul32x32_64(x[7], y[4]) + mul32x32_64(x[8], y[3]); + f = (bignum256modm_element_t)c; q1[2] = (q1[2] | (f << 22)) & 0x3fffffff; q1[3] = (f >> 8) & 0x3fffff; c >>= 30; + c += mul32x32_64(x[4], y[8]) + mul32x32_64(x[5], y[7]) + mul32x32_64(x[6], y[6]) + mul32x32_64(x[7], y[5]) + mul32x32_64(x[8], y[4]); + f = (bignum256modm_element_t)c; q1[3] = (q1[3] | (f << 22)) & 0x3fffffff; q1[4] = (f >> 8) & 0x3fffff; c >>= 30; + c += mul32x32_64(x[5], y[8]) + mul32x32_64(x[6], y[7]) + mul32x32_64(x[7], y[6]) + mul32x32_64(x[8], y[5]); + f = (bignum256modm_element_t)c; q1[4] = (q1[4] | (f << 22)) & 0x3fffffff; q1[5] = (f >> 8) & 0x3fffff; c >>= 30; + c += mul32x32_64(x[6], y[8]) + mul32x32_64(x[7], y[7]) + mul32x32_64(x[8], y[6]); + f = (bignum256modm_element_t)c; q1[5] = (q1[5] | (f << 22)) & 0x3fffffff; q1[6] = (f >> 8) & 0x3fffff; c >>= 30; + c += mul32x32_64(x[7], y[8]) + mul32x32_64(x[8], y[7]); + f = (bignum256modm_element_t)c; q1[6] = (q1[6] | (f << 22)) & 0x3fffffff; q1[7] = (f >> 8) & 0x3fffff; c >>= 30; + c += mul32x32_64(x[8], y[8]); + f = (bignum256modm_element_t)c; q1[7] = (q1[7] | (f << 22)) & 0x3fffffff; q1[8] = (f >> 8) & 0x3fffff; + + barrett_reduce256_modm(r, q1, r1); +} + +static void +expand256_modm(bignum256modm out, const unsigned char *in, size_t len) { + unsigned char work[64] = {0}; + bignum256modm_element_t x[16]; + bignum256modm q1; + + memcpy(work, in, len); + x[0] = U8TO32_LE(work + 0); + x[1] = U8TO32_LE(work + 4); + x[2] = U8TO32_LE(work + 8); + x[3] = U8TO32_LE(work + 12); + x[4] = U8TO32_LE(work + 16); + x[5] = U8TO32_LE(work + 20); + x[6] = U8TO32_LE(work + 24); + x[7] = U8TO32_LE(work + 28); + x[8] = U8TO32_LE(work + 32); + x[9] = U8TO32_LE(work + 36); + x[10] = U8TO32_LE(work + 40); + x[11] = U8TO32_LE(work + 44); + x[12] = U8TO32_LE(work + 48); + x[13] = U8TO32_LE(work + 52); + x[14] = U8TO32_LE(work + 56); + x[15] = U8TO32_LE(work + 60); + + /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) */ + out[0] = ( x[0]) & 0x3fffffff; + out[1] = ((x[ 0] >> 30) | (x[ 1] << 2)) & 0x3fffffff; + out[2] = ((x[ 1] >> 28) | (x[ 2] << 4)) & 0x3fffffff; + out[3] = ((x[ 2] >> 26) | (x[ 3] << 6)) & 0x3fffffff; + out[4] = ((x[ 3] >> 24) | (x[ 4] << 8)) & 0x3fffffff; + out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff; + out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff; + out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff; + out[8] = ((x[ 7] >> 16) | (x[ 8] << 16)) & 0x00ffffff; + + /* 8*31 = 248 bits, no need to reduce */ + if (len < 32) + return; + + /* q1 = x >> 248 = 264 bits = 9 30 bit elements */ + q1[0] = ((x[ 7] >> 24) | (x[ 8] << 8)) & 0x3fffffff; + q1[1] = ((x[ 8] >> 22) | (x[ 9] << 10)) & 0x3fffffff; + q1[2] = ((x[ 9] >> 20) | (x[10] << 12)) & 0x3fffffff; + q1[3] = ((x[10] >> 18) | (x[11] << 14)) & 0x3fffffff; + q1[4] = ((x[11] >> 16) | (x[12] << 16)) & 0x3fffffff; + q1[5] = ((x[12] >> 14) | (x[13] << 18)) & 0x3fffffff; + q1[6] = ((x[13] >> 12) | (x[14] << 20)) & 0x3fffffff; + q1[7] = ((x[14] >> 10) | (x[15] << 22)) & 0x3fffffff; + q1[8] = ((x[15] >> 8) ); + + barrett_reduce256_modm(out, q1, out); +} + +static void +expand_raw256_modm(bignum256modm out, const unsigned char in[32]) { + bignum256modm_element_t x[8]; + + x[0] = U8TO32_LE(in + 0); + x[1] = U8TO32_LE(in + 4); + x[2] = U8TO32_LE(in + 8); + x[3] = U8TO32_LE(in + 12); + x[4] = U8TO32_LE(in + 16); + x[5] = U8TO32_LE(in + 20); + x[6] = U8TO32_LE(in + 24); + x[7] = U8TO32_LE(in + 28); + + out[0] = ( x[0]) & 0x3fffffff; + out[1] = ((x[ 0] >> 30) | (x[ 1] << 2)) & 0x3fffffff; + out[2] = ((x[ 1] >> 28) | (x[ 2] << 4)) & 0x3fffffff; + out[3] = ((x[ 2] >> 26) | (x[ 3] << 6)) & 0x3fffffff; + out[4] = ((x[ 3] >> 24) | (x[ 4] << 8)) & 0x3fffffff; + out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff; + out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff; + out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff; + out[8] = ((x[ 7] >> 16) ) & 0x0000ffff; +} + +static void +contract256_modm(unsigned char out[32], const bignum256modm in) { + U32TO8_LE(out + 0, (in[0] ) | (in[1] << 30)); + U32TO8_LE(out + 4, (in[1] >> 2) | (in[2] << 28)); + U32TO8_LE(out + 8, (in[2] >> 4) | (in[3] << 26)); + U32TO8_LE(out + 12, (in[3] >> 6) | (in[4] << 24)); + U32TO8_LE(out + 16, (in[4] >> 8) | (in[5] << 22)); + U32TO8_LE(out + 20, (in[5] >> 10) | (in[6] << 20)); + U32TO8_LE(out + 24, (in[6] >> 12) | (in[7] << 18)); + U32TO8_LE(out + 28, (in[7] >> 14) | (in[8] << 16)); +} + + + +static void +contract256_window4_modm(signed char r[64], const bignum256modm in) { + char carry; + signed char *quads = r; + bignum256modm_element_t i, j, v; + + for (i = 0; i < 8; i += 2) { + v = in[i]; + for (j = 0; j < 7; j++) { + *quads++ = (v & 15); + v >>= 4; + } + v |= (in[i+1] << 2); + for (j = 0; j < 8; j++) { + *quads++ = (v & 15); + v >>= 4; + } + } + v = in[8]; + *quads++ = (v & 15); v >>= 4; + *quads++ = (v & 15); v >>= 4; + *quads++ = (v & 15); v >>= 4; + *quads++ = (v & 15); v >>= 4; + + /* making it signed */ + carry = 0; + for(i = 0; i < 63; i++) { + r[i] += carry; + r[i+1] += (r[i] >> 4); + r[i] &= 15; + carry = (r[i] >> 3); + r[i] -= (carry << 4); + } + r[63] += carry; +} + +static void +contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize) { + int i,j,k,b; + int m = (1 << (windowsize - 1)) - 1, soplen = 256; + signed char *bits = r; + bignum256modm_element_t v; + + /* first put the binary expansion into r */ + for (i = 0; i < 8; i++) { + v = s[i]; + for (j = 0; j < 30; j++, v >>= 1) + *bits++ = (v & 1); + } + v = s[8]; + for (j = 0; j < 16; j++, v >>= 1) + *bits++ = (v & 1); + + /* Making it sliding window */ + for (j = 0; j < soplen; j++) { + if (!r[j]) + continue; + + for (b = 1; (b < (soplen - j)) && (b <= 6); b++) { + if ((r[j] + (r[j + b] << b)) <= m) { + r[j] += r[j + b] << b; + r[j + b] = 0; + } else if ((r[j] - (r[j + b] << b)) >= -m) { + r[j] -= r[j + b] << b; + for (k = j + b; k < soplen; k++) { + if (!r[k]) { + r[k] = 1; + break; + } + r[k] = 0; + } + } else if (r[j + b]) { + break; + } + } + } +} + + +/* + helpers for batch verifcation, are allowed to be vartime +*/ + +/* out = a - b, a must be larger than b */ +static void +sub256_modm_batch(bignum256modm out, const bignum256modm a, const bignum256modm b, size_t limbsize) { + size_t i = 0; + bignum256modm_element_t carry = 0; + switch (limbsize) { + case 8: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++; + case 7: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++; + case 6: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++; + case 5: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++; + case 4: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++; + case 3: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++; + case 2: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++; + case 1: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++; + case 0: + default: out[i] = (a[i] - b[i]) - carry; + } +} + + +/* is a < b */ +static int +lt256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) { + switch (limbsize) { + case 8: if (a[8] > b[8]) return 0; if (a[8] < b[8]) return 1; + case 7: if (a[7] > b[7]) return 0; if (a[7] < b[7]) return 1; + case 6: if (a[6] > b[6]) return 0; if (a[6] < b[6]) return 1; + case 5: if (a[5] > b[5]) return 0; if (a[5] < b[5]) return 1; + case 4: if (a[4] > b[4]) return 0; if (a[4] < b[4]) return 1; + case 3: if (a[3] > b[3]) return 0; if (a[3] < b[3]) return 1; + case 2: if (a[2] > b[2]) return 0; if (a[2] < b[2]) return 1; + case 1: if (a[1] > b[1]) return 0; if (a[1] < b[1]) return 1; + case 0: if (a[0] > b[0]) return 0; if (a[0] < b[0]) return 1; + } + return 0; +} + +/* is a <= b */ +static int +lte256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) { + switch (limbsize) { + case 8: if (a[8] > b[8]) return 0; if (a[8] < b[8]) return 1; + case 7: if (a[7] > b[7]) return 0; if (a[7] < b[7]) return 1; + case 6: if (a[6] > b[6]) return 0; if (a[6] < b[6]) return 1; + case 5: if (a[5] > b[5]) return 0; if (a[5] < b[5]) return 1; + case 4: if (a[4] > b[4]) return 0; if (a[4] < b[4]) return 1; + case 3: if (a[3] > b[3]) return 0; if (a[3] < b[3]) return 1; + case 2: if (a[2] > b[2]) return 0; if (a[2] < b[2]) return 1; + case 1: if (a[1] > b[1]) return 0; if (a[1] < b[1]) return 1; + case 0: if (a[0] > b[0]) return 0; if (a[0] < b[0]) return 1; + } + return 1; +} + + +/* is a == 0 */ +static int +iszero256_modm_batch(const bignum256modm a) { + size_t i; + for (i = 0; i < 9; i++) + if (a[i]) + return 0; + return 1; +} + +/* is a == 1 */ +static int +isone256_modm_batch(const bignum256modm a) { + size_t i; + if (a[0] != 1) + return 0; + for (i = 1; i < 9; i++) + if (a[i]) + return 0; + return 1; +} + +/* can a fit in to (at most) 128 bits */ +static int +isatmost128bits256_modm_batch(const bignum256modm a) { + uint32_t mask = + ((a[8] ) | /* 16 */ + (a[7] ) | /* 46 */ + (a[6] ) | /* 76 */ + (a[5] ) | /* 106 */ + (a[4] & 0x3fffff00)); /* 128 */ + + return (mask == 0); +} diff --git a/src/ext/ed25519/donna/modm-donna-64bit.h b/src/ext/ed25519/donna/modm-donna-64bit.h new file mode 100644 index 0000000..a47a38a --- /dev/null +++ b/src/ext/ed25519/donna/modm-donna-64bit.h @@ -0,0 +1,361 @@ +/* + Public domain by Andrew M. liquidsun@gmail.com +*/ + + +/* + Arithmetic modulo the group order n = 2^252 + 27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989 + + k = 32 + b = 1 << 8 = 256 + m = 2^252 + 27742317777372353535851937790883648493 = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed + mu = floor( b^(k*2) / m ) = 0xfffffffffffffffffffffffffffffffeb2106215d086329a7ed9ce5a30a2c131b +*/ + +#define bignum256modm_bits_per_limb 56 +#define bignum256modm_limb_size 5 + +typedef uint64_t bignum256modm_element_t; +typedef bignum256modm_element_t bignum256modm[5]; + +static const bignum256modm modm_m = { + 0x12631a5cf5d3ed, + 0xf9dea2f79cd658, + 0x000000000014de, + 0x00000000000000, + 0x00000010000000 +}; + +static const bignum256modm modm_mu = { + 0x9ce5a30a2c131b, + 0x215d086329a7ed, + 0xffffffffeb2106, + 0xffffffffffffff, + 0x00000fffffffff +}; + +static bignum256modm_element_t +lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) { + return (a - b) >> 63; +} + +static void +reduce256_modm(bignum256modm r) { + bignum256modm t; + bignum256modm_element_t b = 0, pb, mask; + + /* t = r - m */ + pb = 0; + pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 56)); pb = b; + pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 56)); pb = b; + pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 56)); pb = b; + pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 56)); pb = b; + pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 32)); + + /* keep r if r was smaller than m */ + mask = b - 1; + + r[0] ^= mask & (r[0] ^ t[0]); + r[1] ^= mask & (r[1] ^ t[1]); + r[2] ^= mask & (r[2] ^ t[2]); + r[3] ^= mask & (r[3] ^ t[3]); + r[4] ^= mask & (r[4] ^ t[4]); +} + +static void +barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) { + bignum256modm q3, r2; + uint128_t c, mul; + bignum256modm_element_t f, b, pb; + + /* q1 = x >> 248 = 264 bits = 5 56 bit elements + q2 = mu * q1 + q3 = (q2 / 256(32+1)) = q2 / (2^8)^(32+1) = q2 >> 264 */ + mul64x64_128(c, modm_mu[0], q1[3]) mul64x64_128(mul, modm_mu[3], q1[0]) add128(c, mul) mul64x64_128(mul, modm_mu[1], q1[2]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[1]) add128(c, mul) shr128(f, c, 56); + mul64x64_128(c, modm_mu[0], q1[4]) add128_64(c, f) mul64x64_128(mul, modm_mu[4], q1[0]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[1]) add128(c, mul) mul64x64_128(mul, modm_mu[1], q1[3]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[2]) add128(c, mul) + f = lo128(c); q3[0] = (f >> 40) & 0xffff; shr128(f, c, 56); + mul64x64_128(c, modm_mu[4], q1[1]) add128_64(c, f) mul64x64_128(mul, modm_mu[1], q1[4]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[3]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[2]) add128(c, mul) + f = lo128(c); q3[0] |= (f << 16) & 0xffffffffffffff; q3[1] = (f >> 40) & 0xffff; shr128(f, c, 56); + mul64x64_128(c, modm_mu[4], q1[2]) add128_64(c, f) mul64x64_128(mul, modm_mu[2], q1[4]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[3]) add128(c, mul) + f = lo128(c); q3[1] |= (f << 16) & 0xffffffffffffff; q3[2] = (f >> 40) & 0xffff; shr128(f, c, 56); + mul64x64_128(c, modm_mu[4], q1[3]) add128_64(c, f) mul64x64_128(mul, modm_mu[3], q1[4]) add128(c, mul) + f = lo128(c); q3[2] |= (f << 16) & 0xffffffffffffff; q3[3] = (f >> 40) & 0xffff; shr128(f, c, 56); + mul64x64_128(c, modm_mu[4], q1[4]) add128_64(c, f) + f = lo128(c); q3[3] |= (f << 16) & 0xffffffffffffff; q3[4] = (f >> 40) & 0xffff; shr128(f, c, 56); + q3[4] |= (f << 16); + + mul64x64_128(c, modm_m[0], q3[0]) + r2[0] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56); + mul64x64_128(c, modm_m[0], q3[1]) add128_64(c, f) mul64x64_128(mul, modm_m[1], q3[0]) add128(c, mul) + r2[1] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56); + mul64x64_128(c, modm_m[0], q3[2]) add128_64(c, f) mul64x64_128(mul, modm_m[2], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[1]) add128(c, mul) + r2[2] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56); + mul64x64_128(c, modm_m[0], q3[3]) add128_64(c, f) mul64x64_128(mul, modm_m[3], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[2]) add128(c, mul) mul64x64_128(mul, modm_m[2], q3[1]) add128(c, mul) + r2[3] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56); + mul64x64_128(c, modm_m[0], q3[4]) add128_64(c, f) mul64x64_128(mul, modm_m[4], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[3], q3[1]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[3]) add128(c, mul) mul64x64_128(mul, modm_m[2], q3[2]) add128(c, mul) + r2[4] = lo128(c) & 0x0000ffffffffff; + + pb = 0; + pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 56)); pb = b; + pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 56)); pb = b; + pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 56)); pb = b; + pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 56)); pb = b; + pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 40)); + + reduce256_modm(r); + reduce256_modm(r); +} + + +static void +add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) { + bignum256modm_element_t c; + + c = x[0] + y[0]; r[0] = c & 0xffffffffffffff; c >>= 56; + c += x[1] + y[1]; r[1] = c & 0xffffffffffffff; c >>= 56; + c += x[2] + y[2]; r[2] = c & 0xffffffffffffff; c >>= 56; + c += x[3] + y[3]; r[3] = c & 0xffffffffffffff; c >>= 56; + c += x[4] + y[4]; r[4] = c; + + reduce256_modm(r); +} + +static void +mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) { + bignum256modm q1, r1; + uint128_t c, mul; + bignum256modm_element_t f; + + mul64x64_128(c, x[0], y[0]) + f = lo128(c); r1[0] = f & 0xffffffffffffff; shr128(f, c, 56); + mul64x64_128(c, x[0], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[0]) add128(c, mul) + f = lo128(c); r1[1] = f & 0xffffffffffffff; shr128(f, c, 56); + mul64x64_128(c, x[0], y[2]) add128_64(c, f) mul64x64_128(mul, x[2], y[0]) add128(c, mul) mul64x64_128(mul, x[1], y[1]) add128(c, mul) + f = lo128(c); r1[2] = f & 0xffffffffffffff; shr128(f, c, 56); + mul64x64_128(c, x[0], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[0]) add128(c, mul) mul64x64_128(mul, x[1], y[2]) add128(c, mul) mul64x64_128(mul, x[2], y[1]) add128(c, mul) + f = lo128(c); r1[3] = f & 0xffffffffffffff; shr128(f, c, 56); + mul64x64_128(c, x[0], y[4]) add128_64(c, f) mul64x64_128(mul, x[4], y[0]) add128(c, mul) mul64x64_128(mul, x[3], y[1]) add128(c, mul) mul64x64_128(mul, x[1], y[3]) add128(c, mul) mul64x64_128(mul, x[2], y[2]) add128(c, mul) + f = lo128(c); r1[4] = f & 0x0000ffffffffff; q1[0] = (f >> 24) & 0xffffffff; shr128(f, c, 56); + mul64x64_128(c, x[4], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[4]) add128(c, mul) mul64x64_128(mul, x[2], y[3]) add128(c, mul) mul64x64_128(mul, x[3], y[2]) add128(c, mul) + f = lo128(c); q1[0] |= (f << 32) & 0xffffffffffffff; q1[1] = (f >> 24) & 0xffffffff; shr128(f, c, 56); + mul64x64_128(c, x[4], y[2]) add128_64(c, f) mul64x64_128(mul, x[2], y[4]) add128(c, mul) mul64x64_128(mul, x[3], y[3]) add128(c, mul) + f = lo128(c); q1[1] |= (f << 32) & 0xffffffffffffff; q1[2] = (f >> 24) & 0xffffffff; shr128(f, c, 56); + mul64x64_128(c, x[4], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[4]) add128(c, mul) + f = lo128(c); q1[2] |= (f << 32) & 0xffffffffffffff; q1[3] = (f >> 24) & 0xffffffff; shr128(f, c, 56); + mul64x64_128(c, x[4], y[4]) add128_64(c, f) + f = lo128(c); q1[3] |= (f << 32) & 0xffffffffffffff; q1[4] = (f >> 24) & 0xffffffff; shr128(f, c, 56); + q1[4] |= (f << 32); + + barrett_reduce256_modm(r, q1, r1); +} + +static void +expand256_modm(bignum256modm out, const unsigned char *in, size_t len) { + unsigned char work[64] = {0}; + bignum256modm_element_t x[16]; + bignum256modm q1; + + memcpy(work, in, len); + x[0] = U8TO64_LE(work + 0); + x[1] = U8TO64_LE(work + 8); + x[2] = U8TO64_LE(work + 16); + x[3] = U8TO64_LE(work + 24); + x[4] = U8TO64_LE(work + 32); + x[5] = U8TO64_LE(work + 40); + x[6] = U8TO64_LE(work + 48); + x[7] = U8TO64_LE(work + 56); + + /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) */ + out[0] = ( x[0]) & 0xffffffffffffff; + out[1] = ((x[ 0] >> 56) | (x[ 1] << 8)) & 0xffffffffffffff; + out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff; + out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff; + out[4] = ((x[ 3] >> 32) | (x[ 4] << 32)) & 0x0000ffffffffff; + + /* under 252 bits, no need to reduce */ + if (len < 32) + return; + + /* q1 = x >> 248 = 264 bits */ + q1[0] = ((x[ 3] >> 56) | (x[ 4] << 8)) & 0xffffffffffffff; + q1[1] = ((x[ 4] >> 48) | (x[ 5] << 16)) & 0xffffffffffffff; + q1[2] = ((x[ 5] >> 40) | (x[ 6] << 24)) & 0xffffffffffffff; + q1[3] = ((x[ 6] >> 32) | (x[ 7] << 32)) & 0xffffffffffffff; + q1[4] = ((x[ 7] >> 24) ); + + barrett_reduce256_modm(out, q1, out); +} + +static void +expand_raw256_modm(bignum256modm out, const unsigned char in[32]) { + bignum256modm_element_t x[4]; + + x[0] = U8TO64_LE(in + 0); + x[1] = U8TO64_LE(in + 8); + x[2] = U8TO64_LE(in + 16); + x[3] = U8TO64_LE(in + 24); + + out[0] = ( x[0]) & 0xffffffffffffff; + out[1] = ((x[ 0] >> 56) | (x[ 1] << 8)) & 0xffffffffffffff; + out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff; + out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff; + out[4] = ((x[ 3] >> 32) ) & 0x000000ffffffff; +} + +static void +contract256_modm(unsigned char out[32], const bignum256modm in) { + U64TO8_LE(out + 0, (in[0] ) | (in[1] << 56)); + U64TO8_LE(out + 8, (in[1] >> 8) | (in[2] << 48)); + U64TO8_LE(out + 16, (in[2] >> 16) | (in[3] << 40)); + U64TO8_LE(out + 24, (in[3] >> 24) | (in[4] << 32)); +} + +static void +contract256_window4_modm(signed char r[64], const bignum256modm in) { + char carry; + signed char *quads = r; + bignum256modm_element_t i, j, v, m; + + for (i = 0; i < 5; i++) { + v = in[i]; + m = (i == 4) ? 8 : 14; + for (j = 0; j < m; j++) { + *quads++ = (v & 15); + v >>= 4; + } + } + + /* making it signed */ + carry = 0; + for(i = 0; i < 63; i++) { + r[i] += carry; + r[i+1] += (r[i] >> 4); + r[i] &= 15; + carry = (r[i] >> 3); + r[i] -= (carry << 4); + } + r[63] += carry; +} + +static void +contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize) { + int i,j,k,b; + int m = (1 << (windowsize - 1)) - 1, soplen = 256; + signed char *bits = r; + bignum256modm_element_t v; + + /* first put the binary expansion into r */ + for (i = 0; i < 4; i++) { + v = s[i]; + for (j = 0; j < 56; j++, v >>= 1) + *bits++ = (v & 1); + } + v = s[4]; + for (j = 0; j < 32; j++, v >>= 1) + *bits++ = (v & 1); + + /* Making it sliding window */ + for (j = 0; j < soplen; j++) { + if (!r[j]) + continue; + + for (b = 1; (b < (soplen - j)) && (b <= 6); b++) { + if ((r[j] + (r[j + b] << b)) <= m) { + r[j] += r[j + b] << b; + r[j + b] = 0; + } else if ((r[j] - (r[j + b] << b)) >= -m) { + r[j] -= r[j + b] << b; + for (k = j + b; k < soplen; k++) { + if (!r[k]) { + r[k] = 1; + break; + } + r[k] = 0; + } + } else if (r[j + b]) { + break; + } + } + } +} + +/* + helpers for batch verifcation, are allowed to be vartime +*/ + +/* out = a - b, a must be larger than b */ +static void +sub256_modm_batch(bignum256modm out, const bignum256modm a, const bignum256modm b, size_t limbsize) { + size_t i = 0; + bignum256modm_element_t carry = 0; + switch (limbsize) { + case 4: out[i] = (a[i] - b[i]) ; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++; + case 3: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++; + case 2: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++; + case 1: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++; + case 0: + default: out[i] = (a[i] - b[i]) - carry; + } +} + + +/* is a < b */ +static int +lt256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) { + size_t i = 0; + bignum256modm_element_t t, carry = 0; + switch (limbsize) { + case 4: t = (a[i] - b[i]) ; carry = (t >> 63); i++; + case 3: t = (a[i] - b[i]) - carry; carry = (t >> 63); i++; + case 2: t = (a[i] - b[i]) - carry; carry = (t >> 63); i++; + case 1: t = (a[i] - b[i]) - carry; carry = (t >> 63); i++; + case 0: t = (a[i] - b[i]) - carry; carry = (t >> 63); + } + return (int)carry; +} + +/* is a <= b */ +static int +lte256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) { + size_t i = 0; + bignum256modm_element_t t, carry = 0; + switch (limbsize) { + case 4: t = (b[i] - a[i]) ; carry = (t >> 63); i++; + case 3: t = (b[i] - a[i]) - carry; carry = (t >> 63); i++; + case 2: t = (b[i] - a[i]) - carry; carry = (t >> 63); i++; + case 1: t = (b[i] - a[i]) - carry; carry = (t >> 63); i++; + case 0: t = (b[i] - a[i]) - carry; carry = (t >> 63); + } + return (int)!carry; +} + +/* is a == 0 */ +static int +iszero256_modm_batch(const bignum256modm a) { + size_t i; + for (i = 0; i < 5; i++) + if (a[i]) + return 0; + return 1; +} + +/* is a == 1 */ +static int +isone256_modm_batch(const bignum256modm a) { + size_t i; + for (i = 0; i < 5; i++) + if (a[i] != ((i) ? 0 : 1)) + return 0; + return 1; +} + +/* can a fit in to (at most) 128 bits */ +static int +isatmost128bits256_modm_batch(const bignum256modm a) { + uint64_t mask = + ((a[4] ) | /* 32 */ + (a[3] ) | /* 88 */ + (a[2] & 0xffffffffff0000)); + + return (mask == 0); +} diff --git a/src/ext/ed25519/donna/regression.h b/src/ext/ed25519/donna/regression.h new file mode 100644 index 0000000..b4c2e62 --- /dev/null +++ b/src/ext/ed25519/donna/regression.h @@ -0,0 +1,1024 @@ 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+#include "ed25519-donna.h" + +static int +test_adds() { +#if defined(HAVE_UINT128) && !defined(ED25519_SSE2) + /* largest result for each limb from a mult or square: all elements except r1 reduced, r1 overflowed as far as possible */ + static const bignum25519 max_bignum = { + 0x7ffffffffffff,0x8000000001230,0x7ffffffffffff,0x7ffffffffffff,0x7ffffffffffff + }; + + /* what max_bignum should fully reduce to */ + static const unsigned char max_bignum_raw[32] = { + 0x12,0x00,0x00,0x00,0x00,0x00,0x88,0x91,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00 + }; + + /* (max_bignum + max_bignum)^2 */ + static const unsigned char max_bignum2_squared_raw[32] = { + 0x10,0x05,0x00,0x00,0x00,0x00,0x80,0xdc,0x51,0x00,0x00,0x00,0x00,0x61,0xed,0x4a, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + }; + + /* ((max_bignum + max_bignum) + max_bignum)^2 */ + static const unsigned char max_bignum3_squared_raw[32] = { + 0x64,0x0b,0x00,0x00,0x00,0x00,0x20,0x30,0xb8,0x00,0x00,0x00,0x40,0x1a,0x96,0xe8, + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + }; +#else + /* largest result for each limb from a mult or square: all elements except r1 reduced, r1 overflowed as far as possible */ + static const bignum25519 ALIGN(16) max_bignum = { + 0x3ffffff,0x2000300,0x3ffffff,0x1ffffff,0x3ffffff, + 0x1ffffff,0x3ffffff,0x1ffffff,0x3ffffff,0x1ffffff + }; + + /* what max_bignum should fully reduce to */ + static const unsigned char max_bignum2_squared_raw[32] = { + 0x10,0x05,0x00,0x40,0xc2,0x06,0x40,0x80,0x41,0x02,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + }; + + /* (max_bignum * max_bignum) */ + static const unsigned char max_bignum3_squared_raw[32] = { + 0x64,0x0b,0x00,0x10,0x35,0x0f,0x90,0x60,0x13,0x05,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + }; +#endif + unsigned char result[32]; + static const bignum25519 ALIGN(16) zero = {0}; + bignum25519 ALIGN(16) a, b, c; + size_t i; + + /* a = (max_bignum + max_bignum) */ + curve25519_add(a, max_bignum, max_bignum); + + /* b = ((max_bignum + max_bignum) * (max_bignum + max_bignum)) */ + curve25519_mul(b, a, a); + curve25519_contract(result, b); + if (memcmp(result, max_bignum2_squared_raw, 32) != 0) + return -1; + curve25519_square(b, a); + curve25519_contract(result, b); + if (memcmp(result, max_bignum2_squared_raw, 32) != 0) + return -1; + + /* b = (max_bignum + max_bignum + max_bignum) */ + curve25519_add_after_basic(b, a, max_bignum); + + /* a = ((max_bignum + max_bignum + max_bignum) * (max_bignum + max_bignum + max_bignum)) */ + curve25519_mul(a, b, b); + curve25519_contract(result, a); + if (memcmp(result, max_bignum3_squared_raw, 32) != 0) + return -1; + curve25519_square(a, b); + curve25519_contract(result, a); + if (memcmp(result, max_bignum3_squared_raw, 32) != 0) + return -1; + + return 0; +} + +static int +test_subs() { +#if defined(HAVE_UINT128) && !defined(ED25519_SSE2) + /* largest result for each limb from a mult or square: all elements except r1 reduced, r1 overflowed as far as possible */ + static const bignum25519 max_bignum = { + 0x7ffffffffffff,0x8000000001230,0x7ffffffffffff,0x7ffffffffffff,0x7ffffffffffff + }; + + /* what max_bignum should fully reduce to */ + static const unsigned char max_bignum_raw[32] = { + 0x12,0x00,0x00,0x00,0x00,0x00,0x88,0x91,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00 + }; + + /* (max_bignum * max_bignum) */ + static const unsigned char max_bignum_squared_raw[32] = { + 0x44,0x01,0x00,0x00,0x00,0x00,0x20,0x77,0x14,0x00,0x00,0x00,0x40,0x58,0xbb,0x52, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00 + }; +#else + /* largest result for each limb from a mult or square: all elements except r1 reduced, r1 overflowed as far as possible */ + static const bignum25519 ALIGN(16) max_bignum = { + 0x3ffffff,0x2000300,0x3ffffff,0x1ffffff,0x3ffffff, + 0x1ffffff,0x3ffffff,0x1ffffff,0x3ffffff,0x1ffffff + }; + + /* what max_bignum should fully reduce to */ + static const unsigned char max_bignum_raw[32] = { + 0x12,0x00,0x00,0x04,0x0c,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + }; + + /* (max_bignum * max_bignum) */ + static const unsigned char max_bignum_squared_raw[32] = { + 0x44,0x01,0x00,0x90,0xb0,0x01,0x10,0x60,0x90,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + }; +#endif + unsigned char result[32]; + static const bignum25519 ALIGN(16) zero = {0}; + bignum25519 ALIGN(16) a, b, c; + size_t i; + + /* a = max_bignum - 0, which expands to 2p + max_bignum - 0 */ + curve25519_sub(a, max_bignum, zero); + curve25519_contract(result, a); + if (memcmp(result, max_bignum_raw, 32) != 0) + return -1; + + /* b = (max_bignum * max_bignum) */ + curve25519_mul(b, a, a); + curve25519_contract(result, b); + if (memcmp(result, max_bignum_squared_raw, 32) != 0) + return -1; + curve25519_square(b, a); + curve25519_contract(result, b); + if (memcmp(result, max_bignum_squared_raw, 32) != 0) + return -1; + + /* b = ((a - 0) - 0) */ + curve25519_sub_after_basic(b, a, zero); + curve25519_contract(result, b); + if (memcmp(result, max_bignum_raw, 32) != 0) + return -1; + + /* a = (max_bignum * max_bignum) */ + curve25519_mul(a, b, b); + curve25519_contract(result, a); + if (memcmp(result, max_bignum_squared_raw, 32) != 0) + return -1; + curve25519_square(a, b); + curve25519_contract(result, a); + if (memcmp(result, max_bignum_squared_raw, 32) != 0) + return -1; + + + return 0; +} + + +int +main() { + int ret = 0; + int single; + single = test_adds(); + if (single) printf("test_adds: FAILED\n"); + ret |= single; + single = test_subs(); + if (single) printf("test_subs: FAILED\n"); + ret |= single; + if (!ret) printf("success\n"); + return ret; +} + + diff --git a/src/ext/ed25519/donna/test-ticks.h b/src/ext/ed25519/donna/test-ticks.h new file mode 100644 index 0000000..0103e03 --- /dev/null +++ b/src/ext/ed25519/donna/test-ticks.h @@ -0,0 +1,50 @@ +#include "ed25519-donna-portable-identify.h" + +/* ticks - not tested on anything other than x86 */ +static uint64_t +get_ticks(void) { +#if defined(CPU_X86) || defined(CPU_X86_64) + #if defined(COMPILER_INTEL) + return _rdtsc(); + #elif defined(COMPILER_MSVC) + return __rdtsc(); + #elif defined(COMPILER_GCC) + uint32_t lo, hi; + __asm__ __volatile__("rdtsc" : "=a" (lo), "=d" (hi)); + return ((uint64_t)lo | ((uint64_t)hi << 32)); + #else + need rdtsc for this compiler + #endif +#elif defined(OS_SOLARIS) + return (uint64_t)gethrtime(); +#elif defined(CPU_SPARC) && !defined(OS_OPENBSD) + uint64_t t; + __asm__ __volatile__("rd %%tick, %0" : "=r" (t)); + return t; +#elif defined(CPU_PPC) + uint32_t lo = 0, hi = 0; + __asm__ __volatile__("mftbu %0; mftb %1" : "=r" (hi), "=r" (lo)); + return ((uint64_t)lo | ((uint64_t)hi << 32)); +#elif defined(CPU_IA64) + uint64_t t; + __asm__ __volatile__("mov %0=ar.itc" : "=r" (t)); + return t; +#elif defined(OS_NIX) + timeval t2; + gettimeofday(&t2, NULL); + t = ((uint64_t)t2.tv_usec << 32) | (uint64_t)t2.tv_sec; + return t; +#else + need ticks for this platform +#endif +} + +#define timeit(x,minvar) \ + ticks = get_ticks(); \ + x; \ + ticks = get_ticks() - ticks; \ + if (ticks < minvar) \ + minvar = ticks; + +#define maxticks 0xffffffffffffffffull + diff --git a/src/ext/ed25519/donna/test.c b/src/ext/ed25519/donna/test.c new file mode 100644 index 0000000..6154492 --- /dev/null +++ b/src/ext/ed25519/donna/test.c @@ -0,0 +1,260 @@ +/* + Validate ed25519 implementation against the official test vectors from + http://ed25519.cr.yp.to/software.html +*/ + +#include <stdio.h> +#include <string.h> +#include "ed25519.h" + +#include "test-ticks.h" + +static void +edassert(int check, int round, const char *failreason) { + if (check) + return; + printf("round %d, %s\n", round, failreason); + exit(1); +} + +static void +edassert_die(const unsigned char *a, const unsigned char *b, size_t len, int round, const char *failreason) { + size_t i; + if (round > 0) + printf("round %d, %s\n", round, failreason); + else + printf("%s\n", failreason); + printf("want: "); for (i = 0; i < len; i++) printf("%02x,", a[i]); printf("\n"); + printf("got : "); for (i = 0; i < len; i++) printf("%02x,", b[i]); printf("\n"); + printf("diff: "); for (i = 0; i < len; i++) if (a[i] ^ b[i]) printf("%02x,", a[i] ^ b[i]); else printf(" ,"); printf("\n\n"); + exit(1); +} + +static void +edassert_equal(const unsigned char *a, const unsigned char *b, size_t len, const char *failreason) { + if (memcmp(a, b, len) == 0) + return; + edassert_die(a, b, len, -1, failreason); +} + +static void +edassert_equal_round(const unsigned char *a, const unsigned char *b, size_t len, int round, const char *failreason) { + if (memcmp(a, b, len) == 0) + return; + edassert_die(a, b, len, round, failreason); +} + + +/* test data */ +typedef struct test_data_t { + unsigned char sk[32], pk[32], sig[64]; + const char *m; +} test_data; + + +test_data dataset[] = { +#include "regression.h" +}; + +/* result of the curve25519 scalarmult ((|255| * basepoint) * basepoint)... 1024 times */ +const curved25519_key curved25519_expected = { + 0xac,0xce,0x24,0xb1,0xd4,0xa2,0x36,0x21, + 0x15,0xe2,0x3e,0x84,0x3c,0x23,0x2b,0x5f, + 0x95,0x6c,0xc0,0x7b,0x95,0x82,0xd7,0x93, + 0xd5,0x19,0xb6,0xf1,0xfb,0x96,0xd6,0x04 +}; + + +/* from ed25519-donna-batchverify.h */ +extern unsigned char batch_point_buffer[3][32]; + +/* y coordinate of the final point from 'amd64-51-30k' with the same random generator */ +static const unsigned char batch_verify_y[32] = { + 0x51,0xe7,0x68,0xe0,0xf7,0xa1,0x88,0x45, + 0xde,0xa1,0xcb,0xd9,0x37,0xd4,0x78,0x53, + 0x1b,0x95,0xdb,0xbe,0x66,0x59,0x29,0x3b, + 0x94,0x51,0x2f,0xbc,0x0d,0x66,0xba,0x3f +}; + +/* +static const unsigned char batch_verify_y[32] = { + 0x5c,0x63,0x96,0x26,0xca,0xfe,0xfd,0xc4, + 0x2d,0x11,0xa8,0xe4,0xc4,0x46,0x42,0x97, + 0x97,0x92,0xbe,0xe0,0x3c,0xef,0x96,0x01, + 0x50,0xa1,0xcc,0x8f,0x50,0x85,0x76,0x7d +}; + +Introducing the 128 bit r scalars to the heap _before_ the largest scalar +fits in to 128 bits alters the heap shape and produces a different, +yet still neutral/valid y/z value. + +This was the value of introducing the r scalars when the largest scalar fit +in to 135-256 bits. You can produce it with amd64-64-24k / amd64-51-32k +with the random sequence used in the first pass by changing + + unsigned long long hlen=((npoints+1)/2)|1; + +to + + unsigned long long hlen=npoints; + +in ge25519_multi_scalarmult.c + +ed25519-donna-batchverify.h has been modified to match the +default amd64-64-24k / amd64-51-32k behaviour +*/ + + + +/* batch test */ +#define test_batch_count 64 +#define test_batch_rounds 96 + +typedef enum batch_test_t { + batch_no_errors = 0, + batch_wrong_message = 1, + batch_wrong_pk = 2, + batch_wrong_sig = 3 +} batch_test; + +static int +test_batch_instance(batch_test type, uint64_t *ticks) { + ed25519_secret_key sks[test_batch_count]; + ed25519_public_key pks[test_batch_count]; + ed25519_signature sigs[test_batch_count]; + unsigned char messages[test_batch_count][128]; + size_t message_lengths[test_batch_count]; + const unsigned char *message_pointers[test_batch_count]; + const unsigned char *pk_pointers[test_batch_count]; + const unsigned char *sig_pointers[test_batch_count]; + int valid[test_batch_count], ret, validret; + size_t i; + uint64_t t; + + /* generate keys */ + for (i = 0; i < test_batch_count; i++) { + ed25519_randombytes_unsafe(sks[i], sizeof(sks[i])); + ed25519_publickey(sks[i], pks[i]); + pk_pointers[i] = pks[i]; + } + + /* generate messages */ + ed25519_randombytes_unsafe(messages, sizeof(messages)); + for (i = 0; i < test_batch_count; i++) { + message_pointers[i] = messages[i]; + message_lengths[i] = (i & 127) + 1; + } + + /* sign messages */ + for (i = 0; i < test_batch_count; i++) { + ed25519_sign(message_pointers[i], message_lengths[i], sks[i], pks[i], sigs[i]); + sig_pointers[i] = sigs[i]; + } + + validret = 0; + if (type == batch_wrong_message) { + message_pointers[0] = message_pointers[1]; + validret = 1|2; + } else if (type == batch_wrong_pk) { + pk_pointers[0] = pk_pointers[1]; + validret = 1|2; + } else if (type == batch_wrong_sig) { + sig_pointers[0] = sig_pointers[1]; + validret = 1|2; + } + + /* batch verify */ + t = get_ticks(); + ret = ed25519_sign_open_batch(message_pointers, message_lengths, pk_pointers, sig_pointers, test_batch_count, valid); + *ticks = get_ticks() - t; + edassert_equal((unsigned char *)&validret, (unsigned char *)&ret, sizeof(int), "batch return code"); + for (i = 0; i < test_batch_count; i++) { + validret = ((type == batch_no_errors) || (i != 0)) ? 1 : 0; + edassert_equal((unsigned char *)&validret, (unsigned char *)&valid[i], sizeof(int), "individual batch return code"); + } + return ret; +} + +static void +test_batch(void) { + uint64_t dummy_ticks, ticks[test_batch_rounds], best = maxticks, sum; + size_t i, count; + + /* check the first pass for the expected result */ + test_batch_instance(batch_no_errors, &dummy_ticks); + edassert_equal(batch_verify_y, batch_point_buffer[1], 32, "failed to generate expected result"); + + /* make sure ge25519_multi_scalarmult_vartime throws an error on the entire batch with wrong data */ + for (i = 0; i < 4; i++) { + test_batch_instance(batch_wrong_message, &dummy_ticks); + test_batch_instance(batch_wrong_pk, &dummy_ticks); + test_batch_instance(batch_wrong_sig, &dummy_ticks); + } + + /* speed test */ + for (i = 0; i < test_batch_rounds; i++) { + test_batch_instance(batch_no_errors, &ticks[i]); + if (ticks[i] < best) + best = ticks[i]; + } + + /* take anything within 1% of the best time */ + for (i = 0, sum = 0, count = 0; i < test_batch_rounds; i++) { + if (ticks[i] < (best * 1.01)) { + sum += ticks[i]; + count++; + } + } + printf("%.0f ticks/verification\n", (double)sum / (count * test_batch_count)); +} + +static void +test_main(void) { + int i, res; + ed25519_public_key pk; + ed25519_signature sig; + unsigned char forge[1024] = {'x'}; + curved25519_key csk[2] = {{255}}; + uint64_t ticks, pkticks = maxticks, signticks = maxticks, openticks = maxticks, curvedticks = maxticks; + + for (i = 0; i < 1024; i++) { + ed25519_publickey(dataset[i].sk, pk); + edassert_equal_round(dataset[i].pk, pk, sizeof(pk), i, "public key didn't match"); + ed25519_sign((unsigned char *)dataset[i].m, i, dataset[i].sk, pk, sig); + edassert_equal_round(dataset[i].sig, sig, sizeof(sig), i, "signature didn't match"); + edassert(!ed25519_sign_open((unsigned char *)dataset[i].m, i, pk, sig), i, "failed to open message"); + + memcpy(forge, dataset[i].m, i); + if (i) + forge[i - 1] += 1; + + edassert(ed25519_sign_open(forge, (i) ? i : 1, pk, sig), i, "opened forged message"); + } + + for (i = 0; i < 1024; i++) + curved25519_scalarmult_basepoint(csk[(i & 1) ^ 1], csk[i & 1]); + edassert_equal(curved25519_expected, csk[0], sizeof(curved25519_key), "curve25519 failed to generate correct value"); + + for (i = 0; i < 2048; i++) { + timeit(ed25519_publickey(dataset[0].sk, pk), pkticks) + edassert_equal_round(dataset[0].pk, pk, sizeof(pk), i, "public key didn't match"); + timeit(ed25519_sign((unsigned char *)dataset[0].m, 0, dataset[0].sk, pk, sig), signticks) + edassert_equal_round(dataset[0].sig, sig, sizeof(sig), i, "signature didn't match"); + timeit(res = ed25519_sign_open((unsigned char *)dataset[0].m, 0, pk, sig), openticks) + edassert(!res, 0, "failed to open message"); + timeit(curved25519_scalarmult_basepoint(csk[1], csk[0]), curvedticks); + } + + printf("%.0f ticks/public key generation\n", (double)pkticks); + printf("%.0f ticks/signature\n", (double)signticks); + printf("%.0f ticks/signature verification\n", (double)openticks); + printf("%.0f ticks/curve25519 basepoint scalarmult\n", (double)curvedticks); +} + +int +main(void) { + test_main(); + test_batch(); + return 0; +} +