tor-commits

Download

tor-commits@lists.torproject.org

September 2014

22 participants
980 discussions

[tor/master] Fix linux compilation of ed25519_ref10
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit 1d3b33e1ede15c787d0c2d1f8823cdad1a196008 Author: Nick Mathewson <nickm(a)torproject.org> Date: Wed Aug 27 20:12:57 2014 -0400 Fix linux compilation of ed25519_ref10 Our integer-definition headers apparently suck in a definition for select(2), which interferes with the select() in ge_scalarmult_base.c --- src/ext/ed25519/ref10/ge_scalarmult_base.c | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/src/ext/ed25519/ref10/ge_scalarmult_base.c b/src/ext/ed25519/ref10/ge_scalarmult_base.c index a55c3c4..ad7aae4 100644 --- a/src/ext/ed25519/ref10/ge_scalarmult_base.c +++ b/src/ext/ed25519/ref10/ge_scalarmult_base.c @@ -1,6 +1,10 @@ #include "ge.h" #include "crypto_uint32.h" +/* Rename this so as not to interfere with select() which torint.h apparently + * grabs. :p */ +#define select ed25519_ref10_select + static unsigned char equal(signed char b,signed char c) { unsigned char ub = b;

1 0

[tor/master] Add a reference implementation of our ed25519 modifications
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit 7ca470e13c70eaff483010e4b5c8f1f3076b3b7e Author: Nick Mathewson <nickm(a)torproject.org> Date: Sun Aug 31 19:39:43 2014 -0400 Add a reference implementation of our ed25519 modifications Also, use it to generate test vectors, and add those test vectors to test_crypto.c This is based on ed25519.py from the ed25519 webpage; the kludgy hacks are my own. --- src/test/ed25519_exts_ref.py | 206 ++++++++++++++++++++++++++++++++++++++++++ src/test/ed25519_vectors.inc | 112 +++++++++++++++++++++++ src/test/include.am | 3 +- src/test/slow_ed25519.py | 6 +- src/test/test_crypto.c | 67 ++++++++++++++ 5 files changed, 392 insertions(+), 2 deletions(-) diff --git a/src/test/ed25519_exts_ref.py b/src/test/ed25519_exts_ref.py new file mode 100644 index 0000000..199e1e1 --- /dev/null +++ b/src/test/ed25519_exts_ref.py @@ -0,0 +1,206 @@ +#!/usr/bin/python +# Copyright 2014, The Tor Project, Inc +# See LICENSE for licensing information + +""" + Reference implementations for the ed25519 tweaks that Tor uses. + + Includes self-tester and test vector generator. +""" + +from slow_ed25519 import * + +import os +import random +import slownacl_curve25519 +import unittest +import binascii + +#define a synonym that doesn't look like 1 +ell = l + +# This replaces expmod above and makes it go a lot faster. +def expmod(b,e,m): + return pow(b,e,m) + +def curve25519ToEd25519(c, sign): + u = decodeint(c) + y = ((u - 1) * inv(u + 1)) % q + x = xrecover(y) + if x & 1 != sign: x = q-x + return encodepoint([x,y]) + +def blindESK(esk, param): + h = H("Derive temporary signing key" + param) + mult = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2)) + s = decodeint(esk[:32]) + s_prime = (s * mult) % ell + k = esk[32:] + assert(len(k) == 32) + k_prime = H("Derive temporary signing key hash input" + k)[:32] + return encodeint(s_prime) + k_prime + +def blindPK(pk, param): + h = H("Derive temporary signing key" + param) + mult = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2)) + P = decodepoint(pk) + return encodepoint(scalarmult(P, mult)) + +def expandSK(sk): + h = H(sk) + a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2)) + k = ''.join([h[i] for i in range(b/8,b/4)]) + assert len(k) == 32 + return encodeint(a)+k + +def publickeyFromESK(h): + a = decodeint(h[:32]) + A = scalarmult(B,a) + return encodepoint(A) + +def signatureWithESK(m,h,pk): + a = decodeint(h[:32]) + r = Hint(''.join([h[i] for i in range(b/8,b/4)]) + m) + R = scalarmult(B,r) + S = (r + Hint(encodepoint(R) + pk + m) * a) % l + return encodepoint(R) + encodeint(S) + +def newSK(): + return os.urandom(32) + +# ------------------------------------------------------------ + +MSG = "This is extremely silly. But it is also incredibly serious business!" + +class SelfTest(unittest.TestCase): + + def _testSignatures(self, esk, pk): + sig = signatureWithESK(MSG, esk, pk) + checkvalid(sig, MSG, pk) + bad = False + try: + checkvalid(sig, MSG*2, pk) + bad = True + except Exception: + pass + + self.failIf(bad) + + def testExpand(self): + sk = newSK() + pk = publickey(sk) + esk = expandSK(sk) + sig1 = signature(MSG, sk, pk) + sig2 = signatureWithESK(MSG, esk, pk) + self.assertEquals(sig1, sig2) + + def testSignatures(self): + sk = newSK() + esk = expandSK(sk) + pk = publickeyFromESK(esk) + pk2 = publickey(sk) + self.assertEquals(pk, pk2) + + self._testSignatures(esk, pk) + + def testDerivation(self): + priv = slownacl_curve25519.Private() + pub = priv.get_public() + + ed_pub0 = publickeyFromESK(priv.private) + sign = (ord(ed_pub0[31]) & 255) >> 7 + ed_pub1 = curve25519ToEd25519(pub.public, sign) + + self.assertEquals(ed_pub0, ed_pub1) + + def testBlinding(self): + sk = newSK() + esk = expandSK(sk) + pk = publickeyFromESK(esk) + param = os.urandom(32) + besk = blindESK(esk, param) + bpk = blindPK(pk, param) + bpk2 = publickeyFromESK(besk) + self.assertEquals(bpk, bpk2) + + self._testSignatures(besk, bpk) + +# ------------------------------------------------------------ + +# From pprint.pprint([ binascii.b2a_hex(os.urandom(32)) for _ in xrange(8) ]) +RAND_INPUTS = [ + '26c76712d89d906e6672dafa614c42e5cb1caac8c6568e4d2493087db51f0d36', + 'fba7a5366b5cb98c2667a18783f5cf8f4f8d1a2ce939ad22a6e685edde85128d', + '67e3aa7a14fac8445d15e45e38a523481a69ae35513c9e4143eb1c2196729a0e', + 'd51385942033a76dc17f089a59e6a5a7fe80d9c526ae8ddd8c3a506b99d3d0a6', + '5c8eac469bb3f1b85bc7cd893f52dc42a9ab66f1b02b5ce6a68e9b175d3bb433', + 'eda433d483059b6d1ff8b7cfbd0fe406bfb23722c8f3c8252629284573b61b86', + '4377c40431c30883c5fbd9bc92ae48d1ed8a47b81d13806beac5351739b5533d', + 'c6bbcce615839756aed2cc78b1de13884dd3618f48367a17597a16c1cd7a290b'] + +# From pprint.pprint([ binascii.b2a_hex(os.urandom(16)) for _ in xrange(8) ]) +BLINDING_PARAMS = [ + '54a513898b471d1d448a2f3c55c1de2c0ef718c447b04497eeb999ed32027823', + '831e9b5325b5d31b7ae6197e9c7a7baf2ec361e08248bce055908971047a2347', + 'ac78a1d46faf3bfbbdc5af5f053dc6dc9023ed78236bec1760dadfd0b2603760', + 'f9c84dc0ac31571507993df94da1b3d28684a12ad14e67d0a068aba5c53019fc', + 'b1fe79d1dec9bc108df69f6612c72812755751f21ecc5af99663b30be8b9081f', + '81f1512b63ab5fb5c1711a4ec83d379c420574aedffa8c3368e1c3989a3a0084', + '97f45142597c473a4b0e9a12d64561133ad9e1155fe5a9807fe6af8a93557818', + '3f44f6a5a92cde816635dfc12ade70539871078d2ff097278be2a555c9859cd0'] + +PREFIX = "ED25519_" + +def writeArray(name, array): + print "static const char *{prefix}{name}[] = {{".format( + prefix=PREFIX,name=name) + for a in array: + h = binascii.b2a_hex(a) + if len(h) > 70: + h1 = h[:70] + h2 = h[70:] + print ' "{0}"\n "{1}",'.format(h1,h2) + else: + print ' "{0}",'.format(h) + print "};\n" + +def makeTestVectors(): + secretKeys = [ binascii.a2b_hex(r) for r in RAND_INPUTS ] + writeArray("SECRET_KEYS", secretKeys) + + expandedSecretKeys = [ expandSK(sk) for sk in secretKeys ] + writeArray("EXPANDED_SECRET_KEYS", expandedSecretKeys) + + publicKeys = [ publickey(sk) for sk in secretKeys ] + writeArray("PUBLIC_KEYS", publicKeys) + + writeArray("CURVE25519_PUBLIC_KEYS", + (slownacl_curve25519.smult_curve25519_base(sk[:32]) + for sk in expandedSecretKeys)) + + blindingParams = [ binascii.a2b_hex(r) for r in BLINDING_PARAMS ] + writeArray("BLINDING_PARAMS", blindingParams) + + writeArray("BLINDED_SECRET_KEYS", + (blindESK(expandSK(sk), bp) + for sk,bp in zip(secretKeys,blindingParams))) + + writeArray("BLINDED_PUBLIC_KEYS", + (blindPK(pk, bp) for pk,bp in zip(publicKeys,blindingParams))) + + writeArray("SELF_SIGNATURES", + (signature(pk, sk, pk) for pk,sk in zip(publicKeys,secretKeys))) + + + +if __name__ == '__main__': + import sys + if len(sys.argv) == 1 or sys.argv[1] not in ("SelfTest", "MakeVectors"): + print "You should specify one of 'SelfTest' or 'MakeVectors'" + sys.exit(1) + if sys.argv[1] == 'SelfTest': + unittest.main() + else: + makeTestVectors() + + diff --git a/src/test/ed25519_vectors.inc b/src/test/ed25519_vectors.inc new file mode 100644 index 0000000..ef0a20b --- /dev/null +++ b/src/test/ed25519_vectors.inc @@ -0,0 +1,112 @@ +static const char *ED25519_SECRET_KEYS[] = { + "26c76712d89d906e6672dafa614c42e5cb1caac8c6568e4d2493087db51f0d36", + "fba7a5366b5cb98c2667a18783f5cf8f4f8d1a2ce939ad22a6e685edde85128d", + "67e3aa7a14fac8445d15e45e38a523481a69ae35513c9e4143eb1c2196729a0e", + "d51385942033a76dc17f089a59e6a5a7fe80d9c526ae8ddd8c3a506b99d3d0a6", + "5c8eac469bb3f1b85bc7cd893f52dc42a9ab66f1b02b5ce6a68e9b175d3bb433", + "eda433d483059b6d1ff8b7cfbd0fe406bfb23722c8f3c8252629284573b61b86", + "4377c40431c30883c5fbd9bc92ae48d1ed8a47b81d13806beac5351739b5533d", + "c6bbcce615839756aed2cc78b1de13884dd3618f48367a17597a16c1cd7a290b", +}; + +static const char *ED25519_EXPANDED_SECRET_KEYS[] = { + "c0a4de23cc64392d85aa1da82b3defddbea946d13bb053bf8489fa9296281f495022f1" + "f7ec0dcf52f07d4c7965c4eaed121d5d88d0a8ff546b06116a20e97755", + "18a8a69a06790dac778e882f7e868baacfa12521a5c058f5194f3a729184514a2a656f" + "e7799c3e41f43d756da8d9cd47a061316cfe6147e23ea2f90d1ca45f30", + "58d84f8862d2ecfa30eb491a81c36d05b574310ea69dae18ecb57e992a896656b98218" + "7ee96c15bf4caeeab2d0b0ae4cd0b8d17470fc7efa98bb26428f4ef36d", + "50702d20b3550c6e16033db5ad4fba16436f1ecc7485be6af62b0732ceb5d173c47ccd" + "9d044b6ea99dd99256adcc9c62191be194e7cb1a5b58ddcec85d876a2b", + "7077464c864c2ed5ed21c9916dc3b3ba6256f8b742fec67658d8d233dadc8d5a7a82c3" + "71083cc86892c2c8782dda2a09b6baf016aec51b689183ae59ce932ff2", + "8883c1387a6c86fc0bd7b9f157b4e4cd83f6885bf55e2706d2235d4527a2f05311a359" + "5953282e436df0349e1bb313a19b3ddbf7a7b91ecce8a2c34abadb38b3", + "186791ac8d03a3ac8efed6ac360467edd5a3bed2d02b3be713ddd5be53b3287ee37436" + "e5fd7ac43794394507ad440ecfdf59c4c255f19b768a273109e06d7d8e", + "b003077c1e52a62308eef7950b2d532e1d4a7eea50ad22d8ac11b892851f1c40ffb9c9" + "ff8dcd0c6c233f665a2e176324d92416bfcfcd1f787424c0c667452d86", +}; + +static const char *ED25519_PUBLIC_KEYS[] = { + "c2247870536a192d142d056abefca68d6193158e7c1a59c1654c954eccaff894", + "1519a3b15816a1aafab0b213892026ebf5c0dc232c58b21088d88cb90e9b940d", + "081faa81992e360ea22c06af1aba096e7a73f1c665bc8b3e4e531c46455fd1dd", + "73cfa1189a723aad7966137cbffa35140bb40d7e16eae4c40b79b5f0360dd65a", + "66c1a77104d86461b6f98f73acf3cd229c80624495d2d74d6fda1e940080a96b", + "d21c294db0e64cb2d8976625786ede1d9754186ae8197a64d72f68c792eecc19", + "c4d58b4cf85a348ff3d410dd936fa460c4f18da962c01b1963792b9dcc8a6ea6", + "95126f14d86494020665face03f2d42ee2b312a85bc729903eb17522954a1c4a", +}; + +static const char *ED25519_CURVE25519_PUBLIC_KEYS[] = { + "17ba77846e04c7ee5ca17cade774ac1884408f9701f439d4df32cbd8736c6a1f", + "022be2124bc1899a78ba2b4167d191af3b59cadf94f0382bc31ce183a117f161", + "bf4fd38ef22f718f03c0a12ba5127bd1e3afd494793753f519728b29cc577571", + "56c493e490261cef31633efd2461d2b896908e90459e4eecde950a895aef681d", + "089675a3e8ff2a7d8b2844a79269c95b7f97a4b8b5ea0cbeec669c6f2dea9b39", + "59e20dcb691c4a345fe86c8a79ac817e5b514d84bbf0512a842a08e43f7f087e", + "9e43b820b320eda35f66f122c155b2bf8e2192c468617b7115bf067d19e08369", + "861f33296cb57f8f01e4a5e8a7e5d5d7043a6247586ab36dea8a1a3c4403ee30", +}; + +static const char *ED25519_BLINDING_PARAMS[] = { + "54a513898b471d1d448a2f3c55c1de2c0ef718c447b04497eeb999ed32027823", + "831e9b5325b5d31b7ae6197e9c7a7baf2ec361e08248bce055908971047a2347", + "ac78a1d46faf3bfbbdc5af5f053dc6dc9023ed78236bec1760dadfd0b2603760", + "f9c84dc0ac31571507993df94da1b3d28684a12ad14e67d0a068aba5c53019fc", + "b1fe79d1dec9bc108df69f6612c72812755751f21ecc5af99663b30be8b9081f", + "81f1512b63ab5fb5c1711a4ec83d379c420574aedffa8c3368e1c3989a3a0084", + "97f45142597c473a4b0e9a12d64561133ad9e1155fe5a9807fe6af8a93557818", + "3f44f6a5a92cde816635dfc12ade70539871078d2ff097278be2a555c9859cd0", +}; + +static const char *ED25519_BLINDED_SECRET_KEYS[] = { + "014e83abadb2ca9a27e0ffe23920333d817729f48700e97656ec2823d694050e171d43" + "f24e3f53e70ec7ac280044ac77d4942dee5d6807118a59bdf3ee647e89", + "fad8cca0b4335847795288b1452508752b253e64e6c7c78d4a02dbbd7d46aa0eb8ceff" + "20dfcf53eb52b891fc078c934efbf0353af7242e7dc51bb32a093afa29", + "116eb0ae0a4a91763365bdf86db427b00862db448487808788cc339ac10e5e089217f5" + "2e92797462bd890fc274672e05c98f2c82970d640084781334aae0f940", + "bd1fbb0ee5acddc4adbcf5f33e95d9445f40326ce579fdd764a24483a9ccb20f509ece" + "e77082ce088f7c19d5a00e955eeef8df6fa41686abc1030c2d76807733", + "237f5345cefe8573ce9fa7e216381a1172796c9e3f70668ab503b1352952530fb57b95" + "a440570659a440a3e4771465022a8e67af86bdf2d0990c54e7bb87ff9a", + "ba8ff23bc4ad2b739e1ccffc9fbc7837053ea81cdfdb15073f56411cfbae1d0ec492fc" + "87d5ec2a1b185ca5a40541fdef0b1e128fd5c2380c888bfa924711bcab", + "0fa68f969de038c7a90a4a74ee6167c77582006f2dedecc1956501ba6b6fb10391b476" + "8f8e556d78f4bdcb9a13b6f6066fe81d3134ae965dc48cd0785b3af2b8", + "deaa3456d1c21944d5dcd361a646858c6cf9336b0a6851d925717eb1ae186902053d9c" + "00c81e1331c06ab50087be8cfc7dc11691b132614474f1aa9c2503cccd", +}; + +static const char *ED25519_BLINDED_PUBLIC_KEYS[] = { + "722d6da6348e618967ef782e71061e27163a8b35f21856475d9d2023f65b6495", + "1dffa0586da6cbfcff2024eedf4fc6c818242d9a82dbbe635d6da1b975a1160d", + "5ed81f98fed5a6acda4ea6da2c34fab0ab359d950c510c256473f1f33ff438b4", + "6e6f92a54fb282120c46d9603df41135f025bc1f58f283809d04be96aeb04040", + "cda236f28edc4c7e02d18007b8dab49d669265b0f7aefb1824d7cc8e73a2cd63", + "367b03b17b67ca7329b89a520bdab91782402a41cd67264e34b5541a4b3f875b", + "8d486b03ac4e3b486b7a1d563706c7fdac75aee789a7cf6f22789eedeff61a31", + "9f297ff0aa2ceda91c5ab1b6446f12533d145940de6d850dc323417afde0cb78", +}; + +static const char *ED25519_SELF_SIGNATURES[] = { + "d23188eac3773a316d46006fa59c095060be8b1a23582a0dd99002a82a0662bd246d84" + "49e172e04c5f46ac0d1404cebe4aabd8a75a1457aa06cae41f3334f104", + "3a785ac1201c97ee5f6f0d99323960d5f264c7825e61aa7cc81262f15bef75eb4fa572" + "3add9b9d45b12311b6d403eb3ac79ff8e4e631fc3cd51e4ad2185b200b", + "cf431fd0416bfbd20c9d95ef9b723e2acddffb33900edc72195dea95965d52d888d30b" + "7b8a677c0bd8ae1417b1e1a0ec6700deadd5d8b54b6689275e04a04509", + "2375380cd72d1a6c642aeddff862be8a5804b916acb72c02d9ed052c1561881aa658a5" + "af856fcd6d43113e42f698cd6687c99efeef7f2ce045824440d26c5d00", + "2385a472f599ca965bbe4d610e391cdeabeba9c336694b0d6249e551458280be122c24" + "41dd9746a81bbfb9cd619364bab0df37ff4ceb7aefd24469c39d3bc508", + "e500cd0b8cfff35442f88008d894f3a2fa26ef7d3a0ca5714ae0d3e2d40caae58ba7cd" + "f69dd126994dad6be536fcda846d89dd8138d1683cc144c8853dce7607", + "d187b9e334b0050154de10bf69b3e4208a584e1a65015ec28b14bcc252cf84b8baa9c9" + "4867daa60f2a82d09ba9652d41e8dde292b624afc8d2c26441b95e3c0e", + "815213640a643d198bd056e02bba74e1c8d2d931643e84497adf3347eb485079c9afe0" + "afce9284cdc084946b561abbb214f1304ca11228ff82702185cf28f60d", +}; + diff --git a/src/test/include.am b/src/test/include.am index d5163aa..3fecbbd 100644 --- a/src/test/include.am +++ b/src/test/include.am @@ -73,7 +73,8 @@ src_test_bench_LDADD = src/or/libtor.a src/common/libor.a \ noinst_HEADERS+= \ src/test/test.h \ - src/test/test_descriptors.inc + src/test/test_descriptors.inc \ + src/test/ed25519_vectors.inc if CURVE25519_ENABLED noinst_PROGRAMS+= src/test/test-ntor-cl diff --git a/src/test/slow_ed25519.py b/src/test/slow_ed25519.py index 3380079..f44708b 100644 --- a/src/test/slow_ed25519.py +++ b/src/test/slow_ed25519.py @@ -2,7 +2,11 @@ # http://ed25519.cr.yp.to/python/ed25519.py . # It is in the public domain. # -# It isn't constant-time. Don't use it except for testing. +# It isn't constant-time. Don't use it except for testing. Also, see +# warnings about how very slow it is. Only use this for generating +# test vectors, I'd suggest. +# +# Don't edit this file. Mess with ed25519_ref.py import hashlib diff --git a/src/test/test_crypto.c b/src/test/test_crypto.c index d4478d5..6c2258e 100644 --- a/src/test/test_crypto.c +++ b/src/test/test_crypto.c @@ -13,6 +13,7 @@ #ifdef CURVE25519_ENABLED #include "crypto_curve25519.h" #include "crypto_ed25519.h" +#include "ed25519_vectors.inc" #endif extern const char AUTHORITY_SIGNKEY_3[]; @@ -1456,6 +1457,71 @@ test_crypto_ed25519_blinding(void *arg) } static void +test_crypto_ed25519_testvectors(void *arg) +{ + unsigned i; + char *mem_op_hex_tmp = NULL; + (void)arg; + + for (i = 0; i < ARRAY_LENGTH(ED25519_SECRET_KEYS); ++i) { + uint8_t sk[32]; + ed25519_secret_key_t esk; + ed25519_public_key_t pk, blind_pk, pkfromcurve; + ed25519_keypair_t keypair, blind_keypair; + curve25519_keypair_t curvekp; + uint8_t blinding_param[32]; + ed25519_signature_t sig; + int sign; + +#define DECODE(p,s) base16_decode((char*)(p),sizeof(p),(s),strlen(s)) +#define EQ(a,h) test_memeq_hex((const char*)(a), (h)) + + tt_int_op(0, ==, DECODE(sk, ED25519_SECRET_KEYS[i])); + tt_int_op(0, ==, DECODE(blinding_param, ED25519_BLINDING_PARAMS[i])); + + tt_int_op(0, ==, ed25519_secret_key_from_seed(&esk, sk)); + EQ(esk.seckey, ED25519_EXPANDED_SECRET_KEYS[i]); + + tt_int_op(0, ==, ed25519_public_key_generate(&pk, &esk)); + EQ(pk.pubkey, ED25519_PUBLIC_KEYS[i]); + + memcpy(&curvekp.seckey.secret_key, esk.seckey, 32); + curve25519_public_key_generate(&curvekp.pubkey, &curvekp.seckey); + + tt_int_op(0, ==, + ed25519_keypair_from_curve25519_keypair(&keypair, &sign, &curvekp)); + tt_int_op(0, ==, ed25519_public_key_from_curve25519_public_key( + &pkfromcurve, &curvekp.pubkey, sign)); + tt_mem_op(keypair.pubkey.pubkey, ==, pkfromcurve.pubkey, 32); + EQ(curvekp.pubkey.public_key, ED25519_CURVE25519_PUBLIC_KEYS[i]); + + /* Self-signing */ + memcpy(&keypair.seckey, &esk, sizeof(esk)); + memcpy(&keypair.pubkey, &pk, sizeof(pk)); + + tt_int_op(0, ==, ed25519_sign(&sig, pk.pubkey, 32, &keypair)); + + EQ(sig.sig, ED25519_SELF_SIGNATURES[i]); + + /* Blinding */ + tt_int_op(0, ==, + ed25519_keypair_blind(&blind_keypair, &keypair, blinding_param)); + tt_int_op(0, ==, + ed25519_public_blind(&blind_pk, &pk, blinding_param)); + + EQ(blind_keypair.seckey.seckey, ED25519_BLINDED_SECRET_KEYS[i]); + EQ(blind_pk.pubkey, ED25519_BLINDED_PUBLIC_KEYS[i]); + + tt_mem_op(blind_pk.pubkey, ==, blind_keypair.pubkey.pubkey, 32); + +#undef DECODE +#undef EQ + } + done: + tor_free(mem_op_hex_tmp); +} + +static void test_crypto_siphash(void *arg) { /* From the reference implementation, taking @@ -1597,6 +1663,7 @@ struct testcase_t crypto_tests[] = { { "ed25519_encode", test_crypto_ed25519_encode, 0, NULL, NULL }, { "ed25519_convert", test_crypto_ed25519_convert, 0, NULL, NULL }, { "ed25519_blinding", test_crypto_ed25519_blinding, 0, NULL, NULL }, + { "ed25519_testvectors", test_crypto_ed25519_testvectors, 0, NULL, NULL }, #endif { "siphash", test_crypto_siphash, 0, NULL, NULL }, END_OF_TESTCASES

1 0

[tor/master] More documentation for ed25519 stuff.
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit f0eb7ae79f54781bc00e51ff5e9630b2103e4df0 Author: Nick Mathewson <nickm(a)torproject.org> Date: Fri Aug 29 09:24:27 2014 -0400 More documentation for ed25519 stuff. --- src/common/crypto_ed25519.c | 43 ++++++++++++++++++++++++++++++++++---- src/common/crypto_ed25519.h | 6 ++++++ src/ext/ed25519/ref10/README.tor | 23 ++++++++++++++++++++ src/ext/ed25519/ref10/blinding.c | 2 +- 4 files changed, 69 insertions(+), 5 deletions(-) diff --git a/src/common/crypto_ed25519.c b/src/common/crypto_ed25519.c index 15fc626..a545cad 100644 --- a/src/common/crypto_ed25519.c +++ b/src/common/crypto_ed25519.c @@ -19,6 +19,11 @@ #include <openssl/sha.h> +/** + * Initialize a new ed25519 secret key in seckey_out. If + * extra_strong, take the RNG inputs directly from the operating + * system. Return 0 on success, -1 on failure. + */ int ed25519_secret_key_generate(ed25519_secret_key_t *seckey_out, int extra_strong) @@ -34,6 +39,10 @@ ed25519_secret_key_generate(ed25519_secret_key_t *seckey_out, return r < 0 ? -1 : 0; } +/** + * Given a 32-byte random seed in seed, expand it into an ed25519 + * secret key in seckey_out. Return 0 on success, -1 on failure. + */ int ed25519_secret_key_from_seed(ed25519_secret_key_t *seckey_out, const uint8_t *seed) @@ -43,6 +52,10 @@ ed25519_secret_key_from_seed(ed25519_secret_key_t *seckey_out, return 0; } +/** + * Given a secret key in seckey, expand it into an + * ed25519 public key. Return 0 on success, -1 on failure. + */ int ed25519_public_key_generate(ed25519_public_key_t *pubkey_out, const ed25519_secret_key_t *seckey) @@ -224,6 +237,10 @@ ed25519_public_key_from_curve25519_public_key(ed25519_public_key_t *pubkey, * ed25519 keypair in out, blinded by the corresponding 32-byte input * in 'param'. * + * Tor uses key blinding for the "next-generation" hidden services design: + * service descriptors are encrypted with a key derived from the service's + * long-term public key, and then signed with (and stored at a position + * indexed by) a short-term key derived by blinding the long-term keys. */ int ed25519_keypair_blind(ed25519_keypair_t *out, @@ -245,6 +262,11 @@ ed25519_keypair_blind(ed25519_keypair_t *out, return 0; } +/** + * Given an ed25519 public key in inp, generate a corresponding blinded + * public key in out, blinded with the 32-byte parameter in + * param. Return 0 on sucess, -1 on railure. + */ int ed25519_public_blind(ed25519_public_key_t *out, const ed25519_public_key_t *inp, @@ -254,7 +276,10 @@ ed25519_public_blind(ed25519_public_key_t *out, return 0; } -/** DOCDOC */ +/** + * Store seckey unencrypted to filename, marking it with tag. + * Return 0 on success, -1 on failure. + */ int ed25519_seckey_write_to_file(const ed25519_secret_key_t *seckey, const char *filename, @@ -267,7 +292,11 @@ ed25519_seckey_write_to_file(const ed25519_secret_key_t *seckey, sizeof(seckey->seckey)); } -/** DOCDOC */ +/** + * Read seckey unencrypted from filename, storing it into + * seckey_out. Set *tag_out</> to the tag it was marked with. + * Return 0 on success, -1 on failure. + */ int ed25519_seckey_read_from_file(ed25519_secret_key_t *seckey_out, char **tag_out, @@ -284,7 +313,10 @@ ed25519_seckey_read_from_file(ed25519_secret_key_t *seckey_out, return 0; } -/** DOCDOC */ +/** + * Store pubkey unencrypted to filename, marking it with tag. + * Return 0 on success, -1 on failure. + */ int ed25519_pubkey_write_to_file(const ed25519_public_key_t *pubkey, const char *filename, @@ -297,7 +329,10 @@ ed25519_pubkey_write_to_file(const ed25519_public_key_t *pubkey, sizeof(pubkey->pubkey)); } -/** DOCDOC */ +/** + * Store pubkey unencrypted to filename, marking it with tag. + * Return 0 on success, -1 on failure. + */ int ed25519_pubkey_read_from_file(ed25519_public_key_t *pubkey_out, char **tag_out, diff --git a/src/common/crypto_ed25519.h b/src/common/crypto_ed25519.h index 1271312..13b05c7 100644 --- a/src/common/crypto_ed25519.h +++ b/src/common/crypto_ed25519.h @@ -24,6 +24,12 @@ typedef struct { /** An Ed25519 secret key */ typedef struct { + /** Note that we store secret keys in an expanded format that doesn't match + * the format from standard ed25519. Ed25519 stores a 32-byte value k and + * expands it into a 64-byte H(k), using the first 32 bytes for a multiplier + * of the base point, and second 32 bytes as an input to a hash function + * for deriving r. But because we implement key blinding, we need to store + * keys in the 64-byte expanded form. */ uint8_t seckey[ED25519_SECKEY_LEN]; } ed25519_secret_key_t; diff --git a/src/ext/ed25519/ref10/README.tor b/src/ext/ed25519/ref10/README.tor new file mode 100644 index 0000000..38ed97b --- /dev/null +++ b/src/ext/ed25519/ref10/README.tor @@ -0,0 +1,23 @@ + +We've made the following changes to the stock ed25519_ref10 from +supercop-20140622: + + * We added the necessary glue to provide integers of fixed bit + sizes, SHA512, and to compile without warnings everywhere we need + to build. + + * Secret keys are stored in expanded format. There are functions + to expand them from the 32-byte seed. + + * Signatures are made and processed detached from the messages that + they sign. (In other words, we support "make signature" and + "check signature", not "create signed message" and "check and + unpack signed message".) + + * There's an implementation of 'convert a curve25519 key to an + ed25519 key' so we can do cross-certification with curve25519 keys. + (keyconv.c) + + * There's an implementation of multiplicative key blinding so we + can use it for next-gen hidden srevice descriptors. (blinding.c) + diff --git a/src/ext/ed25519/ref10/blinding.c b/src/ext/ed25519/ref10/blinding.c index a17dbcd..f0154e0 100644 --- a/src/ext/ed25519/ref10/blinding.c +++ b/src/ext/ed25519/ref10/blinding.c @@ -14,7 +14,7 @@ gettweak(unsigned char *out, const unsigned char *param) { const char str[] = "Derive temporary signing key"; crypto_hash_sha512_2(out, (const unsigned char*)str, strlen(str), param, 32); - out[0] &= 248; /* Necessary ? */ + out[0] &= 248; /* Is this necessary necessary ? */ out[31] &= 63; out[31] |= 64; }

1 0

[tor/master] Merge branch 'ed25519_ref10_squashed'
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit 1c5d680b3d6734e989a92deedbcf2bb46f31f7f9 Merge: 50d15e0 46cda48 Author: Nick Mathewson <nickm(a)torproject.org> Date: Thu Sep 25 15:11:34 2014 -0400 Merge branch 'ed25519_ref10_squashed' Conflicts: src/common/include.am src/ext/README .gitignore | 4 + src/common/crypto_curve25519.c | 174 +++- src/common/crypto_curve25519.h | 14 + src/common/crypto_ed25519.c | 353 +++++++ src/common/crypto_ed25519.h | 116 +++ src/common/crypto_format.c | 22 + src/common/include.am | 7 +- src/ext/README | 7 + src/ext/ed25519/ref10/Makefile | 41 + src/ext/ed25519/ref10/README.tor | 23 + src/ext/ed25519/ref10/api.h | 4 + src/ext/ed25519/ref10/base.h | 1344 ++++++++++++++++++++++++++ src/ext/ed25519/ref10/base.py | 65 ++ src/ext/ed25519/ref10/base2.h | 40 + src/ext/ed25519/ref10/base2.py | 60 ++ src/ext/ed25519/ref10/blinding.c | 76 ++ src/ext/ed25519/ref10/crypto_hash_sha512.h | 30 + src/ext/ed25519/ref10/crypto_int32.h | 3 + src/ext/ed25519/ref10/crypto_int64.h | 3 + src/ext/ed25519/ref10/crypto_sign.h | 9 + src/ext/ed25519/ref10/crypto_uint32.h | 3 + src/ext/ed25519/ref10/crypto_uint64.h | 3 + src/ext/ed25519/ref10/crypto_verify_32.h | 5 + src/ext/ed25519/ref10/d.h | 1 + src/ext/ed25519/ref10/d.py | 28 + src/ext/ed25519/ref10/d2.h | 1 + src/ext/ed25519/ref10/d2.py | 28 + src/ext/ed25519/ref10/ed25519_ref10.h | 30 + src/ext/ed25519/ref10/fe.h | 56 ++ src/ext/ed25519/ref10/fe_0.c | 19 + src/ext/ed25519/ref10/fe_1.c | 19 + src/ext/ed25519/ref10/fe_add.c | 57 ++ src/ext/ed25519/ref10/fe_cmov.c | 63 ++ src/ext/ed25519/ref10/fe_copy.c | 29 + src/ext/ed25519/ref10/fe_frombytes.c | 73 ++ src/ext/ed25519/ref10/fe_invert.c | 14 + src/ext/ed25519/ref10/fe_isnegative.c | 16 + src/ext/ed25519/ref10/fe_isnonzero.c | 19 + src/ext/ed25519/ref10/fe_mul.c | 253 +++++ src/ext/ed25519/ref10/fe_neg.c | 45 + src/ext/ed25519/ref10/fe_pow22523.c | 13 + src/ext/ed25519/ref10/fe_sq.c | 149 +++ src/ext/ed25519/ref10/fe_sq2.c | 160 +++ src/ext/ed25519/ref10/fe_sub.c | 57 ++ src/ext/ed25519/ref10/fe_tobytes.c | 119 +++ src/ext/ed25519/ref10/ge.h | 95 ++ src/ext/ed25519/ref10/ge_add.c | 11 + src/ext/ed25519/ref10/ge_add.h | 97 ++ src/ext/ed25519/ref10/ge_add.q | 49 + src/ext/ed25519/ref10/ge_double_scalarmult.c | 96 ++ src/ext/ed25519/ref10/ge_frombytes.c | 50 + src/ext/ed25519/ref10/ge_madd.c | 11 + src/ext/ed25519/ref10/ge_madd.h | 88 ++ src/ext/ed25519/ref10/ge_madd.q | 46 + src/ext/ed25519/ref10/ge_msub.c | 11 + src/ext/ed25519/ref10/ge_msub.h | 88 ++ src/ext/ed25519/ref10/ge_msub.q | 46 + src/ext/ed25519/ref10/ge_p1p1_to_p2.c | 12 + src/ext/ed25519/ref10/ge_p1p1_to_p3.c | 13 + src/ext/ed25519/ref10/ge_p2_0.c | 8 + src/ext/ed25519/ref10/ge_p2_dbl.c | 11 + src/ext/ed25519/ref10/ge_p2_dbl.h | 73 ++ src/ext/ed25519/ref10/ge_p2_dbl.q | 41 + src/ext/ed25519/ref10/ge_p3_0.c | 9 + src/ext/ed25519/ref10/ge_p3_dbl.c | 12 + src/ext/ed25519/ref10/ge_p3_to_cached.c | 17 + src/ext/ed25519/ref10/ge_p3_to_p2.c | 12 + src/ext/ed25519/ref10/ge_p3_tobytes.c | 14 + src/ext/ed25519/ref10/ge_precomp_0.c | 8 + src/ext/ed25519/ref10/ge_scalarmult_base.c | 109 +++ src/ext/ed25519/ref10/ge_sub.c | 11 + src/ext/ed25519/ref10/ge_sub.h | 97 ++ src/ext/ed25519/ref10/ge_sub.q | 49 + src/ext/ed25519/ref10/ge_tobytes.c | 14 + src/ext/ed25519/ref10/keyconv.c | 37 + src/ext/ed25519/ref10/keypair.c | 51 + src/ext/ed25519/ref10/open.c | 42 + src/ext/ed25519/ref10/pow22523.h | 160 +++ src/ext/ed25519/ref10/pow22523.q | 61 ++ src/ext/ed25519/ref10/pow225521.h | 160 +++ src/ext/ed25519/ref10/pow225521.q | 61 ++ src/ext/ed25519/ref10/q2h.sh | 4 + src/ext/ed25519/ref10/randombytes.h | 4 + src/ext/ed25519/ref10/sc.h | 15 + src/ext/ed25519/ref10/sc_muladd.c | 368 +++++++ src/ext/ed25519/ref10/sc_reduce.c | 275 ++++++ src/ext/ed25519/ref10/sign.c | 29 + src/ext/ed25519/ref10/sqrtm1.h | 1 + src/ext/ed25519/ref10/sqrtm1.py | 28 + src/ext/include.am | 67 ++ src/test/bench.c | 62 ++ src/test/ed25519_exts_ref.py | 234 +++++ src/test/ed25519_vectors.inc | 150 +++ src/test/include.am | 3 +- src/test/slow_ed25519.py | 115 +++ src/test/test_crypto.c | 364 +++++++ 96 files changed, 7101 insertions(+), 43 deletions(-) diff --cc .gitignore index 744c2b8,df94237..9ddd0c5 --- a/.gitignore +++ b/.gitignore @@@ -136,8 -133,11 +136,12 @@@ cscope. /src/config/sample-server-torrc /src/config/torrc /src/config/torrc.sample +/src/config/torrc.minimal + # /src/ext/ + /src/ext/ed25519/ref10/libed25519_ref10.a + /src/ext/ed25519/ref10/libed25519_ref10.lib + # /src/or/ /src/or/Makefile /src/or/Makefile.in diff --cc src/common/include.am index d669cf4,8fc1ff9..5c000e8 --- a/src/common/include.am +++ b/src/common/include.am @@@ -114,8 -114,7 +118,9 @@@ COMMONHEADERS = src/common/container.h \ src/common/crypto.h \ src/common/crypto_curve25519.h \ + src/common/crypto_ed25519.h \ + src/common/crypto_pwbox.h \ + src/common/crypto_s2k.h \ src/common/di_ops.h \ src/common/memarea.h \ src/common/linux_syscalls.inc \ diff --cc src/ext/README index a263dd7,b759fc2..616716e --- a/src/ext/README +++ b/src/ext/README @@@ -50,7 -50,8 +50,14 @@@ siphash. hash algorithm to avoid collision-based DoS attacks against hash tables. +trunnel/*.[ch] + + Headers and runtime code for Trunnel, a system for generating + code to encode and decode binary formats. ++ + ed25519/ref10/* + + Daniel Bernsten's portable ref10 implementation of ed25519. + Public domain. + ++ diff --cc src/test/test_crypto.c index 36af725,6c2258e..0c87c88 --- a/src/test/test_crypto.c +++ b/src/test/test_crypto.c @@@ -13,9 -12,9 +13,11 @@@ #include "siphash.h" #ifdef CURVE25519_ENABLED #include "crypto_curve25519.h" + #include "crypto_ed25519.h" + #include "ed25519_vectors.inc" #endif +#include "crypto_s2k.h" +#include "crypto_pwbox.h" extern const char AUTHORITY_SIGNKEY_3[]; extern const char AUTHORITY_SIGNKEY_A_DIGEST[]; @@@ -1516,9 -1163,365 +1518,365 @@@ test_crypto_curve25519_persist(void *ar tor_free(tag); } + static void + test_crypto_ed25519_simple(void *arg) + { + ed25519_keypair_t kp1, kp2; + ed25519_public_key_t pub1, pub2; + ed25519_secret_key_t sec1, sec2; + ed25519_signature_t sig1, sig2; + const uint8_t msg[] = + "GNU will be able to run Unix programs, " + "but will not be identical to Unix."; + const uint8_t msg2[] = + "Microsoft Windows extends the features of the DOS operating system, " + "yet is compatible with most existing applications that run under DOS."; + size_t msg_len = strlen((const char*)msg); + size_t msg2_len = strlen((const char*)msg2); + + (void)arg; + + tt_int_op(0, ==, ed25519_secret_key_generate(&sec1, 0)); + tt_int_op(0, ==, ed25519_secret_key_generate(&sec2, 1)); + + tt_int_op(0, ==, ed25519_public_key_generate(&pub1, &sec1)); + tt_int_op(0, ==, ed25519_public_key_generate(&pub2, &sec1)); + - test_memeq(pub1.pubkey, pub2.pubkey, sizeof(pub1.pubkey)); ++ tt_mem_op(pub1.pubkey, ==, pub2.pubkey, sizeof(pub1.pubkey)); + + memcpy(&kp1.pubkey, &pub1, sizeof(pub1)); + memcpy(&kp1.seckey, &sec1, sizeof(sec1)); + tt_int_op(0, ==, ed25519_sign(&sig1, msg, msg_len, &kp1)); + tt_int_op(0, ==, ed25519_sign(&sig2, msg, msg_len, &kp1)); + + /* Ed25519 signatures are deterministic */ - test_memeq(sig1.sig, sig2.sig, sizeof(sig1.sig)); ++ tt_mem_op(sig1.sig, ==, sig2.sig, sizeof(sig1.sig)); + + /* Basic signature is valid. */ + tt_int_op(0, ==, ed25519_checksig(&sig1, msg, msg_len, &pub1)); + + /* Altered signature doesn't work. */ + sig1.sig[0] ^= 3; + tt_int_op(-1, ==, ed25519_checksig(&sig1, msg, msg_len, &pub1)); + + /* Wrong public key doesn't work. */ + tt_int_op(0, ==, ed25519_public_key_generate(&pub2, &sec2)); + tt_int_op(-1, ==, ed25519_checksig(&sig2, msg, msg_len, &pub2)); + + /* Wrong message doesn't work. */ + tt_int_op(0, ==, ed25519_checksig(&sig2, msg, msg_len, &pub1)); + tt_int_op(-1, ==, ed25519_checksig(&sig2, msg, msg_len-1, &pub1)); + tt_int_op(-1, ==, ed25519_checksig(&sig2, msg2, msg2_len, &pub1)); + + /* Batch signature checking works with some bad. */ + tt_int_op(0, ==, ed25519_keypair_generate(&kp2, 0)); + tt_int_op(0, ==, ed25519_sign(&sig1, msg, msg_len, &kp2)); + { + ed25519_checkable_t ch[] = { + { &pub1, sig2, msg, msg_len }, /*ok*/ + { &pub1, sig2, msg, msg_len-1 }, /*bad*/ + { &kp2.pubkey, sig2, msg2, msg2_len }, /*bad*/ + { &kp2.pubkey, sig1, msg, msg_len }, /*ok*/ + }; + int okay[4]; + tt_int_op(-2, ==, ed25519_checksig_batch(okay, ch, 4)); + tt_int_op(okay[0], ==, 1); + tt_int_op(okay[1], ==, 0); + tt_int_op(okay[2], ==, 0); + tt_int_op(okay[3], ==, 1); + tt_int_op(-2, ==, ed25519_checksig_batch(NULL, ch, 4)); + } + + /* Batch signature checking works with all good. */ + { + ed25519_checkable_t ch[] = { + { &pub1, sig2, msg, msg_len }, /*ok*/ + { &kp2.pubkey, sig1, msg, msg_len }, /*ok*/ + }; + int okay[2]; + tt_int_op(0, ==, ed25519_checksig_batch(okay, ch, 2)); + tt_int_op(okay[0], ==, 1); + tt_int_op(okay[1], ==, 1); + tt_int_op(0, ==, ed25519_checksig_batch(NULL, ch, 2)); + } + + done: + ; + } + + static void + test_crypto_ed25519_test_vectors(void *arg) + { + char *mem_op_hex_tmp=NULL; + int i; + struct { + const char *sk; + const char *pk; + const char *sig; + const char *msg; + } items[] = { + /* These test vectors were generated with the "ref" implementation of + * ed25519 from SUPERCOP-20130419 */ + { "4c6574277320686f706520746865726520617265206e6f206275677320696e20", + "f3e0e493b30f56e501aeb868fc912fe0c8b76621efca47a78f6d75875193dd87", + "b5d7fd6fd3adf643647ce1fe87a2931dedd1a4e38e6c662bedd35cdd80bfac51" + "1b2c7d1ee6bd929ac213014e1a8dc5373854c7b25dbe15ec96bf6c94196fae06", + "506c6561736520657863757365206d7920667269656e642e2048652069736e2774" + "204e554c2d7465726d696e617465642e" + }, + + { "74686520696d706c656d656e746174696f6e20776869636820617265206e6f74", + "407f0025a1e1351a4cb68e92f5c0ebaf66e7aaf93a4006a4d1a66e3ede1cfeac", + "02884fde1c3c5944d0ecf2d133726fc820c303aae695adceabf3a1e01e95bf28" + "da88c0966f5265e9c6f8edc77b3b96b5c91baec3ca993ccd21a3f64203600601", + "506c6561736520657863757365206d7920667269656e642e2048652069736e2774" + "204e554c2d7465726d696e617465642e" + }, + { "6578706f73656420627920456e676c697368207465787420617320696e707574", + "61681cb5fbd69f9bc5a462a21a7ab319011237b940bc781cdc47fcbe327e7706", + "6a127d0414de7510125d4bc214994ffb9b8857a46330832d05d1355e882344ad" + "f4137e3ca1f13eb9cc75c887ef2309b98c57528b4acd9f6376c6898889603209", + "506c6561736520657863757365206d7920667269656e642e2048652069736e2774" + "204e554c2d7465726d696e617465642e" + }, + + /* These come from "sign.input" in ed25519's page */ + { "5b5a619f8ce1c66d7ce26e5a2ae7b0c04febcd346d286c929e19d0d5973bfef9", + "6fe83693d011d111131c4f3fbaaa40a9d3d76b30012ff73bb0e39ec27ab18257", + "0f9ad9793033a2fa06614b277d37381e6d94f65ac2a5a94558d09ed6ce922258" + "c1a567952e863ac94297aec3c0d0c8ddf71084e504860bb6ba27449b55adc40e", + "5a8d9d0a22357e6655f9c785" + }, + { "940c89fe40a81dafbdb2416d14ae469119869744410c3303bfaa0241dac57800", + "a2eb8c0501e30bae0cf842d2bde8dec7386f6b7fc3981b8c57c9792bb94cf2dd", + "d8bb64aad8c9955a115a793addd24f7f2b077648714f49c4694ec995b330d09d" + "640df310f447fd7b6cb5c14f9fe9f490bcf8cfadbfd2169c8ac20d3b8af49a0c", + "b87d3813e03f58cf19fd0b6395" + }, + { "9acad959d216212d789a119252ebfe0c96512a23c73bd9f3b202292d6916a738", + "cf3af898467a5b7a52d33d53bc037e2642a8da996903fc252217e9c033e2f291", + "6ee3fe81e23c60eb2312b2006b3b25e6838e02106623f844c44edb8dafd66ab0" + "671087fd195df5b8f58a1d6e52af42908053d55c7321010092748795ef94cf06", + "55c7fa434f5ed8cdec2b7aeac173", + }, + { "d5aeee41eeb0e9d1bf8337f939587ebe296161e6bf5209f591ec939e1440c300", + "fd2a565723163e29f53c9de3d5e8fbe36a7ab66e1439ec4eae9c0a604af291a5", + "f68d04847e5b249737899c014d31c805c5007a62c0a10d50bb1538c5f3550395" + "1fbc1e08682f2cc0c92efe8f4985dec61dcbd54d4b94a22547d24451271c8b00", + "0a688e79be24f866286d4646b5d81c" + }, + + { NULL, NULL, NULL, NULL} + }; + + (void)arg; + + for (i = 0; items[i].pk; ++i) { + ed25519_keypair_t kp; + ed25519_signature_t sig; + uint8_t sk_seed[32]; + uint8_t *msg; + size_t msg_len; + base16_decode((char*)sk_seed, sizeof(sk_seed), + items[i].sk, 64); + ed25519_secret_key_from_seed(&kp.seckey, sk_seed); + tt_int_op(0, ==, ed25519_public_key_generate(&kp.pubkey, &kp.seckey)); + test_memeq_hex(kp.pubkey.pubkey, items[i].pk); + + msg_len = strlen(items[i].msg) / 2; + msg = tor_malloc(msg_len); + base16_decode((char*)msg, msg_len, items[i].msg, strlen(items[i].msg)); + + tt_int_op(0, ==, ed25519_sign(&sig, msg, msg_len, &kp)); + test_memeq_hex(sig.sig, items[i].sig); + + tor_free(msg); + } + + done: + tor_free(mem_op_hex_tmp); + } + #endif static void + test_crypto_ed25519_encode(void *arg) + { + char buf[ED25519_BASE64_LEN+1]; + ed25519_keypair_t kp; + ed25519_public_key_t pk; + char *mem_op_hex_tmp = NULL; + (void) arg; + + /* Test roundtrip. */ + tt_int_op(0, ==, ed25519_keypair_generate(&kp, 0)); + tt_int_op(0, ==, ed25519_public_to_base64(buf, &kp.pubkey)); + tt_int_op(ED25519_BASE64_LEN, ==, strlen(buf)); + tt_int_op(0, ==, ed25519_public_from_base64(&pk, buf)); - test_memeq(kp.pubkey.pubkey, pk.pubkey, ED25519_PUBKEY_LEN); ++ tt_mem_op(kp.pubkey.pubkey, ==, pk.pubkey, ED25519_PUBKEY_LEN); + + /* Test known value. */ + tt_int_op(0, ==, ed25519_public_from_base64(&pk, + "lVIuIctLjbGZGU5wKMNXxXlSE3cW4kaqkqm04u6pxvM")); + test_memeq_hex(pk.pubkey, + "95522e21cb4b8db199194e7028c357c57952137716e246aa92a9b4e2eea9c6f3"); + + done: + tor_free(mem_op_hex_tmp); + } + + static void + test_crypto_ed25519_convert(void *arg) + { + const uint8_t msg[] = + "The eyes are not here / There are no eyes here."; + const int N = 30; + int i; + (void)arg; + + for (i = 0; i < N; ++i) { + curve25519_keypair_t curve25519_keypair; + ed25519_keypair_t ed25519_keypair; + ed25519_public_key_t ed25519_pubkey; + + int bit=0; + ed25519_signature_t sig; + + tt_int_op(0,==,curve25519_keypair_generate(&curve25519_keypair, i&1)); + tt_int_op(0,==,ed25519_keypair_from_curve25519_keypair( + &ed25519_keypair, &bit, &curve25519_keypair)); + tt_int_op(0,==,ed25519_public_key_from_curve25519_public_key( + &ed25519_pubkey, &curve25519_keypair.pubkey, bit)); + tt_mem_op(ed25519_pubkey.pubkey, ==, ed25519_keypair.pubkey.pubkey, 32); + + tt_int_op(0,==,ed25519_sign(&sig, msg, sizeof(msg), &ed25519_keypair)); + tt_int_op(0,==,ed25519_checksig(&sig, msg, sizeof(msg), + &ed25519_pubkey)); + + tt_int_op(-1,==,ed25519_checksig(&sig, msg, sizeof(msg)-1, + &ed25519_pubkey)); + sig.sig[0] ^= 15; + tt_int_op(-1,==,ed25519_checksig(&sig, msg, sizeof(msg), + &ed25519_pubkey)); + } + + done: + ; + } + + static void + test_crypto_ed25519_blinding(void *arg) + { + const uint8_t msg[] = + "Eyes I dare not meet in dreams / In death's dream kingdom"; + + const int N = 30; + int i; + (void)arg; + + for (i = 0; i < N; ++i) { + uint8_t blinding[32]; + ed25519_keypair_t ed25519_keypair; + ed25519_keypair_t ed25519_keypair_blinded; + ed25519_public_key_t ed25519_pubkey_blinded; + + ed25519_signature_t sig; + + crypto_rand((char*) blinding, sizeof(blinding)); + + tt_int_op(0,==,ed25519_keypair_generate(&ed25519_keypair, 0)); + tt_int_op(0,==,ed25519_keypair_blind(&ed25519_keypair_blinded, + &ed25519_keypair, blinding)); + + tt_int_op(0,==,ed25519_public_blind(&ed25519_pubkey_blinded, + &ed25519_keypair.pubkey, blinding)); + + tt_mem_op(ed25519_pubkey_blinded.pubkey, ==, + ed25519_keypair_blinded.pubkey.pubkey, 32); + + tt_int_op(0,==,ed25519_sign(&sig, msg, sizeof(msg), + &ed25519_keypair_blinded)); + + tt_int_op(0,==,ed25519_checksig(&sig, msg, sizeof(msg), + &ed25519_pubkey_blinded)); + + tt_int_op(-1,==,ed25519_checksig(&sig, msg, sizeof(msg)-1, + &ed25519_pubkey_blinded)); + sig.sig[0] ^= 15; + tt_int_op(-1,==,ed25519_checksig(&sig, msg, sizeof(msg), + &ed25519_pubkey_blinded)); + } + + done: + ; + } + + static void + test_crypto_ed25519_testvectors(void *arg) + { + unsigned i; + char *mem_op_hex_tmp = NULL; + (void)arg; + + for (i = 0; i < ARRAY_LENGTH(ED25519_SECRET_KEYS); ++i) { + uint8_t sk[32]; + ed25519_secret_key_t esk; + ed25519_public_key_t pk, blind_pk, pkfromcurve; + ed25519_keypair_t keypair, blind_keypair; + curve25519_keypair_t curvekp; + uint8_t blinding_param[32]; + ed25519_signature_t sig; + int sign; + + #define DECODE(p,s) base16_decode((char*)(p),sizeof(p),(s),strlen(s)) + #define EQ(a,h) test_memeq_hex((const char*)(a), (h)) + + tt_int_op(0, ==, DECODE(sk, ED25519_SECRET_KEYS[i])); + tt_int_op(0, ==, DECODE(blinding_param, ED25519_BLINDING_PARAMS[i])); + + tt_int_op(0, ==, ed25519_secret_key_from_seed(&esk, sk)); + EQ(esk.seckey, ED25519_EXPANDED_SECRET_KEYS[i]); + + tt_int_op(0, ==, ed25519_public_key_generate(&pk, &esk)); + EQ(pk.pubkey, ED25519_PUBLIC_KEYS[i]); + + memcpy(&curvekp.seckey.secret_key, esk.seckey, 32); + curve25519_public_key_generate(&curvekp.pubkey, &curvekp.seckey); + + tt_int_op(0, ==, + ed25519_keypair_from_curve25519_keypair(&keypair, &sign, &curvekp)); + tt_int_op(0, ==, ed25519_public_key_from_curve25519_public_key( + &pkfromcurve, &curvekp.pubkey, sign)); + tt_mem_op(keypair.pubkey.pubkey, ==, pkfromcurve.pubkey, 32); + EQ(curvekp.pubkey.public_key, ED25519_CURVE25519_PUBLIC_KEYS[i]); + + /* Self-signing */ + memcpy(&keypair.seckey, &esk, sizeof(esk)); + memcpy(&keypair.pubkey, &pk, sizeof(pk)); + + tt_int_op(0, ==, ed25519_sign(&sig, pk.pubkey, 32, &keypair)); + + EQ(sig.sig, ED25519_SELF_SIGNATURES[i]); + + /* Blinding */ + tt_int_op(0, ==, + ed25519_keypair_blind(&blind_keypair, &keypair, blinding_param)); + tt_int_op(0, ==, + ed25519_public_blind(&blind_pk, &pk, blinding_param)); + + EQ(blind_keypair.seckey.seckey, ED25519_BLINDED_SECRET_KEYS[i]); + EQ(blind_pk.pubkey, ED25519_BLINDED_PUBLIC_KEYS[i]); + + tt_mem_op(blind_pk.pubkey, ==, blind_keypair.pubkey.pubkey, 32); + + #undef DECODE + #undef EQ + } + done: + tor_free(mem_op_hex_tmp); + } + + static void test_crypto_siphash(void *arg) { /* From the reference implementation, taking

1 0

[tor/master] Add comments to ed25519_vectors.inc
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit 9b43a4a122770c7dcb221d11ca7b5799a8274d49 Author: Nick Mathewson <nickm(a)torproject.org> Date: Sun Aug 31 20:01:53 2014 -0400 Add comments to ed25519_vectors.inc --- src/test/ed25519_exts_ref.py | 30 +++++++++++++++++++++++++++++- src/test/ed25519_vectors.inc | 38 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 67 insertions(+), 1 deletion(-) diff --git a/src/test/ed25519_exts_ref.py b/src/test/ed25519_exts_ref.py index 0df5541..93dc49e 100644 --- a/src/test/ed25519_exts_ref.py +++ b/src/test/ed25519_exts_ref.py @@ -16,6 +16,7 @@ import random import slownacl_curve25519 import unittest import binascii +import textwrap #define a synonym that doesn't look like 1 ell = l @@ -138,7 +139,7 @@ RAND_INPUTS = [ '4377c40431c30883c5fbd9bc92ae48d1ed8a47b81d13806beac5351739b5533d', 'c6bbcce615839756aed2cc78b1de13884dd3618f48367a17597a16c1cd7a290b'] -# From pprint.pprint([ binascii.b2a_hex(os.urandom(16)) for _ in xrange(8) ]) +# From pprint.pprint([ binascii.b2a_hex(os.urandom(32)) for _ in xrange(8) ]) BLINDING_PARAMS = [ '54a513898b471d1d448a2f3c55c1de2c0ef718c447b04497eeb999ed32027823', '831e9b5325b5d31b7ae6197e9c7a7baf2ec361e08248bce055908971047a2347', @@ -164,30 +165,57 @@ def writeArray(name, array): print ' "{0}",'.format(h) print "};\n" +def comment(text, initial="/**"): + print initial + print textwrap.fill(text,initial_indent=" * ",subsequent_indent=" * ") + print " */" + def makeTestVectors(): + comment("""Test vectors for our ed25519 implementation and related + functions. These were automatically generated by the + ed25519_exts_ref.py script.""", initial="/*") + + + comment("""Secret key seeds used as inputs for the ed25519 test vectors. + Randomly generated. """) secretKeys = [ binascii.a2b_hex(r) for r in RAND_INPUTS ] writeArray("SECRET_KEYS", secretKeys) + comment("""Secret ed25519 keys after expansion from seeds. This is how Tor + represents them internally.""") expandedSecretKeys = [ expandSK(sk) for sk in secretKeys ] writeArray("EXPANDED_SECRET_KEYS", expandedSecretKeys) + comment("""Public keys derived from the above secret keys""") publicKeys = [ publickey(sk) for sk in secretKeys ] writeArray("PUBLIC_KEYS", publicKeys) + comment("""The curve25519 public keys from which the ed25519 keys can be + derived. Used to test our 'derive ed25519 from curve25519' + code.""") writeArray("CURVE25519_PUBLIC_KEYS", (slownacl_curve25519.smult_curve25519_base(sk[:32]) for sk in expandedSecretKeys)) + comment("""Parameters used for key blinding tests. Randomly generated.""") blindingParams = [ binascii.a2b_hex(r) for r in BLINDING_PARAMS ] writeArray("BLINDING_PARAMS", blindingParams) + comment("""Blinded secret keys for testing key blinding. The nth blinded + key corresponds to the nth secret key blidned with the nth + blinding parameter.""") writeArray("BLINDED_SECRET_KEYS", (blindESK(expandSK(sk), bp) for sk,bp in zip(secretKeys,blindingParams))) + comment("""Blinded public keys for testing key blinding. The nth blinded + key corresponds to the nth public key blidned with the nth + blinding parameter.""") writeArray("BLINDED_PUBLIC_KEYS", (blindPK(pk, bp) for pk,bp in zip(publicKeys,blindingParams))) + comment("""Signatures of the public keys, made with their corresponding + secret keys.""") writeArray("SELF_SIGNATURES", (signature(pk, sk, pk) for pk,sk in zip(publicKeys,secretKeys))) diff --git a/src/test/ed25519_vectors.inc b/src/test/ed25519_vectors.inc index ef0a20b..760bafb 100644 --- a/src/test/ed25519_vectors.inc +++ b/src/test/ed25519_vectors.inc @@ -1,3 +1,12 @@ +/* + * Test vectors for our ed25519 implementation and related + * functions. These were automatically generated by the + * ed25519_exts_ref.py script. + */ +/** + * Secret key seeds used as inputs for the ed25519 test vectors. + * Randomly generated. + */ static const char *ED25519_SECRET_KEYS[] = { "26c76712d89d906e6672dafa614c42e5cb1caac8c6568e4d2493087db51f0d36", "fba7a5366b5cb98c2667a18783f5cf8f4f8d1a2ce939ad22a6e685edde85128d", @@ -9,6 +18,10 @@ static const char *ED25519_SECRET_KEYS[] = { "c6bbcce615839756aed2cc78b1de13884dd3618f48367a17597a16c1cd7a290b", }; +/** + * Secret ed25519 keys after expansion from seeds. This is how Tor + * represents them internally. + */ static const char *ED25519_EXPANDED_SECRET_KEYS[] = { "c0a4de23cc64392d85aa1da82b3defddbea946d13bb053bf8489fa9296281f495022f1" "f7ec0dcf52f07d4c7965c4eaed121d5d88d0a8ff546b06116a20e97755", @@ -28,6 +41,9 @@ static const char *ED25519_EXPANDED_SECRET_KEYS[] = { "ff8dcd0c6c233f665a2e176324d92416bfcfcd1f787424c0c667452d86", }; +/** + * Public keys derived from the above secret keys + */ static const char *ED25519_PUBLIC_KEYS[] = { "c2247870536a192d142d056abefca68d6193158e7c1a59c1654c954eccaff894", "1519a3b15816a1aafab0b213892026ebf5c0dc232c58b21088d88cb90e9b940d", @@ -39,6 +55,11 @@ static const char *ED25519_PUBLIC_KEYS[] = { "95126f14d86494020665face03f2d42ee2b312a85bc729903eb17522954a1c4a", }; +/** + * The curve25519 public keys from which the ed25519 keys can be + * derived. Used to test our 'derive ed25519 from curve25519' + * code. + */ static const char *ED25519_CURVE25519_PUBLIC_KEYS[] = { "17ba77846e04c7ee5ca17cade774ac1884408f9701f439d4df32cbd8736c6a1f", "022be2124bc1899a78ba2b4167d191af3b59cadf94f0382bc31ce183a117f161", @@ -50,6 +71,9 @@ static const char *ED25519_CURVE25519_PUBLIC_KEYS[] = { "861f33296cb57f8f01e4a5e8a7e5d5d7043a6247586ab36dea8a1a3c4403ee30", }; +/** + * Parameters used for key blinding tests. Randomly generated. + */ static const char *ED25519_BLINDING_PARAMS[] = { "54a513898b471d1d448a2f3c55c1de2c0ef718c447b04497eeb999ed32027823", "831e9b5325b5d31b7ae6197e9c7a7baf2ec361e08248bce055908971047a2347", @@ -61,6 +85,11 @@ static const char *ED25519_BLINDING_PARAMS[] = { "3f44f6a5a92cde816635dfc12ade70539871078d2ff097278be2a555c9859cd0", }; +/** + * Blinded secret keys for testing key blinding. The nth blinded + * key corresponds to the nth secret key blidned with the nth + * blinding parameter. + */ static const char *ED25519_BLINDED_SECRET_KEYS[] = { "014e83abadb2ca9a27e0ffe23920333d817729f48700e97656ec2823d694050e171d43" "f24e3f53e70ec7ac280044ac77d4942dee5d6807118a59bdf3ee647e89", @@ -80,6 +109,11 @@ static const char *ED25519_BLINDED_SECRET_KEYS[] = { "00c81e1331c06ab50087be8cfc7dc11691b132614474f1aa9c2503cccd", }; +/** + * Blinded public keys for testing key blinding. The nth blinded + * key corresponds to the nth public key blidned with the nth + * blinding parameter. + */ static const char *ED25519_BLINDED_PUBLIC_KEYS[] = { "722d6da6348e618967ef782e71061e27163a8b35f21856475d9d2023f65b6495", "1dffa0586da6cbfcff2024eedf4fc6c818242d9a82dbbe635d6da1b975a1160d", @@ -91,6 +125,10 @@ static const char *ED25519_BLINDED_PUBLIC_KEYS[] = { "9f297ff0aa2ceda91c5ab1b6446f12533d145940de6d850dc323417afde0cb78", }; +/** + * Signatures of the public keys, made with their corresponding + * secret keys. + */ static const char *ED25519_SELF_SIGNATURES[] = { "d23188eac3773a316d46006fa59c095060be8b1a23582a0dd99002a82a0662bd246d84" "49e172e04c5f46ac0d1404cebe4aabd8a75a1457aa06cae41f3334f104",

1 0

[tor/master] Add benchmarks for ed25519 functions
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit 6dbd451b9f7542b16f64415a57a1af26723f8645 Author: Nick Mathewson <nickm(a)torproject.org> Date: Thu Sep 25 10:13:25 2014 -0400 Add benchmarks for ed25519 functions --- src/test/bench.c | 62 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 62 insertions(+) diff --git a/src/test/bench.c b/src/test/bench.c index f6c3362..98e45d2 100644 --- a/src/test/bench.c +++ b/src/test/bench.c @@ -30,6 +30,7 @@ const char tor_git_revision[] = ""; #include "crypto_curve25519.h" #include "onion_ntor.h" #endif +#include "crypto_ed25519.h" #if defined(HAVE_CLOCK_GETTIME) && defined(CLOCK_PROCESS_CPUTIME_ID) static uint64_t nanostart; @@ -79,6 +80,9 @@ perftime(void) #define NANOCOUNT(start,end,iters) \ ( ((double)((end)-(start))) / (iters) ) +#define MICROCOUNT(start,end,iters) \ + ( NANOCOUNT((start), (end), (iters)) / 1000.0 ) + /** Run AES performance benchmarks. */ static void bench_aes(void) @@ -235,6 +239,63 @@ bench_onion_ntor(void) #endif static void +bench_ed25519(void) +{ + uint64_t start, end; + const int iters = 1<<12; + int i; + const uint8_t msg[] = "but leaving, could not tell what they had heard"; + ed25519_signature_t sig; + ed25519_keypair_t kp; + curve25519_keypair_t curve_kp; + ed25519_public_key_t pubkey_tmp; + + ed25519_secret_key_generate(&kp.seckey, 0); + start = perftime(); + for (i = 0; i < iters; ++i) { + ed25519_public_key_generate(&kp.pubkey, &kp.seckey); + } + end = perftime(); + printf("Generate public key: %.2f usec\n", + MICROCOUNT(start, end, iters)); + + start = perftime(); + for (i = 0; i < iters; ++i) { + ed25519_sign(&sig, msg, sizeof(msg), &kp); + } + end = perftime(); + printf("Sign a short message: %.2f usec\n", + MICROCOUNT(start, end, iters)); + + start = perftime(); + for (i = 0; i < iters; ++i) { + ed25519_checksig(&sig, msg, sizeof(msg), &kp.pubkey); + } + end = perftime(); + printf("Verify signature: %.2f usec\n", + MICROCOUNT(start, end, iters)); + + curve25519_keypair_generate(&curve_kp, 0); + start = perftime(); + for (i = 0; i < iters; ++i) { + ed25519_public_key_from_curve25519_public_key(&pubkey_tmp, + &curve_kp.pubkey, 1); + } + end = perftime(); + printf("Convert public point from curve25519: %.2f usec\n", + MICROCOUNT(start, end, iters)); + + curve25519_keypair_generate(&curve_kp, 0); + start = perftime(); + for (i = 0; i < iters; ++i) { + ed25519_public_blind(&pubkey_tmp, &kp.pubkey, msg); + } + end = perftime(); + printf("Blind a public key: %.2f usec\n", + MICROCOUNT(start, end, iters)); +} + +static void bench_cell_aes(void) { uint64_t start, end; @@ -515,6 +576,7 @@ static struct benchmark_t benchmarks[] = { #ifdef CURVE25519_ENABLED ENT(onion_ntor), #endif + ENT(ed25519), ENT(cell_aes), ENT(cell_ops), ENT(dh),

1 0

[tor/master] Comments and tweaks based on review by asn
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit 46cda485bce60894d3128dcd42831a8c6cc7bcb4 Author: Nick Mathewson <nickm(a)torproject.org> Date: Thu Sep 25 15:03:55 2014 -0400 Comments and tweaks based on review by asn Add some documentation Rename "derive" -> "blind" Check for failure on randombytes(). --- src/common/crypto_curve25519.c | 14 ++++++++++++-- src/common/crypto_ed25519.c | 6 ++++-- src/ext/ed25519/ref10/blinding.c | 9 +++++---- src/ext/ed25519/ref10/crypto_hash_sha512.h | 7 +++++++ src/ext/ed25519/ref10/ed25519_ref10.h | 4 ++-- src/ext/ed25519/ref10/keypair.c | 5 +++-- src/ext/ed25519/ref10/open.c | 2 ++ src/ext/ed25519/ref10/sign.c | 1 + 8 files changed, 36 insertions(+), 12 deletions(-) diff --git a/src/common/crypto_curve25519.c b/src/common/crypto_curve25519.c index 484dd76..44b280a 100644 --- a/src/common/crypto_curve25519.c +++ b/src/common/crypto_curve25519.c @@ -128,7 +128,13 @@ curve25519_keypair_generate(curve25519_keypair_t *keypair_out, return 0; } -/** DOCDOC */ +/** Write the datalen bytes from data to the file named + * fname in the tagged-data format. This format contains a + * 32-byte header, followed by the data itself. The header is the + * NUL-padded string "== typestring: tag ==". The length + * of typestring and tag must therefore be no more than + * 24. + **/ int crypto_write_tagged_contents_to_file(const char *fname, const char *typestring, @@ -159,7 +165,11 @@ crypto_write_tagged_contents_to_file(const char *fname, return r; } -/** DOCDOC */ +/** Read a tagged-data file from fname into the + * data_out_len-byte buffer in data_out. Check that the + * typestring matches typestring; store the tag into a newly allocated + * string in tag_out. Return -1 on failure, and the number of bytes of + * data on success. */ ssize_t crypto_read_tagged_contents_from_file(const char *fname, const char *typestring, diff --git a/src/common/crypto_ed25519.c b/src/common/crypto_ed25519.c index a545cad..408c12b 100644 --- a/src/common/crypto_ed25519.c +++ b/src/common/crypto_ed25519.c @@ -138,6 +138,8 @@ ed25519_checksig_batch(int *okay_out, } #if 0 + /* This is how we'd do it if we were using ed25519_donna. I'll keep this + * code around here in case we ever do that. */ const uint8_t **ms; size_t *lens; const uint8_t **pks; @@ -249,7 +251,7 @@ ed25519_keypair_blind(ed25519_keypair_t *out, { ed25519_public_key_t pubkey_check; - ed25519_ref10_derive_secret_key(out->seckey.seckey, + ed25519_ref10_blind_secret_key(out->seckey.seckey, inp->seckey.seckey, param); ed25519_public_blind(&pubkey_check, &inp->pubkey, param); @@ -272,7 +274,7 @@ ed25519_public_blind(ed25519_public_key_t *out, const ed25519_public_key_t *inp, const uint8_t *param) { - ed25519_ref10_derive_public_key(out->pubkey, inp->pubkey, param); + ed25519_ref10_blind_public_key(out->pubkey, inp->pubkey, param); return 0; } diff --git a/src/ext/ed25519/ref10/blinding.c b/src/ext/ed25519/ref10/blinding.c index f0154e0..4d9a9cb 100644 --- a/src/ext/ed25519/ref10/blinding.c +++ b/src/ext/ed25519/ref10/blinding.c @@ -19,7 +19,7 @@ gettweak(unsigned char *out, const unsigned char *param) out[31] |= 64; } -int ed25519_ref10_derive_secret_key(unsigned char *out, +int ed25519_ref10_blind_secret_key(unsigned char *out, const unsigned char *inp, const unsigned char *param) { @@ -40,7 +40,7 @@ int ed25519_ref10_derive_secret_key(unsigned char *out, return 0; } -int ed25519_ref10_derive_public_key(unsigned char *out, +int ed25519_ref10_blind_public_key(unsigned char *out, const unsigned char *inp, const unsigned char *param) { @@ -58,7 +58,8 @@ int ed25519_ref10_derive_public_key(unsigned char *out, * strongly that I'm about to code my own ge_scalarmult_vartime). */ /* We negate the public key first, so that we can pass it to - * frombytes_negate_vartime, which negates it again. */ + * frombytes_negate_vartime, which negates it again. If there were a + * "ge_frombytes", we'd use that, but there isn't. */ memcpy(pkcopy, inp, 32); pkcopy[31] ^= (1<<7); ge_frombytes_negate_vartime(&A, pkcopy); @@ -69,7 +70,7 @@ int ed25519_ref10_derive_public_key(unsigned char *out, memwipe(tweak, 0, sizeof(tweak)); memwipe(&A, 0, sizeof(A)); memwipe(&Aprime, 0, sizeof(Aprime)); - memwipe(&pkcopy, 0, sizeof(pkcopy)); + memwipe(pkcopy, 0, sizeof(pkcopy)); return 0; } diff --git a/src/ext/ed25519/ref10/crypto_hash_sha512.h b/src/ext/ed25519/ref10/crypto_hash_sha512.h index c819b8d..0278571 100644 --- a/src/ext/ed25519/ref10/crypto_hash_sha512.h +++ b/src/ext/ed25519/ref10/crypto_hash_sha512.h @@ -1,8 +1,12 @@ /* Added for Tor. */ #include <openssl/sha.h> + +/* Set 'out' to the 512-bit SHA512 hash of the 'len'-byte string in 'inp' */ #define crypto_hash_sha512(out, inp, len) \ SHA512((inp), (len), (out)) +/* Set 'out' to the 512-bit SHA512 hash of the 'len1'-byte string in 'inp1', + * concatenated with the 'len2'-byte string in 'inp2'. */ #define crypto_hash_sha512_2(out, inp1, len1, inp2, len2) \ do { \ SHA512_CTX sha_ctx_; \ @@ -12,6 +16,9 @@ SHA512_Final((out), &sha_ctx_); \ } while(0) +/* Set 'out' to the 512-bit SHA512 hash of the 'len1'-byte string in 'inp1', + * concatenated with the 'len2'-byte string in 'inp2', concatenated with + * the 'len3'-byte string in 'len3'. */ #define crypto_hash_sha512_3(out, inp1, len1, inp2, len2, inp3, len3) \ do { \ SHA512_CTX sha_ctx_; \ diff --git a/src/ext/ed25519/ref10/ed25519_ref10.h b/src/ext/ed25519/ref10/ed25519_ref10.h index f4a76e6..8c77b0e 100644 --- a/src/ext/ed25519/ref10/ed25519_ref10.h +++ b/src/ext/ed25519/ref10/ed25519_ref10.h @@ -20,10 +20,10 @@ int ed25519_ref10_sign( int ed25519_ref10_pubkey_from_curve25519_pubkey(unsigned char *out, const unsigned char *inp, int signbit); -int ed25519_ref10_derive_secret_key(unsigned char *out, +int ed25519_ref10_blind_secret_key(unsigned char *out, const unsigned char *inp, const unsigned char *param); -int ed25519_ref10_derive_public_key(unsigned char *out, +int ed25519_ref10_blind_public_key(unsigned char *out, const unsigned char *inp, const unsigned char *param); diff --git a/src/ext/ed25519/ref10/keypair.c b/src/ext/ed25519/ref10/keypair.c index e861998..7ddbaa9 100644 --- a/src/ext/ed25519/ref10/keypair.c +++ b/src/ext/ed25519/ref10/keypair.c @@ -1,4 +1,4 @@ -/* Modified for Tor: new API, 32-byte secret keys. */ +/* Modified for Tor: new API, 64-byte secret keys. */ #include <string.h> #include "randombytes.h" #include "crypto_sign.h" @@ -10,7 +10,8 @@ crypto_sign_seckey(unsigned char *sk) { unsigned char seed[32]; - randombytes(seed,32); + if (randombytes(seed,32) < 0) + return -1; crypto_sign_seckey_expand(sk, seed); diff --git a/src/ext/ed25519/ref10/open.c b/src/ext/ed25519/ref10/open.c index 790f668..0e7abba 100644 --- a/src/ext/ed25519/ref10/open.c +++ b/src/ext/ed25519/ref10/open.c @@ -1,3 +1,4 @@ +/* (Modified by Tor to verify signature separately from message) */ #include <string.h> #include "crypto_sign.h" #include "crypto_hash_sha512.h" @@ -5,6 +6,7 @@ #include "ge.h" #include "sc.h" +/* 'signature' must be 64-bytes long. */ int crypto_sign_open( const unsigned char *signature, const unsigned char *m,uint64_t mlen, diff --git a/src/ext/ed25519/ref10/sign.c b/src/ext/ed25519/ref10/sign.c index c11fca9..e37b0d1 100644 --- a/src/ext/ed25519/ref10/sign.c +++ b/src/ext/ed25519/ref10/sign.c @@ -1,3 +1,4 @@ +/* (Modified by Tor to generate detached signatures.) */ #include <string.h> #include "crypto_sign.h" #include "crypto_hash_sha512.h"

1 0

[tor/master] Integrate ed25519_ref10 into our build system.
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit 4847136d2c56217f639875f168892eac6e914fec Author: Nick Mathewson <nickm(a)torproject.org> Date: Tue Aug 26 10:11:56 2014 -0400 Integrate ed25519_ref10 into our build system. --- src/ext/README | 6 +++++ src/ext/include.am | 63 ++++++++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 69 insertions(+) diff --git a/src/ext/README b/src/ext/README index 5d5a6e1..b759fc2 100644 --- a/src/ext/README +++ b/src/ext/README @@ -49,3 +49,9 @@ siphash.h Marek Majkowski's implementation of siphash 2-4, a secure keyed hash algorithm to avoid collision-based DoS attacks against hash tables. + +ed25519/ref10/* + + Daniel Bernsten's portable ref10 implementation of ed25519. + Public domain. + diff --git a/src/ext/include.am b/src/ext/include.am index 26e194e..88025f6 100644 --- a/src/ext/include.am +++ b/src/ext/include.am @@ -15,4 +15,67 @@ EXTHEADERS = \ noinst_HEADERS+= $(EXTHEADERS) +src_ext_ed25519_ref10_libed25519_ref10_a_CFLAGS= + +src_ext_ed25519_ref10_libed25519_ref10_a_SOURCES= \ + src/ext/ed25519/ref10/fe_0.c \ + src/ext/ed25519/ref10/fe_1.c \ + src/ext/ed25519/ref10/fe_add.c \ + src/ext/ed25519/ref10/fe_cmov.c \ + src/ext/ed25519/ref10/fe_copy.c \ + src/ext/ed25519/ref10/fe_frombytes.c \ + src/ext/ed25519/ref10/fe_invert.c \ + src/ext/ed25519/ref10/fe_isnegative.c \ + src/ext/ed25519/ref10/fe_isnonzero.c \ + src/ext/ed25519/ref10/fe_mul.c \ + src/ext/ed25519/ref10/fe_neg.c \ + src/ext/ed25519/ref10/fe_pow22523.c \ + src/ext/ed25519/ref10/fe_sq.c \ + src/ext/ed25519/ref10/fe_sq2.c \ + src/ext/ed25519/ref10/fe_sub.c \ + src/ext/ed25519/ref10/fe_tobytes.c \ + src/ext/ed25519/ref10/ge_add.c \ + src/ext/ed25519/ref10/ge_double_scalarmult.c \ + src/ext/ed25519/ref10/ge_frombytes.c \ + src/ext/ed25519/ref10/ge_madd.c \ + src/ext/ed25519/ref10/ge_msub.c \ + src/ext/ed25519/ref10/ge_p1p1_to_p2.c \ + src/ext/ed25519/ref10/ge_p1p1_to_p3.c \ + src/ext/ed25519/ref10/ge_p2_0.c \ + src/ext/ed25519/ref10/ge_p2_dbl.c \ + src/ext/ed25519/ref10/ge_p3_0.c \ + src/ext/ed25519/ref10/ge_p3_dbl.c \ + src/ext/ed25519/ref10/ge_p3_to_cached.c \ + src/ext/ed25519/ref10/ge_p3_to_p2.c \ + src/ext/ed25519/ref10/ge_p3_tobytes.c \ + src/ext/ed25519/ref10/ge_precomp_0.c \ + src/ext/ed25519/ref10/ge_scalarmult_base.c \ + src/ext/ed25519/ref10/ge_sub.c \ + src/ext/ed25519/ref10/ge_tobytes.c \ + src/ext/ed25519/ref10/keypair.c \ + src/ext/ed25519/ref10/open.c \ + src/ext/ed25519/ref10/sc_muladd.c \ + src/ext/ed25519/ref10/sc_reduce.c \ + src/ext/ed25519/ref10/sign.c + +ED25519_REF10_HDRS = \ + src/ext/ed25519/ref10/api.h \ + src/ext/ed25519/ref10/base.h \ + src/ext/ed25519/ref10/base2.h \ + src/ext/ed25519/ref10/d.h \ + src/ext/ed25519/ref10/d2.h \ + src/ext/ed25519/ref10/fe.h \ + src/ext/ed25519/ref10/ge.h \ + src/ext/ed25519/ref10/ge_add.h \ + src/ext/ed25519/ref10/ge_madd.h \ + src/ext/ed25519/ref10/ge_msub.h \ + src/ext/ed25519/ref10/ge_p2_dbl.h \ + src/ext/ed25519/ref10/ge_sub.h \ + src/ext/ed25519/ref10/pow22523.h \ + src/ext/ed25519/ref10/pow225521.h \ + src/ext/ed25519/ref10/sc.h \ + src/ext/ed25519/ref10/sqrtm1.h + +noinst_HEADERS += $(ED25519_REF10_HDRS) +noinst_LIBRARIES += src/ext/ed25519/ref10/libed25519_ref10.a

1 0

[tor/master] Add headers as needed to make ed25519_ref10 compile.
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit 8b36bb92998d4081ae99ea733a8f4ec57c0a8f04 Author: Nick Mathewson <nickm(a)torproject.org> Date: Tue Aug 26 10:56:22 2014 -0400 Add headers as needed to make ed25519_ref10 compile. --- src/ext/ed25519/ref10/crypto_hash_sha512.h | 4 ++++ src/ext/ed25519/ref10/crypto_int32.h | 3 +++ src/ext/ed25519/ref10/crypto_int64.h | 3 +++ src/ext/ed25519/ref10/crypto_sign.h | 6 ++++++ src/ext/ed25519/ref10/crypto_uint32.h | 3 +++ src/ext/ed25519/ref10/crypto_uint64.h | 3 +++ src/ext/ed25519/ref10/crypto_verify_32.h | 5 +++++ src/ext/ed25519/ref10/ed25519_ref10.h | 16 ++++++++++++++++ src/ext/ed25519/ref10/randombytes.h | 4 ++++ 9 files changed, 47 insertions(+) diff --git a/src/ext/ed25519/ref10/crypto_hash_sha512.h b/src/ext/ed25519/ref10/crypto_hash_sha512.h new file mode 100644 index 0000000..fa768ac --- /dev/null +++ b/src/ext/ed25519/ref10/crypto_hash_sha512.h @@ -0,0 +1,4 @@ +/* Added for Tor. */ +#include <openssl/sha.h> +#define crypto_hash_sha512(out, inp, len) \ + SHA512((inp), (len), (out)) diff --git a/src/ext/ed25519/ref10/crypto_int32.h b/src/ext/ed25519/ref10/crypto_int32.h new file mode 100644 index 0000000..cd5c7c2 --- /dev/null +++ b/src/ext/ed25519/ref10/crypto_int32.h @@ -0,0 +1,3 @@ +/* Added for Tor. */ +#include "torint.h" +#define crypto_int32 int32_t diff --git a/src/ext/ed25519/ref10/crypto_int64.h b/src/ext/ed25519/ref10/crypto_int64.h new file mode 100644 index 0000000..de0b602 --- /dev/null +++ b/src/ext/ed25519/ref10/crypto_int64.h @@ -0,0 +1,3 @@ +/* Added for Tor. */ +#include "torint.h" +#define crypto_int64 int64_t diff --git a/src/ext/ed25519/ref10/crypto_sign.h b/src/ext/ed25519/ref10/crypto_sign.h new file mode 100644 index 0000000..627ba0a --- /dev/null +++ b/src/ext/ed25519/ref10/crypto_sign.h @@ -0,0 +1,6 @@ +/* Added for Tor */ +#define crypto_sign ed25519_ref10_sign +#define crypto_sign_keypair ed25519_ref10_keygen +#define crypto_sign_open ed25519_ref10_open + +#include "ed25519_ref10.h" diff --git a/src/ext/ed25519/ref10/crypto_uint32.h b/src/ext/ed25519/ref10/crypto_uint32.h new file mode 100644 index 0000000..62655a5 --- /dev/null +++ b/src/ext/ed25519/ref10/crypto_uint32.h @@ -0,0 +1,3 @@ +/* Added for Tor. */ +#include "torint.h" +#define crypto_uint32 uint32_t diff --git a/src/ext/ed25519/ref10/crypto_uint64.h b/src/ext/ed25519/ref10/crypto_uint64.h new file mode 100644 index 0000000..cbda882 --- /dev/null +++ b/src/ext/ed25519/ref10/crypto_uint64.h @@ -0,0 +1,3 @@ +/* Added for Tor. */ +#include "torint.h" +#define crypto_uint64 uint64_t diff --git a/src/ext/ed25519/ref10/crypto_verify_32.h b/src/ext/ed25519/ref10/crypto_verify_32.h new file mode 100644 index 0000000..0f63efc --- /dev/null +++ b/src/ext/ed25519/ref10/crypto_verify_32.h @@ -0,0 +1,5 @@ +/* Added for Tor. */ +#include "di_ops.h" +#define crypto_verify_32(a,b) \ + (! tor_memeq((a), (b), 32)) + diff --git a/src/ext/ed25519/ref10/ed25519_ref10.h b/src/ext/ed25519/ref10/ed25519_ref10.h new file mode 100644 index 0000000..fc10a26 --- /dev/null +++ b/src/ext/ed25519/ref10/ed25519_ref10.h @@ -0,0 +1,16 @@ +/* Added for Tor */ +#ifndef SRC_EXT_ED25519_REF10_H_INCLUDED_ +#define SRC_EXT_ED25519_REF10_H_INCLUDED_ +#include <torint.h> + +int ed25519_ref10_keygen(unsigned char *pk,unsigned char *sk); +int ed25519_ref10_open( + unsigned char *m,uint64_t *mlen, + const unsigned char *sm,uint64_t smlen, + const unsigned char *pk); +int ed25519_ref10_sign( + unsigned char *sm,uint64_t *smlen, + const unsigned char *m,uint64_t mlen, + const unsigned char *sk); + +#endif diff --git a/src/ext/ed25519/ref10/randombytes.h b/src/ext/ed25519/ref10/randombytes.h new file mode 100644 index 0000000..fc709fc --- /dev/null +++ b/src/ext/ed25519/ref10/randombytes.h @@ -0,0 +1,4 @@ +/* Added for Tor. */ +#include "crypto.h" +#define randombytes(b, n) \ + (crypto_strongest_rand((b), (n)))

1 0

[tor/master] Add the ed25519 ref10 code verbatim from supercop-20140622
by nickm＠torproject.org 25 Sep '14

25 Sep '14

commit b40ac6808f8a31f2f95de435036a6a7af111fdff Author: Nick Mathewson <nickm(a)torproject.org> Date: Tue Aug 26 10:08:44 2014 -0400 Add the ed25519 ref10 code verbatim from supercop-20140622 We might use libsodium or ed25519-donna later on, but for now, let's see whether this is fast enough. We should use it in all cases when performance doesn't matter. --- src/ext/ed25519/ref10/Makefile | 41 + src/ext/ed25519/ref10/api.h | 4 + src/ext/ed25519/ref10/base.h | 1344 ++++++++++++++++++++++++++ src/ext/ed25519/ref10/base.py | 65 ++ src/ext/ed25519/ref10/base2.h | 40 + src/ext/ed25519/ref10/base2.py | 60 ++ src/ext/ed25519/ref10/d.h | 1 + src/ext/ed25519/ref10/d.py | 28 + src/ext/ed25519/ref10/d2.h | 1 + src/ext/ed25519/ref10/d2.py | 28 + src/ext/ed25519/ref10/fe.h | 56 ++ src/ext/ed25519/ref10/fe_0.c | 19 + src/ext/ed25519/ref10/fe_1.c | 19 + src/ext/ed25519/ref10/fe_add.c | 57 ++ src/ext/ed25519/ref10/fe_cmov.c | 63 ++ src/ext/ed25519/ref10/fe_copy.c | 29 + src/ext/ed25519/ref10/fe_frombytes.c | 73 ++ src/ext/ed25519/ref10/fe_invert.c | 14 + src/ext/ed25519/ref10/fe_isnegative.c | 16 + src/ext/ed25519/ref10/fe_isnonzero.c | 19 + src/ext/ed25519/ref10/fe_mul.c | 253 +++++ src/ext/ed25519/ref10/fe_neg.c | 45 + src/ext/ed25519/ref10/fe_pow22523.c | 13 + src/ext/ed25519/ref10/fe_sq.c | 149 +++ src/ext/ed25519/ref10/fe_sq2.c | 160 +++ src/ext/ed25519/ref10/fe_sub.c | 57 ++ src/ext/ed25519/ref10/fe_tobytes.c | 119 +++ src/ext/ed25519/ref10/ge.h | 95 ++ src/ext/ed25519/ref10/ge_add.c | 11 + src/ext/ed25519/ref10/ge_add.h | 97 ++ src/ext/ed25519/ref10/ge_add.q | 49 + src/ext/ed25519/ref10/ge_double_scalarmult.c | 96 ++ src/ext/ed25519/ref10/ge_frombytes.c | 50 + src/ext/ed25519/ref10/ge_madd.c | 11 + src/ext/ed25519/ref10/ge_madd.h | 88 ++ src/ext/ed25519/ref10/ge_madd.q | 46 + src/ext/ed25519/ref10/ge_msub.c | 11 + src/ext/ed25519/ref10/ge_msub.h | 88 ++ src/ext/ed25519/ref10/ge_msub.q | 46 + src/ext/ed25519/ref10/ge_p1p1_to_p2.c | 12 + src/ext/ed25519/ref10/ge_p1p1_to_p3.c | 13 + src/ext/ed25519/ref10/ge_p2_0.c | 8 + src/ext/ed25519/ref10/ge_p2_dbl.c | 11 + src/ext/ed25519/ref10/ge_p2_dbl.h | 73 ++ src/ext/ed25519/ref10/ge_p2_dbl.q | 41 + src/ext/ed25519/ref10/ge_p3_0.c | 9 + src/ext/ed25519/ref10/ge_p3_dbl.c | 12 + src/ext/ed25519/ref10/ge_p3_to_cached.c | 17 + src/ext/ed25519/ref10/ge_p3_to_p2.c | 12 + src/ext/ed25519/ref10/ge_p3_tobytes.c | 14 + src/ext/ed25519/ref10/ge_precomp_0.c | 8 + src/ext/ed25519/ref10/ge_scalarmult_base.c | 105 ++ src/ext/ed25519/ref10/ge_sub.c | 11 + src/ext/ed25519/ref10/ge_sub.h | 97 ++ src/ext/ed25519/ref10/ge_sub.q | 49 + src/ext/ed25519/ref10/ge_tobytes.c | 14 + src/ext/ed25519/ref10/keypair.c | 23 + src/ext/ed25519/ref10/open.c | 48 + src/ext/ed25519/ref10/pow22523.h | 160 +++ src/ext/ed25519/ref10/pow22523.q | 61 ++ src/ext/ed25519/ref10/pow225521.h | 160 +++ src/ext/ed25519/ref10/pow225521.q | 61 ++ src/ext/ed25519/ref10/q2h.sh | 4 + src/ext/ed25519/ref10/sc.h | 15 + src/ext/ed25519/ref10/sc_muladd.c | 368 +++++++ src/ext/ed25519/ref10/sc_reduce.c | 275 ++++++ src/ext/ed25519/ref10/sign.c | 41 + src/ext/ed25519/ref10/sqrtm1.h | 1 + src/ext/ed25519/ref10/sqrtm1.py | 28 + 69 files changed, 5212 insertions(+) diff --git a/src/ext/ed25519/ref10/Makefile b/src/ext/ed25519/ref10/Makefile new file mode 100644 index 0000000..9b0ba7a --- /dev/null +++ b/src/ext/ed25519/ref10/Makefile @@ -0,0 +1,41 @@ +all: d.h d2.h sqrtm1.h base.h base2.h \ +ge_add.h ge_sub.h \ +ge_madd.h ge_msub.h \ +ge_p2_dbl.h \ +pow225521.h pow22523.h + +d.h: d.py + python d.py > d.h + +d2.h: d2.py + python d2.py > d2.h + +sqrtm1.h: sqrtm1.py + python sqrtm1.py > sqrtm1.h + +base.h: base.py + python base.py > base.h + +base2.h: base2.py + python base2.py > base2.h + +ge_add.h: ge_add.q q2h.sh + ./q2h.sh < ge_add.q > ge_add.h + +ge_sub.h: ge_sub.q q2h.sh + ./q2h.sh < ge_sub.q > ge_sub.h + +ge_madd.h: ge_madd.q q2h.sh + ./q2h.sh < ge_madd.q > ge_madd.h + +ge_msub.h: ge_msub.q q2h.sh + ./q2h.sh < ge_msub.q > ge_msub.h + +ge_p2_dbl.h: ge_p2_dbl.q q2h.sh + ./q2h.sh < ge_p2_dbl.q > ge_p2_dbl.h + +pow22523.h: pow22523.q q2h.sh + ./q2h.sh < pow22523.q > pow22523.h + +pow225521.h: pow225521.q q2h.sh + ./q2h.sh < pow225521.q > pow225521.h diff --git a/src/ext/ed25519/ref10/api.h b/src/ext/ed25519/ref10/api.h new file mode 100644 index 0000000..d88dae0 --- /dev/null +++ b/src/ext/ed25519/ref10/api.h @@ -0,0 +1,4 @@ +#define CRYPTO_SECRETKEYBYTES 64 +#define CRYPTO_PUBLICKEYBYTES 32 +#define CRYPTO_BYTES 64 +#define CRYPTO_DETERMINISTIC 1 diff --git a/src/ext/ed25519/ref10/base.h b/src/ext/ed25519/ref10/base.h new file mode 100644 index 0000000..573bd8a --- /dev/null +++ b/src/ext/ed25519/ref10/base.h @@ -0,0 +1,1344 @@ +{ + { + { 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 }, + { 23152971,775386,27395463,14006635,-9701118,4649512,1689819,892185,-11513277,-15205948 }, + }, + { + { 9770129,9586738,26496094,4324120,1556511,-3550024,27453819,4763127,-19179614,5867134 }, + { -32765025,1927590,31726409,-4753295,23962434,-16019500,27846559,5931263,-29749703,-16108455 }, + { 27461885,-2977536,22380810,1815854,-23033753,-3031938,7283490,-15148073,-19526700,7734629 }, + }, +}, +{ + { + { -8010264,-9590817,-11120403,6196038,29344158,-13430885,7585295,-3176626,18549497,15302069 }, + { -32658337,-6171222,-7672793,-11051681,6258878,13504381,10458790,-6418461,-8872242,8424746 }, + { 24687205,8613276,-30667046,-3233545,1863892,-1830544,19206234,7134917,-11284482,-828919 }, + }, + { + { 11334899,-9218022,8025293,12707519,17523892,-10476071,10243738,-14685461,-5066034,16498837 }, + { 8911542,6887158,-9584260,-6958590,11145641,-9543680,17303925,-14124238,6536641,10543906 }, + { -28946384,15479763,-17466835,568876,-1497683,11223454,-2669190,-16625574,-27235709,8876771 }, + }, + { + { -25742899,-12566864,-15649966,-846607,-33026686,-796288,-33481822,15824474,-604426,-9039817 }, + { 10330056,70051,7957388,-9002667,9764902,15609756,27698697,-4890037,1657394,3084098 }, + { 10477963,-7470260,12119566,-13250805,29016247,-5365589,31280319,14396151,-30233575,15272409 }, + }, + { + { -12288309,3169463,28813183,16658753,25116432,-5630466,-25173957,-12636138,-25014757,1950504 }, + { -26180358,9489187,11053416,-14746161,-31053720,5825630,-8384306,-8767532,15341279,8373727 }, + { 28685821,7759505,-14378516,-12002860,-31971820,4079242,298136,-10232602,-2878207,15190420 }, + }, + { + { -32932876,13806336,-14337485,-15794431,-24004620,10940928,8669718,2742393,-26033313,-6875003 }, + { -1580388,-11729417,-25979658,-11445023,-17411874,-10912854,9291594,-16247779,-12154742,6048605 }, + { -30305315,14843444,1539301,11864366,20201677,1900163,13934231,5128323,11213262,9168384 }, + }, + { + { -26280513,11007847,19408960,-940758,-18592965,-4328580,-5088060,-11105150,20470157,-16398701 }, + { -23136053,9282192,14855179,-15390078,-7362815,-14408560,-22783952,14461608,14042978,5230683 }, + { 29969567,-2741594,-16711867,-8552442,9175486,-2468974,21556951,3506042,-5933891,-12449708 }, + }, + { + { -3144746,8744661,19704003,4581278,-20430686,6830683,-21284170,8971513,-28539189,15326563 }, + { -19464629,10110288,-17262528,-3503892,-23500387,1355669,-15523050,15300988,-20514118,9168260 }, + { -5353335,4488613,-23803248,16314347,7780487,-15638939,-28948358,9601605,33087103,-9011387 }, + }, + { + { -19443170,-15512900,-20797467,-12445323,-29824447,10229461,-27444329,-15000531,-5996870,15664672 }, + { 23294591,-16632613,-22650781,-8470978,27844204,11461195,13099750,-2460356,18151676,13417686 }, + { -24722913,-4176517,-31150679,5988919,-26858785,6685065,1661597,-12551441,15271676,-15452665 }, + }, +}, +{ + { + { 11433042,-13228665,8239631,-5279517,-1985436,-725718,-18698764,2167544,-6921301,-13440182 }, + { -31436171,15575146,30436815,12192228,-22463353,9395379,-9917708,-8638997,12215110,12028277 }, + { 14098400,6555944,23007258,5757252,-15427832,-12950502,30123440,4617780,-16900089,-655628 }, + }, + { + { -4026201,-15240835,11893168,13718664,-14809462,1847385,-15819999,10154009,23973261,-12684474 }, + { -26531820,-3695990,-1908898,2534301,-31870557,-16550355,18341390,-11419951,32013174,-10103539 }, + { -25479301,10876443,-11771086,-14625140,-12369567,1838104,21911214,6354752,4425632,-837822 }, + }, + { + { -10433389,-14612966,22229858,-3091047,-13191166,776729,-17415375,-12020462,4725005,14044970 }, + { 19268650,-7304421,1555349,8692754,-21474059,-9910664,6347390,-1411784,-19522291,-16109756 }, + { -24864089,12986008,-10898878,-5558584,-11312371,-148526,19541418,8180106,9282262,10282508 }, + }, + { + { -26205082,4428547,-8661196,-13194263,4098402,-14165257,15522535,8372215,5542595,-10702683 }, + { -10562541,14895633,26814552,-16673850,-17480754,-2489360,-2781891,6993761,-18093885,10114655 }, + { -20107055,-929418,31422704,10427861,-7110749,6150669,-29091755,-11529146,25953725,-106158 }, + }, + { + { -4234397,-8039292,-9119125,3046000,2101609,-12607294,19390020,6094296,-3315279,12831125 }, + { -15998678,7578152,5310217,14408357,-33548620,-224739,31575954,6326196,7381791,-2421839 }, + { -20902779,3296811,24736065,-16328389,18374254,7318640,6295303,8082724,-15362489,12339664 }, + }, + { + { 27724736,2291157,6088201,-14184798,1792727,5857634,13848414,15768922,25091167,14856294 }, + { -18866652,8331043,24373479,8541013,-701998,-9269457,12927300,-12695493,-22182473,-9012899 }, + { -11423429,-5421590,11632845,3405020,30536730,-11674039,-27260765,13866390,30146206,9142070 }, + }, + { + { 3924129,-15307516,-13817122,-10054960,12291820,-668366,-27702774,9326384,-8237858,4171294 }, + { -15921940,16037937,6713787,16606682,-21612135,2790944,26396185,3731949,345228,-5462949 }, + { -21327538,13448259,25284571,1143661,20614966,-8849387,2031539,-12391231,-16253183,-13582083 }, + }, + { + { 31016211,-16722429,26371392,-14451233,-5027349,14854137,17477601,3842657,28012650,-16405420 }, + { -5075835,9368966,-8562079,-4600902,-15249953,6970560,-9189873,16292057,-8867157,3507940 }, + { 29439664,3537914,23333589,6997794,-17555561,-11018068,-15209202,-15051267,-9164929,6580396 }, + }, +}, +{ + { + { -12185861,-7679788,16438269,10826160,-8696817,-6235611,17860444,-9273846,-2095802,9304567 }, + { 20714564,-4336911,29088195,7406487,11426967,-5095705,14792667,-14608617,5289421,-477127 }, + { -16665533,-10650790,-6160345,-13305760,9192020,-1802462,17271490,12349094,26939669,-3752294 }, + }, + { + { -12889898,9373458,31595848,16374215,21471720,13221525,-27283495,-12348559,-3698806,117887 }, + { 22263325,-6560050,3984570,-11174646,-15114008,-566785,28311253,5358056,-23319780,541964 }, + { 16259219,3261970,2309254,-15534474,-16885711,-4581916,24134070,-16705829,-13337066,-13552195 }, + }, + { + { 9378160,-13140186,-22845982,-12745264,28198281,-7244098,-2399684,-717351,690426,14876244 }, + { 24977353,-314384,-8223969,-13465086,28432343,-1176353,-13068804,-12297348,-22380984,6618999 }, + { -1538174,11685646,12944378,13682314,-24389511,-14413193,8044829,-13817328,32239829,-5652762 }, + }, + { + { -18603066,4762990,-926250,8885304,-28412480,-3187315,9781647,-10350059,32779359,5095274 }, + { -33008130,-5214506,-32264887,-3685216,9460461,-9327423,-24601656,14506724,21639561,-2630236 }, + { -16400943,-13112215,25239338,15531969,3987758,-4499318,-1289502,-6863535,17874574,558605 }, + }, + { + { -13600129,10240081,9171883,16131053,-20869254,9599700,33499487,5080151,2085892,5119761 }, + { -22205145,-2519528,-16381601,414691,-25019550,2170430,30634760,-8363614,-31999993,-5759884 }, + { -6845704,15791202,8550074,-1312654,29928809,-12092256,27534430,-7192145,-22351378,12961482 }, + }, + { + { -24492060,-9570771,10368194,11582341,-23397293,-2245287,16533930,8206996,-30194652,-5159638 }, + { -11121496,-3382234,2307366,6362031,-135455,8868177,-16835630,7031275,7589640,8945490 }, + { -32152748,8917967,6661220,-11677616,-1192060,-15793393,7251489,-11182180,24099109,-14456170 }, + }, + { + { 5019558,-7907470,4244127,-14714356,-26933272,6453165,-19118182,-13289025,-6231896,-10280736 }, + { 10853594,10721687,26480089,5861829,-22995819,1972175,-1866647,-10557898,-3363451,-6441124 }, + { -17002408,5906790,221599,-6563147,7828208,-13248918,24362661,-2008168,-13866408,7421392 }, + }, + { + { 8139927,-6546497,32257646,-5890546,30375719,1886181,-21175108,15441252,28826358,-4123029 }, + { 6267086,9695052,7709135,-16603597,-32869068,-1886135,14795160,-7840124,13746021,-1742048 }, + { 28584902,7787108,-6732942,-15050729,22846041,-7571236,-3181936,-363524,4771362,-8419958 }, + }, +}, +{ + { + { 24949256,6376279,-27466481,-8174608,-18646154,-9930606,33543569,-12141695,3569627,11342593 }, + { 26514989,4740088,27912651,3697550,19331575,-11472339,6809886,4608608,7325975,-14801071 }, + { -11618399,-14554430,-24321212,7655128,-1369274,5214312,-27400540,10258390,-17646694,-8186692 }, + }, + { + { 11431204,15823007,26570245,14329124,18029990,4796082,-31446179,15580664,9280358,-3973687 }, + { -160783,-10326257,-22855316,-4304997,-20861367,-13621002,-32810901,-11181622,-15545091,4387441 }, + { -20799378,12194512,3937617,-5805892,-27154820,9340370,-24513992,8548137,20617071,-7482001 }, + }, + { + { -938825,-3930586,-8714311,16124718,24603125,-6225393,-13775352,-11875822,24345683,10325460 }, + { -19855277,-1568885,-22202708,8714034,14007766,6928528,16318175,-1010689,4766743,3552007 }, + { -21751364,-16730916,1351763,-803421,-4009670,3950935,3217514,14481909,10988822,-3994762 }, + }, + { + { 15564307,-14311570,3101243,5684148,30446780,-8051356,12677127,-6505343,-8295852,13296005 }, + { -9442290,6624296,-30298964,-11913677,-4670981,-2057379,31521204,9614054,-30000824,12074674 }, + { 4771191,-135239,14290749,-13089852,27992298,14998318,-1413936,-1556716,29832613,-16391035 }, + }, + { + { 7064884,-7541174,-19161962,-5067537,-18891269,-2912736,25825242,5293297,-27122660,13101590 }, + { -2298563,2439670,-7466610,1719965,-27267541,-16328445,32512469,-5317593,-30356070,-4190957 }, + { -30006540,10162316,-33180176,3981723,-16482138,-13070044,14413974,9515896,19568978,9628812 }, + }, + { + { 33053803,199357,15894591,1583059,27380243,-4580435,-17838894,-6106839,-6291786,3437740 }, + { -18978877,3884493,19469877,12726490,15913552,13614290,-22961733,70104,7463304,4176122 }, + { -27124001,10659917,11482427,-16070381,12771467,-6635117,-32719404,-5322751,24216882,5944158 }, + }, + { + { 8894125,7450974,-2664149,-9765752,-28080517,-12389115,19345746,14680796,11632993,5847885 }, + { 26942781,-2315317,9129564,-4906607,26024105,11769399,-11518837,6367194,-9727230,4782140 }, + { 19916461,-4828410,-22910704,-11414391,25606324,-5972441,33253853,8220911,6358847,-1873857 }, + }, + { + { 801428,-2081702,16569428,11065167,29875704,96627,7908388,-4480480,-13538503,1387155 }, + { 19646058,5720633,-11416706,12814209,11607948,12749789,14147075,15156355,-21866831,11835260 }, + { 19299512,1155910,28703737,14890794,2925026,7269399,26121523,15467869,-26560550,5052483 }, + }, +}, +{ + { + { -3017432,10058206,1980837,3964243,22160966,12322533,-6431123,-12618185,12228557,-7003677 }, + { 32944382,14922211,-22844894,5188528,21913450,-8719943,4001465,13238564,-6114803,8653815 }, + { 22865569,-4652735,27603668,-12545395,14348958,8234005,24808405,5719875,28483275,2841751 }, + }, + { + { -16420968,-1113305,-327719,-12107856,21886282,-15552774,-1887966,-315658,19932058,-12739203 }, + { -11656086,10087521,-8864888,-5536143,-19278573,-3055912,3999228,13239134,-4777469,-13910208 }, + { 1382174,-11694719,17266790,9194690,-13324356,9720081,20403944,11284705,-14013818,3093230 }, + }, + { + { 16650921,-11037932,-1064178,1570629,-8329746,7352753,-302424,16271225,-24049421,-6691850 }, + { -21911077,-5927941,-4611316,-5560156,-31744103,-10785293,24123614,15193618,-21652117,-16739389 }, + { -9935934,-4289447,-25279823,4372842,2087473,10399484,31870908,14690798,17361620,11864968 }, + }, + { + { -11307610,6210372,13206574,5806320,-29017692,-13967200,-12331205,-7486601,-25578460,-16240689 }, + { 14668462,-12270235,26039039,15305210,25515617,4542480,10453892,6577524,9145645,-6443880 }, + { 5974874,3053895,-9433049,-10385191,-31865124,3225009,-7972642,3936128,-5652273,-3050304 }, + }, + { + { 30625386,-4729400,-25555961,-12792866,-20484575,7695099,17097188,-16303496,-27999779,1803632 }, + { -3553091,9865099,-5228566,4272701,-5673832,-16689700,14911344,12196514,-21405489,7047412 }, + { 20093277,9920966,-11138194,-5343857,13161587,12044805,-32856851,4124601,-32343828,-10257566 }, + }, + { + { -20788824,14084654,-13531713,7842147,19119038,-13822605,4752377,-8714640,-21679658,2288038 }, + { -26819236,-3283715,29965059,3039786,-14473765,2540457,29457502,14625692,-24819617,12570232 }, + { -1063558,-11551823,16920318,12494842,1278292,-5869109,-21159943,-3498680,-11974704,4724943 }, + }, + { + { 17960970,-11775534,-4140968,-9702530,-8876562,-1410617,-12907383,-8659932,-29576300,1903856 }, + { 23134274,-14279132,-10681997,-1611936,20684485,15770816,-12989750,3190296,26955097,14109738 }, + { 15308788,5320727,-30113809,-14318877,22902008,7767164,29425325,-11277562,31960942,11934971 }, + }, + { + { -27395711,8435796,4109644,12222639,-24627868,14818669,20638173,4875028,10491392,1379718 }, + { -13159415,9197841,3875503,-8936108,-1383712,-5879801,33518459,16176658,21432314,12180697 }, + { -11787308,11500838,13787581,-13832590,-22430679,10140205,1465425,12689540,-10301319,-13872883 }, + }, +}, +{ + { + { 5414091,-15386041,-21007664,9643570,12834970,1186149,-2622916,-1342231,26128231,6032912 }, + { -26337395,-13766162,32496025,-13653919,17847801,-12669156,3604025,8316894,-25875034,-10437358 }, + { 3296484,6223048,24680646,-12246460,-23052020,5903205,-8862297,-4639164,12376617,3188849 }, + }, + { + { 29190488,-14659046,27549113,-1183516,3520066,-10697301,32049515,-7309113,-16109234,-9852307 }, + { -14744486,-9309156,735818,-598978,-20407687,-5057904,25246078,-15795669,18640741,-960977 }, + { -6928835,-16430795,10361374,5642961,4910474,12345252,-31638386,-494430,10530747,1053335 }, + }, + { + { -29265967,-14186805,-13538216,-12117373,-19457059,-10655384,-31462369,-2948985,24018831,15026644 }, + { -22592535,-3145277,-2289276,5953843,-13440189,9425631,25310643,13003497,-2314791,-15145616 }, + { -27419985,-603321,-8043984,-1669117,-26092265,13987819,-27297622,187899,-23166419,-2531735 }, + }, + { + { -21744398,-13810475,1844840,5021428,-10434399,-15911473,9716667,16266922,-5070217,726099 }, + { 29370922,-6053998,7334071,-15342259,9385287,2247707,-13661962,-4839461,30007388,-15823341 }, + { -936379,16086691,23751945,-543318,-1167538,-5189036,9137109,730663,9835848,4555336 }, + }, + { + { -23376435,1410446,-22253753,-12899614,30867635,15826977,17693930,544696,-11985298,12422646 }, + { 31117226,-12215734,-13502838,6561947,-9876867,-12757670,-5118685,-4096706,29120153,13924425 }, + { -17400879,-14233209,19675799,-2734756,-11006962,-5858820,-9383939,-11317700,7240931,-237388 }, + }, + { + { -31361739,-11346780,-15007447,-5856218,-22453340,-12152771,1222336,4389483,3293637,-15551743 }, + { -16684801,-14444245,11038544,11054958,-13801175,-3338533,-24319580,7733547,12796905,-6335822 }, + { -8759414,-10817836,-25418864,10783769,-30615557,-9746811,-28253339,3647836,3222231,-11160462 }, + }, + { + { 18606113,1693100,-25448386,-15170272,4112353,10045021,23603893,-2048234,-7550776,2484985 }, + { 9255317,-3131197,-12156162,-1004256,13098013,-9214866,16377220,-2102812,-19802075,-3034702 }, + { -22729289,7496160,-5742199,11329249,19991973,-3347502,-31718148,9936966,-30097688,-10618797 }, + }, + { + { 21878590,-5001297,4338336,13643897,-3036865,13160960,19708896,5415497,-7360503,-4109293 }, + { 27736861,10103576,12500508,8502413,-3413016,-9633558,10436918,-1550276,-23659143,-8132100 }, + { 19492550,-12104365,-29681976,-852630,-3208171,12403437,30066266,8367329,13243957,8709688 }, + }, +}, +{ + { + { 12015105,2801261,28198131,10151021,24818120,-4743133,-11194191,-5645734,5150968,7274186 }, + { 2831366,-12492146,1478975,6122054,23825128,-12733586,31097299,6083058,31021603,-9793610 }, + { -2529932,-2229646,445613,10720828,-13849527,-11505937,-23507731,16354465,15067285,-14147707 }, + }, + { + { 7840942,14037873,-33364863,15934016,-728213,-3642706,21403988,1057586,-19379462,-12403220 }, + { 915865,-16469274,15608285,-8789130,-24357026,6060030,-17371319,8410997,-7220461,16527025 }, + { 32922597,-556987,20336074,-16184568,10903705,-5384487,16957574,52992,23834301,6588044 }, + }, + { + { 32752030,11232950,3381995,-8714866,22652988,-10744103,17159699,16689107,-20314580,-1305992 }, + { -4689649,9166776,-25710296,-10847306,11576752,12733943,7924251,-2752281,1976123,-7249027 }, + { 21251222,16309901,-2983015,-6783122,30810597,12967303,156041,-3371252,12331345,-8237197 }, + }, + { + { 8651614,-4477032,-16085636,-4996994,13002507,2950805,29054427,-5106970,10008136,-4667901 }, + { 31486080,15114593,-14261250,12951354,14369431,-7387845,16347321,-13662089,8684155,-10532952 }, + { 19443825,11385320,24468943,-9659068,-23919258,2187569,-26263207,-6086921,31316348,14219878 }, + }, + { + { -28594490,1193785,32245219,11392485,31092169,15722801,27146014,6992409,29126555,9207390 }, + { 32382935,1110093,18477781,11028262,-27411763,-7548111,-4980517,10843782,-7957600,-14435730 }, + { 2814918,7836403,27519878,-7868156,-20894015,-11553689,-21494559,8550130,28346258,1994730 }, + }, + { + { -19578299,8085545,-14000519,-3948622,2785838,-16231307,-19516951,7174894,22628102,8115180 }, + { -30405132,955511,-11133838,-15078069,-32447087,-13278079,-25651578,3317160,-9943017,930272 }, + { -15303681,-6833769,28856490,1357446,23421993,1057177,24091212,-1388970,-22765376,-10650715 }, + }, + { + { -22751231,-5303997,-12907607,-12768866,-15811511,-7797053,-14839018,-16554220,-1867018,8398970 }, + { -31969310,2106403,-4736360,1362501,12813763,16200670,22981545,-6291273,18009408,-15772772 }, + { -17220923,-9545221,-27784654,14166835,29815394,7444469,29551787,-3727419,19288549,1325865 }, + }, + { + { 15100157,-15835752,-23923978,-1005098,-26450192,15509408,12376730,-3479146,33166107,-8042750 }, + { 20909231,13023121,-9209752,16251778,-5778415,-8094914,12412151,10018715,2213263,-13878373 }, + { 32529814,-11074689,30361439,-16689753,-9135940,1513226,22922121,6382134,-5766928,8371348 }, + }, +}, +{ + { + { 9923462,11271500,12616794,3544722,-29998368,-1721626,12891687,-8193132,-26442943,10486144 }, + { -22597207,-7012665,8587003,-8257861,4084309,-12970062,361726,2610596,-23921530,-11455195 }, + { 5408411,-1136691,-4969122,10561668,24145918,14240566,31319731,-4235541,19985175,-3436086 }, + }, + { + { -13994457,16616821,14549246,3341099,32155958,13648976,-17577068,8849297,65030,8370684 }, + { -8320926,-12049626,31204563,5839400,-20627288,-1057277,-19442942,6922164,12743482,-9800518 }, + { -2361371,12678785,28815050,4759974,-23893047,4884717,23783145,11038569,18800704,255233 }, + }, + { + { -5269658,-1773886,13957886,7990715,23132995,728773,13393847,9066957,19258688,-14753793 }, + { -2936654,-10827535,-10432089,14516793,-3640786,4372541,-31934921,2209390,-1524053,2055794 }, + { 580882,16705327,5468415,-2683018,-30926419,-14696000,-7203346,-8994389,-30021019,7394435 }, + }, + { + { 23838809,1822728,-15738443,15242727,8318092,-3733104,-21672180,-3492205,-4821741,14799921 }, + { 13345610,9759151,3371034,-16137791,16353039,8577942,31129804,13496856,-9056018,7402518 }, + { 2286874,-4435931,-20042458,-2008336,-13696227,5038122,11006906,-15760352,8205061,1607563 }, + }, + { + { 14414086,-8002132,3331830,-3208217,22249151,-5594188,18364661,-2906958,30019587,-9029278 }, + { -27688051,1585953,-10775053,931069,-29120221,-11002319,-14410829,12029093,9944378,8024 }, + { 4368715,-3709630,29874200,-15022983,-20230386,-11410704,-16114594,-999085,-8142388,5640030 }, + }, + { + { 10299610,13746483,11661824,16234854,7630238,5998374,9809887,-16694564,15219798,-14327783 }, + { 27425505,-5719081,3055006,10660664,23458024,595578,-15398605,-1173195,-18342183,9742717 }, + { 6744077,2427284,26042789,2720740,-847906,1118974,32324614,7406442,12420155,1994844 }, + }, + { + { 14012521,-5024720,-18384453,-9578469,-26485342,-3936439,-13033478,-10909803,24319929,-6446333 }, + { 16412690,-4507367,10772641,15929391,-17068788,-4658621,10555945,-10484049,-30102368,-4739048 }, + { 22397382,-7767684,-9293161,-12792868,17166287,-9755136,-27333065,6199366,21880021,-12250760 }, + }, + { + { -4283307,5368523,-31117018,8163389,-30323063,3209128,16557151,8890729,8840445,4957760 }, + { -15447727,709327,-6919446,-10870178,-29777922,6522332,-21720181,12130072,-14796503,5005757 }, + { -2114751,-14308128,23019042,15765735,-25269683,6002752,10183197,-13239326,-16395286,-2176112 }, + }, +}, +{ + { + { -19025756,1632005,13466291,-7995100,-23640451,16573537,-32013908,-3057104,22208662,2000468 }, + { 3065073,-1412761,-25598674,-361432,-17683065,-5703415,-8164212,11248527,-3691214,-7414184 }, + { 10379208,-6045554,8877319,1473647,-29291284,-12507580,16690915,2553332,-3132688,16400289 }, + }, + { + { 15716668,1254266,-18472690,7446274,-8448918,6344164,-22097271,-7285580,26894937,9132066 }, + { 24158887,12938817,11085297,-8177598,-28063478,-4457083,-30576463,64452,-6817084,-2692882 }, + { 13488534,7794716,22236231,5989356,25426474,-12578208,2350710,-3418511,-4688006,2364226 }, + }, + { + { 16335052,9132434,25640582,6678888,1725628,8517937,-11807024,-11697457,15445875,-7798101 }, + { 29004207,-7867081,28661402,-640412,-12794003,-7943086,31863255,-4135540,-278050,-15759279 }, + { -6122061,-14866665,-28614905,14569919,-10857999,-3591829,10343412,-6976290,-29828287,-10815811 }, + }, + { + { 27081650,3463984,14099042,-4517604,1616303,-6205604,29542636,15372179,17293797,960709 }, + { 20263915,11434237,-5765435,11236810,13505955,-10857102,-16111345,6493122,-19384511,7639714 }, + { -2830798,-14839232,25403038,-8215196,-8317012,-16173699,18006287,-16043750,29994677,-15808121 }, + }, + { + { 9769828,5202651,-24157398,-13631392,-28051003,-11561624,-24613141,-13860782,-31184575,709464 }, + { 12286395,13076066,-21775189,-1176622,-25003198,4057652,-32018128,-8890874,16102007,13205847 }, + { 13733362,5599946,10557076,3195751,-5557991,8536970,-25540170,8525972,10151379,10394400 }, + }, + { + { 4024660,-16137551,22436262,12276534,-9099015,-2686099,19698229,11743039,-33302334,8934414 }, + { -15879800,-4525240,-8580747,-2934061,14634845,-698278,-9449077,3137094,-11536886,11721158 }, + { 17555939,-5013938,8268606,2331751,-22738815,9761013,9319229,8835153,-9205489,-1280045 }, + }, + { + { -461409,-7830014,20614118,16688288,-7514766,-4807119,22300304,505429,6108462,-6183415 }, + { -5070281,12367917,-30663534,3234473,32617080,-8422642,29880583,-13483331,-26898490,-7867459 }, + { -31975283,5726539,26934134,10237677,-3173717,-605053,24199304,3795095,7592688,-14992079 }, + }, + { + { 21594432,-14964228,17466408,-4077222,32537084,2739898,6407723,12018833,-28256052,4298412 }, + { -20650503,-11961496,-27236275,570498,3767144,-1717540,13891942,-1569194,13717174,10805743 }, + { -14676630,-15644296,15287174,11927123,24177847,-8175568,-796431,14860609,-26938930,-5863836 }, + }, +}, +{ + { + { 12962541,5311799,-10060768,11658280,18855286,-7954201,13286263,-12808704,-4381056,9882022 }, + { 18512079,11319350,-20123124,15090309,18818594,5271736,-22727904,3666879,-23967430,-3299429 }, + { -6789020,-3146043,16192429,13241070,15898607,-14206114,-10084880,-6661110,-2403099,5276065 }, + }, + { + { 30169808,-5317648,26306206,-11750859,27814964,7069267,7152851,3684982,1449224,13082861 }, + { 10342826,3098505,2119311,193222,25702612,12233820,23697382,15056736,-21016438,-8202000 }, + { -33150110,3261608,22745853,7948688,19370557,-15177665,-26171976,6482814,-10300080,-11060101 }, + }, + { + { 32869458,-5408545,25609743,15678670,-10687769,-15471071,26112421,2521008,-22664288,6904815 }, + { 29506923,4457497,3377935,-9796444,-30510046,12935080,1561737,3841096,-29003639,-6657642 }, + { 10340844,-6630377,-18656632,-2278430,12621151,-13339055,30878497,-11824370,-25584551,5181966 }, + }, + { + { 25940115,-12658025,17324188,-10307374,-8671468,15029094,24396252,-16450922,-2322852,-12388574 }, + { -21765684,9916823,-1300409,4079498,-1028346,11909559,1782390,12641087,20603771,-6561742 }, + { -18882287,-11673380,24849422,11501709,13161720,-4768874,1925523,11914390,4662781,7820689 }, + }, + { + { 12241050,-425982,8132691,9393934,32846760,-1599620,29749456,12172924,16136752,15264020 }, + { -10349955,-14680563,-8211979,2330220,-17662549,-14545780,10658213,6671822,19012087,3772772 }, + { 3753511,-3421066,10617074,2028709,14841030,-6721664,28718732,-15762884,20527771,12988982 }, + }, + { + { -14822485,-5797269,-3707987,12689773,-898983,-10914866,-24183046,-10564943,3299665,-12424953 }, + { -16777703,-15253301,-9642417,4978983,3308785,8755439,6943197,6461331,-25583147,8991218 }, + { -17226263,1816362,-1673288,-6086439,31783888,-8175991,-32948145,7417950,-30242287,1507265 }, + }, + { + { 29692663,6829891,-10498800,4334896,20945975,-11906496,-28887608,8209391,14606362,-10647073 }, + { -3481570,8707081,32188102,5672294,22096700,1711240,-33020695,9761487,4170404,-2085325 }, + { -11587470,14855945,-4127778,-1531857,-26649089,15084046,22186522,16002000,-14276837,-8400798 }, + }, + { + { -4811456,13761029,-31703877,-2483919,-3312471,7869047,-7113572,-9620092,13240845,10965870 }, + { -7742563,-8256762,-14768334,-13656260,-23232383,12387166,4498947,14147411,29514390,4302863 }, + { -13413405,-12407859,20757302,-13801832,14785143,8976368,-5061276,-2144373,17846988,-13971927 }, + }, +}, +{ + { + { -2244452,-754728,-4597030,-1066309,-6247172,1455299,-21647728,-9214789,-5222701,12650267 }, + { -9906797,-16070310,21134160,12198166,-27064575,708126,387813,13770293,-19134326,10958663 }, + { 22470984,12369526,23446014,-5441109,-21520802,-9698723,-11772496,-11574455,-25083830,4271862 }, + }, + { + { -25169565,-10053642,-19909332,15361595,-5984358,2159192,75375,-4278529,-32526221,8469673 }, + { 15854970,4148314,-8893890,7259002,11666551,13824734,-30531198,2697372,24154791,-9460943 }, + { 15446137,-15806644,29759747,14019369,30811221,-9610191,-31582008,12840104,24913809,9815020 }, + }, + { + { -4709286,-5614269,-31841498,-12288893,-14443537,10799414,-9103676,13438769,18735128,9466238 }, + { 11933045,9281483,5081055,-5183824,-2628162,-4905629,-7727821,-10896103,-22728655,16199064 }, + { 14576810,379472,-26786533,-8317236,-29426508,-10812974,-102766,1876699,30801119,2164795 }, + }, + { + { 15995086,3199873,13672555,13712240,-19378835,-4647646,-13081610,-15496269,-13492807,1268052 }, + { -10290614,-3659039,-3286592,10948818,23037027,3794475,-3470338,-12600221,-17055369,3565904 }, + { 29210088,-9419337,-5919792,-4952785,10834811,-13327726,-16512102,-10820713,-27162222,-14030531 }, + }, + { + { -13161890,15508588,16663704,-8156150,-28349942,9019123,-29183421,-3769423,2244111,-14001979 }, + { -5152875,-3800936,-9306475,-6071583,16243069,14684434,-25673088,-16180800,13491506,4641841 }, + { 10813417,643330,-19188515,-728916,30292062,-16600078,27548447,-7721242,14476989,-12767431 }, + }, + { + { 10292079,9984945,6481436,8279905,-7251514,7032743,27282937,-1644259,-27912810,12651324 }, + { -31185513,-813383,22271204,11835308,10201545,15351028,17099662,3988035,21721536,-3148940 }, + { 10202177,-6545839,-31373232,-9574638,-32150642,-8119683,-12906320,3852694,13216206,14842320 }, + }, + { + { -15815640,-10601066,-6538952,-7258995,-6984659,-6581778,-31500847,13765824,-27434397,9900184 }, + { 14465505,-13833331,-32133984,-14738873,-27443187,12990492,33046193,15796406,-7051866,-8040114 }, + { 30924417,-8279620,6359016,-12816335,16508377,9071735,-25488601,15413635,9524356,-7018878 }, + }, + { + { 12274201,-13175547,32627641,-1785326,6736625,13267305,5237659,-5109483,15663516,4035784 }, + { -2951309,8903985,17349946,601635,-16432815,-4612556,-13732739,-15889334,-22258478,4659091 }, + { -16916263,-4952973,-30393711,-15158821,20774812,15897498,5736189,15026997,-2178256,-13455585 }, + }, +}, +{ + { + { -8858980,-2219056,28571666,-10155518,-474467,-10105698,-3801496,278095,23440562,-290208 }, + { 10226241,-5928702,15139956,120818,-14867693,5218603,32937275,11551483,-16571960,-7442864 }, + { 17932739,-12437276,-24039557,10749060,11316803,7535897,22503767,5561594,-3646624,3898661 }, + }, + { + { 7749907,-969567,-16339731,-16464,-25018111,15122143,-1573531,7152530,21831162,1245233 }, + { 26958459,-14658026,4314586,8346991,-5677764,11960072,-32589295,-620035,-30402091,-16716212 }, + { -12165896,9166947,33491384,13673479,29787085,13096535,6280834,14587357,-22338025,13987525 }, + }, + { + { -24349909,7778775,21116000,15572597,-4833266,-5357778,-4300898,-5124639,-7469781,-2858068 }, + { 9681908,-6737123,-31951644,13591838,-6883821,386950,31622781,6439245,-14581012,4091397 }, + { -8426427,1470727,-28109679,-1596990,3978627,-5123623,-19622683,12092163,29077877,-14741988 }, + }, + { + { 5269168,-6859726,-13230211,-8020715,25932563,1763552,-5606110,-5505881,-20017847,2357889 }, + { 32264008,-15407652,-5387735,-1160093,-2091322,-3946900,23104804,-12869908,5727338,189038 }, + { 14609123,-8954470,-6000566,-16622781,-14577387,-7743898,-26745169,10942115,-25888931,-14884697 }, + }, + { + { 20513500,5557931,-15604613,7829531,26413943,-2019404,-21378968,7471781,13913677,-5137875 }, + { -25574376,11967826,29233242,12948236,-6754465,4713227,-8940970,14059180,12878652,8511905 }, + { -25656801,3393631,-2955415,-7075526,-2250709,9366908,-30223418,6812974,5568676,-3127656 }, + }, + { + { 11630004,12144454,2116339,13606037,27378885,15676917,-17408753,-13504373,-14395196,8070818 }, + { 27117696,-10007378,-31282771,-5570088,1127282,12772488,-29845906,10483306,-11552749,-1028714 }, + { 10637467,-5688064,5674781,1072708,-26343588,-6982302,-1683975,9177853,-27493162,15431203 }, + }, + { + { 20525145,10892566,-12742472,12779443,-29493034,16150075,-28240519,14943142,-15056790,-7935931 }, + { -30024462,5626926,-551567,-9981087,753598,11981191,25244767,-3239766,-3356550,9594024 }, + { -23752644,2636870,-5163910,-10103818,585134,7877383,11345683,-6492290,13352335,-10977084 }, + }, + { + { -1931799,-5407458,3304649,-12884869,17015806,-4877091,-29783850,-7752482,-13215537,-319204 }, + { 20239939,6607058,6203985,3483793,-18386976,-779229,-20723742,15077870,-22750759,14523817 }, + { 27406042,-6041657,27423596,-4497394,4996214,10002360,-28842031,-4545494,-30172742,-4805667 }, + }, +}, +{ + { + { 11374242,12660715,17861383,-12540833,10935568,1099227,-13886076,-9091740,-27727044,11358504 }, + { -12730809,10311867,1510375,10778093,-2119455,-9145702,32676003,11149336,-26123651,4985768 }, + { -19096303,341147,-6197485,-239033,15756973,-8796662,-983043,13794114,-19414307,-15621255 }, + }, + { + { 6490081,11940286,25495923,-7726360,8668373,-8751316,3367603,6970005,-1691065,-9004790 }, + { 1656497,13457317,15370807,6364910,13605745,8362338,-19174622,-5475723,-16796596,-5031438 }, + { -22273315,-13524424,-64685,-4334223,-18605636,-10921968,-20571065,-7007978,-99853,-10237333 }, + }, + { + { 17747465,10039260,19368299,-4050591,-20630635,-16041286,31992683,-15857976,-29260363,-5511971 }, + { 31932027,-4986141,-19612382,16366580,22023614,88450,11371999,-3744247,4882242,-10626905 }, + { 29796507,37186,19818052,10115756,-11829032,3352736,18551198,3272828,-5190932,-4162409 }, + }, + { + { 12501286,4044383,-8612957,-13392385,-32430052,5136599,-19230378,-3529697,330070,-3659409 }, + { 6384877,2899513,17807477,7663917,-2358888,12363165,25366522,-8573892,-271295,12071499 }, + { -8365515,-4042521,25133448,-4517355,-6211027,2265927,-32769618,1936675,-5159697,3829363 }, + }, + { + { 28425966,-5835433,-577090,-4697198,-14217555,6870930,7921550,-6567787,26333140,14267664 }, + { -11067219,11871231,27385719,-10559544,-4585914,-11189312,10004786,-8709488,-21761224,8930324 }, + { -21197785,-16396035,25654216,-1725397,12282012,11008919,1541940,4757911,-26491501,-16408940 }, + }, + { + { 13537262,-7759490,-20604840,10961927,-5922820,-13218065,-13156584,6217254,-15943699,13814990 }, + { -17422573,15157790,18705543,29619,24409717,-260476,27361681,9257833,-1956526,-1776914 }, + { -25045300,-10191966,15366585,15166509,-13105086,8423556,-29171540,12361135,-18685978,4578290 }, + }, + { + { 24579768,3711570,1342322,-11180126,-27005135,14124956,-22544529,14074919,21964432,8235257 }, + { -6528613,-2411497,9442966,-5925588,12025640,-1487420,-2981514,-1669206,13006806,2355433 }, + { -16304899,-13605259,-6632427,-5142349,16974359,-10911083,27202044,1719366,1141648,-12796236 }, + }, + { + { -12863944,-13219986,-8318266,-11018091,-6810145,-4843894,13475066,-3133972,32674895,13715045 }, + { 11423335,-5468059,32344216,8962751,24989809,9241752,-13265253,16086212,-28740881,-15642093 }, + { -1409668,12530728,-6368726,10847387,19531186,-14132160,-11709148,7791794,-27245943,4383347 }, + }, +}, +{ + { + { -28970898,5271447,-1266009,-9736989,-12455236,16732599,-4862407,-4906449,27193557,6245191 }, + { -15193956,5362278,-1783893,2695834,4960227,12840725,23061898,3260492,22510453,8577507 }, + { -12632451,11257346,-32692994,13548177,-721004,10879011,31168030,13952092,-29571492,-3635906 }, + }, + { + { 3877321,-9572739,32416692,5405324,-11004407,-13656635,3759769,11935320,5611860,8164018 }, + { -16275802,14667797,15906460,12155291,-22111149,-9039718,32003002,-8832289,5773085,-8422109 }, + { -23788118,-8254300,1950875,8937633,18686727,16459170,-905725,12376320,31632953,190926 }, + }, + { + { -24593607,-16138885,-8423991,13378746,14162407,6901328,-8288749,4508564,-25341555,-3627528 }, + { 8884438,-5884009,6023974,10104341,-6881569,-4941533,18722941,-14786005,-1672488,827625 }, + { -32720583,-16289296,-32503547,7101210,13354605,2659080,-1800575,-14108036,-24878478,1541286 }, + }, + { + { 2901347,-1117687,3880376,-10059388,-17620940,-3612781,-21802117,-3567481,20456845,-1885033 }, + { 27019610,12299467,-13658288,-1603234,-12861660,-4861471,-19540150,-5016058,29439641,15138866 }, + { 21536104,-6626420,-32447818,-10690208,-22408077,5175814,-5420040,-16361163,7779328,109896 }, + }, + { + { 30279744,14648750,-8044871,6425558,13639621,-743509,28698390,12180118,23177719,-554075 }, + { 26572847,3405927,-31701700,12890905,-19265668,5335866,-6493768,2378492,4439158,-13279347 }, + { -22716706,3489070,-9225266,-332753,18875722,-1140095,14819434,-12731527,-17717757,-5461437 }, + }, + { + { -5056483,16566551,15953661,3767752,-10436499,15627060,-820954,2177225,8550082,-15114165 }, + { -18473302,16596775,-381660,15663611,22860960,15585581,-27844109,-3582739,-23260460,-8428588 }, + { -32480551,15707275,-8205912,-5652081,29464558,2713815,-22725137,15860482,-21902570,1494193 }, + }, + { + { -19562091,-14087393,-25583872,-9299552,13127842,759709,21923482,16529112,8742704,12967017 }, + { -28464899,1553205,32536856,-10473729,-24691605,-406174,-8914625,-2933896,-29903758,15553883 }, + { 21877909,3230008,9881174,10539357,-4797115,2841332,11543572,14513274,19375923,-12647961 }, + }, + { + { 8832269,-14495485,13253511,5137575,5037871,4078777,24880818,-6222716,2862653,9455043 }, + { 29306751,5123106,20245049,-14149889,9592566,8447059,-2077124,-2990080,15511449,4789663 }, + { -20679756,7004547,8824831,-9434977,-4045704,-3750736,-5754762,108893,23513200,16652362 }, + }, +}, +{ + { + { -33256173,4144782,-4476029,-6579123,10770039,-7155542,-6650416,-12936300,-18319198,10212860 }, + { 2756081,8598110,7383731,-6859892,22312759,-1105012,21179801,2600940,-9988298,-12506466 }, + { -24645692,13317462,-30449259,-15653928,21365574,-10869657,11344424,864440,-2499677,-16710063 }, + }, + { + { -26432803,6148329,-17184412,-14474154,18782929,-275997,-22561534,211300,2719757,4940997 }, + { -1323882,3911313,-6948744,14759765,-30027150,7851207,21690126,8518463,26699843,5276295 }, + { -13149873,-6429067,9396249,365013,24703301,-10488939,1321586,149635,-15452774,7159369 }, + }, + { + { 9987780,-3404759,17507962,9505530,9731535,-2165514,22356009,8312176,22477218,-8403385 }, + { 18155857,-16504990,19744716,9006923,15154154,-10538976,24256460,-4864995,-22548173,9334109 }, + { 2986088,-4911893,10776628,-3473844,10620590,-7083203,-21413845,14253545,-22587149,536906 }, + }, + { + { 4377756,8115836,24567078,15495314,11625074,13064599,7390551,10589625,10838060,-15420424 }, + { -19342404,867880,9277171,-3218459,-14431572,-1986443,19295826,-15796950,6378260,699185 }, + { 7895026,4057113,-7081772,-13077756,-17886831,-323126,-716039,15693155,-5045064,-13373962 }, + }, + { + { -7737563,-5869402,-14566319,-7406919,11385654,13201616,31730678,-10962840,-3918636,-9669325 }, + { 10188286,-15770834,-7336361,13427543,22223443,14896287,30743455,7116568,-21786507,5427593 }, + { 696102,13206899,27047647,-10632082,15285305,-9853179,10798490,-4578720,19236243,12477404 }, + }, + { + { -11229439,11243796,-17054270,-8040865,-788228,-8167967,-3897669,11180504,-23169516,7733644 }, + { 17800790,-14036179,-27000429,-11766671,23887827,3149671,23466177,-10538171,10322027,15313801 }, + { 26246234,11968874,32263343,-5468728,6830755,-13323031,-15794704,-101982,-24449242,10890804 }, + }, + { + { -31365647,10271363,-12660625,-6267268,16690207,-13062544,-14982212,16484931,25180797,-5334884 }, + { -586574,10376444,-32586414,-11286356,19801893,10997610,2276632,9482883,316878,13820577 }, + { -9882808,-4510367,-2115506,16457136,-11100081,11674996,30756178,-7515054,30696930,-3712849 }, + }, + { + { 32988917,-9603412,12499366,7910787,-10617257,-11931514,-7342816,-9985397,-32349517,7392473 }, + { -8855661,15927861,9866406,-3649411,-2396914,-16655781,-30409476,-9134995,25112947,-2926644 }, + { -2504044,-436966,25621774,-5678772,15085042,-5479877,-24884878,-13526194,5537438,-13914319 }, + }, +}, +{ + { + { -11225584,2320285,-9584280,10149187,-33444663,5808648,-14876251,-1729667,31234590,6090599 }, + { -9633316,116426,26083934,2897444,-6364437,-2688086,609721,15878753,-6970405,-9034768 }, + { -27757857,247744,-15194774,-9002551,23288161,-10011936,-23869595,6503646,20650474,1804084 }, + }, + { + { -27589786,15456424,8972517,8469608,15640622,4439847,3121995,-10329713,27842616,-202328 }, + { -15306973,2839644,22530074,10026331,4602058,5048462,28248656,5031932,-11375082,12714369 }, + { 20807691,-7270825,29286141,11421711,-27876523,-13868230,-21227475,1035546,-19733229,12796920 }, + }, + { + { 12076899,-14301286,-8785001,-11848922,-25012791,16400684,-17591495,-12899438,3480665,-15182815 }, + { -32361549,5457597,28548107,7833186,7303070,-11953545,-24363064,-15921875,-33374054,2771025 }, + { -21389266,421932,26597266,6860826,22486084,-6737172,-17137485,-4210226,-24552282,15673397 }, + }, + { + { -20184622,2338216,19788685,-9620956,-4001265,-8740893,-20271184,4733254,3727144,-12934448 }, + { 6120119,814863,-11794402,-622716,6812205,-15747771,2019594,7975683,31123697,-10958981 }, + { 30069250,-11435332,30434654,2958439,18399564,-976289,12296869,9204260,-16432438,9648165 }, + }, + { + { 32705432,-1550977,30705658,7451065,-11805606,9631813,3305266,5248604,-26008332,-11377501 }, + { 17219865,2375039,-31570947,-5575615,-19459679,9219903,294711,15298639,2662509,-16297073 }, + { -1172927,-7558695,-4366770,-4287744,-21346413,-8434326,32087529,-1222777,32247248,-14389861 }, + }, + { + { 14312628,1221556,17395390,-8700143,-4945741,-8684635,-28197744,-9637817,-16027623,-13378845 }, + { -1428825,-9678990,-9235681,6549687,-7383069,-468664,23046502,9803137,17597934,2346211 }, + { 18510800,15337574,26171504,981392,-22241552,7827556,-23491134,-11323352,3059833,-11782870 }, + }, + { + { 10141598,6082907,17829293,-1947643,9830092,13613136,-25556636,-5544586,-33502212,3592096 }, + { 33114168,-15889352,-26525686,-13343397,33076705,8716171,1151462,1521897,-982665,-6837803 }, + { -32939165,-4255815,23947181,-324178,-33072974,-12305637,-16637686,3891704,26353178,693168 }, + }, + { + { 30374239,1595580,-16884039,13186931,4600344,406904,9585294,-400668,31375464,14369965 }, + { -14370654,-7772529,1510301,6434173,-18784789,-6262728,32732230,-13108839,17901441,16011505 }, + { 18171223,-11934626,-12500402,15197122,-11038147,-15230035,-19172240,-16046376,8764035,12309598 }, + }, +}, +{ + { + { 5975908,-5243188,-19459362,-9681747,-11541277,14015782,-23665757,1228319,17544096,-10593782 }, + { 5811932,-1715293,3442887,-2269310,-18367348,-8359541,-18044043,-15410127,-5565381,12348900 }, + { -31399660,11407555,25755363,6891399,-3256938,14872274,-24849353,8141295,-10632534,-585479 }, + }, + { + { -12675304,694026,-5076145,13300344,14015258,-14451394,-9698672,-11329050,30944593,1130208 }, + { 8247766,-6710942,-26562381,-7709309,-14401939,-14648910,4652152,2488540,23550156,-271232 }, + { 17294316,-3788438,7026748,15626851,22990044,113481,2267737,-5908146,-408818,-137719 }, + }, + { + { 16091085,-16253926,18599252,7340678,2137637,-1221657,-3364161,14550936,3260525,-7166271 }, + { -4910104,-13332887,18550887,10864893,-16459325,-7291596,-23028869,-13204905,-12748722,2701326 }, + { -8574695,16099415,4629974,-16340524,-20786213,-6005432,-10018363,9276971,11329923,1862132 }, + }, + { + { 14763076,-15903608,-30918270,3689867,3511892,10313526,-21951088,12219231,-9037963,-940300 }, + { 8894987,-3446094,6150753,3013931,301220,15693451,-31981216,-2909717,-15438168,11595570 }, + { 15214962,3537601,-26238722,-14058872,4418657,-15230761,13947276,10730794,-13489462,-4363670 }, + }, + { + { -2538306,7682793,32759013,263109,-29984731,-7955452,-22332124,-10188635,977108,699994 }, + { -12466472,4195084,-9211532,550904,-15565337,12917920,19118110,-439841,-30534533,-14337913 }, + { 31788461,-14507657,4799989,7372237,8808585,-14747943,9408237,-10051775,12493932,-5409317 }, + }, + { + { -25680606,5260744,-19235809,-6284470,-3695942,16566087,27218280,2607121,29375955,6024730 }, + { 842132,-2794693,-4763381,-8722815,26332018,-12405641,11831880,6985184,-9940361,2854096 }, + { -4847262,-7969331,2516242,-5847713,9695691,-7221186,16512645,960770,12121869,16648078 }, + }, + { + { -15218652,14667096,-13336229,2013717,30598287,-464137,-31504922,-7882064,20237806,2838411 }, + { -19288047,4453152,15298546,-16178388,22115043,-15972604,12544294,-13470457,1068881,-12499905 }, + { -9558883,-16518835,33238498,13506958,30505848,-1114596,-8486907,-2630053,12521378,4845654 }, + }, + { + { -28198521,10744108,-2958380,10199664,7759311,-13088600,3409348,-873400,-6482306,-12885870 }, + { -23561822,6230156,-20382013,10655314,-24040585,-11621172,10477734,-1240216,-3113227,13974498 }, + { 12966261,15550616,-32038948,-1615346,21025980,-629444,5642325,7188737,18895762,12629579 }, + }, +}, +{ + { + { 14741879,-14946887,22177208,-11721237,1279741,8058600,11758140,789443,32195181,3895677 }, + { 10758205,15755439,-4509950,9243698,-4879422,6879879,-2204575,-3566119,-8982069,4429647 }, + { -2453894,15725973,-20436342,-10410672,-5803908,-11040220,-7135870,-11642895,18047436,-15281743 }, + }, + { + { -25173001,-11307165,29759956,11776784,-22262383,-15820455,10993114,-12850837,-17620701,-9408468 }, + { 21987233,700364,-24505048,14972008,-7774265,-5718395,32155026,2581431,-29958985,8773375 }, + { -25568350,454463,-13211935,16126715,25240068,8594567,20656846,12017935,-7874389,-13920155 }, + }, + { + { 6028182,6263078,-31011806,-11301710,-818919,2461772,-31841174,-5468042,-1721788,-2776725 }, + { -12278994,16624277,987579,-5922598,32908203,1248608,7719845,-4166698,28408820,6816612 }, + { -10358094,-8237829,19549651,-12169222,22082623,16147817,20613181,13982702,-10339570,5067943 }, + }, + { + { -30505967,-3821767,12074681,13582412,-19877972,2443951,-19719286,12746132,5331210,-10105944 }, + { 30528811,3601899,-1957090,4619785,-27361822,-15436388,24180793,-12570394,27679908,-1648928 }, + { 9402404,-13957065,32834043,10838634,-26580150,-13237195,26653274,-8685565,22611444,-12715406 }, + }, + { + { 22190590,1118029,22736441,15130463,-30460692,-5991321,19189625,-4648942,4854859,6622139 }, + { -8310738,-2953450,-8262579,-3388049,-10401731,-271929,13424426,-3567227,26404409,13001963 }, + { -31241838,-15415700,-2994250,8939346,11562230,-12840670,-26064365,-11621720,-15405155,11020693 }, + }, + { + { 1866042,-7949489,-7898649,-10301010,12483315,13477547,3175636,-12424163,28761762,1406734 }, + { -448555,-1777666,13018551,3194501,-9580420,-11161737,24760585,-4347088,25577411,-13378680 }, + { -24290378,4759345,-690653,-1852816,2066747,10693769,-29595790,9884936,-9368926,4745410 }, + }, + { + { -9141284,6049714,-19531061,-4341411,-31260798,9944276,-15462008,-11311852,10931924,-11931931 }, + { -16561513,14112680,-8012645,4817318,-8040464,-11414606,-22853429,10856641,-20470770,13434654 }, + { 22759489,-10073434,-16766264,-1871422,13637442,-10168091,1765144,-12654326,28445307,-5364710 }, + }, + { + { 29875063,12493613,2795536,-3786330,1710620,15181182,-10195717,-8788675,9074234,1167180 }, + { -26205683,11014233,-9842651,-2635485,-26908120,7532294,-18716888,-9535498,3843903,9367684 }, + { -10969595,-6403711,9591134,9582310,11349256,108879,16235123,8601684,-139197,4242895 }, + }, +}, +{ + { + { 22092954,-13191123,-2042793,-11968512,32186753,-11517388,-6574341,2470660,-27417366,16625501 }, + { -11057722,3042016,13770083,-9257922,584236,-544855,-7770857,2602725,-27351616,14247413 }, + { 6314175,-10264892,-32772502,15957557,-10157730,168750,-8618807,14290061,27108877,-1180880 }, + }, + { + { -8586597,-7170966,13241782,10960156,-32991015,-13794596,33547976,-11058889,-27148451,981874 }, + { 22833440,9293594,-32649448,-13618667,-9136966,14756819,-22928859,-13970780,-10479804,-16197962 }, + { -7768587,3326786,-28111797,10783824,19178761,14905060,22680049,13906969,-15933690,3797899 }, + }, + { + { 21721356,-4212746,-12206123,9310182,-3882239,-13653110,23740224,-2709232,20491983,-8042152 }, + { 9209270,-15135055,-13256557,-6167798,-731016,15289673,25947805,15286587,30997318,-6703063 }, + { 7392032,16618386,23946583,-8039892,-13265164,-1533858,-14197445,-2321576,17649998,-250080 }, + }, + { + { -9301088,-14193827,30609526,-3049543,-25175069,-1283752,-15241566,-9525724,-2233253,7662146 }, + { -17558673,1763594,-33114336,15908610,-30040870,-12174295,7335080,-8472199,-3174674,3440183 }, + { -19889700,-5977008,-24111293,-9688870,10799743,-16571957,40450,-4431835,4862400,1133 }, + }, + { + { -32856209,-7873957,-5422389,14860950,-16319031,7956142,7258061,311861,-30594991,-7379421 }, + { -3773428,-1565936,28985340,7499440,24445838,9325937,29727763,16527196,18278453,15405622 }, + { -4381906,8508652,-19898366,-3674424,-5984453,15149970,-13313598,843523,-21875062,13626197 }, + }, + { + { 2281448,-13487055,-10915418,-2609910,1879358,16164207,-10783882,3953792,13340839,15928663 }, + { 31727126,-7179855,-18437503,-8283652,2875793,-16390330,-25269894,-7014826,-23452306,5964753 }, + { 4100420,-5959452,-17179337,6017714,-18705837,12227141,-26684835,11344144,2538215,-7570755 }, + }, + { + { -9433605,6123113,11159803,-2156608,30016280,14966241,-20474983,1485421,-629256,-15958862 }, + { -26804558,4260919,11851389,9658551,-32017107,16367492,-20205425,-13191288,11659922,-11115118 }, + { 26180396,10015009,-30844224,-8581293,5418197,9480663,2231568,-10170080,33100372,-1306171 }, + }, + { + { 15121113,-5201871,-10389905,15427821,-27509937,-15992507,21670947,4486675,-5931810,-14466380 }, + { 16166486,-9483733,-11104130,6023908,-31926798,-1364923,2340060,-16254968,-10735770,-10039824 }, + { 28042865,-3557089,-12126526,12259706,-3717498,-6945899,6766453,-8689599,18036436,5803270 }, + }, +}, +{ + { + { -817581,6763912,11803561,1585585,10958447,-2671165,23855391,4598332,-6159431,-14117438 }, + { -31031306,-14256194,17332029,-2383520,31312682,-5967183,696309,50292,-20095739,11763584 }, + { -594563,-2514283,-32234153,12643980,12650761,14811489,665117,-12613632,-19773211,-10713562 }, + }, + { + { 30464590,-11262872,-4127476,-12734478,19835327,-7105613,-24396175,2075773,-17020157,992471 }, + { 18357185,-6994433,7766382,16342475,-29324918,411174,14578841,8080033,-11574335,-10601610 }, + { 19598397,10334610,12555054,2555664,18821899,-10339780,21873263,16014234,26224780,16452269 }, + }, + { + { -30223925,5145196,5944548,16385966,3976735,2009897,-11377804,-7618186,-20533829,3698650 }, + { 14187449,3448569,-10636236,-10810935,-22663880,-3433596,7268410,-10890444,27394301,12015369 }, + { 19695761,16087646,28032085,12999827,6817792,11427614,20244189,-1312777,-13259127,-3402461 }, + }, + { + { 30860103,12735208,-1888245,-4699734,-16974906,2256940,-8166013,12298312,-8550524,-10393462 }, + { -5719826,-11245325,-1910649,15569035,26642876,-7587760,-5789354,-15118654,-4976164,12651793 }, + { -2848395,9953421,11531313,-5282879,26895123,-12697089,-13118820,-16517902,9768698,-2533218 }, + }, + { + { -24719459,1894651,-287698,-4704085,15348719,-8156530,32767513,12765450,4940095,10678226 }, + { 18860224,15980149,-18987240,-1562570,-26233012,-11071856,-7843882,13944024,-24372348,16582019 }, + { -15504260,4970268,-29893044,4175593,-20993212,-2199756,-11704054,15444560,-11003761,7989037 }, + }, + { + { 31490452,5568061,-2412803,2182383,-32336847,4531686,-32078269,6200206,-19686113,-14800171 }, + { -17308668,-15879940,-31522777,-2831,-32887382,16375549,8680158,-16371713,28550068,-6857132 }, + { -28126887,-5688091,16837845,-1820458,-6850681,12700016,-30039981,4364038,1155602,5988841 }, + }, + { + { 21890435,-13272907,-12624011,12154349,-7831873,15300496,23148983,-4470481,24618407,8283181 }, + { -33136107,-10512751,9975416,6841041,-31559793,16356536,3070187,-7025928,1466169,10740210 }, + { -1509399,-15488185,-13503385,-10655916,32799044,909394,-13938903,-5779719,-32164649,-15327040 }, + }, + { + { 3960823,-14267803,-28026090,-15918051,-19404858,13146868,15567327,951507,-3260321,-573935 }, + { 24740841,5052253,-30094131,8961361,25877428,6165135,-24368180,14397372,-7380369,-6144105 }, + { -28888365,3510803,-28103278,-1158478,-11238128,-10631454,-15441463,-14453128,-1625486,-6494814 }, + }, +}, +{ + { + { 793299,-9230478,8836302,-6235707,-27360908,-2369593,33152843,-4885251,-9906200,-621852 }, + { 5666233,525582,20782575,-8038419,-24538499,14657740,16099374,1468826,-6171428,-15186581 }, + { -4859255,-3779343,-2917758,-6748019,7778750,11688288,-30404353,-9871238,-1558923,-9863646 }, + }, + { + { 10896332,-7719704,824275,472601,-19460308,3009587,25248958,14783338,-30581476,-15757844 }, + { 10566929,12612572,-31944212,11118703,-12633376,12362879,21752402,8822496,24003793,14264025 }, + { 27713862,-7355973,-11008240,9227530,27050101,2504721,23886875,-13117525,13958495,-5732453 }, + }, + { + { -23481610,4867226,-27247128,3900521,29838369,-8212291,-31889399,-10041781,7340521,-15410068 }, + { 4646514,-8011124,-22766023,-11532654,23184553,8566613,31366726,-1381061,-15066784,-10375192 }, + { -17270517,12723032,-16993061,14878794,21619651,-6197576,27584817,3093888,-8843694,3849921 }, + }, + { + { -9064912,2103172,25561640,-15125738,-5239824,9582958,32477045,-9017955,5002294,-15550259 }, + { -12057553,-11177906,21115585,-13365155,8808712,-12030708,16489530,13378448,-25845716,12741426 }, + { -5946367,10645103,-30911586,15390284,-3286982,-7118677,24306472,15852464,28834118,-7646072 }, + }, + { + { -17335748,-9107057,-24531279,9434953,-8472084,-583362,-13090771,455841,20461858,5491305 }, + { 13669248,-16095482,-12481974,-10203039,-14569770,-11893198,-24995986,11293807,-28588204,-9421832 }, + { 28497928,6272777,-33022994,14470570,8906179,-1225630,18504674,-14165166,29867745,-8795943 }, + }, + { + { -16207023,13517196,-27799630,-13697798,24009064,-6373891,-6367600,-13175392,22853429,-4012011 }, + { 24191378,16712145,-13931797,15217831,14542237,1646131,18603514,-11037887,12876623,-2112447 }, + { 17902668,4518229,-411702,-2829247,26878217,5258055,-12860753,608397,16031844,3723494 }, + }, + { + { -28632773,12763728,-20446446,7577504,33001348,-13017745,17558842,-7872890,23896954,-4314245 }, + { -20005381,-12011952,31520464,605201,2543521,5991821,-2945064,7229064,-9919646,-8826859 }, + { 28816045,298879,-28165016,-15920938,19000928,-1665890,-12680833,-2949325,-18051778,-2082915 }, + }, + { + { 16000882,-344896,3493092,-11447198,-29504595,-13159789,12577740,16041268,-19715240,7847707 }, + { 10151868,10572098,27312476,7922682,14825339,4723128,-32855931,-6519018,-10020567,3852848 }, + { -11430470,15697596,-21121557,-4420647,5386314,15063598,16514493,-15932110,29330899,-15076224 }, + }, +}, +{ + { + { -25499735,-4378794,-15222908,-6901211,16615731,2051784,3303702,15490,-27548796,12314391 }, + { 15683520,-6003043,18109120,-9980648,15337968,-5997823,-16717435,15921866,16103996,-3731215 }, + { -23169824,-10781249,13588192,-1628807,-3798557,-1074929,-19273607,5402699,-29815713,-9841101 }, + }, + { + { 23190676,2384583,-32714340,3462154,-29903655,-1529132,-11266856,8911517,-25205859,2739713 }, + { 21374101,-3554250,-33524649,9874411,15377179,11831242,-33529904,6134907,4931255,11987849 }, + { -7732,-2978858,-16223486,7277597,105524,-322051,-31480539,13861388,-30076310,10117930 }, + }, + { + { -29501170,-10744872,-26163768,13051539,-25625564,5089643,-6325503,6704079,12890019,15728940 }, + { -21972360,-11771379,-951059,-4418840,14704840,2695116,903376,-10428139,12885167,8311031 }, + { -17516482,5352194,10384213,-13811658,7506451,13453191,26423267,4384730,1888765,-5435404 }, + }, + { + { -25817338,-3107312,-13494599,-3182506,30896459,-13921729,-32251644,-12707869,-19464434,-3340243 }, + { -23607977,-2665774,-526091,4651136,5765089,4618330,6092245,14845197,17151279,-9854116 }, + { -24830458,-12733720,-15165978,10367250,-29530908,-265356,22825805,-7087279,-16866484,16176525 }, + }, + { + { -23583256,6564961,20063689,3798228,-4740178,7359225,2006182,-10363426,-28746253,-10197509 }, + { -10626600,-4486402,-13320562,-5125317,3432136,-6393229,23632037,-1940610,32808310,1099883 }, + { 15030977,5768825,-27451236,-2887299,-6427378,-15361371,-15277896,-6809350,2051441,-15225865 }, + }, + { + { -3362323,-7239372,7517890,9824992,23555850,295369,5148398,-14154188,-22686354,16633660 }, + { 4577086,-16752288,13249841,-15304328,19958763,-14537274,18559670,-10759549,8402478,-9864273 }, + { -28406330,-1051581,-26790155,-907698,-17212414,-11030789,9453451,-14980072,17983010,9967138 }, + }, + { + { -25762494,6524722,26585488,9969270,24709298,1220360,-1677990,7806337,17507396,3651560 }, + { -10420457,-4118111,14584639,15971087,-15768321,8861010,26556809,-5574557,-18553322,-11357135 }, + { 2839101,14284142,4029895,3472686,14402957,12689363,-26642121,8459447,-5605463,-7621941 }, + }, + { + { -4839289,-3535444,9744961,2871048,25113978,3187018,-25110813,-849066,17258084,-7977739 }, + { 18164541,-10595176,-17154882,-1542417,19237078,-9745295,23357533,-15217008,26908270,12150756 }, + { -30264870,-7647865,5112249,-7036672,-1499807,-6974257,43168,-5537701,-32302074,16215819 }, + }, +}, +{ + { + { -6898905,9824394,-12304779,-4401089,-31397141,-6276835,32574489,12532905,-7503072,-8675347 }, + { -27343522,-16515468,-27151524,-10722951,946346,16291093,254968,7168080,21676107,-1943028 }, + { 21260961,-8424752,-16831886,-11920822,-23677961,3968121,-3651949,-6215466,-3556191,-7913075 }, + }, + { + { 16544754,13250366,-16804428,15546242,-4583003,12757258,-2462308,-8680336,-18907032,-9662799 }, + { -2415239,-15577728,18312303,4964443,-15272530,-12653564,26820651,16690659,25459437,-4564609 }, + { -25144690,11425020,28423002,-11020557,-6144921,-15826224,9142795,-2391602,-6432418,-1644817 }, + }, + { + { -23104652,6253476,16964147,-3768872,-25113972,-12296437,-27457225,-16344658,6335692,7249989 }, + { -30333227,13979675,7503222,-12368314,-11956721,-4621693,-30272269,2682242,25993170,-12478523 }, + { 4364628,5930691,32304656,-10044554,-8054781,15091131,22857016,-10598955,31820368,15075278 }, + }, + { + { 31879134,-8918693,17258761,90626,-8041836,-4917709,24162788,-9650886,-17970238,12833045 }, + { 19073683,14851414,-24403169,-11860168,7625278,11091125,-19619190,2074449,-9413939,14905377 }, + { 24483667,-11935567,-2518866,-11547418,-1553130,15355506,-25282080,9253129,27628530,-7555480 }, + }, + { + { 17597607,8340603,19355617,552187,26198470,-3176583,4593324,-9157582,-14110875,15297016 }, + { 510886,14337390,-31785257,16638632,6328095,2713355,-20217417,-11864220,8683221,2921426 }, + { 18606791,11874196,27155355,-5281482,-24031742,6265446,-25178240,-1278924,4674690,13890525 }, + }, + { + { 13609624,13069022,-27372361,-13055908,24360586,9592974,14977157,9835105,4389687,288396 }, + { 9922506,-519394,13613107,5883594,-18758345,-434263,-12304062,8317628,23388070,16052080 }, + { 12720016,11937594,-31970060,-5028689,26900120,8561328,-20155687,-11632979,-14754271,-10812892 }, + }, + { + { 15961858,14150409,26716931,-665832,-22794328,13603569,11829573,7467844,-28822128,929275 }, + { 11038231,-11582396,-27310482,-7316562,-10498527,-16307831,-23479533,-9371869,-21393143,2465074 }, + { 20017163,-4323226,27915242,1529148,12396362,15675764,13817261,-9658066,2463391,-4622140 }, + }, + { + { -16358878,-12663911,-12065183,4996454,-1256422,1073572,9583558,12851107,4003896,12673717 }, + { -1731589,-15155870,-3262930,16143082,19294135,13385325,14741514,-9103726,7903886,2348101 }, + { 24536016,-16515207,12715592,-3862155,1511293,10047386,-3842346,-7129159,-28377538,10048127 }, + }, +}, +{ + { + { -12622226,-6204820,30718825,2591312,-10617028,12192840,18873298,-7297090,-32297756,15221632 }, + { -26478122,-11103864,11546244,-1852483,9180880,7656409,-21343950,2095755,29769758,6593415 }, + { -31994208,-2907461,4176912,3264766,12538965,-868111,26312345,-6118678,30958054,8292160 }, + }, + { + { 31429822,-13959116,29173532,15632448,12174511,-2760094,32808831,3977186,26143136,-3148876 }, + { 22648901,1402143,-22799984,13746059,7936347,365344,-8668633,-1674433,-3758243,-2304625 }, + { -15491917,8012313,-2514730,-12702462,-23965846,-10254029,-1612713,-1535569,-16664475,8194478 }, + }, + { + { 27338066,-7507420,-7414224,10140405,-19026427,-6589889,27277191,8855376,28572286,3005164 }, + { 26287124,4821776,25476601,-4145903,-3764513,-15788984,-18008582,1182479,-26094821,-13079595 }, + { -7171154,3178080,23970071,6201893,-17195577,-4489192,-21876275,-13982627,32208683,-1198248 }, + }, + { + { -16657702,2817643,-10286362,14811298,6024667,13349505,-27315504,-10497842,-27672585,-11539858 }, + { 15941029,-9405932,-21367050,8062055,31876073,-238629,-15278393,-1444429,15397331,-4130193 }, + { 8934485,-13485467,-23286397,-13423241,-32446090,14047986,31170398,-1441021,-27505566,15087184 }, + }, + { + { -18357243,-2156491,24524913,-16677868,15520427,-6360776,-15502406,11461896,16788528,-5868942 }, + { -1947386,16013773,21750665,3714552,-17401782,-16055433,-3770287,-10323320,31322514,-11615635 }, + { 21426655,-5650218,-13648287,-5347537,-28812189,-4920970,-18275391,-14621414,13040862,-12112948 }, + }, + { + { 11293895,12478086,-27136401,15083750,-29307421,14748872,14555558,-13417103,1613711,4896935 }, + { -25894883,15323294,-8489791,-8057900,25967126,-13425460,2825960,-4897045,-23971776,-11267415 }, + { -15924766,-5229880,-17443532,6410664,3622847,10243618,20615400,12405433,-23753030,-8436416 }, + }, + { + { -7091295,12556208,-20191352,9025187,-17072479,4333801,4378436,2432030,23097949,-566018 }, + { 4565804,-16025654,20084412,-7842817,1724999,189254,24767264,10103221,-18512313,2424778 }, + { 366633,-11976806,8173090,-6890119,30788634,5745705,-7168678,1344109,-3642553,12412659 }, + }, + { + { -24001791,7690286,14929416,-168257,-32210835,-13412986,24162697,-15326504,-3141501,11179385 }, + { 18289522,-14724954,8056945,16430056,-21729724,7842514,-6001441,-1486897,-18684645,-11443503 }, + { 476239,6601091,-6152790,-9723375,17503545,-4863900,27672959,13403813,11052904,5219329 }, + }, +}, +{ + { + { 20678546,-8375738,-32671898,8849123,-5009758,14574752,31186971,-3973730,9014762,-8579056 }, + { -13644050,-10350239,-15962508,5075808,-1514661,-11534600,-33102500,9160280,8473550,-3256838 }, + { 24900749,14435722,17209120,-15292541,-22592275,9878983,-7689309,-16335821,-24568481,11788948 }, + }, + { + { -3118155,-11395194,-13802089,14797441,9652448,-6845904,-20037437,10410733,-24568470,-1458691 }, + { -15659161,16736706,-22467150,10215878,-9097177,7563911,11871841,-12505194,-18513325,8464118 }, + { -23400612,8348507,-14585951,-861714,-3950205,-6373419,14325289,8628612,33313881,-8370517 }, + }, + { + { -20186973,-4967935,22367356,5271547,-1097117,-4788838,-24805667,-10236854,-8940735,-5818269 }, + { -6948785,-1795212,-32625683,-16021179,32635414,-7374245,15989197,-12838188,28358192,-4253904 }, + { -23561781,-2799059,-32351682,-1661963,-9147719,10429267,-16637684,4072016,-5351664,5596589 }, + }, + { + { -28236598,-3390048,12312896,6213178,3117142,16078565,29266239,2557221,1768301,15373193 }, + { -7243358,-3246960,-4593467,-7553353,-127927,-912245,-1090902,-4504991,-24660491,3442910 }, + { -30210571,5124043,14181784,8197961,18964734,-11939093,22597931,7176455,-18585478,13365930 }, + }, + { + { -7877390,-1499958,8324673,4690079,6261860,890446,24538107,-8570186,-9689599,-3031667 }, + { 25008904,-10771599,-4305031,-9638010,16265036,15721635,683793,-11823784,15723479,-15163481 }, + { -9660625,12374379,-27006999,-7026148,-7724114,-12314514,11879682,5400171,519526,-1235876 }, + }, + { + { 22258397,-16332233,-7869817,14613016,-22520255,-2950923,-20353881,7315967,16648397,7605640 }, + { -8081308,-8464597,-8223311,9719710,19259459,-15348212,23994942,-5281555,-9468848,4763278 }, + { -21699244,9220969,-15730624,1084137,-25476107,-2852390,31088447,-7764523,-11356529,728112 }, + }, + { + { 26047220,-11751471,-6900323,-16521798,24092068,9158119,-4273545,-12555558,-29365436,-5498272 }, + { 17510331,-322857,5854289,8403524,17133918,-3112612,-28111007,12327945,10750447,10014012 }, + { -10312768,3936952,9156313,-8897683,16498692,-994647,-27481051,-666732,3424691,7540221 }, + }, + { + { 30322361,-6964110,11361005,-4143317,7433304,4989748,-7071422,-16317219,-9244265,15258046 }, + { 13054562,-2779497,19155474,469045,-12482797,4566042,5631406,2711395,1062915,-5136345 }, + { -19240248,-11254599,-29509029,-7499965,-5835763,13005411,-6066489,12194497,32960380,1459310 }, + }, +}, +{ + { + { 19852034,7027924,23669353,10020366,8586503,-6657907,394197,-6101885,18638003,-11174937 }, + { 31395534,15098109,26581030,8030562,-16527914,-5007134,9012486,-7584354,-6643087,-5442636 }, + { -9192165,-2347377,-1997099,4529534,25766844,607986,-13222,9677543,-32294889,-6456008 }, + }, + { + { -2444496,-149937,29348902,8186665,1873760,12489863,-30934579,-7839692,-7852844,-8138429 }, + { -15236356,-15433509,7766470,746860,26346930,-10221762,-27333451,10754588,-9431476,5203576 }, + { 31834314,14135496,-770007,5159118,20917671,-16768096,-7467973,-7337524,31809243,7347066 }, + }, + { + { -9606723,-11874240,20414459,13033986,13716524,-11691881,19797970,-12211255,15192876,-2087490 }, + { -12663563,-2181719,1168162,-3804809,26747877,-14138091,10609330,12694420,33473243,-13382104 }, + { 33184999,11180355,15832085,-11385430,-1633671,225884,15089336,-11023903,-6135662,14480053 }, + }, + { + { 31308717,-5619998,31030840,-1897099,15674547,-6582883,5496208,13685227,27595050,8737275 }, + { -20318852,-15150239,10933843,-16178022,8335352,-7546022,-31008351,-12610604,26498114,66511 }, + { 22644454,-8761729,-16671776,4884562,-3105614,-13559366,30540766,-4286747,-13327787,-7515095 }, + }, + { + { -28017847,9834845,18617207,-2681312,-3401956,-13307506,8205540,13585437,-17127465,15115439 }, + { 23711543,-672915,31206561,-8362711,6164647,-9709987,-33535882,-1426096,8236921,16492939 }, + { -23910559,-13515526,-26299483,-4503841,25005590,-7687270,19574902,10071562,6708380,-6222424 }, + }, + { + { 2101391,-4930054,19702731,2367575,-15427167,1047675,5301017,9328700,29955601,-11678310 }, + { 3096359,9271816,-21620864,-15521844,-14847996,-7592937,-25892142,-12635595,-9917575,6216608 }, + { -32615849,338663,-25195611,2510422,-29213566,-13820213,24822830,-6146567,-26767480,7525079 }, + }, + { + { -23066649,-13985623,16133487,-7896178,-3389565,778788,-910336,-2782495,-19386633,11994101 }, + { 21691500,-13624626,-641331,-14367021,3285881,-3483596,-25064666,9718258,-7477437,13381418 }, + { 18445390,-4202236,14979846,11622458,-1727110,-3582980,23111648,-6375247,28535282,15779576 }, + }, + { + { 30098053,3089662,-9234387,16662135,-21306940,11308411,-14068454,12021730,9955285,-16303356 }, + { 9734894,-14576830,-7473633,-9138735,2060392,11313496,-18426029,9924399,20194861,13380996 }, + { -26378102,-7965207,-22167821,15789297,-18055342,-6168792,-1984914,15707771,26342023,10146099 }, + }, +}, +{ + { + { -26016874,-219943,21339191,-41388,19745256,-2878700,-29637280,2227040,21612326,-545728 }, + { -13077387,1184228,23562814,-5970442,-20351244,-6348714,25764461,12243797,-20856566,11649658 }, + { -10031494,11262626,27384172,2271902,26947504,-15997771,39944,6114064,33514190,2333242 }, + }, + { + { -21433588,-12421821,8119782,7219913,-21830522,-9016134,-6679750,-12670638,24350578,-13450001 }, + { -4116307,-11271533,-23886186,4843615,-30088339,690623,-31536088,-10406836,8317860,12352766 }, + { 18200138,-14475911,-33087759,-2696619,-23702521,-9102511,-23552096,-2287550,20712163,6719373 }, + }, + { + { 26656208,6075253,-7858556,1886072,-28344043,4262326,11117530,-3763210,26224235,-3297458 }, + { -17168938,-14854097,-3395676,-16369877,-19954045,14050420,21728352,9493610,18620611,-16428628 }, + { -13323321,13325349,11432106,5964811,18609221,6062965,-5269471,-9725556,-30701573,-16479657 }, + }, + { + { -23860538,-11233159,26961357,1640861,-32413112,-16737940,12248509,-5240639,13735342,1934062 }, + { 25089769,6742589,17081145,-13406266,21909293,-16067981,-15136294,-3765346,-21277997,5473616 }, + { 31883677,-7961101,1083432,-11572403,22828471,13290673,-7125085,12469656,29111212,-5451014 }, + }, + { + { 24244947,-15050407,-26262976,2791540,-14997599,16666678,24367466,6388839,-10295587,452383 }, + { -25640782,-3417841,5217916,16224624,19987036,-4082269,-24236251,-5915248,15766062,8407814 }, + { -20406999,13990231,15495425,16395525,5377168,15166495,-8917023,-4388953,-8067909,2276718 }, + }, + { + { 30157918,12924066,-17712050,9245753,19895028,3368142,-23827587,5096219,22740376,-7303417 }, + { 2041139,-14256350,7783687,13876377,-25946985,-13352459,24051124,13742383,-15637599,13295222 }, + { 33338237,-8505733,12532113,7977527,9106186,-1715251,-17720195,-4612972,-4451357,-14669444 }, + }, + { + { -20045281,5454097,-14346548,6447146,28862071,1883651,-2469266,-4141880,7770569,9620597 }, + { 23208068,7979712,33071466,8149229,1758231,-10834995,30945528,-1694323,-33502340,-14767970 }, + { 1439958,-16270480,-1079989,-793782,4625402,10647766,-5043801,1220118,30494170,-11440799 }, + }, + { + { -5037580,-13028295,-2970559,-3061767,15640974,-6701666,-26739026,926050,-1684339,-13333647 }, + { 13908495,-3549272,30919928,-6273825,-21521863,7989039,9021034,9078865,3353509,4033511 }, + { -29663431,-15113610,32259991,-344482,24295849,-12912123,23161163,8839127,27485041,7356032 }, + }, +}, +{ + { + { 9661027,705443,11980065,-5370154,-1628543,14661173,-6346142,2625015,28431036,-16771834 }, + { -23839233,-8311415,-25945511,7480958,-17681669,-8354183,-22545972,14150565,15970762,4099461 }, + { 29262576,16756590,26350592,-8793563,8529671,-11208050,13617293,-9937143,11465739,8317062 }, + }, + { + { -25493081,-6962928,32500200,-9419051,-23038724,-2302222,14898637,3848455,20969334,-5157516 }, + { -20384450,-14347713,-18336405,13884722,-33039454,2842114,-21610826,-3649888,11177095,14989547 }, + { -24496721,-11716016,16959896,2278463,12066309,10137771,13515641,2581286,-28487508,9930240 }, + }, + { + { -17751622,-2097826,16544300,-13009300,-15914807,-14949081,18345767,-13403753,16291481,-5314038 }, + { -33229194,2553288,32678213,9875984,8534129,6889387,-9676774,6957617,4368891,9788741 }, + { 16660756,7281060,-10830758,12911820,20108584,-8101676,-21722536,-8613148,16250552,-11111103 }, + }, + { + { -19765507,2390526,-16551031,14161980,1905286,6414907,4689584,10604807,-30190403,4782747 }, + { -1354539,14736941,-7367442,-13292886,7710542,-14155590,-9981571,4383045,22546403,437323 }, + { 31665577,-12180464,-16186830,1491339,-18368625,3294682,27343084,2786261,-30633590,-14097016 }, + }, + { + { -14467279,-683715,-33374107,7448552,19294360,14334329,-19690631,2355319,-19284671,-6114373 }, + { 15121312,-15796162,6377020,-6031361,-10798111,-12957845,18952177,15496498,-29380133,11754228 }, + { -2637277,-13483075,8488727,-14303896,12728761,-1622493,7141596,11724556,22761615,-10134141 }, + }, + { + { 16918416,11729663,-18083579,3022987,-31015732,-13339659,-28741185,-12227393,32851222,11717399 }, + { 11166634,7338049,-6722523,4531520,-29468672,-7302055,31474879,3483633,-1193175,-4030831 }, + { -185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376 }, + }, + { + { -32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313 }, + { -18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958 }, + { -6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577 }, + }, + { + { -22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743 }, + { 29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684 }, + { -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 }, + }, +}, diff --git a/src/ext/ed25519/ref10/base.py b/src/ext/ed25519/ref10/base.py new file mode 100644 index 0000000..84accc8 --- /dev/null +++ b/src/ext/ed25519/ref10/base.py @@ -0,0 +1,65 @@ +b = 256 +q = 2**255 - 19 +l = 2**252 + 27742317777372353535851937790883648493 + +def expmod(b,e,m): + if e == 0: return 1 + t = expmod(b,e/2,m)**2 % m + if e & 1: t = (t*b) % m + return t + +def inv(x): + return expmod(x,q-2,q) + +d = -121665 * inv(121666) +I = expmod(2,(q-1)/4,q) + +def xrecover(y): + xx = (y*y-1) * inv(d*y*y+1) + x = expmod(xx,(q+3)/8,q) + if (x*x - xx) % q != 0: x = (x*I) % q + if x % 2 != 0: x = q-x + return x + +By = 4 * inv(5) +Bx = xrecover(By) +B = [Bx % q,By % q] + +def edwards(P,Q): + x1 = P[0] + y1 = P[1] + x2 = Q[0] + y2 = Q[1] + x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2) + y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2) + return [x3 % q,y3 % q] + +def radix255(x): + x = x % q + if x + x > q: x -= q + x = [x,0,0,0,0,0,0,0,0,0] + bits = [26,25,26,25,26,25,26,25,26,25] + for i in range(9): + carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i] + x[i] -= carry * 2**bits[i] + x[i + 1] += carry + result = "" + for i in range(9): + result = result+str(x[i])+"," + result = result+str(x[9]) + return result + +Bi = B +for i in range(32): + print "{" + Bij = Bi + for j in range(8): + print " {" + print " {",radix255(Bij[1]+Bij[0]),"}," + print " {",radix255(Bij[1]-Bij[0]),"}," + print " {",radix255(2*d*Bij[0]*Bij[1]),"}," + Bij = edwards(Bij,Bi) + print " }," + print "}," + for k in range(8): + Bi = edwards(Bi,Bi) diff --git a/src/ext/ed25519/ref10/base2.h b/src/ext/ed25519/ref10/base2.h new file mode 100644 index 0000000..8c53844 --- /dev/null +++ b/src/ext/ed25519/ref10/base2.h @@ -0,0 +1,40 @@ + { + { 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 }, + }, diff --git a/src/ext/ed25519/ref10/base2.py b/src/ext/ed25519/ref10/base2.py new file mode 100644 index 0000000..5e4e873 --- /dev/null +++ b/src/ext/ed25519/ref10/base2.py @@ -0,0 +1,60 @@ +b = 256 +q = 2**255 - 19 +l = 2**252 + 27742317777372353535851937790883648493 + +def expmod(b,e,m): + if e == 0: return 1 + t = expmod(b,e/2,m)**2 % m + if e & 1: t = (t*b) % m + return t + +def inv(x): + return expmod(x,q-2,q) + +d = -121665 * inv(121666) +I = expmod(2,(q-1)/4,q) + +def xrecover(y): + xx = (y*y-1) * inv(d*y*y+1) + x = expmod(xx,(q+3)/8,q) + if (x*x - xx) % q != 0: x = (x*I) % q + if x % 2 != 0: x = q-x + return x + +By = 4 * inv(5) +Bx = xrecover(By) +B = [Bx % q,By % q] + +def edwards(P,Q): + x1 = P[0] + y1 = P[1] + x2 = Q[0] + y2 = Q[1] + x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2) + y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2) + return [x3 % q,y3 % q] + +def radix255(x): + x = x % q + if x + x > q: x -= q + x = [x,0,0,0,0,0,0,0,0,0] + bits = [26,25,26,25,26,25,26,25,26,25] + for i in range(9): + carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i] + x[i] -= carry * 2**bits[i] + x[i + 1] += carry + result = "" + for i in range(9): + result = result+str(x[i])+"," + result = result+str(x[9]) + return result + +Bi = B + +for i in range(8): + print " {" + print " {",radix255(Bi[1]+Bi[0]),"}," + print " {",radix255(Bi[1]-Bi[0]),"}," + print " {",radix255(2*d*Bi[0]*Bi[1]),"}," + print " }," + Bi = edwards(B,edwards(B,Bi)) diff --git a/src/ext/ed25519/ref10/d.h b/src/ext/ed25519/ref10/d.h new file mode 100644 index 0000000..e25f578 --- /dev/null +++ b/src/ext/ed25519/ref10/d.h @@ -0,0 +1 @@ +-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116 diff --git a/src/ext/ed25519/ref10/d.py b/src/ext/ed25519/ref10/d.py new file mode 100644 index 0000000..8995bb8 --- /dev/null +++ b/src/ext/ed25519/ref10/d.py @@ -0,0 +1,28 @@ +q = 2**255 - 19 + +def expmod(b,e,m): + if e == 0: return 1 + t = expmod(b,e/2,m)**2 % m + if e & 1: t = (t*b) % m + return t + +def inv(x): + return expmod(x,q-2,q) + +def radix255(x): + x = x % q + if x + x > q: x -= q + x = [x,0,0,0,0,0,0,0,0,0] + bits = [26,25,26,25,26,25,26,25,26,25] + for i in range(9): + carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i] + x[i] -= carry * 2**bits[i] + x[i + 1] += carry + result = "" + for i in range(9): + result = result+str(x[i])+"," + result = result+str(x[9]) + return result + +d = -121665 * inv(121666) +print radix255(d) diff --git a/src/ext/ed25519/ref10/d2.h b/src/ext/ed25519/ref10/d2.h new file mode 100644 index 0000000..01aaec7 --- /dev/null +++ b/src/ext/ed25519/ref10/d2.h @@ -0,0 +1 @@ +-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199 diff --git a/src/ext/ed25519/ref10/d2.py b/src/ext/ed25519/ref10/d2.py new file mode 100644 index 0000000..7984175 --- /dev/null +++ b/src/ext/ed25519/ref10/d2.py @@ -0,0 +1,28 @@ +q = 2**255 - 19 + +def expmod(b,e,m): + if e == 0: return 1 + t = expmod(b,e/2,m)**2 % m + if e & 1: t = (t*b) % m + return t + +def inv(x): + return expmod(x,q-2,q) + +def radix255(x): + x = x % q + if x + x > q: x -= q + x = [x,0,0,0,0,0,0,0,0,0] + bits = [26,25,26,25,26,25,26,25,26,25] + for i in range(9): + carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i] + x[i] -= carry * 2**bits[i] + x[i + 1] += carry + result = "" + for i in range(9): + result = result+str(x[i])+"," + result = result+str(x[9]) + return result + +d = -121665 * inv(121666) +print radix255(d*2) diff --git a/src/ext/ed25519/ref10/fe.h b/src/ext/ed25519/ref10/fe.h new file mode 100644 index 0000000..60c308b --- /dev/null +++ b/src/ext/ed25519/ref10/fe.h @@ -0,0 +1,56 @@ +#ifndef FE_H +#define FE_H + +#include "crypto_int32.h" + +typedef crypto_int32 fe[10]; + +/* +fe means field element. +Here the field is \Z/(2^255-19). +An element t, entries t[0]...t[9], represents the integer +t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9]. +Bounds on each t[i] vary depending on context. +*/ + +#define fe_frombytes crypto_sign_ed25519_ref10_fe_frombytes +#define fe_tobytes crypto_sign_ed25519_ref10_fe_tobytes +#define fe_copy crypto_sign_ed25519_ref10_fe_copy +#define fe_isnonzero crypto_sign_ed25519_ref10_fe_isnonzero +#define fe_isnegative crypto_sign_ed25519_ref10_fe_isnegative +#define fe_0 crypto_sign_ed25519_ref10_fe_0 +#define fe_1 crypto_sign_ed25519_ref10_fe_1 +#define fe_cswap crypto_sign_ed25519_ref10_fe_cswap +#define fe_cmov crypto_sign_ed25519_ref10_fe_cmov +#define fe_add crypto_sign_ed25519_ref10_fe_add +#define fe_sub crypto_sign_ed25519_ref10_fe_sub +#define fe_neg crypto_sign_ed25519_ref10_fe_neg +#define fe_mul crypto_sign_ed25519_ref10_fe_mul +#define fe_sq crypto_sign_ed25519_ref10_fe_sq +#define fe_sq2 crypto_sign_ed25519_ref10_fe_sq2 +#define fe_mul121666 crypto_sign_ed25519_ref10_fe_mul121666 +#define fe_invert crypto_sign_ed25519_ref10_fe_invert +#define fe_pow22523 crypto_sign_ed25519_ref10_fe_pow22523 + +extern void fe_frombytes(fe,const unsigned char *); +extern void fe_tobytes(unsigned char *,const fe); + +extern void fe_copy(fe,const fe); +extern int fe_isnonzero(const fe); +extern int fe_isnegative(const fe); +extern void fe_0(fe); +extern void fe_1(fe); +extern void fe_cswap(fe,fe,unsigned int); +extern void fe_cmov(fe,const fe,unsigned int); + +extern void fe_add(fe,const fe,const fe); +extern void fe_sub(fe,const fe,const fe); +extern void fe_neg(fe,const fe); +extern void fe_mul(fe,const fe,const fe); +extern void fe_sq(fe,const fe); +extern void fe_sq2(fe,const fe); +extern void fe_mul121666(fe,const fe); +extern void fe_invert(fe,const fe); +extern void fe_pow22523(fe,const fe); + +#endif diff --git a/src/ext/ed25519/ref10/fe_0.c b/src/ext/ed25519/ref10/fe_0.c new file mode 100644 index 0000000..ec879d7 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_0.c @@ -0,0 +1,19 @@ +#include "fe.h" + +/* +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; +} diff --git a/src/ext/ed25519/ref10/fe_1.c b/src/ext/ed25519/ref10/fe_1.c new file mode 100644 index 0000000..8cf7784 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_1.c @@ -0,0 +1,19 @@ +#include "fe.h" + +/* +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; +} diff --git a/src/ext/ed25519/ref10/fe_add.c b/src/ext/ed25519/ref10/fe_add.c new file mode 100644 index 0000000..e6a81da --- /dev/null +++ b/src/ext/ed25519/ref10/fe_add.c @@ -0,0 +1,57 @@ +#include "fe.h" + +/* +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,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; +} diff --git a/src/ext/ed25519/ref10/fe_cmov.c b/src/ext/ed25519/ref10/fe_cmov.c new file mode 100644 index 0000000..8ca584f --- /dev/null +++ b/src/ext/ed25519/ref10/fe_cmov.c @@ -0,0 +1,63 @@ +#include "fe.h" + +/* +Replace (f,g) with (g,g) if b == 1; +replace (f,g) with (f,g) if b == 0. + +Preconditions: b in {0,1}. +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/fe_copy.c b/src/ext/ed25519/ref10/fe_copy.c new file mode 100644 index 0000000..9c5bf86 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_copy.c @@ -0,0 +1,29 @@ +#include "fe.h" + +/* +h = f +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/fe_frombytes.c b/src/ext/ed25519/ref10/fe_frombytes.c new file mode 100644 index 0000000..5c17917 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_frombytes.c @@ -0,0 +1,73 @@ +#include "fe.h" +#include "crypto_int64.h" +#include "crypto_uint64.h" + +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. +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/fe_invert.c b/src/ext/ed25519/ref10/fe_invert.c new file mode 100644 index 0000000..bcfdb8f --- /dev/null +++ b/src/ext/ed25519/ref10/fe_invert.c @@ -0,0 +1,14 @@ +#include "fe.h" + +void fe_invert(fe out,const fe z) +{ + fe t0; + fe t1; + fe t2; + fe t3; + int i; + +#include "pow225521.h" + + return; +} diff --git a/src/ext/ed25519/ref10/fe_isnegative.c b/src/ext/ed25519/ref10/fe_isnegative.c new file mode 100644 index 0000000..3b2c8b8 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_isnegative.c @@ -0,0 +1,16 @@ +#include "fe.h" + +/* +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. +*/ + +int fe_isnegative(const fe f) +{ + unsigned char s[32]; + fe_tobytes(s,f); + return s[0] & 1; +} diff --git a/src/ext/ed25519/ref10/fe_isnonzero.c b/src/ext/ed25519/ref10/fe_isnonzero.c new file mode 100644 index 0000000..4756800 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_isnonzero.c @@ -0,0 +1,19 @@ +#include "fe.h" +#include "crypto_verify_32.h" + +/* +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]; + +int fe_isnonzero(const fe f) +{ + unsigned char s[32]; + fe_tobytes(s,f); + return crypto_verify_32(s,zero); +} diff --git a/src/ext/ed25519/ref10/fe_mul.c b/src/ext/ed25519/ref10/fe_mul.c new file mode 100644 index 0000000..26ca8b3 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_mul.c @@ -0,0 +1,253 @@ +#include "fe.h" +#include "crypto_int64.h" + +/* +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. +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/fe_neg.c b/src/ext/ed25519/ref10/fe_neg.c new file mode 100644 index 0000000..2078ce5 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_neg.c @@ -0,0 +1,45 @@ +#include "fe.h" + +/* +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. +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/fe_pow22523.c b/src/ext/ed25519/ref10/fe_pow22523.c new file mode 100644 index 0000000..56675a5 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_pow22523.c @@ -0,0 +1,13 @@ +#include "fe.h" + +void fe_pow22523(fe out,const fe z) +{ + fe t0; + fe t1; + fe t2; + int i; + +#include "pow22523.h" + + return; +} diff --git a/src/ext/ed25519/ref10/fe_sq.c b/src/ext/ed25519/ref10/fe_sq.c new file mode 100644 index 0000000..8dd1198 --- /dev/null +++ b/src/ext/ed25519/ref10/fe_sq.c @@ -0,0 +1,149 @@ +#include "fe.h" +#include "crypto_int64.h" + +/* +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. +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/fe_sq2.c b/src/ext/ed25519/ref10/fe_sq2.c new file mode 100644 index 0000000..026ed3a --- /dev/null +++ b/src/ext/ed25519/ref10/fe_sq2.c @@ -0,0 +1,160 @@ +#include "fe.h" +#include "crypto_int64.h" + +/* +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. +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/fe_sub.c b/src/ext/ed25519/ref10/fe_sub.c new file mode 100644 index 0000000..6e26b7d --- /dev/null +++ b/src/ext/ed25519/ref10/fe_sub.c @@ -0,0 +1,57 @@ +#include "fe.h" + +/* +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,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; +} diff --git a/src/ext/ed25519/ref10/fe_tobytes.c b/src/ext/ed25519/ref10/fe_tobytes.c new file mode 100644 index 0000000..0a63baf --- /dev/null +++ b/src/ext/ed25519/ref10/fe_tobytes.c @@ -0,0 +1,119 @@ +#include "fe.h" + +/* +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. +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/ge.h b/src/ext/ed25519/ref10/ge.h new file mode 100644 index 0000000..55e95f9 --- /dev/null +++ b/src/ext/ed25519/ref10/ge.h @@ -0,0 +1,95 @@ +#ifndef GE_H +#define GE_H + +/* +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) +*/ + +#include "fe.h" + +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; + +#define ge_frombytes_negate_vartime crypto_sign_ed25519_ref10_ge_frombytes_negate_vartime +#define ge_tobytes crypto_sign_ed25519_ref10_ge_tobytes +#define ge_p3_tobytes crypto_sign_ed25519_ref10_ge_p3_tobytes + +#define ge_p2_0 crypto_sign_ed25519_ref10_ge_p2_0 +#define ge_p3_0 crypto_sign_ed25519_ref10_ge_p3_0 +#define ge_precomp_0 crypto_sign_ed25519_ref10_ge_precomp_0 +#define ge_p3_to_p2 crypto_sign_ed25519_ref10_ge_p3_to_p2 +#define ge_p3_to_cached crypto_sign_ed25519_ref10_ge_p3_to_cached +#define ge_p1p1_to_p2 crypto_sign_ed25519_ref10_ge_p1p1_to_p2 +#define ge_p1p1_to_p3 crypto_sign_ed25519_ref10_ge_p1p1_to_p3 +#define ge_p2_dbl crypto_sign_ed25519_ref10_ge_p2_dbl +#define ge_p3_dbl crypto_sign_ed25519_ref10_ge_p3_dbl + +#define ge_madd crypto_sign_ed25519_ref10_ge_madd +#define ge_msub crypto_sign_ed25519_ref10_ge_msub +#define ge_add crypto_sign_ed25519_ref10_ge_add +#define ge_sub crypto_sign_ed25519_ref10_ge_sub +#define ge_scalarmult_base crypto_sign_ed25519_ref10_ge_scalarmult_base +#define ge_double_scalarmult_vartime crypto_sign_ed25519_ref10_ge_double_scalarmult_vartime + +extern void ge_tobytes(unsigned char *,const ge_p2 *); +extern void ge_p3_tobytes(unsigned char *,const ge_p3 *); +extern int ge_frombytes_negate_vartime(ge_p3 *,const unsigned char *); + +extern void ge_p2_0(ge_p2 *); +extern void ge_p3_0(ge_p3 *); +extern void ge_precomp_0(ge_precomp *); +extern void ge_p3_to_p2(ge_p2 *,const ge_p3 *); +extern void ge_p3_to_cached(ge_cached *,const ge_p3 *); +extern void ge_p1p1_to_p2(ge_p2 *,const ge_p1p1 *); +extern void ge_p1p1_to_p3(ge_p3 *,const ge_p1p1 *); +extern void ge_p2_dbl(ge_p1p1 *,const ge_p2 *); +extern void ge_p3_dbl(ge_p1p1 *,const ge_p3 *); + +extern void ge_madd(ge_p1p1 *,const ge_p3 *,const ge_precomp *); +extern void ge_msub(ge_p1p1 *,const ge_p3 *,const ge_precomp *); +extern void ge_add(ge_p1p1 *,const ge_p3 *,const ge_cached *); +extern void ge_sub(ge_p1p1 *,const ge_p3 *,const ge_cached *); +extern void ge_scalarmult_base(ge_p3 *,const unsigned char *); +extern void ge_double_scalarmult_vartime(ge_p2 *,const unsigned char *,const ge_p3 *,const unsigned char *); + +#endif diff --git a/src/ext/ed25519/ref10/ge_add.c b/src/ext/ed25519/ref10/ge_add.c new file mode 100644 index 0000000..da7ff5d --- /dev/null +++ b/src/ext/ed25519/ref10/ge_add.c @@ -0,0 +1,11 @@ +#include "ge.h" + +/* +r = p + q +*/ + +void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) +{ + fe t0; +#include "ge_add.h" +} diff --git a/src/ext/ed25519/ref10/ge_add.h b/src/ext/ed25519/ref10/ge_add.h new file mode 100644 index 0000000..7481f8f --- /dev/null +++ b/src/ext/ed25519/ref10/ge_add.h @@ -0,0 +1,97 @@ + +/* 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 */ diff --git a/src/ext/ed25519/ref10/ge_add.q b/src/ext/ed25519/ref10/ge_add.q new file mode 100644 index 0000000..a6572ab --- /dev/null +++ b/src/ext/ed25519/ref10/ge_add.q @@ -0,0 +1,49 @@ +:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->YplusX:q->YminusX:q->Z:q->T2d: +fe r:var/r=fe: + +enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>YpX2=fe#15:>YmX2=fe#16:>Z2=fe#17:>T2d2=fe#18: +return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave: + +h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);: +h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);: +h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);: +h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);: +h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);: + +: + +enter ge_add + +fe X1 +fe Y1 +fe Z1 +fe Z2 +fe T1 +fe ZZ +fe YpX2 +fe YmX2 +fe T2d2 +fe X3 +fe Y3 +fe Z3 +fe T3 +fe YpX1 +fe YmX1 +fe A +fe B +fe C +fe D + +YpX1 = Y1+X1 +YmX1 = Y1-X1 +A = YpX1*YpX2 +B = YmX1*YmX2 +C = T2d2*T1 +ZZ = Z1*Z2 +D = 2*ZZ +X3 = A-B +Y3 = A+B +Z3 = D+C +T3 = D-C + +return diff --git a/src/ext/ed25519/ref10/ge_double_scalarmult.c b/src/ext/ed25519/ref10/ge_double_scalarmult.c new file mode 100644 index 0000000..f8bf4bf --- /dev/null +++ b/src/ext/ed25519/ref10/ge_double_scalarmult.c @@ -0,0 +1,96 @@ +#include "ge.h" + +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; + } + } + } + +} + +static ge_precomp Bi[8] = { +#include "base2.h" +} ; + +/* +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. +*/ + +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); + } +} diff --git a/src/ext/ed25519/ref10/ge_frombytes.c b/src/ext/ed25519/ref10/ge_frombytes.c new file mode 100644 index 0000000..1a059ee --- /dev/null +++ b/src/ext/ed25519/ref10/ge_frombytes.c @@ -0,0 +1,50 @@ +#include "ge.h" + +static const fe d = { +#include "d.h" +} ; + +static const fe sqrtm1 = { +#include "sqrtm1.h" +} ; + +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; +} diff --git a/src/ext/ed25519/ref10/ge_madd.c b/src/ext/ed25519/ref10/ge_madd.c new file mode 100644 index 0000000..6225717 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_madd.c @@ -0,0 +1,11 @@ +#include "ge.h" + +/* +r = p + q +*/ + +void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) +{ + fe t0; +#include "ge_madd.h" +} diff --git a/src/ext/ed25519/ref10/ge_madd.h b/src/ext/ed25519/ref10/ge_madd.h new file mode 100644 index 0000000..ecae849 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_madd.h @@ -0,0 +1,88 @@ + +/* 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 */ diff --git a/src/ext/ed25519/ref10/ge_madd.q b/src/ext/ed25519/ref10/ge_madd.q new file mode 100644 index 0000000..aa3db45 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_madd.q @@ -0,0 +1,46 @@ +:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->yplusx:q->yminusx:q->xy2d: +fe r:var/r=fe: + +enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>ypx2=fe#15:>ymx2=fe#16:>xy2d2=fe#17: +return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave: + +h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);: +h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);: +h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);: +h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);: +h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);: + +: + +enter ge_madd + +fe X1 +fe Y1 +fe Z1 +fe T1 +fe ypx2 +fe ymx2 +fe xy2d2 +fe X3 +fe Y3 +fe Z3 +fe T3 +fe YpX1 +fe YmX1 +fe A +fe B +fe C +fe D + +YpX1 = Y1+X1 +YmX1 = Y1-X1 +A = YpX1*ypx2 +B = YmX1*ymx2 +C = xy2d2*T1 +D = 2*Z1 +X3 = A-B +Y3 = A+B +Z3 = D+C +T3 = D-C + +return diff --git a/src/ext/ed25519/ref10/ge_msub.c b/src/ext/ed25519/ref10/ge_msub.c new file mode 100644 index 0000000..741ecbf --- /dev/null +++ b/src/ext/ed25519/ref10/ge_msub.c @@ -0,0 +1,11 @@ +#include "ge.h" + +/* +r = p - q +*/ + +void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) +{ + fe t0; +#include "ge_msub.h" +} diff --git a/src/ext/ed25519/ref10/ge_msub.h b/src/ext/ed25519/ref10/ge_msub.h new file mode 100644 index 0000000..500f986 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_msub.h @@ -0,0 +1,88 @@ + +/* 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 */ diff --git a/src/ext/ed25519/ref10/ge_msub.q b/src/ext/ed25519/ref10/ge_msub.q new file mode 100644 index 0000000..e3cadd8 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_msub.q @@ -0,0 +1,46 @@ +:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->yplusx:q->yminusx:q->xy2d: +fe r:var/r=fe: + +enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>ypx2=fe#15:>ymx2=fe#16:>xy2d2=fe#17: +return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave: + +h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);: +h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);: +h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);: +h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);: +h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);: + +: + +enter ge_msub + +fe X1 +fe Y1 +fe Z1 +fe T1 +fe ypx2 +fe ymx2 +fe xy2d2 +fe X3 +fe Y3 +fe Z3 +fe T3 +fe YpX1 +fe YmX1 +fe A +fe B +fe C +fe D + +YpX1 = Y1+X1 +YmX1 = Y1-X1 +A = YpX1*ymx2 +B = YmX1*ypx2 +C = xy2d2*T1 +D = 2*Z1 +X3 = A-B +Y3 = A+B +Z3 = D-C +T3 = D+C + +return diff --git a/src/ext/ed25519/ref10/ge_p1p1_to_p2.c b/src/ext/ed25519/ref10/ge_p1p1_to_p2.c new file mode 100644 index 0000000..9bb5013 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p1p1_to_p2.c @@ -0,0 +1,12 @@ +#include "ge.h" + +/* +r = p +*/ + +extern void ge_p1p1_to_p2(ge_p2 *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); +} diff --git a/src/ext/ed25519/ref10/ge_p1p1_to_p3.c b/src/ext/ed25519/ref10/ge_p1p1_to_p3.c new file mode 100644 index 0000000..2f57b10 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p1p1_to_p3.c @@ -0,0 +1,13 @@ +#include "ge.h" + +/* +r = p +*/ + +extern void ge_p1p1_to_p3(ge_p3 *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); +} diff --git a/src/ext/ed25519/ref10/ge_p2_0.c b/src/ext/ed25519/ref10/ge_p2_0.c new file mode 100644 index 0000000..6191d1e --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p2_0.c @@ -0,0 +1,8 @@ +#include "ge.h" + +void ge_p2_0(ge_p2 *h) +{ + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); +} diff --git a/src/ext/ed25519/ref10/ge_p2_dbl.c b/src/ext/ed25519/ref10/ge_p2_dbl.c new file mode 100644 index 0000000..2e332b5 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p2_dbl.c @@ -0,0 +1,11 @@ +#include "ge.h" + +/* +r = 2 * p +*/ + +void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p) +{ + fe t0; +#include "ge_p2_dbl.h" +} diff --git a/src/ext/ed25519/ref10/ge_p2_dbl.h b/src/ext/ed25519/ref10/ge_p2_dbl.h new file mode 100644 index 0000000..128efed --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p2_dbl.h @@ -0,0 +1,73 @@ + +/* 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 */ diff --git a/src/ext/ed25519/ref10/ge_p2_dbl.q b/src/ext/ed25519/ref10/ge_p2_dbl.q new file mode 100644 index 0000000..170d42f --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p2_dbl.q @@ -0,0 +1,41 @@ +:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z: +fe r:var/r=fe: + +enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13: +return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave: + +h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);: +h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);: +h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);: +h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);: +h=2*f^2:<f=fe:>h=fe:asm/fe_sq2(>h,<f);: +h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);: + +: + +enter ge_p2_dbl + +fe X1 +fe Y1 +fe Z1 +fe A +fe AA +fe XX +fe YY +fe B +fe X3 +fe Y3 +fe Z3 +fe T3 + +XX=X1^2 +YY=Y1^2 +B=2*Z1^2 +A=X1+Y1 +AA=A^2 +Y3=YY+XX +Z3=YY-XX +X3=AA-Y3 +T3=B-Z3 + +return diff --git a/src/ext/ed25519/ref10/ge_p3_0.c b/src/ext/ed25519/ref10/ge_p3_0.c new file mode 100644 index 0000000..401b293 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p3_0.c @@ -0,0 +1,9 @@ +#include "ge.h" + +void ge_p3_0(ge_p3 *h) +{ + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); + fe_0(h->T); +} diff --git a/src/ext/ed25519/ref10/ge_p3_dbl.c b/src/ext/ed25519/ref10/ge_p3_dbl.c new file mode 100644 index 0000000..0d8a059 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p3_dbl.c @@ -0,0 +1,12 @@ +#include "ge.h" + +/* +r = 2 * p +*/ + +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); +} diff --git a/src/ext/ed25519/ref10/ge_p3_to_cached.c b/src/ext/ed25519/ref10/ge_p3_to_cached.c new file mode 100644 index 0000000..bde6422 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p3_to_cached.c @@ -0,0 +1,17 @@ +#include "ge.h" + +/* +r = p +*/ + +static const fe d2 = { +#include "d2.h" +} ; + +extern 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); +} diff --git a/src/ext/ed25519/ref10/ge_p3_to_p2.c b/src/ext/ed25519/ref10/ge_p3_to_p2.c new file mode 100644 index 0000000..e532a9e --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p3_to_p2.c @@ -0,0 +1,12 @@ +#include "ge.h" + +/* +r = p +*/ + +extern 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); +} diff --git a/src/ext/ed25519/ref10/ge_p3_tobytes.c b/src/ext/ed25519/ref10/ge_p3_tobytes.c new file mode 100644 index 0000000..21cb2fc --- /dev/null +++ b/src/ext/ed25519/ref10/ge_p3_tobytes.c @@ -0,0 +1,14 @@ +#include "ge.h" + +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; +} diff --git a/src/ext/ed25519/ref10/ge_precomp_0.c b/src/ext/ed25519/ref10/ge_precomp_0.c new file mode 100644 index 0000000..2e21886 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_precomp_0.c @@ -0,0 +1,8 @@ +#include "ge.h" + +void ge_precomp_0(ge_precomp *h) +{ + fe_1(h->yplusx); + fe_1(h->yminusx); + fe_0(h->xy2d); +} diff --git a/src/ext/ed25519/ref10/ge_scalarmult_base.c b/src/ext/ed25519/ref10/ge_scalarmult_base.c new file mode 100644 index 0000000..421e4fa --- /dev/null +++ b/src/ext/ed25519/ref10/ge_scalarmult_base.c @@ -0,0 +1,105 @@ +#include "ge.h" +#include "crypto_uint32.h" + +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); +} + +/* base[i][j] = (j+1)*256^i*B */ +static ge_precomp base[32][8] = { +#include "base.h" +} ; + +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 +*/ + +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); + } +} diff --git a/src/ext/ed25519/ref10/ge_sub.c b/src/ext/ed25519/ref10/ge_sub.c new file mode 100644 index 0000000..69f3d54 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_sub.c @@ -0,0 +1,11 @@ +#include "ge.h" + +/* +r = p - q +*/ + +void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) +{ + fe t0; +#include "ge_sub.h" +} diff --git a/src/ext/ed25519/ref10/ge_sub.h b/src/ext/ed25519/ref10/ge_sub.h new file mode 100644 index 0000000..b4ef1f5 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_sub.h @@ -0,0 +1,97 @@ + +/* 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 */ diff --git a/src/ext/ed25519/ref10/ge_sub.q b/src/ext/ed25519/ref10/ge_sub.q new file mode 100644 index 0000000..2779a4a --- /dev/null +++ b/src/ext/ed25519/ref10/ge_sub.q @@ -0,0 +1,49 @@ +:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->YplusX:q->YminusX:q->Z:q->T2d: +fe r:var/r=fe: + +enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>YpX2=fe#15:>YmX2=fe#16:>Z2=fe#17:>T2d2=fe#18: +return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave: + +h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);: +h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);: +h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);: +h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);: +h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);: + +: + +enter ge_sub + +fe X1 +fe Y1 +fe Z1 +fe Z2 +fe T1 +fe ZZ +fe YpX2 +fe YmX2 +fe T2d2 +fe X3 +fe Y3 +fe Z3 +fe T3 +fe YpX1 +fe YmX1 +fe A +fe B +fe C +fe D + +YpX1 = Y1+X1 +YmX1 = Y1-X1 +A = YpX1*YmX2 +B = YmX1*YpX2 +C = T2d2*T1 +ZZ = Z1*Z2 +D = 2*ZZ +X3 = A-B +Y3 = A+B +Z3 = D-C +T3 = D+C + +return diff --git a/src/ext/ed25519/ref10/ge_tobytes.c b/src/ext/ed25519/ref10/ge_tobytes.c new file mode 100644 index 0000000..31b3d33 --- /dev/null +++ b/src/ext/ed25519/ref10/ge_tobytes.c @@ -0,0 +1,14 @@ +#include "ge.h" + +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; +} diff --git a/src/ext/ed25519/ref10/keypair.c b/src/ext/ed25519/ref10/keypair.c new file mode 100644 index 0000000..ac6cea2 --- /dev/null +++ b/src/ext/ed25519/ref10/keypair.c @@ -0,0 +1,23 @@ +#include <string.h> +#include "randombytes.h" +#include "crypto_sign.h" +#include "crypto_hash_sha512.h" +#include "ge.h" + +int crypto_sign_keypair(unsigned char *pk,unsigned char *sk) +{ + unsigned char az[64]; + ge_p3 A; + + randombytes(sk,32); + crypto_hash_sha512(az,sk,32); + az[0] &= 248; + az[31] &= 63; + az[31] |= 64; + + ge_scalarmult_base(&A,az); + ge_p3_tobytes(pk,&A); + + memmove(sk + 32,pk,32); + return 0; +} diff --git a/src/ext/ed25519/ref10/open.c b/src/ext/ed25519/ref10/open.c new file mode 100644 index 0000000..1ec4cd2 --- /dev/null +++ b/src/ext/ed25519/ref10/open.c @@ -0,0 +1,48 @@ +#include <string.h> +#include "crypto_sign.h" +#include "crypto_hash_sha512.h" +#include "crypto_verify_32.h" +#include "ge.h" +#include "sc.h" + +int crypto_sign_open( + unsigned char *m,unsigned long long *mlen, + const unsigned char *sm,unsigned long long smlen, + const unsigned char *pk +) +{ + unsigned char pkcopy[32]; + unsigned char rcopy[32]; + unsigned char scopy[32]; + unsigned char h[64]; + unsigned char rcheck[32]; + ge_p3 A; + ge_p2 R; + + if (smlen < 64) goto badsig; + if (sm[63] & 224) goto badsig; + if (ge_frombytes_negate_vartime(&A,pk) != 0) goto badsig; + + memmove(pkcopy,pk,32); + memmove(rcopy,sm,32); + memmove(scopy,sm + 32,32); + + memmove(m,sm,smlen); + memmove(m + 32,pkcopy,32); + crypto_hash_sha512(h,m,smlen); + sc_reduce(h); + + ge_double_scalarmult_vartime(&R,h,&A,scopy); + ge_tobytes(rcheck,&R); + if (crypto_verify_32(rcheck,rcopy) == 0) { + memmove(m,m + 64,smlen - 64); + memset(m + smlen - 64,0,64); + *mlen = smlen - 64; + return 0; + } + +badsig: + *mlen = -1; + memset(m,0,smlen); + return -1; +} diff --git a/src/ext/ed25519/ref10/pow22523.h b/src/ext/ed25519/ref10/pow22523.h new file mode 100644 index 0000000..60ffe0d --- /dev/null +++ b/src/ext/ed25519/ref10/pow22523.h @@ -0,0 +1,160 @@ + +/* 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 */ diff --git a/src/ext/ed25519/ref10/pow22523.q b/src/ext/ed25519/ref10/pow22523.q new file mode 100644 index 0000000..2ce1da9 --- /dev/null +++ b/src/ext/ed25519/ref10/pow22523.q @@ -0,0 +1,61 @@ +:name:fe:t0:t1:t2:t3:t4:t5:t6:t7:t8:t9:z:out: +fe r:var/r=fe: + +enter f:enter/f:>z1=fe#11: +return:nofallthrough:<z_252_3=fe#12:leave: + +h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);: +h=f^2^k:<f=fe:>h=fe:#k:asm/fe_sq(>h,<f); for (i = 1;i !lt; #k;++i) fe_sq(>h,>h);: + +: + +fe z1 +fe z2 +fe z8 +fe z9 +fe z11 +fe z22 +fe z_5_0 +fe z_10_5 +fe z_10_0 +fe z_20_10 +fe z_20_0 +fe z_40_20 +fe z_40_0 +fe z_50_10 +fe z_50_0 +fe z_100_50 +fe z_100_0 +fe z_200_100 +fe z_200_0 +fe z_250_50 +fe z_250_0 +fe z_252_2 +fe z_252_3 + +enter pow22523 + +z2 = z1^2^1 +z8 = z2^2^2 +z9 = z1*z8 +z11 = z2*z9 +z22 = z11^2^1 +z_5_0 = z9*z22 +z_10_5 = z_5_0^2^5 +z_10_0 = z_10_5*z_5_0 +z_20_10 = z_10_0^2^10 +z_20_0 = z_20_10*z_10_0 +z_40_20 = z_20_0^2^20 +z_40_0 = z_40_20*z_20_0 +z_50_10 = z_40_0^2^10 +z_50_0 = z_50_10*z_10_0 +z_100_50 = z_50_0^2^50 +z_100_0 = z_100_50*z_50_0 +z_200_100 = z_100_0^2^100 +z_200_0 = z_200_100*z_100_0 +z_250_50 = z_200_0^2^50 +z_250_0 = z_250_50*z_50_0 +z_252_2 = z_250_0^2^2 +z_252_3 = z_252_2*z1 + +return diff --git a/src/ext/ed25519/ref10/pow225521.h b/src/ext/ed25519/ref10/pow225521.h new file mode 100644 index 0000000..109df77 --- /dev/null +++ b/src/ext/ed25519/ref10/pow225521.h @@ -0,0 +1,160 @@ + +/* 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 */ diff --git a/src/ext/ed25519/ref10/pow225521.q b/src/ext/ed25519/ref10/pow225521.q new file mode 100644 index 0000000..45be57c --- /dev/null +++ b/src/ext/ed25519/ref10/pow225521.q @@ -0,0 +1,61 @@ +:name:fe:t0:t1:t2:t3:t4:t5:t6:t7:t8:t9:z:out: +fe r:var/r=fe: + +enter f:enter/f:>z1=fe#11: +return:nofallthrough:<z_255_21=fe#12:leave: + +h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);: +h=f^2^k:<f=fe:>h=fe:#k:asm/fe_sq(>h,<f); for (i = 1;i !lt; #k;++i) fe_sq(>h,>h);: + +: + +fe z1 +fe z2 +fe z8 +fe z9 +fe z11 +fe z22 +fe z_5_0 +fe z_10_5 +fe z_10_0 +fe z_20_10 +fe z_20_0 +fe z_40_20 +fe z_40_0 +fe z_50_10 +fe z_50_0 +fe z_100_50 +fe z_100_0 +fe z_200_100 +fe z_200_0 +fe z_250_50 +fe z_250_0 +fe z_255_5 +fe z_255_21 + +enter pow225521 + +z2 = z1^2^1 +z8 = z2^2^2 +z9 = z1*z8 +z11 = z2*z9 +z22 = z11^2^1 +z_5_0 = z9*z22 +z_10_5 = z_5_0^2^5 +z_10_0 = z_10_5*z_5_0 +z_20_10 = z_10_0^2^10 +z_20_0 = z_20_10*z_10_0 +z_40_20 = z_20_0^2^20 +z_40_0 = z_40_20*z_20_0 +z_50_10 = z_40_0^2^10 +z_50_0 = z_50_10*z_10_0 +z_100_50 = z_50_0^2^50 +z_100_0 = z_100_50*z_50_0 +z_200_100 = z_100_0^2^100 +z_200_0 = z_200_100*z_100_0 +z_250_50 = z_200_0^2^50 +z_250_0 = z_250_50*z_50_0 +z_255_5 = z_250_0^2^5 +z_255_21 = z_255_5*z11 + +return diff --git a/src/ext/ed25519/ref10/q2h.sh b/src/ext/ed25519/ref10/q2h.sh new file mode 100755 index 0000000..47ec511 --- /dev/null +++ b/src/ext/ed25519/ref10/q2h.sh @@ -0,0 +1,4 @@ +#!/bin/sh +sed 's/^#.*//' \ +| qhasm-generic \ +| sed 's_//$.*$$_/*\1 */_' diff --git a/src/ext/ed25519/ref10/sc.h b/src/ext/ed25519/ref10/sc.h new file mode 100644 index 0000000..d32ed2e --- /dev/null +++ b/src/ext/ed25519/ref10/sc.h @@ -0,0 +1,15 @@ +#ifndef SC_H +#define SC_H + +/* +The set of scalars is \Z/l +where l = 2^252 + 27742317777372353535851937790883648493. +*/ + +#define sc_reduce crypto_sign_ed25519_ref10_sc_reduce +#define sc_muladd crypto_sign_ed25519_ref10_sc_muladd + +extern void sc_reduce(unsigned char *); +extern void sc_muladd(unsigned char *,const unsigned char *,const unsigned char *,const unsigned char *); + +#endif diff --git a/src/ext/ed25519/ref10/sc_muladd.c b/src/ext/ed25519/ref10/sc_muladd.c new file mode 100644 index 0000000..6f1e9d0 --- /dev/null +++ b/src/ext/ed25519/ref10/sc_muladd.c @@ -0,0 +1,368 @@ +#include "sc.h" +#include "crypto_int64.h" +#include "crypto_uint32.h" +#include "crypto_uint64.h" + +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; +} + +/* +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. +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/sc_reduce.c b/src/ext/ed25519/ref10/sc_reduce.c new file mode 100644 index 0000000..d01f5a5 --- /dev/null +++ b/src/ext/ed25519/ref10/sc_reduce.c @@ -0,0 +1,275 @@ +#include "sc.h" +#include "crypto_int64.h" +#include "crypto_uint32.h" +#include "crypto_uint64.h" + +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; +} + +/* +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. +*/ + +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; +} diff --git a/src/ext/ed25519/ref10/sign.c b/src/ext/ed25519/ref10/sign.c new file mode 100644 index 0000000..de53742 --- /dev/null +++ b/src/ext/ed25519/ref10/sign.c @@ -0,0 +1,41 @@ +#include <string.h> +#include "crypto_sign.h" +#include "crypto_hash_sha512.h" +#include "ge.h" +#include "sc.h" + +int crypto_sign( + unsigned char *sm,unsigned long long *smlen, + const unsigned char *m,unsigned long long mlen, + const unsigned char *sk +) +{ + unsigned char pk[32]; + unsigned char az[64]; + unsigned char nonce[64]; + unsigned char hram[64]; + ge_p3 R; + + memmove(pk,sk + 32,32); + + crypto_hash_sha512(az,sk,32); + az[0] &= 248; + az[31] &= 63; + az[31] |= 64; + + *smlen = mlen + 64; + memmove(sm + 64,m,mlen); + memmove(sm + 32,az + 32,32); + crypto_hash_sha512(nonce,sm + 32,mlen + 32); + memmove(sm + 32,pk,32); + + sc_reduce(nonce); + ge_scalarmult_base(&R,nonce); + ge_p3_tobytes(sm,&R); + + crypto_hash_sha512(hram,sm,mlen + 64); + sc_reduce(hram); + sc_muladd(sm + 32,hram,az,nonce); + + return 0; +} diff --git a/src/ext/ed25519/ref10/sqrtm1.h b/src/ext/ed25519/ref10/sqrtm1.h new file mode 100644 index 0000000..d8caa23 --- /dev/null +++ b/src/ext/ed25519/ref10/sqrtm1.h @@ -0,0 +1 @@ +-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482 diff --git a/src/ext/ed25519/ref10/sqrtm1.py b/src/ext/ed25519/ref10/sqrtm1.py new file mode 100644 index 0000000..9a47fbc --- /dev/null +++ b/src/ext/ed25519/ref10/sqrtm1.py @@ -0,0 +1,28 @@ +q = 2**255 - 19 + +def expmod(b,e,m): + if e == 0: return 1 + t = expmod(b,e/2,m)**2 % m + if e & 1: t = (t*b) % m + return t + +def inv(x): + return expmod(x,q-2,q) + +def radix255(x): + x = x % q + if x + x > q: x -= q + x = [x,0,0,0,0,0,0,0,0,0] + bits = [26,25,26,25,26,25,26,25,26,25] + for i in range(9): + carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i] + x[i] -= carry * 2**bits[i] + x[i + 1] += carry + result = "" + for i in range(9): + result = result+str(x[i])+"," + result = result+str(x[9]) + return result + +I = expmod(2,(q-1)/4,q) +print radix255(I)

1 0

← Newer
1
...
13
14
15
16
17
18
19
...
98
Older →

Jump to page: