commit f638c33f6c6f697498150d5f0dfbf26453759262
Author: Philipp Winter <phw(a)nymity.ch>
Date: Mon Dec 7 10:23:44 2020 -0800
Actually support unsafe logging.
Obfs4proxy implements the -unsafeLogging switch but it's been ignored so
far. This patch makes it work.
---
ChangeLog | 1 +
common/log/log.go | 1 +
2 files changed, 2 insertions(+)
diff --git a/ChangeLog b/ChangeLog
index 5b16201..467f7d7 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,6 +1,7 @@
Changes in version 0.0.12 - UNRELEASED:
- Replace the extra25519 import with an internal package.
- Update the Azure TLS certificate digest (Thanks to Philipp Winter).
+ - Make the -unsafeLogging command line switch work.
Changes in version 0.0.11 - 2019-06-21:
- Update my e-mail address.
diff --git a/common/log/log.go b/common/log/log.go
index 61d8d8c..5e08c64 100644
--- a/common/log/log.go
+++ b/common/log/log.go
@@ -70,6 +70,7 @@ func Init(enable bool, logFilePath string, unsafe bool) error {
log.SetOutput(ioutil.Discard)
}
enableLogging = enable
+ unsafeLogging = unsafe
return nil
}
1
0
24 Jan '22
commit a564bc3840bc788605e1a8155f4b95ce0d70c6db
Author: Yawning Angel <yawning(a)schwanenlied.me>
Date: Fri Dec 31 02:43:14 2021 +0000
Do the release ritual for obfs4proxy-0.0.12
---
ChangeLog | 2 +-
go.mod | 2 +-
obfs4proxy/obfs4proxy.go | 2 +-
3 files changed, 3 insertions(+), 3 deletions(-)
diff --git a/ChangeLog b/ChangeLog
index 5253fe6..fca34df 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,4 +1,4 @@
-Changes in version 0.0.12 - UNRELEASED:
+Changes in version 0.0.12 - 2021-12-31:
- Fix the long standing distinguishers associated with agl's Elligator2
implementation (Thanks to Loup Vaillant).
- Replace the extra25519 import with an internal package.
diff --git a/go.mod b/go.mod
index 037082a..622ac6f 100644
--- a/go.mod
+++ b/go.mod
@@ -10,4 +10,4 @@ require (
golang.org/x/net v0.0.0-20210226172049-e18ecbb05110
)
-go 1.13
+go 1.16
diff --git a/obfs4proxy/obfs4proxy.go b/obfs4proxy/obfs4proxy.go
index 1dd00b2..c4982ce 100644
--- a/obfs4proxy/obfs4proxy.go
+++ b/obfs4proxy/obfs4proxy.go
@@ -50,7 +50,7 @@ import (
)
const (
- obfs4proxyVersion = "0.0.12-dev"
+ obfs4proxyVersion = "0.0.12"
obfs4proxyLogFile = "obfs4proxy.log"
socksAddr = "127.0.0.1:0"
)
1
0
[obfs4/main] transports/meek_lite: Bump the version of the utls fork
by cohosh＠torproject.org 24 Jan '22
by cohosh＠torproject.org 24 Jan '22
24 Jan '22
commit e330d1b7024b4ab04f7d96cc1afc61325744fafc
Author: Yawning Angel <yawning(a)schwanenlied.me>
Date: Tue May 11 22:07:00 2021 +0000
transports/meek_lite: Bump the version of the utls fork
And add the Chrome 83 fingerprint.
---
ChangeLog | 1 +
go.mod | 2 +-
go.sum | 12 ++++++------
transports/meeklite/transport.go | 1 +
4 files changed, 9 insertions(+), 7 deletions(-)
diff --git a/ChangeLog b/ChangeLog
index 467f7d7..53253ef 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -2,6 +2,7 @@ Changes in version 0.0.12 - UNRELEASED:
- Replace the extra25519 import with an internal package.
- Update the Azure TLS certificate digest (Thanks to Philipp Winter).
- Make the -unsafeLogging command line switch work.
+ - Bump the version of the utls fork, add the Chrome 83 fingerprint.
Changes in version 0.0.11 - 2019-06-21:
- Update my e-mail address.
diff --git a/go.mod b/go.mod
index a90d67d..1a64cb6 100644
--- a/go.mod
+++ b/go.mod
@@ -3,7 +3,7 @@ module gitlab.com/yawning/obfs4.git
require (
git.torproject.org/pluggable-transports/goptlib.git v1.0.0
github.com/dchest/siphash v1.2.1
- gitlab.com/yawning/utls.git v0.0.11-1
+ gitlab.com/yawning/utls.git v0.0.12-1
golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c
golang.org/x/net v0.0.0-20190328230028-74de082e2cca
)
diff --git a/go.sum b/go.sum
index bffa15e..5e192a8 100644
--- a/go.sum
+++ b/go.sum
@@ -1,5 +1,3 @@
-git.schwanenlied.me/yawning/bsaes.git v0.0.0-20190320102049-26d1add596b6 h1:zOrl5/RvK48MxMrif6Z+/OpuYyRnvB+ZTrQWEV9VYb0=
-git.schwanenlied.me/yawning/bsaes.git v0.0.0-20190320102049-26d1add596b6/go.mod h1:BWqTsj8PgcPriQJGl7el20J/7TuT1d/hSyFDXMEpoEo=
git.torproject.org/pluggable-transports/goptlib.git v1.0.0 h1:ElTwFFPKf/tA6x5nuIk9g49JZzS4T5WN+eTQTjqd00A=
git.torproject.org/pluggable-transports/goptlib.git v1.0.0/go.mod h1:YT4XMSkuEXbtqlydr9+OxqFAyspUv0Gr9qhM3B++o/Q=
github.com/dchest/siphash v1.2.1 h1:4cLinnzVJDKxTCl9B01807Yiy+W7ZzVHj/KIroQRvT4=
@@ -10,15 +8,17 @@ github.com/dsnet/golib v0.0.0-20171103203638-1ea166775780/go.mod h1:Lj+Z9rebOhdf
github.com/klauspost/compress v1.4.1/go.mod h1:RyIbtBH6LamlWaDj8nUwkbUhJ87Yi3uG0guNDohfE1A=
github.com/klauspost/cpuid v1.2.0/go.mod h1:Pj4uuM528wm8OyEC2QMXAi2YiTZ96dNQPGgoMS4s3ek=
github.com/ulikunitz/xz v0.5.6/go.mod h1:2bypXElzHzzJZwzH67Y6wb67pO62Rzfn7BSiF4ABRW8=
-gitlab.com/yawning/utls.git v0.0.11-1 h1:cQLJ4sN+u07Rn9M7RpvCEWUPndtrsQsy6U3ZaEHeDvI=
-gitlab.com/yawning/utls.git v0.0.11-1/go.mod h1:eYdrOOCoedNc3xw50kJ/s8JquyxeS5kr3vkFZFPTI9w=
+gitlab.com/yawning/bsaes.git v0.0.0-20190805113838-0a714cd429ec h1:FpfFs4EhNehiVfzQttTuxanPIT43FtkkCFypIod8LHo=
+gitlab.com/yawning/bsaes.git v0.0.0-20190805113838-0a714cd429ec/go.mod h1:BZ1RAoRPbCxum9Grlv5aeksu2H8BiKehBYooU2LFiOQ=
+gitlab.com/yawning/utls.git v0.0.12-1 h1:RL6O0MP2YI0KghuEU/uGN6+8b4183eqNWoYgx7CXD0U=
+gitlab.com/yawning/utls.git v0.0.12-1/go.mod h1:3ONKiSFR9Im/c3t5RKmMJTVdmZN496FNyk3mjrY1dyo=
golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c h1:Vj5n4GlwjmQteupaxJ9+0FNOmBrHfq7vN4btdGoDZgI=
golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
golang.org/x/net v0.0.0-20190328230028-74de082e2cca h1:hyA6yiAgbUwuWqtscNvWAI7U1CtlaD1KilQ6iudt1aI=
golang.org/x/net v0.0.0-20190328230028-74de082e2cca/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
-golang.org/x/sys v0.0.0-20190329044733-9eb1bfa1ce65 h1:hOY+O8MxdkPV10pNf7/XEHaySCiPKxixMKUshfHsGn0=
-golang.org/x/sys v0.0.0-20190329044733-9eb1bfa1ce65/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20190804053845-51ab0e2deafa h1:KIDDMLT1O0Nr7TSxp8xM5tJcdn8tgyAONntO829og1M=
+golang.org/x/sys v0.0.0-20190804053845-51ab0e2deafa/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
golang.org/x/text v0.3.0 h1:g61tztE5qeGQ89tm6NTjjM9VPIm088od1l6aSorWRWg=
golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
diff --git a/transports/meeklite/transport.go b/transports/meeklite/transport.go
index 4e4907a..8ff02a5 100644
--- a/transports/meeklite/transport.go
+++ b/transports/meeklite/transport.go
@@ -54,6 +54,7 @@ var (
"hellochrome_62": &utls.HelloChrome_62,
"hellochrome_70": &utls.HelloChrome_70,
"hellochrome_72": &utls.HelloChrome_72,
+ "hellochrome_83": &utls.HelloChrome_83,
"helloios_auto": &utls.HelloIOS_Auto,
"helloios_11_1": &utls.HelloIOS_11_1,
"helloios_12_1": &utls.HelloIOS_12_1,
1
0
commit 393aca86cc3b1a5263018c10f87ece09ac3fd5ed
Author: Yawning Angel <yawning(a)schwanenlied.me>
Date: Wed Dec 29 08:44:20 2021 +0000
internal/x25519ell2: Initial import
Replace agl's Elligator2 implementation with a different one, that fixes
the various distinguishers stemming from bugs in the original
implementation and "The Elligator paper is extremely hard to read".
All releases prior to this commit are trivially distinguishable with
simple math, so upgrading is strongly recommended. The upgrade is fully
backward-compatible with existing implementations, however the
non-upgraded side will emit traffic that is trivially distinguishable
from random.
Special thanks to Loup Vaillant for his body of work on this primitive,
and for motivating me to fix it.
---
ChangeLog | 2 +
README.md | 4 +-
common/ntor/ntor.go | 19 +-
go.mod | 6 +-
go.sum | 19 +-
internal/README-extra25519.md | 21 -
internal/README.md | 37 +
internal/edwards25519/const.go | 1411 -------------------------
internal/edwards25519/edwards25519.go | 1773 --------------------------------
internal/extra25519/extra25519.go | 291 ------
internal/extra25519/extra25519_test.go | 61 --
internal/x25519ell2/x25519ell2.go | 177 ++++
internal/x25519ell2/x25519ell2_test.go | 153 +++
13 files changed, 404 insertions(+), 3570 deletions(-)
diff --git a/ChangeLog b/ChangeLog
index 53253ef..5253fe6 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,4 +1,6 @@
Changes in version 0.0.12 - UNRELEASED:
+ - Fix the long standing distinguishers associated with agl's Elligator2
+ implementation (Thanks to Loup Vaillant).
- Replace the extra25519 import with an internal package.
- Update the Azure TLS certificate digest (Thanks to Philipp Winter).
- Make the -unsafeLogging command line switch work.
diff --git a/README.md b/README.md
index 621fe21..af211af 100644
--- a/README.md
+++ b/README.md
@@ -90,7 +90,9 @@ ServerTransportPlugin obfs4 exec /usr/local/bin/obfs4proxy
### Thanks
+ * Loup Vaillant for motivating me to replace the Elligator implementation
+ and a body of code I could draw on to accelerate the replacement process.
* David Fifield for goptlib.
- * Adam Langley for his Elligator implementation.
+ * Adam Langley for his initial Elligator implementation.
* Philipp Winter for the ScrambleSuit protocol which provided much of the
design.
diff --git a/common/ntor/ntor.go b/common/ntor/ntor.go
index 851cc1e..af24b68 100644
--- a/common/ntor/ntor.go
+++ b/common/ntor/ntor.go
@@ -38,6 +38,7 @@ import (
"bytes"
"crypto/hmac"
"crypto/sha256"
+ "crypto/sha512"
"crypto/subtle"
"encoding/hex"
"fmt"
@@ -47,7 +48,7 @@ import (
"golang.org/x/crypto/hkdf"
"gitlab.com/yawning/obfs4.git/common/csrand"
- "gitlab.com/yawning/obfs4.git/internal/extra25519"
+ "gitlab.com/yawning/obfs4.git/internal/x25519ell2"
)
const (
@@ -204,7 +205,7 @@ func (repr *Representative) Bytes() *[RepresentativeLength]byte {
func (repr *Representative) ToPublic() *PublicKey {
pub := new(PublicKey)
- extra25519.UnsafeBrokenRepresentativeToPublicKey(pub.Bytes(), repr.Bytes())
+ x25519ell2.RepresentativeToPublicKey(pub.Bytes(), repr.Bytes())
return pub
}
@@ -263,22 +264,28 @@ func NewKeypair(elligator bool) (*Keypair, error) {
for {
// Generate a Curve25519 private key. Like everyone who does this,
- // run the CSPRNG output through SHA256 for extra tinfoil hattery.
+ // run the CSPRNG output through SHA512 for extra tinfoil hattery.
+ //
+ // Also use part of the digest that gets truncated off for the
+ // obfuscation tweak.
priv := keypair.private.Bytes()[:]
if err := csrand.Bytes(priv); err != nil {
return nil, err
}
- digest := sha256.Sum256(priv)
+ digest := sha512.Sum512(priv)
digest[0] &= 248
digest[31] &= 127
digest[31] |= 64
copy(priv, digest[:])
if elligator {
+ tweak := digest[63]
+
// Apply the Elligator transform. This fails ~50% of the time.
- if !extra25519.UnsafeBrokenScalarBaseMult(keypair.public.Bytes(),
+ if !x25519ell2.ScalarBaseMult(keypair.public.Bytes(),
keypair.representative.Bytes(),
- keypair.private.Bytes()) {
+ keypair.private.Bytes(),
+ tweak) {
continue
}
} else {
diff --git a/go.mod b/go.mod
index 1a64cb6..037082a 100644
--- a/go.mod
+++ b/go.mod
@@ -1,11 +1,13 @@
module gitlab.com/yawning/obfs4.git
require (
+ filippo.io/edwards25519 v1.0.0-rc.1.0.20210721174708-390f27c3be20
git.torproject.org/pluggable-transports/goptlib.git v1.0.0
github.com/dchest/siphash v1.2.1
+ gitlab.com/yawning/edwards25519-extra.git v0.0.0-20211229043746-2f91fcc9fbdb
gitlab.com/yawning/utls.git v0.0.12-1
- golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c
- golang.org/x/net v0.0.0-20190328230028-74de082e2cca
+ golang.org/x/crypto v0.0.0-20210711020723-a769d52b0f97
+ golang.org/x/net v0.0.0-20210226172049-e18ecbb05110
)
go 1.13
diff --git a/go.sum b/go.sum
index 5e192a8..5de7fd9 100644
--- a/go.sum
+++ b/go.sum
@@ -1,3 +1,5 @@
+filippo.io/edwards25519 v1.0.0-rc.1.0.20210721174708-390f27c3be20 h1:iJoUgXvhagsNMrJrvavw7vu1eG8+hm6jLOxlLFcoODw=
+filippo.io/edwards25519 v1.0.0-rc.1.0.20210721174708-390f27c3be20/go.mod h1:N1IkdkCkiLB6tki+MYJoSx2JTY9NUlxZE7eHn5EwJns=
git.torproject.org/pluggable-transports/goptlib.git v1.0.0 h1:ElTwFFPKf/tA6x5nuIk9g49JZzS4T5WN+eTQTjqd00A=
git.torproject.org/pluggable-transports/goptlib.git v1.0.0/go.mod h1:YT4XMSkuEXbtqlydr9+OxqFAyspUv0Gr9qhM3B++o/Q=
github.com/dchest/siphash v1.2.1 h1:4cLinnzVJDKxTCl9B01807Yiy+W7ZzVHj/KIroQRvT4=
@@ -10,15 +12,24 @@ github.com/klauspost/cpuid v1.2.0/go.mod h1:Pj4uuM528wm8OyEC2QMXAi2YiTZ96dNQPGgo
github.com/ulikunitz/xz v0.5.6/go.mod h1:2bypXElzHzzJZwzH67Y6wb67pO62Rzfn7BSiF4ABRW8=
gitlab.com/yawning/bsaes.git v0.0.0-20190805113838-0a714cd429ec h1:FpfFs4EhNehiVfzQttTuxanPIT43FtkkCFypIod8LHo=
gitlab.com/yawning/bsaes.git v0.0.0-20190805113838-0a714cd429ec/go.mod h1:BZ1RAoRPbCxum9Grlv5aeksu2H8BiKehBYooU2LFiOQ=
+gitlab.com/yawning/edwards25519-extra.git v0.0.0-20211229043746-2f91fcc9fbdb h1:qRSZHsODmAP5qDvb3YsO7Qnf3TRiVbGxNG/WYnlM4/o=
+gitlab.com/yawning/edwards25519-extra.git v0.0.0-20211229043746-2f91fcc9fbdb/go.mod h1:gvdJuZuO/tPZyhEV8K3Hmoxv/DWud5L4qEQxfYjEUTo=
gitlab.com/yawning/utls.git v0.0.12-1 h1:RL6O0MP2YI0KghuEU/uGN6+8b4183eqNWoYgx7CXD0U=
gitlab.com/yawning/utls.git v0.0.12-1/go.mod h1:3ONKiSFR9Im/c3t5RKmMJTVdmZN496FNyk3mjrY1dyo=
golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
-golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c h1:Vj5n4GlwjmQteupaxJ9+0FNOmBrHfq7vN4btdGoDZgI=
golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
-golang.org/x/net v0.0.0-20190328230028-74de082e2cca h1:hyA6yiAgbUwuWqtscNvWAI7U1CtlaD1KilQ6iudt1aI=
+golang.org/x/crypto v0.0.0-20210711020723-a769d52b0f97 h1:/UOmuWzQfxxo9UtlXMwuQU8CMgg1eZXqTRwkSQJWKOI=
+golang.org/x/crypto v0.0.0-20210711020723-a769d52b0f97/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc=
golang.org/x/net v0.0.0-20190328230028-74de082e2cca/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
+golang.org/x/net v0.0.0-20210226172049-e18ecbb05110 h1:qWPm9rbaAMKs8Bq/9LRpbMqxWRVUAQwMI9fVrssnTfw=
+golang.org/x/net v0.0.0-20210226172049-e18ecbb05110/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg=
golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
-golang.org/x/sys v0.0.0-20190804053845-51ab0e2deafa h1:KIDDMLT1O0Nr7TSxp8xM5tJcdn8tgyAONntO829og1M=
golang.org/x/sys v0.0.0-20190804053845-51ab0e2deafa/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
-golang.org/x/text v0.3.0 h1:g61tztE5qeGQ89tm6NTjjM9VPIm088od1l6aSorWRWg=
+golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1 h1:SrN+KX8Art/Sf4HNj6Zcz06G7VEz+7w9tdXTPOZ7+l4=
+golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
+golang.org/x/text v0.3.3 h1:cokOdA+Jmi5PJGXLlLllQSgYigAEfHXJAERHVMaCc2k=
+golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
+golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
diff --git a/internal/README-extra25519.md b/internal/README-extra25519.md
deleted file mode 100644
index f02418c..0000000
--- a/internal/README-extra25519.md
+++ /dev/null
@@ -1,21 +0,0 @@
-This includes a copy of the edwards25519 and extra25519 packages authored
-by agl, that formerly lived at github.com/agl/ed25519 as of the commit
-5312a61534124124185d41f09206b9fef1d88403 with the following changes:
-
- * Import paths fixed up.
-
- * The unused Ed25519->X25519 key conversion routines were removed.
-
- * `UnsafeBroken` was prefixed to the routines that are known to be
- severely flawed.
-
-The only reason this is being done (despite agl's wishes that the code
-base dies, which I wanted to respect) is so people stop bothering me
-about it.
-
-Do not ask me questions about this.
-Do not use it in other projects.
-Do not use it in anything new.
-Do not expect me to maintain this beyond ensuring it continues to build.
-
-All I want is to be left alone.
diff --git a/internal/README.md b/internal/README.md
new file mode 100644
index 0000000..05aa472
--- /dev/null
+++ b/internal/README.md
@@ -0,0 +1,37 @@
+The x25519ell2 package provides X25519 obfuscated with Elligator 2, with
+special care taken to handle cofactor related issues, and fixes for the
+bugs in agl's original Elligator2 implementation.
+
+All existing versions prior to the migration to the new code (anything
+that uses agl's code) are fatally broken, and trivial to distinguish via
+some simple math. For more details see Loup Vaillant's writings on the
+subject. Any bugs in the implementation are mine, and not his.
+
+Representatives created by this implementation will correctly be decoded
+by existing implementations. Public keys created by this implementation
+be it via the modified scalar basepoint multiply or via decoding a
+representative will be somewhat non-standard, but will interoperate with
+a standard X25519 scalar-multiply.
+
+As the obfs4 handshake does not include the decoded representative in
+any of it's authenticated handshake digest calculations, this change is
+fully-backward compatible (though the non-upgraded side of the connection
+will still be trivially distinguishable from random).
+
+##### Maintainer's rant
+
+Honestly, it is possible to create a better obfuscation protocol than
+obfs4, and it's shelf-life expired years ago. No one should be using
+it for anything at this point, and no one should have been using it
+for anything for the past however many years since I first started
+telling people to stop using it.
+
+People should also have listened when I told them repeatedly that there
+are massive issues in the protocol.
+
+ * Do not ask me questions about this.
+ * Do not use it in other projects.
+ * Do not use it in anything new.
+ * Use a prime order group instead of this nonsense especially if you
+ are doing something new.
+ * All I want is to be left alone.
diff --git a/internal/edwards25519/const.go b/internal/edwards25519/const.go
deleted file mode 100644
index ea5b77a..0000000
--- a/internal/edwards25519/const.go
+++ /dev/null
@@ -1,1411 +0,0 @@
-// Copyright 2013 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package edwards25519
-
-var d = FieldElement{
- -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116,
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-
-var d2 = FieldElement{
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-}
-
-var SqrtM1 = FieldElement{
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-}
-
-var A = FieldElement{
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-}
-
-var bi = [8]PreComputedGroupElement{
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- {
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- FieldElement{-10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221},
- },
- {
- FieldElement{30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046},
- FieldElement{13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345},
- FieldElement{-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310},
- },
- },
- {
- {
- FieldElement{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937},
- FieldElement{31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636},
- FieldElement{-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008},
- },
- {
- FieldElement{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429},
- FieldElement{-15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576},
- FieldElement{31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066},
- },
- {
- FieldElement{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490},
- FieldElement{-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104},
- FieldElement{33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053},
- },
- {
- FieldElement{31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275},
- FieldElement{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511},
- FieldElement{22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095},
- },
- {
- FieldElement{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439},
- FieldElement{23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939},
- FieldElement{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424},
- },
- {
- FieldElement{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310},
- FieldElement{3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608},
- FieldElement{-32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079},
- },
- {
- FieldElement{-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101},
- FieldElement{21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418},
- FieldElement{18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576},
- },
- {
- FieldElement{30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356},
- FieldElement{9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996},
- FieldElement{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099},
- },
- },
- {
- {
- FieldElement{-26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728},
- FieldElement{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658},
- FieldElement{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242},
- },
- {
- FieldElement{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001},
- FieldElement{-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766},
- FieldElement{18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373},
- },
- {
- FieldElement{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458},
- FieldElement{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628},
- FieldElement{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657},
- },
- {
- FieldElement{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062},
- FieldElement{25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616},
- FieldElement{31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014},
- },
- {
- FieldElement{24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383},
- FieldElement{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814},
- FieldElement{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718},
- },
- {
- FieldElement{30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417},
- FieldElement{2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222},
- FieldElement{33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444},
- },
- {
- FieldElement{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597},
- FieldElement{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970},
- FieldElement{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799},
- },
- {
- FieldElement{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647},
- FieldElement{13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511},
- FieldElement{-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032},
- },
- },
- {
- {
- FieldElement{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834},
- FieldElement{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461},
- FieldElement{29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062},
- },
- {
- FieldElement{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516},
- FieldElement{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547},
- FieldElement{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240},
- },
- {
- FieldElement{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038},
- FieldElement{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741},
- FieldElement{16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103},
- },
- {
- FieldElement{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747},
- FieldElement{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323},
- FieldElement{31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016},
- },
- {
- FieldElement{-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373},
- FieldElement{15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228},
- FieldElement{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141},
- },
- {
- FieldElement{16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399},
- FieldElement{11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831},
- FieldElement{-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376},
- },
- {
- FieldElement{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313},
- FieldElement{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958},
- FieldElement{-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577},
- },
- {
- FieldElement{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743},
- FieldElement{29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684},
- FieldElement{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476},
- },
- },
-}
diff --git a/internal/edwards25519/edwards25519.go b/internal/edwards25519/edwards25519.go
deleted file mode 100644
index 9079818..0000000
--- a/internal/edwards25519/edwards25519.go
+++ /dev/null
@@ -1,1773 +0,0 @@
-// Copyright 2013 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// Package edwards25519 implements operations in GF(2**255-19) and on an
-// Edwards curve that is isomorphic to curve25519. See
-// http://ed25519.cr.yp.to/.
-package edwards25519
-
-// This code is a port of the public domain, "ref10" implementation of ed25519
-// from SUPERCOP.
-
-// FieldElement represents an element of the field GF(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.
-type FieldElement [10]int32
-
-var zero FieldElement
-
-func FeZero(fe *FieldElement) {
- copy(fe[:], zero[:])
-}
-
-func FeOne(fe *FieldElement) {
- FeZero(fe)
- fe[0] = 1
-}
-
-func FeAdd(dst, a, b *FieldElement) {
- dst[0] = a[0] + b[0]
- dst[1] = a[1] + b[1]
- dst[2] = a[2] + b[2]
- dst[3] = a[3] + b[3]
- dst[4] = a[4] + b[4]
- dst[5] = a[5] + b[5]
- dst[6] = a[6] + b[6]
- dst[7] = a[7] + b[7]
- dst[8] = a[8] + b[8]
- dst[9] = a[9] + b[9]
-}
-
-func FeSub(dst, a, b *FieldElement) {
- dst[0] = a[0] - b[0]
- dst[1] = a[1] - b[1]
- dst[2] = a[2] - b[2]
- dst[3] = a[3] - b[3]
- dst[4] = a[4] - b[4]
- dst[5] = a[5] - b[5]
- dst[6] = a[6] - b[6]
- dst[7] = a[7] - b[7]
- dst[8] = a[8] - b[8]
- dst[9] = a[9] - b[9]
-}
-
-func FeCopy(dst, src *FieldElement) {
- copy(dst[:], src[:])
-}
-
-// Replace (f,g) with (g,g) if b == 1;
-// replace (f,g) with (f,g) if b == 0.
-//
-// Preconditions: b in {0,1}.
-func FeCMove(f, g *FieldElement, b int32) {
- b = -b
- f[0] ^= b & (f[0] ^ g[0])
- f[1] ^= b & (f[1] ^ g[1])
- f[2] ^= b & (f[2] ^ g[2])
- f[3] ^= b & (f[3] ^ g[3])
- f[4] ^= b & (f[4] ^ g[4])
- f[5] ^= b & (f[5] ^ g[5])
- f[6] ^= b & (f[6] ^ g[6])
- f[7] ^= b & (f[7] ^ g[7])
- f[8] ^= b & (f[8] ^ g[8])
- f[9] ^= b & (f[9] ^ g[9])
-}
-
-func load3(in []byte) int64 {
- var r int64
- r = int64(in[0])
- r |= int64(in[1]) << 8
- r |= int64(in[2]) << 16
- return r
-}
-
-func load4(in []byte) int64 {
- var r int64
- r = int64(in[0])
- r |= int64(in[1]) << 8
- r |= int64(in[2]) << 16
- r |= int64(in[3]) << 24
- return r
-}
-
-func FeFromBytes(dst *FieldElement, src *[32]byte) {
- h0 := load4(src[:])
- h1 := load3(src[4:]) << 6
- h2 := load3(src[7:]) << 5
- h3 := load3(src[10:]) << 3
- h4 := load3(src[13:]) << 2
- h5 := load4(src[16:])
- h6 := load3(src[20:]) << 7
- h7 := load3(src[23:]) << 5
- h8 := load3(src[26:]) << 4
- h9 := (load3(src[29:]) & 8388607) << 2
-
- FeCombine(dst, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-// FeToBytes marshals h to s.
-// Preconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Write p=2^255-19; q=floor(h/p).
-// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
-//
-// Proof:
-// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
-// Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
-//
-// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
-// Then 0<y<1.
-//
-// Write r=h-pq.
-// Have 0<=r<=p-1=2^255-20.
-// Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
-//
-// Write x=r+19(2^-255)r+y.
-// Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
-//
-// Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
-// so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
-func FeToBytes(s *[32]byte, h *FieldElement) {
- var carry [10]int32
-
- q := (19*h[9] + (1 << 24)) >> 25
- q = (h[0] + q) >> 26
- q = (h[1] + q) >> 25
- q = (h[2] + q) >> 26
- q = (h[3] + q) >> 25
- q = (h[4] + q) >> 26
- q = (h[5] + q) >> 25
- q = (h[6] + q) >> 26
- q = (h[7] + q) >> 25
- q = (h[8] + q) >> 26
- q = (h[9] + q) >> 25
-
- // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
- h[0] += 19 * q
- // Goal: Output h-2^255 q, which is between 0 and 2^255-20.
-
- carry[0] = h[0] >> 26
- h[1] += carry[0]
- h[0] -= carry[0] << 26
- carry[1] = h[1] >> 25
- h[2] += carry[1]
- h[1] -= carry[1] << 25
- carry[2] = h[2] >> 26
- h[3] += carry[2]
- h[2] -= carry[2] << 26
- carry[3] = h[3] >> 25
- h[4] += carry[3]
- h[3] -= carry[3] << 25
- carry[4] = h[4] >> 26
- h[5] += carry[4]
- h[4] -= carry[4] << 26
- carry[5] = h[5] >> 25
- h[6] += carry[5]
- h[5] -= carry[5] << 25
- carry[6] = h[6] >> 26
- h[7] += carry[6]
- h[6] -= carry[6] << 26
- carry[7] = h[7] >> 25
- h[8] += carry[7]
- h[7] -= carry[7] << 25
- carry[8] = h[8] >> 26
- h[9] += carry[8]
- h[8] -= carry[8] << 26
- carry[9] = h[9] >> 25
- h[9] -= carry[9] << 25
- // h10 = carry9
-
- // Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
- // Have h[0]+...+2^230 h[9] between 0 and 2^255-1;
- // evidently 2^255 h10-2^255 q = 0.
- // Goal: Output h[0]+...+2^230 h[9].
-
- s[0] = byte(h[0] >> 0)
- s[1] = byte(h[0] >> 8)
- s[2] = byte(h[0] >> 16)
- s[3] = byte((h[0] >> 24) | (h[1] << 2))
- s[4] = byte(h[1] >> 6)
- s[5] = byte(h[1] >> 14)
- s[6] = byte((h[1] >> 22) | (h[2] << 3))
- s[7] = byte(h[2] >> 5)
- s[8] = byte(h[2] >> 13)
- s[9] = byte((h[2] >> 21) | (h[3] << 5))
- s[10] = byte(h[3] >> 3)
- s[11] = byte(h[3] >> 11)
- s[12] = byte((h[3] >> 19) | (h[4] << 6))
- s[13] = byte(h[4] >> 2)
- s[14] = byte(h[4] >> 10)
- s[15] = byte(h[4] >> 18)
- s[16] = byte(h[5] >> 0)
- s[17] = byte(h[5] >> 8)
- s[18] = byte(h[5] >> 16)
- s[19] = byte((h[5] >> 24) | (h[6] << 1))
- s[20] = byte(h[6] >> 7)
- s[21] = byte(h[6] >> 15)
- s[22] = byte((h[6] >> 23) | (h[7] << 3))
- s[23] = byte(h[7] >> 5)
- s[24] = byte(h[7] >> 13)
- s[25] = byte((h[7] >> 21) | (h[8] << 4))
- s[26] = byte(h[8] >> 4)
- s[27] = byte(h[8] >> 12)
- s[28] = byte((h[8] >> 20) | (h[9] << 6))
- s[29] = byte(h[9] >> 2)
- s[30] = byte(h[9] >> 10)
- s[31] = byte(h[9] >> 18)
-}
-
-func FeIsNegative(f *FieldElement) byte {
- var s [32]byte
- FeToBytes(&s, f)
- return s[0] & 1
-}
-
-func FeIsNonZero(f *FieldElement) int32 {
- var s [32]byte
- FeToBytes(&s, f)
- var x uint8
- for _, b := range s {
- x |= b
- }
- x |= x >> 4
- x |= x >> 2
- x |= x >> 1
- return int32(x & 1)
-}
-
-// FeNeg sets 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.
-func FeNeg(h, f *FieldElement) {
- h[0] = -f[0]
- h[1] = -f[1]
- h[2] = -f[2]
- h[3] = -f[3]
- h[4] = -f[4]
- h[5] = -f[5]
- h[6] = -f[6]
- h[7] = -f[7]
- h[8] = -f[8]
- h[9] = -f[9]
-}
-
-func FeCombine(h *FieldElement, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
- var c0, c1, c2, c3, c4, c5, c6, c7, c8, c9 int64
-
- /*
- |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
- i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
- |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
- i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
- */
-
- c0 = (h0 + (1 << 25)) >> 26
- h1 += c0
- h0 -= c0 << 26
- c4 = (h4 + (1 << 25)) >> 26
- h5 += c4
- h4 -= c4 << 26
- /* |h0| <= 2^25 */
- /* |h4| <= 2^25 */
- /* |h1| <= 1.51*2^58 */
- /* |h5| <= 1.51*2^58 */
-
- c1 = (h1 + (1 << 24)) >> 25
- h2 += c1
- h1 -= c1 << 25
- c5 = (h5 + (1 << 24)) >> 25
- h6 += c5
- h5 -= c5 << 25
- /* |h1| <= 2^24; from now on fits into int32 */
- /* |h5| <= 2^24; from now on fits into int32 */
- /* |h2| <= 1.21*2^59 */
- /* |h6| <= 1.21*2^59 */
-
- c2 = (h2 + (1 << 25)) >> 26
- h3 += c2
- h2 -= c2 << 26
- c6 = (h6 + (1 << 25)) >> 26
- h7 += c6
- h6 -= c6 << 26
- /* |h2| <= 2^25; from now on fits into int32 unchanged */
- /* |h6| <= 2^25; from now on fits into int32 unchanged */
- /* |h3| <= 1.51*2^58 */
- /* |h7| <= 1.51*2^58 */
-
- c3 = (h3 + (1 << 24)) >> 25
- h4 += c3
- h3 -= c3 << 25
- c7 = (h7 + (1 << 24)) >> 25
- h8 += c7
- h7 -= c7 << 25
- /* |h3| <= 2^24; from now on fits into int32 unchanged */
- /* |h7| <= 2^24; from now on fits into int32 unchanged */
- /* |h4| <= 1.52*2^33 */
- /* |h8| <= 1.52*2^33 */
-
- c4 = (h4 + (1 << 25)) >> 26
- h5 += c4
- h4 -= c4 << 26
- c8 = (h8 + (1 << 25)) >> 26
- h9 += c8
- h8 -= c8 << 26
- /* |h4| <= 2^25; from now on fits into int32 unchanged */
- /* |h8| <= 2^25; from now on fits into int32 unchanged */
- /* |h5| <= 1.01*2^24 */
- /* |h9| <= 1.51*2^58 */
-
- c9 = (h9 + (1 << 24)) >> 25
- h0 += c9 * 19
- h9 -= c9 << 25
- /* |h9| <= 2^24; from now on fits into int32 unchanged */
- /* |h0| <= 1.8*2^37 */
-
- c0 = (h0 + (1 << 25)) >> 26
- h1 += c0
- h0 -= c0 << 26
- /* |h0| <= 2^25; from now on fits into int32 unchanged */
- /* |h1| <= 1.01*2^24 */
-
- h[0] = int32(h0)
- h[1] = int32(h1)
- h[2] = int32(h2)
- h[3] = int32(h3)
- h[4] = int32(h4)
- h[5] = int32(h5)
- h[6] = int32(h6)
- h[7] = int32(h7)
- h[8] = int32(h8)
- h[9] = int32(h9)
-}
-
-// FeMul calculates h = f * g
-// Can overlap h with f or g.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-// |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Notes on implementation strategy:
-//
-// Using schoolbook multiplication.
-// Karatsuba would save a little in some cost models.
-//
-// Most multiplications by 2 and 19 are 32-bit precomputations;
-// cheaper than 64-bit postcomputations.
-//
-// There is one remaining multiplication by 19 in the carry chain;
-// one *19 precomputation can be merged into this,
-// but the resulting data flow is considerably less clean.
-//
-// There are 12 carries below.
-// 10 of them are 2-way parallelizable and vectorizable.
-// Can get away with 11 carries, but then data flow is much deeper.
-//
-// With tighter constraints on inputs can squeeze carries into int32.
-func FeMul(h, f, g *FieldElement) {
- f0 := int64(f[0])
- f1 := int64(f[1])
- f2 := int64(f[2])
- f3 := int64(f[3])
- f4 := int64(f[4])
- f5 := int64(f[5])
- f6 := int64(f[6])
- f7 := int64(f[7])
- f8 := int64(f[8])
- f9 := int64(f[9])
-
- f1_2 := int64(2 * f[1])
- f3_2 := int64(2 * f[3])
- f5_2 := int64(2 * f[5])
- f7_2 := int64(2 * f[7])
- f9_2 := int64(2 * f[9])
-
- g0 := int64(g[0])
- g1 := int64(g[1])
- g2 := int64(g[2])
- g3 := int64(g[3])
- g4 := int64(g[4])
- g5 := int64(g[5])
- g6 := int64(g[6])
- g7 := int64(g[7])
- g8 := int64(g[8])
- g9 := int64(g[9])
-
- g1_19 := int64(19 * g[1]) /* 1.4*2^29 */
- g2_19 := int64(19 * g[2]) /* 1.4*2^30; still ok */
- g3_19 := int64(19 * g[3])
- g4_19 := int64(19 * g[4])
- g5_19 := int64(19 * g[5])
- g6_19 := int64(19 * g[6])
- g7_19 := int64(19 * g[7])
- g8_19 := int64(19 * g[8])
- g9_19 := int64(19 * g[9])
-
- h0 := f0*g0 + f1_2*g9_19 + f2*g8_19 + f3_2*g7_19 + f4*g6_19 + f5_2*g5_19 + f6*g4_19 + f7_2*g3_19 + f8*g2_19 + f9_2*g1_19
- h1 := f0*g1 + f1*g0 + f2*g9_19 + f3*g8_19 + f4*g7_19 + f5*g6_19 + f6*g5_19 + f7*g4_19 + f8*g3_19 + f9*g2_19
- h2 := f0*g2 + f1_2*g1 + f2*g0 + f3_2*g9_19 + f4*g8_19 + f5_2*g7_19 + f6*g6_19 + f7_2*g5_19 + f8*g4_19 + f9_2*g3_19
- h3 := f0*g3 + f1*g2 + f2*g1 + f3*g0 + f4*g9_19 + f5*g8_19 + f6*g7_19 + f7*g6_19 + f8*g5_19 + f9*g4_19
- h4 := f0*g4 + f1_2*g3 + f2*g2 + f3_2*g1 + f4*g0 + f5_2*g9_19 + f6*g8_19 + f7_2*g7_19 + f8*g6_19 + f9_2*g5_19
- h5 := f0*g5 + f1*g4 + f2*g3 + f3*g2 + f4*g1 + f5*g0 + f6*g9_19 + f7*g8_19 + f8*g7_19 + f9*g6_19
- h6 := f0*g6 + f1_2*g5 + f2*g4 + f3_2*g3 + f4*g2 + f5_2*g1 + f6*g0 + f7_2*g9_19 + f8*g8_19 + f9_2*g7_19
- h7 := f0*g7 + f1*g6 + f2*g5 + f3*g4 + f4*g3 + f5*g2 + f6*g1 + f7*g0 + f8*g9_19 + f9*g8_19
- h8 := f0*g8 + f1_2*g7 + f2*g6 + f3_2*g5 + f4*g4 + f5_2*g3 + f6*g2 + f7_2*g1 + f8*g0 + f9_2*g9_19
- h9 := f0*g9 + f1*g8 + f2*g7 + f3*g6 + f4*g5 + f5*g4 + f6*g3 + f7*g2 + f8*g1 + f9*g0
-
- FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-func feSquare(f *FieldElement) (h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
- f0 := int64(f[0])
- f1 := int64(f[1])
- f2 := int64(f[2])
- f3 := int64(f[3])
- f4 := int64(f[4])
- f5 := int64(f[5])
- f6 := int64(f[6])
- f7 := int64(f[7])
- f8 := int64(f[8])
- f9 := int64(f[9])
- f0_2 := int64(2 * f[0])
- f1_2 := int64(2 * f[1])
- f2_2 := int64(2 * f[2])
- f3_2 := int64(2 * f[3])
- f4_2 := int64(2 * f[4])
- f5_2 := int64(2 * f[5])
- f6_2 := int64(2 * f[6])
- f7_2 := int64(2 * f[7])
- f5_38 := 38 * f5 // 1.31*2^30
- f6_19 := 19 * f6 // 1.31*2^30
- f7_38 := 38 * f7 // 1.31*2^30
- f8_19 := 19 * f8 // 1.31*2^30
- f9_38 := 38 * f9 // 1.31*2^30
-
- h0 = f0*f0 + f1_2*f9_38 + f2_2*f8_19 + f3_2*f7_38 + f4_2*f6_19 + f5*f5_38
- h1 = f0_2*f1 + f2*f9_38 + f3_2*f8_19 + f4*f7_38 + f5_2*f6_19
- h2 = f0_2*f2 + f1_2*f1 + f3_2*f9_38 + f4_2*f8_19 + f5_2*f7_38 + f6*f6_19
- h3 = f0_2*f3 + f1_2*f2 + f4*f9_38 + f5_2*f8_19 + f6*f7_38
- h4 = f0_2*f4 + f1_2*f3_2 + f2*f2 + f5_2*f9_38 + f6_2*f8_19 + f7*f7_38
- h5 = f0_2*f5 + f1_2*f4 + f2_2*f3 + f6*f9_38 + f7_2*f8_19
- h6 = f0_2*f6 + f1_2*f5_2 + f2_2*f4 + f3_2*f3 + f7_2*f9_38 + f8*f8_19
- h7 = f0_2*f7 + f1_2*f6 + f2_2*f5 + f3_2*f4 + f8*f9_38
- h8 = f0_2*f8 + f1_2*f7_2 + f2_2*f6 + f3_2*f5_2 + f4*f4 + f9*f9_38
- h9 = f0_2*f9 + f1_2*f8 + f2_2*f7 + f3_2*f6 + f4_2*f5
-
- return
-}
-
-// FeSquare calculates h = f*f. Can overlap h with f.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-func FeSquare(h, f *FieldElement) {
- h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
- FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-// FeSquare2 sets 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.
-func FeSquare2(h, f *FieldElement) {
- h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
-
- h0 += h0
- h1 += h1
- h2 += h2
- h3 += h3
- h4 += h4
- h5 += h5
- h6 += h6
- h7 += h7
- h8 += h8
- h9 += h9
-
- FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-func FeInvert(out, z *FieldElement) {
- var t0, t1, t2, t3 FieldElement
- var i int
-
- FeSquare(&t0, z) // 2^1
- FeSquare(&t1, &t0) // 2^2
- for i = 1; i < 2; i++ { // 2^3
- FeSquare(&t1, &t1)
- }
- FeMul(&t1, z, &t1) // 2^3 + 2^0
- FeMul(&t0, &t0, &t1) // 2^3 + 2^1 + 2^0
- FeSquare(&t2, &t0) // 2^4 + 2^2 + 2^1
- FeMul(&t1, &t1, &t2) // 2^4 + 2^3 + 2^2 + 2^1 + 2^0
- FeSquare(&t2, &t1) // 5,4,3,2,1
- for i = 1; i < 5; i++ { // 9,8,7,6,5
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
- FeSquare(&t2, &t1) // 10..1
- for i = 1; i < 10; i++ { // 19..10
- FeSquare(&t2, &t2)
- }
- FeMul(&t2, &t2, &t1) // 19..0
- FeSquare(&t3, &t2) // 20..1
- for i = 1; i < 20; i++ { // 39..20
- FeSquare(&t3, &t3)
- }
- FeMul(&t2, &t3, &t2) // 39..0
- FeSquare(&t2, &t2) // 40..1
- for i = 1; i < 10; i++ { // 49..10
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1) // 49..0
- FeSquare(&t2, &t1) // 50..1
- for i = 1; i < 50; i++ { // 99..50
- FeSquare(&t2, &t2)
- }
- FeMul(&t2, &t2, &t1) // 99..0
- FeSquare(&t3, &t2) // 100..1
- for i = 1; i < 100; i++ { // 199..100
- FeSquare(&t3, &t3)
- }
- FeMul(&t2, &t3, &t2) // 199..0
- FeSquare(&t2, &t2) // 200..1
- for i = 1; i < 50; i++ { // 249..50
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1) // 249..0
- FeSquare(&t1, &t1) // 250..1
- for i = 1; i < 5; i++ { // 254..5
- FeSquare(&t1, &t1)
- }
- FeMul(out, &t1, &t0) // 254..5,3,1,0
-}
-
-func fePow22523(out, z *FieldElement) {
- var t0, t1, t2 FieldElement
- var i int
-
- FeSquare(&t0, z)
- for i = 1; i < 1; i++ {
- FeSquare(&t0, &t0)
- }
- FeSquare(&t1, &t0)
- for i = 1; i < 2; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t1, z, &t1)
- FeMul(&t0, &t0, &t1)
- FeSquare(&t0, &t0)
- for i = 1; i < 1; i++ {
- FeSquare(&t0, &t0)
- }
- FeMul(&t0, &t1, &t0)
- FeSquare(&t1, &t0)
- for i = 1; i < 5; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t0, &t1, &t0)
- FeSquare(&t1, &t0)
- for i = 1; i < 10; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t1, &t1, &t0)
- FeSquare(&t2, &t1)
- for i = 1; i < 20; i++ {
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1)
- FeSquare(&t1, &t1)
- for i = 1; i < 10; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t0, &t1, &t0)
- FeSquare(&t1, &t0)
- for i = 1; i < 50; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t1, &t1, &t0)
- FeSquare(&t2, &t1)
- for i = 1; i < 100; i++ {
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1)
- FeSquare(&t1, &t1)
- for i = 1; i < 50; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t0, &t1, &t0)
- FeSquare(&t0, &t0)
- for i = 1; i < 2; i++ {
- FeSquare(&t0, &t0)
- }
- FeMul(out, &t0, z)
-}
-
-// Group elements are members of the elliptic curve -x^2 + y^2 = 1 + d * x^2 *
-// y^2 where d = -121665/121666.
-//
-// Several representations are used:
-// ProjectiveGroupElement: (X:Y:Z) satisfying x=X/Z, y=Y/Z
-// ExtendedGroupElement: (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
-// CompletedGroupElement: ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
-// PreComputedGroupElement: (y+x,y-x,2dxy)
-
-type ProjectiveGroupElement struct {
- X, Y, Z FieldElement
-}
-
-type ExtendedGroupElement struct {
- X, Y, Z, T FieldElement
-}
-
-type CompletedGroupElement struct {
- X, Y, Z, T FieldElement
-}
-
-type PreComputedGroupElement struct {
- yPlusX, yMinusX, xy2d FieldElement
-}
-
-type CachedGroupElement struct {
- yPlusX, yMinusX, Z, T2d FieldElement
-}
-
-func (p *ProjectiveGroupElement) Zero() {
- FeZero(&p.X)
- FeOne(&p.Y)
- FeOne(&p.Z)
-}
-
-func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement) {
- var t0 FieldElement
-
- FeSquare(&r.X, &p.X)
- FeSquare(&r.Z, &p.Y)
- FeSquare2(&r.T, &p.Z)
- FeAdd(&r.Y, &p.X, &p.Y)
- FeSquare(&t0, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.X)
- FeSub(&r.Z, &r.Z, &r.X)
- FeSub(&r.X, &t0, &r.Y)
- FeSub(&r.T, &r.T, &r.Z)
-}
-
-func (p *ProjectiveGroupElement) ToBytes(s *[32]byte) {
- var recip, x, y FieldElement
-
- FeInvert(&recip, &p.Z)
- FeMul(&x, &p.X, &recip)
- FeMul(&y, &p.Y, &recip)
- FeToBytes(s, &y)
- s[31] ^= FeIsNegative(&x) << 7
-}
-
-func (p *ExtendedGroupElement) Zero() {
- FeZero(&p.X)
- FeOne(&p.Y)
- FeOne(&p.Z)
- FeZero(&p.T)
-}
-
-func (p *ExtendedGroupElement) Double(r *CompletedGroupElement) {
- var q ProjectiveGroupElement
- p.ToProjective(&q)
- q.Double(r)
-}
-
-func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement) {
- FeAdd(&r.yPlusX, &p.Y, &p.X)
- FeSub(&r.yMinusX, &p.Y, &p.X)
- FeCopy(&r.Z, &p.Z)
- FeMul(&r.T2d, &p.T, &d2)
-}
-
-func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement) {
- FeCopy(&r.X, &p.X)
- FeCopy(&r.Y, &p.Y)
- FeCopy(&r.Z, &p.Z)
-}
-
-func (p *ExtendedGroupElement) ToBytes(s *[32]byte) {
- var recip, x, y FieldElement
-
- FeInvert(&recip, &p.Z)
- FeMul(&x, &p.X, &recip)
- FeMul(&y, &p.Y, &recip)
- FeToBytes(s, &y)
- s[31] ^= FeIsNegative(&x) << 7
-}
-
-func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool {
- var u, v, v3, vxx, check FieldElement
-
- FeFromBytes(&p.Y, s)
- FeOne(&p.Z)
- FeSquare(&u, &p.Y)
- FeMul(&v, &u, &d)
- FeSub(&u, &u, &p.Z) // y = y^2-1
- FeAdd(&v, &v, &p.Z) // v = dy^2+1
-
- FeSquare(&v3, &v)
- FeMul(&v3, &v3, &v) // v3 = v^3
- FeSquare(&p.X, &v3)
- FeMul(&p.X, &p.X, &v)
- FeMul(&p.X, &p.X, &u) // x = uv^7
-
- fePow22523(&p.X, &p.X) // x = (uv^7)^((q-5)/8)
- FeMul(&p.X, &p.X, &v3)
- FeMul(&p.X, &p.X, &u) // x = uv^3(uv^7)^((q-5)/8)
-
- var tmpX, tmp2 [32]byte
-
- FeSquare(&vxx, &p.X)
- FeMul(&vxx, &vxx, &v)
- FeSub(&check, &vxx, &u) // vx^2-u
- if FeIsNonZero(&check) == 1 {
- FeAdd(&check, &vxx, &u) // vx^2+u
- if FeIsNonZero(&check) == 1 {
- return false
- }
- FeMul(&p.X, &p.X, &SqrtM1)
-
- FeToBytes(&tmpX, &p.X)
- for i, v := range tmpX {
- tmp2[31-i] = v
- }
- }
-
- if FeIsNegative(&p.X) != (s[31] >> 7) {
- FeNeg(&p.X, &p.X)
- }
-
- FeMul(&p.T, &p.X, &p.Y)
- return true
-}
-
-func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement) {
- FeMul(&r.X, &p.X, &p.T)
- FeMul(&r.Y, &p.Y, &p.Z)
- FeMul(&r.Z, &p.Z, &p.T)
-}
-
-func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement) {
- FeMul(&r.X, &p.X, &p.T)
- FeMul(&r.Y, &p.Y, &p.Z)
- FeMul(&r.Z, &p.Z, &p.T)
- FeMul(&r.T, &p.X, &p.Y)
-}
-
-func (p *PreComputedGroupElement) Zero() {
- FeOne(&p.yPlusX)
- FeOne(&p.yMinusX)
- FeZero(&p.xy2d)
-}
-
-func geAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
- var t0 FieldElement
-
- FeAdd(&r.X, &p.Y, &p.X)
- FeSub(&r.Y, &p.Y, &p.X)
- FeMul(&r.Z, &r.X, &q.yPlusX)
- FeMul(&r.Y, &r.Y, &q.yMinusX)
- FeMul(&r.T, &q.T2d, &p.T)
- FeMul(&r.X, &p.Z, &q.Z)
- FeAdd(&t0, &r.X, &r.X)
- FeSub(&r.X, &r.Z, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.Y)
- FeAdd(&r.Z, &t0, &r.T)
- FeSub(&r.T, &t0, &r.T)
-}
-
-func geSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
- var t0 FieldElement
-
- FeAdd(&r.X, &p.Y, &p.X)
- FeSub(&r.Y, &p.Y, &p.X)
- FeMul(&r.Z, &r.X, &q.yMinusX)
- FeMul(&r.Y, &r.Y, &q.yPlusX)
- FeMul(&r.T, &q.T2d, &p.T)
- FeMul(&r.X, &p.Z, &q.Z)
- FeAdd(&t0, &r.X, &r.X)
- FeSub(&r.X, &r.Z, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.Y)
- FeSub(&r.Z, &t0, &r.T)
- FeAdd(&r.T, &t0, &r.T)
-}
-
-func geMixedAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
- var t0 FieldElement
-
- FeAdd(&r.X, &p.Y, &p.X)
- FeSub(&r.Y, &p.Y, &p.X)
- FeMul(&r.Z, &r.X, &q.yPlusX)
- FeMul(&r.Y, &r.Y, &q.yMinusX)
- FeMul(&r.T, &q.xy2d, &p.T)
- FeAdd(&t0, &p.Z, &p.Z)
- FeSub(&r.X, &r.Z, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.Y)
- FeAdd(&r.Z, &t0, &r.T)
- FeSub(&r.T, &t0, &r.T)
-}
-
-func geMixedSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
- var t0 FieldElement
-
- FeAdd(&r.X, &p.Y, &p.X)
- FeSub(&r.Y, &p.Y, &p.X)
- FeMul(&r.Z, &r.X, &q.yMinusX)
- FeMul(&r.Y, &r.Y, &q.yPlusX)
- FeMul(&r.T, &q.xy2d, &p.T)
- FeAdd(&t0, &p.Z, &p.Z)
- FeSub(&r.X, &r.Z, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.Y)
- FeSub(&r.Z, &t0, &r.T)
- FeAdd(&r.T, &t0, &r.T)
-}
-
-func slide(r *[256]int8, a *[32]byte) {
- for i := range r {
- r[i] = int8(1 & (a[i>>3] >> uint(i&7)))
- }
-
- for i := range r {
- if r[i] != 0 {
- for b := 1; b <= 6 && i+b < 256; b++ {
- if r[i+b] != 0 {
- if r[i]+(r[i+b]<<uint(b)) <= 15 {
- r[i] += r[i+b] << uint(b)
- r[i+b] = 0
- } else if r[i]-(r[i+b]<<uint(b)) >= -15 {
- r[i] -= r[i+b] << uint(b)
- for k := i + b; k < 256; k++ {
- if r[k] == 0 {
- r[k] = 1
- break
- }
- r[k] = 0
- }
- } else {
- break
- }
- }
- }
- }
- }
-}
-
-// GeDoubleScalarMultVartime sets 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.
-func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte) {
- var aSlide, bSlide [256]int8
- var Ai [8]CachedGroupElement // A,3A,5A,7A,9A,11A,13A,15A
- var t CompletedGroupElement
- var u, A2 ExtendedGroupElement
- var i int
-
- slide(&aSlide, a)
- slide(&bSlide, b)
-
- A.ToCached(&Ai[0])
- A.Double(&t)
- t.ToExtended(&A2)
-
- for i := 0; i < 7; i++ {
- geAdd(&t, &A2, &Ai[i])
- t.ToExtended(&u)
- u.ToCached(&Ai[i+1])
- }
-
- r.Zero()
-
- for i = 255; i >= 0; i-- {
- if aSlide[i] != 0 || bSlide[i] != 0 {
- break
- }
- }
-
- for ; i >= 0; i-- {
- r.Double(&t)
-
- if aSlide[i] > 0 {
- t.ToExtended(&u)
- geAdd(&t, &u, &Ai[aSlide[i]/2])
- } else if aSlide[i] < 0 {
- t.ToExtended(&u)
- geSub(&t, &u, &Ai[(-aSlide[i])/2])
- }
-
- if bSlide[i] > 0 {
- t.ToExtended(&u)
- geMixedAdd(&t, &u, &bi[bSlide[i]/2])
- } else if bSlide[i] < 0 {
- t.ToExtended(&u)
- geMixedSub(&t, &u, &bi[(-bSlide[i])/2])
- }
-
- t.ToProjective(r)
- }
-}
-
-// equal returns 1 if b == c and 0 otherwise.
-func equal(b, c int32) int32 {
- x := uint32(b ^ c)
- x--
- return int32(x >> 31)
-}
-
-// negative returns 1 if b < 0 and 0 otherwise.
-func negative(b int32) int32 {
- return (b >> 31) & 1
-}
-
-func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32) {
- FeCMove(&t.yPlusX, &u.yPlusX, b)
- FeCMove(&t.yMinusX, &u.yMinusX, b)
- FeCMove(&t.xy2d, &u.xy2d, b)
-}
-
-func selectPoint(t *PreComputedGroupElement, pos int32, b int32) {
- var minusT PreComputedGroupElement
- bNegative := negative(b)
- bAbs := b - (((-bNegative) & b) << 1)
-
- t.Zero()
- for i := int32(0); i < 8; i++ {
- PreComputedGroupElementCMove(t, &base[pos][i], equal(bAbs, i+1))
- }
- FeCopy(&minusT.yPlusX, &t.yMinusX)
- FeCopy(&minusT.yMinusX, &t.yPlusX)
- FeNeg(&minusT.xy2d, &t.xy2d)
- PreComputedGroupElementCMove(t, &minusT, bNegative)
-}
-
-// GeScalarMultBase computes 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
-func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte) {
- var e [64]int8
-
- for i, v := range a {
- e[2*i] = int8(v & 15)
- e[2*i+1] = int8((v >> 4) & 15)
- }
-
- // each e[i] is between 0 and 15 and e[63] is between 0 and 7.
-
- carry := int8(0)
- for i := 0; i < 63; i++ {
- e[i] += carry
- carry = (e[i] + 8) >> 4
- e[i] -= carry << 4
- }
- e[63] += carry
- // each e[i] is between -8 and 8.
-
- h.Zero()
- var t PreComputedGroupElement
- var r CompletedGroupElement
- for i := int32(1); i < 64; i += 2 {
- selectPoint(&t, i/2, int32(e[i]))
- geMixedAdd(&r, h, &t)
- r.ToExtended(h)
- }
-
- var s ProjectiveGroupElement
-
- h.Double(&r)
- r.ToProjective(&s)
- s.Double(&r)
- r.ToProjective(&s)
- s.Double(&r)
- r.ToProjective(&s)
- s.Double(&r)
- r.ToExtended(h)
-
- for i := int32(0); i < 64; i += 2 {
- selectPoint(&t, i/2, int32(e[i]))
- geMixedAdd(&r, h, &t)
- r.ToExtended(h)
- }
-}
-
-// The scalars are GF(2^252 + 27742317777372353535851937790883648493).
-
-// 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.
-func ScMulAdd(s, a, b, c *[32]byte) {
- a0 := 2097151 & load3(a[:])
- a1 := 2097151 & (load4(a[2:]) >> 5)
- a2 := 2097151 & (load3(a[5:]) >> 2)
- a3 := 2097151 & (load4(a[7:]) >> 7)
- a4 := 2097151 & (load4(a[10:]) >> 4)
- a5 := 2097151 & (load3(a[13:]) >> 1)
- a6 := 2097151 & (load4(a[15:]) >> 6)
- a7 := 2097151 & (load3(a[18:]) >> 3)
- a8 := 2097151 & load3(a[21:])
- a9 := 2097151 & (load4(a[23:]) >> 5)
- a10 := 2097151 & (load3(a[26:]) >> 2)
- a11 := (load4(a[28:]) >> 7)
- b0 := 2097151 & load3(b[:])
- b1 := 2097151 & (load4(b[2:]) >> 5)
- b2 := 2097151 & (load3(b[5:]) >> 2)
- b3 := 2097151 & (load4(b[7:]) >> 7)
- b4 := 2097151 & (load4(b[10:]) >> 4)
- b5 := 2097151 & (load3(b[13:]) >> 1)
- b6 := 2097151 & (load4(b[15:]) >> 6)
- b7 := 2097151 & (load3(b[18:]) >> 3)
- b8 := 2097151 & load3(b[21:])
- b9 := 2097151 & (load4(b[23:]) >> 5)
- b10 := 2097151 & (load3(b[26:]) >> 2)
- b11 := (load4(b[28:]) >> 7)
- c0 := 2097151 & load3(c[:])
- c1 := 2097151 & (load4(c[2:]) >> 5)
- c2 := 2097151 & (load3(c[5:]) >> 2)
- c3 := 2097151 & (load4(c[7:]) >> 7)
- c4 := 2097151 & (load4(c[10:]) >> 4)
- c5 := 2097151 & (load3(c[13:]) >> 1)
- c6 := 2097151 & (load4(c[15:]) >> 6)
- c7 := 2097151 & (load3(c[18:]) >> 3)
- c8 := 2097151 & load3(c[21:])
- c9 := 2097151 & (load4(c[23:]) >> 5)
- c10 := 2097151 & (load3(c[26:]) >> 2)
- c11 := (load4(c[28:]) >> 7)
- var carry [23]int64
-
- 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 := int64(0)
-
- carry[0] = (s0 + (1 << 20)) >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[2] = (s2 + (1 << 20)) >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[4] = (s4 + (1 << 20)) >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[12] = (s12 + (1 << 20)) >> 21
- s13 += carry[12]
- s12 -= carry[12] << 21
- carry[14] = (s14 + (1 << 20)) >> 21
- s15 += carry[14]
- s14 -= carry[14] << 21
- carry[16] = (s16 + (1 << 20)) >> 21
- s17 += carry[16]
- s16 -= carry[16] << 21
- carry[18] = (s18 + (1 << 20)) >> 21
- s19 += carry[18]
- s18 -= carry[18] << 21
- carry[20] = (s20 + (1 << 20)) >> 21
- s21 += carry[20]
- s20 -= carry[20] << 21
- carry[22] = (s22 + (1 << 20)) >> 21
- s23 += carry[22]
- s22 -= carry[22] << 21
-
- carry[1] = (s1 + (1 << 20)) >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[3] = (s3 + (1 << 20)) >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[5] = (s5 + (1 << 20)) >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
- carry[13] = (s13 + (1 << 20)) >> 21
- s14 += carry[13]
- s13 -= carry[13] << 21
- carry[15] = (s15 + (1 << 20)) >> 21
- s16 += carry[15]
- s15 -= carry[15] << 21
- carry[17] = (s17 + (1 << 20)) >> 21
- s18 += carry[17]
- s17 -= carry[17] << 21
- carry[19] = (s19 + (1 << 20)) >> 21
- s20 += carry[19]
- s19 -= carry[19] << 21
- carry[21] = (s21 + (1 << 20)) >> 21
- s22 += carry[21]
- s21 -= carry[21] << 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
-
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[12] = (s12 + (1 << 20)) >> 21
- s13 += carry[12]
- s12 -= carry[12] << 21
- carry[14] = (s14 + (1 << 20)) >> 21
- s15 += carry[14]
- s14 -= carry[14] << 21
- carry[16] = (s16 + (1 << 20)) >> 21
- s17 += carry[16]
- s16 -= carry[16] << 21
-
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
- carry[13] = (s13 + (1 << 20)) >> 21
- s14 += carry[13]
- s13 -= carry[13] << 21
- carry[15] = (s15 + (1 << 20)) >> 21
- s16 += carry[15]
- s15 -= carry[15] << 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
-
- carry[0] = (s0 + (1 << 20)) >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[2] = (s2 + (1 << 20)) >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[4] = (s4 + (1 << 20)) >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- carry[1] = (s1 + (1 << 20)) >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[3] = (s3 + (1 << 20)) >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[5] = (s5 + (1 << 20)) >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[11] = s11 >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- s[0] = byte(s0 >> 0)
- s[1] = byte(s0 >> 8)
- s[2] = byte((s0 >> 16) | (s1 << 5))
- s[3] = byte(s1 >> 3)
- s[4] = byte(s1 >> 11)
- s[5] = byte((s1 >> 19) | (s2 << 2))
- s[6] = byte(s2 >> 6)
- s[7] = byte((s2 >> 14) | (s3 << 7))
- s[8] = byte(s3 >> 1)
- s[9] = byte(s3 >> 9)
- s[10] = byte((s3 >> 17) | (s4 << 4))
- s[11] = byte(s4 >> 4)
- s[12] = byte(s4 >> 12)
- s[13] = byte((s4 >> 20) | (s5 << 1))
- s[14] = byte(s5 >> 7)
- s[15] = byte((s5 >> 15) | (s6 << 6))
- s[16] = byte(s6 >> 2)
- s[17] = byte(s6 >> 10)
- s[18] = byte((s6 >> 18) | (s7 << 3))
- s[19] = byte(s7 >> 5)
- s[20] = byte(s7 >> 13)
- s[21] = byte(s8 >> 0)
- s[22] = byte(s8 >> 8)
- s[23] = byte((s8 >> 16) | (s9 << 5))
- s[24] = byte(s9 >> 3)
- s[25] = byte(s9 >> 11)
- s[26] = byte((s9 >> 19) | (s10 << 2))
- s[27] = byte(s10 >> 6)
- s[28] = byte((s10 >> 14) | (s11 << 7))
- s[29] = byte(s11 >> 1)
- s[30] = byte(s11 >> 9)
- s[31] = byte(s11 >> 17)
-}
-
-// 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.
-func ScReduce(out *[32]byte, s *[64]byte) {
- s0 := 2097151 & load3(s[:])
- s1 := 2097151 & (load4(s[2:]) >> 5)
- s2 := 2097151 & (load3(s[5:]) >> 2)
- s3 := 2097151 & (load4(s[7:]) >> 7)
- s4 := 2097151 & (load4(s[10:]) >> 4)
- s5 := 2097151 & (load3(s[13:]) >> 1)
- s6 := 2097151 & (load4(s[15:]) >> 6)
- s7 := 2097151 & (load3(s[18:]) >> 3)
- s8 := 2097151 & load3(s[21:])
- s9 := 2097151 & (load4(s[23:]) >> 5)
- s10 := 2097151 & (load3(s[26:]) >> 2)
- s11 := 2097151 & (load4(s[28:]) >> 7)
- s12 := 2097151 & (load4(s[31:]) >> 4)
- s13 := 2097151 & (load3(s[34:]) >> 1)
- s14 := 2097151 & (load4(s[36:]) >> 6)
- s15 := 2097151 & (load3(s[39:]) >> 3)
- s16 := 2097151 & load3(s[42:])
- s17 := 2097151 & (load4(s[44:]) >> 5)
- s18 := 2097151 & (load3(s[47:]) >> 2)
- s19 := 2097151 & (load4(s[49:]) >> 7)
- s20 := 2097151 & (load4(s[52:]) >> 4)
- s21 := 2097151 & (load3(s[55:]) >> 1)
- s22 := 2097151 & (load4(s[57:]) >> 6)
- s23 := (load4(s[60:]) >> 3)
-
- 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
-
- var carry [17]int64
-
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[12] = (s12 + (1 << 20)) >> 21
- s13 += carry[12]
- s12 -= carry[12] << 21
- carry[14] = (s14 + (1 << 20)) >> 21
- s15 += carry[14]
- s14 -= carry[14] << 21
- carry[16] = (s16 + (1 << 20)) >> 21
- s17 += carry[16]
- s16 -= carry[16] << 21
-
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
- carry[13] = (s13 + (1 << 20)) >> 21
- s14 += carry[13]
- s13 -= carry[13] << 21
- carry[15] = (s15 + (1 << 20)) >> 21
- s16 += carry[15]
- s15 -= carry[15] << 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
-
- carry[0] = (s0 + (1 << 20)) >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[2] = (s2 + (1 << 20)) >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[4] = (s4 + (1 << 20)) >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- carry[1] = (s1 + (1 << 20)) >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[3] = (s3 + (1 << 20)) >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[5] = (s5 + (1 << 20)) >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[11] = s11 >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- out[0] = byte(s0 >> 0)
- out[1] = byte(s0 >> 8)
- out[2] = byte((s0 >> 16) | (s1 << 5))
- out[3] = byte(s1 >> 3)
- out[4] = byte(s1 >> 11)
- out[5] = byte((s1 >> 19) | (s2 << 2))
- out[6] = byte(s2 >> 6)
- out[7] = byte((s2 >> 14) | (s3 << 7))
- out[8] = byte(s3 >> 1)
- out[9] = byte(s3 >> 9)
- out[10] = byte((s3 >> 17) | (s4 << 4))
- out[11] = byte(s4 >> 4)
- out[12] = byte(s4 >> 12)
- out[13] = byte((s4 >> 20) | (s5 << 1))
- out[14] = byte(s5 >> 7)
- out[15] = byte((s5 >> 15) | (s6 << 6))
- out[16] = byte(s6 >> 2)
- out[17] = byte(s6 >> 10)
- out[18] = byte((s6 >> 18) | (s7 << 3))
- out[19] = byte(s7 >> 5)
- out[20] = byte(s7 >> 13)
- out[21] = byte(s8 >> 0)
- out[22] = byte(s8 >> 8)
- out[23] = byte((s8 >> 16) | (s9 << 5))
- out[24] = byte(s9 >> 3)
- out[25] = byte(s9 >> 11)
- out[26] = byte((s9 >> 19) | (s10 << 2))
- out[27] = byte(s10 >> 6)
- out[28] = byte((s10 >> 14) | (s11 << 7))
- out[29] = byte(s11 >> 1)
- out[30] = byte(s11 >> 9)
- out[31] = byte(s11 >> 17)
-}
diff --git a/internal/extra25519/extra25519.go b/internal/extra25519/extra25519.go
deleted file mode 100644
index 7e1d227..0000000
--- a/internal/extra25519/extra25519.go
+++ /dev/null
@@ -1,291 +0,0 @@
-// Copyright 2013 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package extra25519
-
-import "gitlab.com/yawning/obfs4.git/internal/edwards25519"
-
-// sqrtMinusAPlus2 is sqrt(-(486662+2))
-var sqrtMinusAPlus2 = edwards25519.FieldElement{
- -12222970, -8312128, -11511410, 9067497, -15300785, -241793, 25456130, 14121551, -12187136, 3972024,
-}
-
-// sqrtMinusHalf is sqrt(-1/2)
-var sqrtMinusHalf = edwards25519.FieldElement{
- -17256545, 3971863, 28865457, -1750208, 27359696, -16640980, 12573105, 1002827, -163343, 11073975,
-}
-
-// halfQMinus1Bytes is (2^255-20)/2 expressed in little endian form.
-var halfQMinus1Bytes = [32]byte{
- 0xf6, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f,
-}
-
-// feBytesLess returns one if a <= b and zero otherwise.
-func feBytesLE(a, b *[32]byte) int32 {
- equalSoFar := int32(-1)
- greater := int32(0)
-
- for i := uint(31); i < 32; i-- {
- x := int32(a[i])
- y := int32(b[i])
-
- greater = (^equalSoFar & greater) | (equalSoFar & ((x - y) >> 31))
- equalSoFar = equalSoFar & (((x ^ y) - 1) >> 31)
- }
-
- return int32(^equalSoFar & 1 & greater)
-}
-
-// UnsafeBrokenScalarBaseMult computes a curve25519 public key from a private
-// key and also a uniform representative for that public key. Note that this
-// function will fail and return false for about half of private keys.
-// See http://elligator.cr.yp.to/elligator-20130828.pdf.
-func UnsafeBrokenScalarBaseMult(publicKey, representative, privateKey *[32]byte) bool {
- var maskedPrivateKey [32]byte
- copy(maskedPrivateKey[:], privateKey[:])
-
- maskedPrivateKey[0] &= 248
- maskedPrivateKey[31] &= 127
- maskedPrivateKey[31] |= 64
-
- var A edwards25519.ExtendedGroupElement
- edwards25519.GeScalarMultBase(&A, &maskedPrivateKey)
-
- var inv1 edwards25519.FieldElement
- edwards25519.FeSub(&inv1, &A.Z, &A.Y)
- edwards25519.FeMul(&inv1, &inv1, &A.X)
- edwards25519.FeInvert(&inv1, &inv1)
-
- var t0, u edwards25519.FieldElement
- edwards25519.FeMul(&u, &inv1, &A.X)
- edwards25519.FeAdd(&t0, &A.Y, &A.Z)
- edwards25519.FeMul(&u, &u, &t0)
-
- var v edwards25519.FieldElement
- edwards25519.FeMul(&v, &t0, &inv1)
- edwards25519.FeMul(&v, &v, &A.Z)
- edwards25519.FeMul(&v, &v, &sqrtMinusAPlus2)
-
- var b edwards25519.FieldElement
- edwards25519.FeAdd(&b, &u, &edwards25519.A)
-
- var c, b3, b7, b8 edwards25519.FieldElement
- edwards25519.FeSquare(&b3, &b) // 2
- edwards25519.FeMul(&b3, &b3, &b) // 3
- edwards25519.FeSquare(&c, &b3) // 6
- edwards25519.FeMul(&b7, &c, &b) // 7
- edwards25519.FeMul(&b8, &b7, &b) // 8
- edwards25519.FeMul(&c, &b7, &u)
- q58(&c, &c)
-
- var chi edwards25519.FieldElement
- edwards25519.FeSquare(&chi, &c)
- edwards25519.FeSquare(&chi, &chi)
-
- edwards25519.FeSquare(&t0, &u)
- edwards25519.FeMul(&chi, &chi, &t0)
-
- edwards25519.FeSquare(&t0, &b7) // 14
- edwards25519.FeMul(&chi, &chi, &t0)
- edwards25519.FeNeg(&chi, &chi)
-
- var chiBytes [32]byte
- edwards25519.FeToBytes(&chiBytes, &chi)
- // chi[1] is either 0 or 0xff
- if chiBytes[1] == 0xff {
- return false
- }
-
- // Calculate r1 = sqrt(-u/(2*(u+A)))
- var r1 edwards25519.FieldElement
- edwards25519.FeMul(&r1, &c, &u)
- edwards25519.FeMul(&r1, &r1, &b3)
- edwards25519.FeMul(&r1, &r1, &sqrtMinusHalf)
-
- var maybeSqrtM1 edwards25519.FieldElement
- edwards25519.FeSquare(&t0, &r1)
- edwards25519.FeMul(&t0, &t0, &b)
- edwards25519.FeAdd(&t0, &t0, &t0)
- edwards25519.FeAdd(&t0, &t0, &u)
-
- edwards25519.FeOne(&maybeSqrtM1)
- edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
- edwards25519.FeMul(&r1, &r1, &maybeSqrtM1)
-
- // Calculate r = sqrt(-(u+A)/(2u))
- var r edwards25519.FieldElement
- edwards25519.FeSquare(&t0, &c) // 2
- edwards25519.FeMul(&t0, &t0, &c) // 3
- edwards25519.FeSquare(&t0, &t0) // 6
- edwards25519.FeMul(&r, &t0, &c) // 7
-
- edwards25519.FeSquare(&t0, &u) // 2
- edwards25519.FeMul(&t0, &t0, &u) // 3
- edwards25519.FeMul(&r, &r, &t0)
-
- edwards25519.FeSquare(&t0, &b8) // 16
- edwards25519.FeMul(&t0, &t0, &b8) // 24
- edwards25519.FeMul(&t0, &t0, &b) // 25
- edwards25519.FeMul(&r, &r, &t0)
- edwards25519.FeMul(&r, &r, &sqrtMinusHalf)
-
- edwards25519.FeSquare(&t0, &r)
- edwards25519.FeMul(&t0, &t0, &u)
- edwards25519.FeAdd(&t0, &t0, &t0)
- edwards25519.FeAdd(&t0, &t0, &b)
- edwards25519.FeOne(&maybeSqrtM1)
- edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
- edwards25519.FeMul(&r, &r, &maybeSqrtM1)
-
- var vBytes [32]byte
- edwards25519.FeToBytes(&vBytes, &v)
- vInSquareRootImage := feBytesLE(&vBytes, &halfQMinus1Bytes)
- edwards25519.FeCMove(&r, &r1, vInSquareRootImage)
-
- edwards25519.FeToBytes(publicKey, &u)
- edwards25519.FeToBytes(representative, &r)
- return true
-}
-
-// q58 calculates out = z^((p-5)/8).
-func q58(out, z *edwards25519.FieldElement) {
- var t1, t2, t3 edwards25519.FieldElement
- var i int
-
- edwards25519.FeSquare(&t1, z) // 2^1
- edwards25519.FeMul(&t1, &t1, z) // 2^1 + 2^0
- edwards25519.FeSquare(&t1, &t1) // 2^2 + 2^1
- edwards25519.FeSquare(&t2, &t1) // 2^3 + 2^2
- edwards25519.FeSquare(&t2, &t2) // 2^4 + 2^3
- edwards25519.FeMul(&t2, &t2, &t1) // 4,3,2,1
- edwards25519.FeMul(&t1, &t2, z) // 4..0
- edwards25519.FeSquare(&t2, &t1) // 5..1
- for i = 1; i < 5; i++ { // 9,8,7,6,5
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
- edwards25519.FeSquare(&t2, &t1) // 10..1
- for i = 1; i < 10; i++ { // 19..10
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t2, &t2, &t1) // 19..0
- edwards25519.FeSquare(&t3, &t2) // 20..1
- for i = 1; i < 20; i++ { // 39..20
- edwards25519.FeSquare(&t3, &t3)
- }
- edwards25519.FeMul(&t2, &t3, &t2) // 39..0
- edwards25519.FeSquare(&t2, &t2) // 40..1
- for i = 1; i < 10; i++ { // 49..10
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 49..0
- edwards25519.FeSquare(&t2, &t1) // 50..1
- for i = 1; i < 50; i++ { // 99..50
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t2, &t2, &t1) // 99..0
- edwards25519.FeSquare(&t3, &t2) // 100..1
- for i = 1; i < 100; i++ { // 199..100
- edwards25519.FeSquare(&t3, &t3)
- }
- edwards25519.FeMul(&t2, &t3, &t2) // 199..0
- edwards25519.FeSquare(&t2, &t2) // 200..1
- for i = 1; i < 50; i++ { // 249..50
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 249..0
- edwards25519.FeSquare(&t1, &t1) // 250..1
- edwards25519.FeSquare(&t1, &t1) // 251..2
- edwards25519.FeMul(out, &t1, z) // 251..2,0
-}
-
-// chi calculates out = z^((p-1)/2). The result is either 1, 0, or -1 depending
-// on whether z is a non-zero square, zero, or a non-square.
-func chi(out, z *edwards25519.FieldElement) {
- var t0, t1, t2, t3 edwards25519.FieldElement
- var i int
-
- edwards25519.FeSquare(&t0, z) // 2^1
- edwards25519.FeMul(&t1, &t0, z) // 2^1 + 2^0
- edwards25519.FeSquare(&t0, &t1) // 2^2 + 2^1
- edwards25519.FeSquare(&t2, &t0) // 2^3 + 2^2
- edwards25519.FeSquare(&t2, &t2) // 4,3
- edwards25519.FeMul(&t2, &t2, &t0) // 4,3,2,1
- edwards25519.FeMul(&t1, &t2, z) // 4..0
- edwards25519.FeSquare(&t2, &t1) // 5..1
- for i = 1; i < 5; i++ { // 9,8,7,6,5
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
- edwards25519.FeSquare(&t2, &t1) // 10..1
- for i = 1; i < 10; i++ { // 19..10
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t2, &t2, &t1) // 19..0
- edwards25519.FeSquare(&t3, &t2) // 20..1
- for i = 1; i < 20; i++ { // 39..20
- edwards25519.FeSquare(&t3, &t3)
- }
- edwards25519.FeMul(&t2, &t3, &t2) // 39..0
- edwards25519.FeSquare(&t2, &t2) // 40..1
- for i = 1; i < 10; i++ { // 49..10
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 49..0
- edwards25519.FeSquare(&t2, &t1) // 50..1
- for i = 1; i < 50; i++ { // 99..50
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t2, &t2, &t1) // 99..0
- edwards25519.FeSquare(&t3, &t2) // 100..1
- for i = 1; i < 100; i++ { // 199..100
- edwards25519.FeSquare(&t3, &t3)
- }
- edwards25519.FeMul(&t2, &t3, &t2) // 199..0
- edwards25519.FeSquare(&t2, &t2) // 200..1
- for i = 1; i < 50; i++ { // 249..50
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 249..0
- edwards25519.FeSquare(&t1, &t1) // 250..1
- for i = 1; i < 4; i++ { // 253..4
- edwards25519.FeSquare(&t1, &t1)
- }
- edwards25519.FeMul(out, &t1, &t0) // 253..4,2,1
-}
-
-// UnsafeBrokenRepresentativeToPublicKey converts a uniform representative
-// value for a curve25519 public key, as produced by UnsafeBrokenScalarBaseMult,
-// to a curve25519 public key.
-func UnsafeBrokenRepresentativeToPublicKey(publicKey, representative *[32]byte) {
- var rr2, v, e edwards25519.FieldElement
- edwards25519.FeFromBytes(&rr2, representative)
-
- edwards25519.FeSquare2(&rr2, &rr2)
- rr2[0]++
- edwards25519.FeInvert(&rr2, &rr2)
- edwards25519.FeMul(&v, &edwards25519.A, &rr2)
- edwards25519.FeNeg(&v, &v)
-
- var v2, v3 edwards25519.FieldElement
- edwards25519.FeSquare(&v2, &v)
- edwards25519.FeMul(&v3, &v, &v2)
- edwards25519.FeAdd(&e, &v3, &v)
- edwards25519.FeMul(&v2, &v2, &edwards25519.A)
- edwards25519.FeAdd(&e, &v2, &e)
- chi(&e, &e)
- var eBytes [32]byte
- edwards25519.FeToBytes(&eBytes, &e)
- // eBytes[1] is either 0 (for e = 1) or 0xff (for e = -1)
- eIsMinus1 := int32(eBytes[1]) & 1
- var negV edwards25519.FieldElement
- edwards25519.FeNeg(&negV, &v)
- edwards25519.FeCMove(&v, &negV, eIsMinus1)
-
- edwards25519.FeZero(&v2)
- edwards25519.FeCMove(&v2, &edwards25519.A, eIsMinus1)
- edwards25519.FeSub(&v, &v, &v2)
-
- edwards25519.FeToBytes(publicKey, &v)
-}
diff --git a/internal/extra25519/extra25519_test.go b/internal/extra25519/extra25519_test.go
deleted file mode 100644
index 7cf1e97..0000000
--- a/internal/extra25519/extra25519_test.go
+++ /dev/null
@@ -1,61 +0,0 @@
-// Copyright 2013 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package extra25519
-
-import (
- "bytes"
- "crypto/rand"
- "testing"
-
- "golang.org/x/crypto/curve25519"
-)
-
-func TestElligator(t *testing.T) {
- var publicKey, publicKey2, publicKey3, representative, privateKey [32]byte
-
- for i := 0; i < 1000; i++ {
- rand.Reader.Read(privateKey[:])
-
- if !UnsafeBrokenScalarBaseMult(&publicKey, &representative, &privateKey) {
- continue
- }
- UnsafeBrokenRepresentativeToPublicKey(&publicKey2, &representative)
- if !bytes.Equal(publicKey[:], publicKey2[:]) {
- t.Fatal("The resulting public key doesn't match the initial one.")
- }
-
- curve25519.ScalarBaseMult(&publicKey3, &privateKey)
- if !bytes.Equal(publicKey[:], publicKey3[:]) {
- t.Fatal("The public key doesn't match the value that curve25519 produced.")
- }
- }
-}
-
-func BenchmarkKeyGeneration(b *testing.B) {
- var publicKey, representative, privateKey [32]byte
-
- // Find the private key that results in a point that's in the image of the map.
- for {
- rand.Reader.Read(privateKey[:])
- if UnsafeBrokenScalarBaseMult(&publicKey, &representative, &privateKey) {
- break
- }
- }
-
- b.ResetTimer()
- for i := 0; i < b.N; i++ {
- UnsafeBrokenScalarBaseMult(&publicKey, &representative, &privateKey)
- }
-}
-
-func BenchmarkMap(b *testing.B) {
- var publicKey, representative [32]byte
- rand.Reader.Read(representative[:])
-
- b.ResetTimer()
- for i := 0; i < b.N; i++ {
- UnsafeBrokenRepresentativeToPublicKey(&publicKey, &representative)
- }
-}
diff --git a/internal/x25519ell2/x25519ell2.go b/internal/x25519ell2/x25519ell2.go
new file mode 100644
index 0000000..cbf0ad6
--- /dev/null
+++ b/internal/x25519ell2/x25519ell2.go
@@ -0,0 +1,177 @@
+// Copyright (c) 2021 Yawning Angel <yawning at schwanenlied dot me>
+//
+// This program is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program. If not, see <https://www.gnu.org/licenses/>.
+
+// Package x25519ell2 implements obfuscated X25519 ECDH, via the Elligator2
+// mapping.
+package x25519ell2
+
+import (
+ "encoding/binary"
+
+ "filippo.io/edwards25519"
+ "filippo.io/edwards25519/field"
+
+ "gitlab.com/yawning/edwards25519-extra.git/elligator2"
+)
+
+// The corrected version of this that solves the implementation errors
+// present in the historical implementation by agl is derived from
+// Monocypher (CC-0 or BSD-2) by Loup Vaillant. Without their efforts
+// and prodding, this would likely have stayed broken forever.
+
+var (
+ feOne = new(field.Element).One()
+
+ feNegTwo = mustFeFromBytes([]byte{
+ 0xeb, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f,
+ })
+
+ feA = mustFeFromUint64(486662)
+
+ feSqrtM1 = mustFeFromBytes([]byte{
+ 0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4, 0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f,
+ 0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, 0x4d, 0x2b, 0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b,
+ })
+
+ // Low order point Edwards x-coordinate `sqrt((sqrt(d + 1) + 1) / d)`.
+ feLopX = mustFeFromBytes([]byte{
+ 0x4a, 0xd1, 0x45, 0xc5, 0x46, 0x46, 0xa1, 0xde, 0x38, 0xe2, 0xe5, 0x13, 0x70, 0x3c, 0x19, 0x5c,
+ 0xbb, 0x4a, 0xde, 0x38, 0x32, 0x99, 0x33, 0xe9, 0x28, 0x4a, 0x39, 0x06, 0xa0, 0xb9, 0xd5, 0x1f,
+ })
+
+ // Low order point Edwards y-coordinate `-lop_x * sqrtm1`
+ feLopY = mustFeFromBytes([]byte{
+ 0x26, 0xe8, 0x95, 0x8f, 0xc2, 0xb2, 0x27, 0xb0, 0x45, 0xc3, 0xf4, 0x89, 0xf2, 0xef, 0x98, 0xf0,
+ 0xd5, 0xdf, 0xac, 0x05, 0xd3, 0xc6, 0x33, 0x39, 0xb1, 0x38, 0x02, 0x88, 0x6d, 0x53, 0xfc, 0x05,
+ })
+)
+
+func mustFeFromBytes(b []byte) *field.Element {
+ fe, err := new(field.Element).SetBytes(b)
+ if err != nil {
+ panic("internal/x25519ell2: failed to deserialize constant: " + err.Error())
+ }
+ return fe
+}
+
+func mustFeFromUint64(x uint64) *field.Element {
+ var b [32]byte
+ binary.LittleEndian.PutUint64(b[:], x)
+ return mustFeFromBytes(b[:])
+}
+
+func selectLowOrderPoint(out, x, k *field.Element, cofactor uint8) {
+ out.Zero()
+ out.Select(k, out, int((cofactor>>1)&1)) // bit 1
+ out.Select(x, out, int((cofactor>>0)&1)) // bit 1
+ var tmp field.Element
+ tmp.Negate(out)
+ out.Select(&tmp, out, int((cofactor>>2)&1)) // bit 2
+}
+
+func scalarBaseMultDirty(privateKey *[32]byte) *field.Element {
+ // Compute clean scalar multiplication
+ scalar, err := new(edwards25519.Scalar).SetBytesWithClamping(privateKey[:])
+ if err != nil {
+ panic("internal/x25519ell2: failed to deserialize scalar: " + err.Error())
+ }
+ pk := new(edwards25519.Point).ScalarBaseMult(scalar)
+
+ // Compute low order point
+ var lopX, lopY, lopT field.Element
+ selectLowOrderPoint(&lopX, feLopX, feSqrtM1, privateKey[0])
+ selectLowOrderPoint(&lopY, feLopY, feOne, privateKey[0]+2)
+ // Z = one
+ lopT.Multiply(&lopX, &lopY)
+ lop, err := new(edwards25519.Point).SetExtendedCoordinates(&lopX, &lopY, feOne, &lopT)
+ if err != nil {
+ panic("interal/x25519ell2: failed to create edwards point from x, y: " + err.Error())
+ }
+
+ // Add low order point to the public key
+ pk.Add(pk, lop)
+
+ // Convert to Montgomery u coordinate (we ignore the sign)
+ _, yExt, zExt, _ := pk.ExtendedCoordinates()
+ var t1, t2 field.Element
+ t1.Add(zExt, yExt)
+ t2.Subtract(zExt, yExt)
+ t2.Invert(&t2)
+ t1.Multiply(&t1, &t2)
+
+ return &t1
+}
+
+func uToRepresentative(representative *[32]byte, u *field.Element, tweak byte) bool {
+ t1 := new(field.Element).Set(u)
+
+ t2 := new(field.Element).Add(t1, feA)
+ t3 := new(field.Element).Multiply(t1, t2)
+ t3.Multiply(t3, feNegTwo)
+ if _, isSquare := t3.SqrtRatio(feOne, t3); isSquare == 1 {
+ t1.Select(t2, t1, int(tweak&1))
+ t3.Multiply(t1, t3)
+ t1.Mult32(t3, 2)
+ t2.Negate(t3)
+ tmp := t1.Bytes()
+ t3.Select(t2, t3, int(tmp[0]&1))
+ copy(representative[:], t3.Bytes())
+
+ // Pad with two random bits
+ representative[31] |= tweak & 0xc0
+
+ return true
+ }
+
+ return false
+}
+
+// ScalarBaseMult computes a curve25519 public key from a private
+// key and also a uniform representative for that public key.
+// Note that this function will fail and return false for about
+// half of private keys.
+//
+// WARNING: The underlying scalar multiply explicitly does not clear
+// the cofactor, and thus the public keys will be different from
+// those produced by normal implementations.
+func ScalarBaseMult(publicKey, representative, privateKey *[32]byte, tweak byte) bool {
+ u := scalarBaseMultDirty(privateKey)
+ if !uToRepresentative(representative, u, tweak) {
+ // No representative.
+ return false
+ }
+ copy(publicKey[:], u.Bytes())
+ return true
+}
+
+// RepresentativeToPublicKey converts a uniform representative value for
+// a curve25519 public key, as produced by ScalarBaseMult, to a curve25519
+// public key.
+func RepresentativeToPublicKey(publicKey, representative *[32]byte) {
+ // Representatives are encoded in 254 bits.
+ var clamped [32]byte
+ copy(clamped[:], representative[:])
+ clamped[31] &= 63
+
+ var fe field.Element
+ if _, err := fe.SetBytes(clamped[:]); err != nil {
+ // Panic is fine, the only way this fails is if the representative
+ // is not 32-bytes.
+ panic("internal/x25519ell2: failed to deserialize representative: " + err.Error())
+ }
+ u, _ := elligator2.MontgomeryFlavor(&fe)
+ copy(publicKey[:], u.Bytes())
+}
diff --git a/internal/x25519ell2/x25519ell2_test.go b/internal/x25519ell2/x25519ell2_test.go
new file mode 100644
index 0000000..4598538
--- /dev/null
+++ b/internal/x25519ell2/x25519ell2_test.go
@@ -0,0 +1,153 @@
+// Copyright (c) 2021 Yawning Angel <yawning at schwanenlied dot me>
+//
+// This program is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program. If not, see <https://www.gnu.org/licenses/>.
+
+package x25519ell2
+
+import (
+ "bytes"
+ "crypto/rand"
+ "testing"
+
+ "filippo.io/edwards25519/field"
+ "golang.org/x/crypto/curve25519"
+)
+
+func TestX25519Ell2(t *testing.T) {
+ t.Run("Constants", testConstants)
+ t.Run("KeyExchage", testKeyExchange)
+}
+
+func testConstants(t *testing.T) {
+ // While the constants were calculated and serialized with a known
+ // correct implementation of the field arithmetic, re-derive them
+ // to be sure.
+
+ t.Run("NegTwo", func(t *testing.T) {
+ expected := new(field.Element).Add(feOne, feOne)
+ expected.Negate(expected)
+
+ if expected.Equal(feNegTwo) != 1 {
+ t.Fatalf("invalid value for -2: %x", feNegTwo.Bytes())
+ }
+ })
+
+ t.Run("LopX", func(t *testing.T) {
+ // d = -121665/121666
+ d := mustFeFromUint64(121666)
+ d.Invert(d)
+ d.Multiply(d, mustFeFromUint64(121665))
+ d.Negate(d)
+
+ // lop_x = sqrt((sqrt(d + 1) + 1) / d)
+ expected := new(field.Element).Add(d, feOne)
+ expected.Invert(expected)
+ expected.SqrtRatio(feOne, expected)
+ expected.Add(expected, feOne)
+ expected.SqrtRatio(expected, d)
+
+ if expected.Equal(feLopX) != 1 {
+ t.Fatalf("invalid value for low order point X: %x", feLopX.Bytes())
+ }
+ })
+
+ t.Run("LopY", func(t *testing.T) {
+ // lop_y = -lop_x * sqrtm1
+ expected := new(field.Element).Negate(feLopX)
+ expected.Multiply(expected, feSqrtM1)
+
+ if expected.Equal(feLopY) != 1 {
+ t.Fatalf("invalid value for low order point Y: %x", feLopY.Bytes())
+ }
+ })
+}
+
+func testKeyExchange(t *testing.T) {
+ var randSk [32]byte
+ _, _ = rand.Read(randSk[:])
+
+ var good, bad int
+ for i := 0; i < 1000; i++ {
+ var (
+ publicKey, privateKey, representative [32]byte
+ publicKeyClean [32]byte
+ tweak [1]byte
+ )
+ _, _ = rand.Read(privateKey[:])
+ _, _ = rand.Read(tweak[:])
+
+ // This won't match the public key from the Elligator2-ed scalar
+ // basepoint multiply, but we want to ensure that the public keys
+ // we do happen to generate are interoperable (otherwise something
+ // is badly broken).
+ curve25519.ScalarBaseMult(&publicKeyClean, &privateKey)
+
+ if !ScalarBaseMult(&publicKey, &representative, &privateKey, tweak[0]) {
+ t.Logf("bad: %x", privateKey)
+ bad++
+ continue
+ }
+ t.Logf("good: %x", privateKey)
+
+ t.Logf("publicKey: %x, repr: %x", publicKey, representative)
+
+ var shared, sharedRep, sharedClean, pkFromRep [32]byte
+ RepresentativeToPublicKey(&pkFromRep, &representative)
+ if !bytes.Equal(pkFromRep[:], publicKey[:]) {
+ t.Fatalf("public key mismatch(repr): expected %x, actual: %x", publicKey, pkFromRep)
+ }
+
+ curve25519.ScalarMult(&sharedClean, &randSk, &publicKeyClean) //nolint: staticcheck
+ curve25519.ScalarMult(&shared, &randSk, &publicKey) //nolint: staticcheck
+ curve25519.ScalarMult(&sharedRep, &randSk, &pkFromRep) //nolint: staticcheck
+
+ if !bytes.Equal(shared[:], sharedRep[:]) {
+ t.Fatalf("shared secret mismatch: expected %x, actual: %x", shared, sharedRep)
+ }
+ if !bytes.Equal(shared[:], sharedClean[:]) {
+ t.Fatalf("shared secret mismatch(clean): expected %x, actual: %x", shared, sharedClean)
+ }
+
+ good++
+ }
+
+ t.Logf("good: %d, bad: %d", good, bad)
+}
+
+func BenchmarkKeyGeneration(b *testing.B) {
+ var publicKey, representative, privateKey [32]byte
+
+ // Find the private key that results in a point that's in the image of the map.
+ for {
+ _, _ = rand.Reader.Read(privateKey[:])
+ if ScalarBaseMult(&publicKey, &representative, &privateKey, 0) {
+ break
+ }
+ }
+
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ ScalarBaseMult(&publicKey, &representative, &privateKey, 0)
+ }
+}
+
+func BenchmarkMap(b *testing.B) {
+ var publicKey, representative [32]byte
+ _, _ = rand.Reader.Read(representative[:])
+
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ RepresentativeToPublicKey(&publicKey, &representative)
+ }
+}
1
0
[obfs4/master] transports/meek_lite: Bump the version of the utls fork
by cohosh＠torproject.org 24 Jan '22
by cohosh＠torproject.org 24 Jan '22
24 Jan '22
commit e330d1b7024b4ab04f7d96cc1afc61325744fafc
Author: Yawning Angel <yawning(a)schwanenlied.me>
Date: Tue May 11 22:07:00 2021 +0000
transports/meek_lite: Bump the version of the utls fork
And add the Chrome 83 fingerprint.
---
ChangeLog | 1 +
go.mod | 2 +-
go.sum | 12 ++++++------
transports/meeklite/transport.go | 1 +
4 files changed, 9 insertions(+), 7 deletions(-)
diff --git a/ChangeLog b/ChangeLog
index 467f7d7..53253ef 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -2,6 +2,7 @@ Changes in version 0.0.12 - UNRELEASED:
- Replace the extra25519 import with an internal package.
- Update the Azure TLS certificate digest (Thanks to Philipp Winter).
- Make the -unsafeLogging command line switch work.
+ - Bump the version of the utls fork, add the Chrome 83 fingerprint.
Changes in version 0.0.11 - 2019-06-21:
- Update my e-mail address.
diff --git a/go.mod b/go.mod
index a90d67d..1a64cb6 100644
--- a/go.mod
+++ b/go.mod
@@ -3,7 +3,7 @@ module gitlab.com/yawning/obfs4.git
require (
git.torproject.org/pluggable-transports/goptlib.git v1.0.0
github.com/dchest/siphash v1.2.1
- gitlab.com/yawning/utls.git v0.0.11-1
+ gitlab.com/yawning/utls.git v0.0.12-1
golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c
golang.org/x/net v0.0.0-20190328230028-74de082e2cca
)
diff --git a/go.sum b/go.sum
index bffa15e..5e192a8 100644
--- a/go.sum
+++ b/go.sum
@@ -1,5 +1,3 @@
-git.schwanenlied.me/yawning/bsaes.git v0.0.0-20190320102049-26d1add596b6 h1:zOrl5/RvK48MxMrif6Z+/OpuYyRnvB+ZTrQWEV9VYb0=
-git.schwanenlied.me/yawning/bsaes.git v0.0.0-20190320102049-26d1add596b6/go.mod h1:BWqTsj8PgcPriQJGl7el20J/7TuT1d/hSyFDXMEpoEo=
git.torproject.org/pluggable-transports/goptlib.git v1.0.0 h1:ElTwFFPKf/tA6x5nuIk9g49JZzS4T5WN+eTQTjqd00A=
git.torproject.org/pluggable-transports/goptlib.git v1.0.0/go.mod h1:YT4XMSkuEXbtqlydr9+OxqFAyspUv0Gr9qhM3B++o/Q=
github.com/dchest/siphash v1.2.1 h1:4cLinnzVJDKxTCl9B01807Yiy+W7ZzVHj/KIroQRvT4=
@@ -10,15 +8,17 @@ github.com/dsnet/golib v0.0.0-20171103203638-1ea166775780/go.mod h1:Lj+Z9rebOhdf
github.com/klauspost/compress v1.4.1/go.mod h1:RyIbtBH6LamlWaDj8nUwkbUhJ87Yi3uG0guNDohfE1A=
github.com/klauspost/cpuid v1.2.0/go.mod h1:Pj4uuM528wm8OyEC2QMXAi2YiTZ96dNQPGgoMS4s3ek=
github.com/ulikunitz/xz v0.5.6/go.mod h1:2bypXElzHzzJZwzH67Y6wb67pO62Rzfn7BSiF4ABRW8=
-gitlab.com/yawning/utls.git v0.0.11-1 h1:cQLJ4sN+u07Rn9M7RpvCEWUPndtrsQsy6U3ZaEHeDvI=
-gitlab.com/yawning/utls.git v0.0.11-1/go.mod h1:eYdrOOCoedNc3xw50kJ/s8JquyxeS5kr3vkFZFPTI9w=
+gitlab.com/yawning/bsaes.git v0.0.0-20190805113838-0a714cd429ec h1:FpfFs4EhNehiVfzQttTuxanPIT43FtkkCFypIod8LHo=
+gitlab.com/yawning/bsaes.git v0.0.0-20190805113838-0a714cd429ec/go.mod h1:BZ1RAoRPbCxum9Grlv5aeksu2H8BiKehBYooU2LFiOQ=
+gitlab.com/yawning/utls.git v0.0.12-1 h1:RL6O0MP2YI0KghuEU/uGN6+8b4183eqNWoYgx7CXD0U=
+gitlab.com/yawning/utls.git v0.0.12-1/go.mod h1:3ONKiSFR9Im/c3t5RKmMJTVdmZN496FNyk3mjrY1dyo=
golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c h1:Vj5n4GlwjmQteupaxJ9+0FNOmBrHfq7vN4btdGoDZgI=
golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
golang.org/x/net v0.0.0-20190328230028-74de082e2cca h1:hyA6yiAgbUwuWqtscNvWAI7U1CtlaD1KilQ6iudt1aI=
golang.org/x/net v0.0.0-20190328230028-74de082e2cca/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
-golang.org/x/sys v0.0.0-20190329044733-9eb1bfa1ce65 h1:hOY+O8MxdkPV10pNf7/XEHaySCiPKxixMKUshfHsGn0=
-golang.org/x/sys v0.0.0-20190329044733-9eb1bfa1ce65/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20190804053845-51ab0e2deafa h1:KIDDMLT1O0Nr7TSxp8xM5tJcdn8tgyAONntO829og1M=
+golang.org/x/sys v0.0.0-20190804053845-51ab0e2deafa/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
golang.org/x/text v0.3.0 h1:g61tztE5qeGQ89tm6NTjjM9VPIm088od1l6aSorWRWg=
golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
diff --git a/transports/meeklite/transport.go b/transports/meeklite/transport.go
index 4e4907a..8ff02a5 100644
--- a/transports/meeklite/transport.go
+++ b/transports/meeklite/transport.go
@@ -54,6 +54,7 @@ var (
"hellochrome_62": &utls.HelloChrome_62,
"hellochrome_70": &utls.HelloChrome_70,
"hellochrome_72": &utls.HelloChrome_72,
+ "hellochrome_83": &utls.HelloChrome_83,
"helloios_auto": &utls.HelloIOS_Auto,
"helloios_11_1": &utls.HelloIOS_11_1,
"helloios_12_1": &utls.HelloIOS_12_1,
1
0
commit f638c33f6c6f697498150d5f0dfbf26453759262
Author: Philipp Winter <phw(a)nymity.ch>
Date: Mon Dec 7 10:23:44 2020 -0800
Actually support unsafe logging.
Obfs4proxy implements the -unsafeLogging switch but it's been ignored so
far. This patch makes it work.
---
ChangeLog | 1 +
common/log/log.go | 1 +
2 files changed, 2 insertions(+)
diff --git a/ChangeLog b/ChangeLog
index 5b16201..467f7d7 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,6 +1,7 @@
Changes in version 0.0.12 - UNRELEASED:
- Replace the extra25519 import with an internal package.
- Update the Azure TLS certificate digest (Thanks to Philipp Winter).
+ - Make the -unsafeLogging command line switch work.
Changes in version 0.0.11 - 2019-06-21:
- Update my e-mail address.
diff --git a/common/log/log.go b/common/log/log.go
index 61d8d8c..5e08c64 100644
--- a/common/log/log.go
+++ b/common/log/log.go
@@ -70,6 +70,7 @@ func Init(enable bool, logFilePath string, unsafe bool) error {
log.SetOutput(ioutil.Discard)
}
enableLogging = enable
+ unsafeLogging = unsafe
return nil
}
1
0
24 Jan '22
commit a564bc3840bc788605e1a8155f4b95ce0d70c6db
Author: Yawning Angel <yawning(a)schwanenlied.me>
Date: Fri Dec 31 02:43:14 2021 +0000
Do the release ritual for obfs4proxy-0.0.12
---
ChangeLog | 2 +-
go.mod | 2 +-
obfs4proxy/obfs4proxy.go | 2 +-
3 files changed, 3 insertions(+), 3 deletions(-)
diff --git a/ChangeLog b/ChangeLog
index 5253fe6..fca34df 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,4 +1,4 @@
-Changes in version 0.0.12 - UNRELEASED:
+Changes in version 0.0.12 - 2021-12-31:
- Fix the long standing distinguishers associated with agl's Elligator2
implementation (Thanks to Loup Vaillant).
- Replace the extra25519 import with an internal package.
diff --git a/go.mod b/go.mod
index 037082a..622ac6f 100644
--- a/go.mod
+++ b/go.mod
@@ -10,4 +10,4 @@ require (
golang.org/x/net v0.0.0-20210226172049-e18ecbb05110
)
-go 1.13
+go 1.16
diff --git a/obfs4proxy/obfs4proxy.go b/obfs4proxy/obfs4proxy.go
index 1dd00b2..c4982ce 100644
--- a/obfs4proxy/obfs4proxy.go
+++ b/obfs4proxy/obfs4proxy.go
@@ -50,7 +50,7 @@ import (
)
const (
- obfs4proxyVersion = "0.0.12-dev"
+ obfs4proxyVersion = "0.0.12"
obfs4proxyLogFile = "obfs4proxy.log"
socksAddr = "127.0.0.1:0"
)
1
0
commit 393aca86cc3b1a5263018c10f87ece09ac3fd5ed
Author: Yawning Angel <yawning(a)schwanenlied.me>
Date: Wed Dec 29 08:44:20 2021 +0000
internal/x25519ell2: Initial import
Replace agl's Elligator2 implementation with a different one, that fixes
the various distinguishers stemming from bugs in the original
implementation and "The Elligator paper is extremely hard to read".
All releases prior to this commit are trivially distinguishable with
simple math, so upgrading is strongly recommended. The upgrade is fully
backward-compatible with existing implementations, however the
non-upgraded side will emit traffic that is trivially distinguishable
from random.
Special thanks to Loup Vaillant for his body of work on this primitive,
and for motivating me to fix it.
---
ChangeLog | 2 +
README.md | 4 +-
common/ntor/ntor.go | 19 +-
go.mod | 6 +-
go.sum | 19 +-
internal/README-extra25519.md | 21 -
internal/README.md | 37 +
internal/edwards25519/const.go | 1411 -------------------------
internal/edwards25519/edwards25519.go | 1773 --------------------------------
internal/extra25519/extra25519.go | 291 ------
internal/extra25519/extra25519_test.go | 61 --
internal/x25519ell2/x25519ell2.go | 177 ++++
internal/x25519ell2/x25519ell2_test.go | 153 +++
13 files changed, 404 insertions(+), 3570 deletions(-)
diff --git a/ChangeLog b/ChangeLog
index 53253ef..5253fe6 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,4 +1,6 @@
Changes in version 0.0.12 - UNRELEASED:
+ - Fix the long standing distinguishers associated with agl's Elligator2
+ implementation (Thanks to Loup Vaillant).
- Replace the extra25519 import with an internal package.
- Update the Azure TLS certificate digest (Thanks to Philipp Winter).
- Make the -unsafeLogging command line switch work.
diff --git a/README.md b/README.md
index 621fe21..af211af 100644
--- a/README.md
+++ b/README.md
@@ -90,7 +90,9 @@ ServerTransportPlugin obfs4 exec /usr/local/bin/obfs4proxy
### Thanks
+ * Loup Vaillant for motivating me to replace the Elligator implementation
+ and a body of code I could draw on to accelerate the replacement process.
* David Fifield for goptlib.
- * Adam Langley for his Elligator implementation.
+ * Adam Langley for his initial Elligator implementation.
* Philipp Winter for the ScrambleSuit protocol which provided much of the
design.
diff --git a/common/ntor/ntor.go b/common/ntor/ntor.go
index 851cc1e..af24b68 100644
--- a/common/ntor/ntor.go
+++ b/common/ntor/ntor.go
@@ -38,6 +38,7 @@ import (
"bytes"
"crypto/hmac"
"crypto/sha256"
+ "crypto/sha512"
"crypto/subtle"
"encoding/hex"
"fmt"
@@ -47,7 +48,7 @@ import (
"golang.org/x/crypto/hkdf"
"gitlab.com/yawning/obfs4.git/common/csrand"
- "gitlab.com/yawning/obfs4.git/internal/extra25519"
+ "gitlab.com/yawning/obfs4.git/internal/x25519ell2"
)
const (
@@ -204,7 +205,7 @@ func (repr *Representative) Bytes() *[RepresentativeLength]byte {
func (repr *Representative) ToPublic() *PublicKey {
pub := new(PublicKey)
- extra25519.UnsafeBrokenRepresentativeToPublicKey(pub.Bytes(), repr.Bytes())
+ x25519ell2.RepresentativeToPublicKey(pub.Bytes(), repr.Bytes())
return pub
}
@@ -263,22 +264,28 @@ func NewKeypair(elligator bool) (*Keypair, error) {
for {
// Generate a Curve25519 private key. Like everyone who does this,
- // run the CSPRNG output through SHA256 for extra tinfoil hattery.
+ // run the CSPRNG output through SHA512 for extra tinfoil hattery.
+ //
+ // Also use part of the digest that gets truncated off for the
+ // obfuscation tweak.
priv := keypair.private.Bytes()[:]
if err := csrand.Bytes(priv); err != nil {
return nil, err
}
- digest := sha256.Sum256(priv)
+ digest := sha512.Sum512(priv)
digest[0] &= 248
digest[31] &= 127
digest[31] |= 64
copy(priv, digest[:])
if elligator {
+ tweak := digest[63]
+
// Apply the Elligator transform. This fails ~50% of the time.
- if !extra25519.UnsafeBrokenScalarBaseMult(keypair.public.Bytes(),
+ if !x25519ell2.ScalarBaseMult(keypair.public.Bytes(),
keypair.representative.Bytes(),
- keypair.private.Bytes()) {
+ keypair.private.Bytes(),
+ tweak) {
continue
}
} else {
diff --git a/go.mod b/go.mod
index 1a64cb6..037082a 100644
--- a/go.mod
+++ b/go.mod
@@ -1,11 +1,13 @@
module gitlab.com/yawning/obfs4.git
require (
+ filippo.io/edwards25519 v1.0.0-rc.1.0.20210721174708-390f27c3be20
git.torproject.org/pluggable-transports/goptlib.git v1.0.0
github.com/dchest/siphash v1.2.1
+ gitlab.com/yawning/edwards25519-extra.git v0.0.0-20211229043746-2f91fcc9fbdb
gitlab.com/yawning/utls.git v0.0.12-1
- golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c
- golang.org/x/net v0.0.0-20190328230028-74de082e2cca
+ golang.org/x/crypto v0.0.0-20210711020723-a769d52b0f97
+ golang.org/x/net v0.0.0-20210226172049-e18ecbb05110
)
go 1.13
diff --git a/go.sum b/go.sum
index 5e192a8..5de7fd9 100644
--- a/go.sum
+++ b/go.sum
@@ -1,3 +1,5 @@
+filippo.io/edwards25519 v1.0.0-rc.1.0.20210721174708-390f27c3be20 h1:iJoUgXvhagsNMrJrvavw7vu1eG8+hm6jLOxlLFcoODw=
+filippo.io/edwards25519 v1.0.0-rc.1.0.20210721174708-390f27c3be20/go.mod h1:N1IkdkCkiLB6tki+MYJoSx2JTY9NUlxZE7eHn5EwJns=
git.torproject.org/pluggable-transports/goptlib.git v1.0.0 h1:ElTwFFPKf/tA6x5nuIk9g49JZzS4T5WN+eTQTjqd00A=
git.torproject.org/pluggable-transports/goptlib.git v1.0.0/go.mod h1:YT4XMSkuEXbtqlydr9+OxqFAyspUv0Gr9qhM3B++o/Q=
github.com/dchest/siphash v1.2.1 h1:4cLinnzVJDKxTCl9B01807Yiy+W7ZzVHj/KIroQRvT4=
@@ -10,15 +12,24 @@ github.com/klauspost/cpuid v1.2.0/go.mod h1:Pj4uuM528wm8OyEC2QMXAi2YiTZ96dNQPGgo
github.com/ulikunitz/xz v0.5.6/go.mod h1:2bypXElzHzzJZwzH67Y6wb67pO62Rzfn7BSiF4ABRW8=
gitlab.com/yawning/bsaes.git v0.0.0-20190805113838-0a714cd429ec h1:FpfFs4EhNehiVfzQttTuxanPIT43FtkkCFypIod8LHo=
gitlab.com/yawning/bsaes.git v0.0.0-20190805113838-0a714cd429ec/go.mod h1:BZ1RAoRPbCxum9Grlv5aeksu2H8BiKehBYooU2LFiOQ=
+gitlab.com/yawning/edwards25519-extra.git v0.0.0-20211229043746-2f91fcc9fbdb h1:qRSZHsODmAP5qDvb3YsO7Qnf3TRiVbGxNG/WYnlM4/o=
+gitlab.com/yawning/edwards25519-extra.git v0.0.0-20211229043746-2f91fcc9fbdb/go.mod h1:gvdJuZuO/tPZyhEV8K3Hmoxv/DWud5L4qEQxfYjEUTo=
gitlab.com/yawning/utls.git v0.0.12-1 h1:RL6O0MP2YI0KghuEU/uGN6+8b4183eqNWoYgx7CXD0U=
gitlab.com/yawning/utls.git v0.0.12-1/go.mod h1:3ONKiSFR9Im/c3t5RKmMJTVdmZN496FNyk3mjrY1dyo=
golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
-golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c h1:Vj5n4GlwjmQteupaxJ9+0FNOmBrHfq7vN4btdGoDZgI=
golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
-golang.org/x/net v0.0.0-20190328230028-74de082e2cca h1:hyA6yiAgbUwuWqtscNvWAI7U1CtlaD1KilQ6iudt1aI=
+golang.org/x/crypto v0.0.0-20210711020723-a769d52b0f97 h1:/UOmuWzQfxxo9UtlXMwuQU8CMgg1eZXqTRwkSQJWKOI=
+golang.org/x/crypto v0.0.0-20210711020723-a769d52b0f97/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc=
golang.org/x/net v0.0.0-20190328230028-74de082e2cca/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
+golang.org/x/net v0.0.0-20210226172049-e18ecbb05110 h1:qWPm9rbaAMKs8Bq/9LRpbMqxWRVUAQwMI9fVrssnTfw=
+golang.org/x/net v0.0.0-20210226172049-e18ecbb05110/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg=
golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
-golang.org/x/sys v0.0.0-20190804053845-51ab0e2deafa h1:KIDDMLT1O0Nr7TSxp8xM5tJcdn8tgyAONntO829og1M=
golang.org/x/sys v0.0.0-20190804053845-51ab0e2deafa/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
-golang.org/x/text v0.3.0 h1:g61tztE5qeGQ89tm6NTjjM9VPIm088od1l6aSorWRWg=
+golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1 h1:SrN+KX8Art/Sf4HNj6Zcz06G7VEz+7w9tdXTPOZ7+l4=
+golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
+golang.org/x/text v0.3.3 h1:cokOdA+Jmi5PJGXLlLllQSgYigAEfHXJAERHVMaCc2k=
+golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
+golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
diff --git a/internal/README-extra25519.md b/internal/README-extra25519.md
deleted file mode 100644
index f02418c..0000000
--- a/internal/README-extra25519.md
+++ /dev/null
@@ -1,21 +0,0 @@
-This includes a copy of the edwards25519 and extra25519 packages authored
-by agl, that formerly lived at github.com/agl/ed25519 as of the commit
-5312a61534124124185d41f09206b9fef1d88403 with the following changes:
-
- * Import paths fixed up.
-
- * The unused Ed25519->X25519 key conversion routines were removed.
-
- * `UnsafeBroken` was prefixed to the routines that are known to be
- severely flawed.
-
-The only reason this is being done (despite agl's wishes that the code
-base dies, which I wanted to respect) is so people stop bothering me
-about it.
-
-Do not ask me questions about this.
-Do not use it in other projects.
-Do not use it in anything new.
-Do not expect me to maintain this beyond ensuring it continues to build.
-
-All I want is to be left alone.
diff --git a/internal/README.md b/internal/README.md
new file mode 100644
index 0000000..05aa472
--- /dev/null
+++ b/internal/README.md
@@ -0,0 +1,37 @@
+The x25519ell2 package provides X25519 obfuscated with Elligator 2, with
+special care taken to handle cofactor related issues, and fixes for the
+bugs in agl's original Elligator2 implementation.
+
+All existing versions prior to the migration to the new code (anything
+that uses agl's code) are fatally broken, and trivial to distinguish via
+some simple math. For more details see Loup Vaillant's writings on the
+subject. Any bugs in the implementation are mine, and not his.
+
+Representatives created by this implementation will correctly be decoded
+by existing implementations. Public keys created by this implementation
+be it via the modified scalar basepoint multiply or via decoding a
+representative will be somewhat non-standard, but will interoperate with
+a standard X25519 scalar-multiply.
+
+As the obfs4 handshake does not include the decoded representative in
+any of it's authenticated handshake digest calculations, this change is
+fully-backward compatible (though the non-upgraded side of the connection
+will still be trivially distinguishable from random).
+
+##### Maintainer's rant
+
+Honestly, it is possible to create a better obfuscation protocol than
+obfs4, and it's shelf-life expired years ago. No one should be using
+it for anything at this point, and no one should have been using it
+for anything for the past however many years since I first started
+telling people to stop using it.
+
+People should also have listened when I told them repeatedly that there
+are massive issues in the protocol.
+
+ * Do not ask me questions about this.
+ * Do not use it in other projects.
+ * Do not use it in anything new.
+ * Use a prime order group instead of this nonsense especially if you
+ are doing something new.
+ * All I want is to be left alone.
diff --git a/internal/edwards25519/const.go b/internal/edwards25519/const.go
deleted file mode 100644
index ea5b77a..0000000
--- a/internal/edwards25519/const.go
+++ /dev/null
@@ -1,1411 +0,0 @@
-// Copyright 2013 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package edwards25519
-
-var d = FieldElement{
- -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116,
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- FieldElement{33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053},
- },
- {
- FieldElement{31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275},
- FieldElement{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511},
- FieldElement{22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095},
- },
- {
- FieldElement{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439},
- FieldElement{23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939},
- FieldElement{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424},
- },
- {
- FieldElement{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310},
- FieldElement{3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608},
- FieldElement{-32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079},
- },
- {
- FieldElement{-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101},
- FieldElement{21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418},
- FieldElement{18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576},
- },
- {
- FieldElement{30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356},
- FieldElement{9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996},
- FieldElement{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099},
- },
- },
- {
- {
- FieldElement{-26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728},
- FieldElement{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658},
- FieldElement{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242},
- },
- {
- FieldElement{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001},
- FieldElement{-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766},
- FieldElement{18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373},
- },
- {
- FieldElement{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458},
- FieldElement{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628},
- FieldElement{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657},
- },
- {
- FieldElement{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062},
- FieldElement{25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616},
- FieldElement{31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014},
- },
- {
- FieldElement{24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383},
- FieldElement{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814},
- FieldElement{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718},
- },
- {
- FieldElement{30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417},
- FieldElement{2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222},
- FieldElement{33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444},
- },
- {
- FieldElement{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597},
- FieldElement{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970},
- FieldElement{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799},
- },
- {
- FieldElement{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647},
- FieldElement{13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511},
- FieldElement{-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032},
- },
- },
- {
- {
- FieldElement{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834},
- FieldElement{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461},
- FieldElement{29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062},
- },
- {
- FieldElement{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516},
- FieldElement{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547},
- FieldElement{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240},
- },
- {
- FieldElement{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038},
- FieldElement{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741},
- FieldElement{16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103},
- },
- {
- FieldElement{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747},
- FieldElement{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323},
- FieldElement{31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016},
- },
- {
- FieldElement{-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373},
- FieldElement{15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228},
- FieldElement{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141},
- },
- {
- FieldElement{16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399},
- FieldElement{11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831},
- FieldElement{-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376},
- },
- {
- FieldElement{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313},
- FieldElement{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958},
- FieldElement{-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577},
- },
- {
- FieldElement{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743},
- FieldElement{29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684},
- FieldElement{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476},
- },
- },
-}
diff --git a/internal/edwards25519/edwards25519.go b/internal/edwards25519/edwards25519.go
deleted file mode 100644
index 9079818..0000000
--- a/internal/edwards25519/edwards25519.go
+++ /dev/null
@@ -1,1773 +0,0 @@
-// Copyright 2013 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// Package edwards25519 implements operations in GF(2**255-19) and on an
-// Edwards curve that is isomorphic to curve25519. See
-// http://ed25519.cr.yp.to/.
-package edwards25519
-
-// This code is a port of the public domain, "ref10" implementation of ed25519
-// from SUPERCOP.
-
-// FieldElement represents an element of the field GF(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.
-type FieldElement [10]int32
-
-var zero FieldElement
-
-func FeZero(fe *FieldElement) {
- copy(fe[:], zero[:])
-}
-
-func FeOne(fe *FieldElement) {
- FeZero(fe)
- fe[0] = 1
-}
-
-func FeAdd(dst, a, b *FieldElement) {
- dst[0] = a[0] + b[0]
- dst[1] = a[1] + b[1]
- dst[2] = a[2] + b[2]
- dst[3] = a[3] + b[3]
- dst[4] = a[4] + b[4]
- dst[5] = a[5] + b[5]
- dst[6] = a[6] + b[6]
- dst[7] = a[7] + b[7]
- dst[8] = a[8] + b[8]
- dst[9] = a[9] + b[9]
-}
-
-func FeSub(dst, a, b *FieldElement) {
- dst[0] = a[0] - b[0]
- dst[1] = a[1] - b[1]
- dst[2] = a[2] - b[2]
- dst[3] = a[3] - b[3]
- dst[4] = a[4] - b[4]
- dst[5] = a[5] - b[5]
- dst[6] = a[6] - b[6]
- dst[7] = a[7] - b[7]
- dst[8] = a[8] - b[8]
- dst[9] = a[9] - b[9]
-}
-
-func FeCopy(dst, src *FieldElement) {
- copy(dst[:], src[:])
-}
-
-// Replace (f,g) with (g,g) if b == 1;
-// replace (f,g) with (f,g) if b == 0.
-//
-// Preconditions: b in {0,1}.
-func FeCMove(f, g *FieldElement, b int32) {
- b = -b
- f[0] ^= b & (f[0] ^ g[0])
- f[1] ^= b & (f[1] ^ g[1])
- f[2] ^= b & (f[2] ^ g[2])
- f[3] ^= b & (f[3] ^ g[3])
- f[4] ^= b & (f[4] ^ g[4])
- f[5] ^= b & (f[5] ^ g[5])
- f[6] ^= b & (f[6] ^ g[6])
- f[7] ^= b & (f[7] ^ g[7])
- f[8] ^= b & (f[8] ^ g[8])
- f[9] ^= b & (f[9] ^ g[9])
-}
-
-func load3(in []byte) int64 {
- var r int64
- r = int64(in[0])
- r |= int64(in[1]) << 8
- r |= int64(in[2]) << 16
- return r
-}
-
-func load4(in []byte) int64 {
- var r int64
- r = int64(in[0])
- r |= int64(in[1]) << 8
- r |= int64(in[2]) << 16
- r |= int64(in[3]) << 24
- return r
-}
-
-func FeFromBytes(dst *FieldElement, src *[32]byte) {
- h0 := load4(src[:])
- h1 := load3(src[4:]) << 6
- h2 := load3(src[7:]) << 5
- h3 := load3(src[10:]) << 3
- h4 := load3(src[13:]) << 2
- h5 := load4(src[16:])
- h6 := load3(src[20:]) << 7
- h7 := load3(src[23:]) << 5
- h8 := load3(src[26:]) << 4
- h9 := (load3(src[29:]) & 8388607) << 2
-
- FeCombine(dst, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-// FeToBytes marshals h to s.
-// Preconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Write p=2^255-19; q=floor(h/p).
-// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
-//
-// Proof:
-// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
-// Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
-//
-// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
-// Then 0<y<1.
-//
-// Write r=h-pq.
-// Have 0<=r<=p-1=2^255-20.
-// Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
-//
-// Write x=r+19(2^-255)r+y.
-// Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
-//
-// Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
-// so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
-func FeToBytes(s *[32]byte, h *FieldElement) {
- var carry [10]int32
-
- q := (19*h[9] + (1 << 24)) >> 25
- q = (h[0] + q) >> 26
- q = (h[1] + q) >> 25
- q = (h[2] + q) >> 26
- q = (h[3] + q) >> 25
- q = (h[4] + q) >> 26
- q = (h[5] + q) >> 25
- q = (h[6] + q) >> 26
- q = (h[7] + q) >> 25
- q = (h[8] + q) >> 26
- q = (h[9] + q) >> 25
-
- // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
- h[0] += 19 * q
- // Goal: Output h-2^255 q, which is between 0 and 2^255-20.
-
- carry[0] = h[0] >> 26
- h[1] += carry[0]
- h[0] -= carry[0] << 26
- carry[1] = h[1] >> 25
- h[2] += carry[1]
- h[1] -= carry[1] << 25
- carry[2] = h[2] >> 26
- h[3] += carry[2]
- h[2] -= carry[2] << 26
- carry[3] = h[3] >> 25
- h[4] += carry[3]
- h[3] -= carry[3] << 25
- carry[4] = h[4] >> 26
- h[5] += carry[4]
- h[4] -= carry[4] << 26
- carry[5] = h[5] >> 25
- h[6] += carry[5]
- h[5] -= carry[5] << 25
- carry[6] = h[6] >> 26
- h[7] += carry[6]
- h[6] -= carry[6] << 26
- carry[7] = h[7] >> 25
- h[8] += carry[7]
- h[7] -= carry[7] << 25
- carry[8] = h[8] >> 26
- h[9] += carry[8]
- h[8] -= carry[8] << 26
- carry[9] = h[9] >> 25
- h[9] -= carry[9] << 25
- // h10 = carry9
-
- // Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
- // Have h[0]+...+2^230 h[9] between 0 and 2^255-1;
- // evidently 2^255 h10-2^255 q = 0.
- // Goal: Output h[0]+...+2^230 h[9].
-
- s[0] = byte(h[0] >> 0)
- s[1] = byte(h[0] >> 8)
- s[2] = byte(h[0] >> 16)
- s[3] = byte((h[0] >> 24) | (h[1] << 2))
- s[4] = byte(h[1] >> 6)
- s[5] = byte(h[1] >> 14)
- s[6] = byte((h[1] >> 22) | (h[2] << 3))
- s[7] = byte(h[2] >> 5)
- s[8] = byte(h[2] >> 13)
- s[9] = byte((h[2] >> 21) | (h[3] << 5))
- s[10] = byte(h[3] >> 3)
- s[11] = byte(h[3] >> 11)
- s[12] = byte((h[3] >> 19) | (h[4] << 6))
- s[13] = byte(h[4] >> 2)
- s[14] = byte(h[4] >> 10)
- s[15] = byte(h[4] >> 18)
- s[16] = byte(h[5] >> 0)
- s[17] = byte(h[5] >> 8)
- s[18] = byte(h[5] >> 16)
- s[19] = byte((h[5] >> 24) | (h[6] << 1))
- s[20] = byte(h[6] >> 7)
- s[21] = byte(h[6] >> 15)
- s[22] = byte((h[6] >> 23) | (h[7] << 3))
- s[23] = byte(h[7] >> 5)
- s[24] = byte(h[7] >> 13)
- s[25] = byte((h[7] >> 21) | (h[8] << 4))
- s[26] = byte(h[8] >> 4)
- s[27] = byte(h[8] >> 12)
- s[28] = byte((h[8] >> 20) | (h[9] << 6))
- s[29] = byte(h[9] >> 2)
- s[30] = byte(h[9] >> 10)
- s[31] = byte(h[9] >> 18)
-}
-
-func FeIsNegative(f *FieldElement) byte {
- var s [32]byte
- FeToBytes(&s, f)
- return s[0] & 1
-}
-
-func FeIsNonZero(f *FieldElement) int32 {
- var s [32]byte
- FeToBytes(&s, f)
- var x uint8
- for _, b := range s {
- x |= b
- }
- x |= x >> 4
- x |= x >> 2
- x |= x >> 1
- return int32(x & 1)
-}
-
-// FeNeg sets 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.
-func FeNeg(h, f *FieldElement) {
- h[0] = -f[0]
- h[1] = -f[1]
- h[2] = -f[2]
- h[3] = -f[3]
- h[4] = -f[4]
- h[5] = -f[5]
- h[6] = -f[6]
- h[7] = -f[7]
- h[8] = -f[8]
- h[9] = -f[9]
-}
-
-func FeCombine(h *FieldElement, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
- var c0, c1, c2, c3, c4, c5, c6, c7, c8, c9 int64
-
- /*
- |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
- i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
- |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
- i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
- */
-
- c0 = (h0 + (1 << 25)) >> 26
- h1 += c0
- h0 -= c0 << 26
- c4 = (h4 + (1 << 25)) >> 26
- h5 += c4
- h4 -= c4 << 26
- /* |h0| <= 2^25 */
- /* |h4| <= 2^25 */
- /* |h1| <= 1.51*2^58 */
- /* |h5| <= 1.51*2^58 */
-
- c1 = (h1 + (1 << 24)) >> 25
- h2 += c1
- h1 -= c1 << 25
- c5 = (h5 + (1 << 24)) >> 25
- h6 += c5
- h5 -= c5 << 25
- /* |h1| <= 2^24; from now on fits into int32 */
- /* |h5| <= 2^24; from now on fits into int32 */
- /* |h2| <= 1.21*2^59 */
- /* |h6| <= 1.21*2^59 */
-
- c2 = (h2 + (1 << 25)) >> 26
- h3 += c2
- h2 -= c2 << 26
- c6 = (h6 + (1 << 25)) >> 26
- h7 += c6
- h6 -= c6 << 26
- /* |h2| <= 2^25; from now on fits into int32 unchanged */
- /* |h6| <= 2^25; from now on fits into int32 unchanged */
- /* |h3| <= 1.51*2^58 */
- /* |h7| <= 1.51*2^58 */
-
- c3 = (h3 + (1 << 24)) >> 25
- h4 += c3
- h3 -= c3 << 25
- c7 = (h7 + (1 << 24)) >> 25
- h8 += c7
- h7 -= c7 << 25
- /* |h3| <= 2^24; from now on fits into int32 unchanged */
- /* |h7| <= 2^24; from now on fits into int32 unchanged */
- /* |h4| <= 1.52*2^33 */
- /* |h8| <= 1.52*2^33 */
-
- c4 = (h4 + (1 << 25)) >> 26
- h5 += c4
- h4 -= c4 << 26
- c8 = (h8 + (1 << 25)) >> 26
- h9 += c8
- h8 -= c8 << 26
- /* |h4| <= 2^25; from now on fits into int32 unchanged */
- /* |h8| <= 2^25; from now on fits into int32 unchanged */
- /* |h5| <= 1.01*2^24 */
- /* |h9| <= 1.51*2^58 */
-
- c9 = (h9 + (1 << 24)) >> 25
- h0 += c9 * 19
- h9 -= c9 << 25
- /* |h9| <= 2^24; from now on fits into int32 unchanged */
- /* |h0| <= 1.8*2^37 */
-
- c0 = (h0 + (1 << 25)) >> 26
- h1 += c0
- h0 -= c0 << 26
- /* |h0| <= 2^25; from now on fits into int32 unchanged */
- /* |h1| <= 1.01*2^24 */
-
- h[0] = int32(h0)
- h[1] = int32(h1)
- h[2] = int32(h2)
- h[3] = int32(h3)
- h[4] = int32(h4)
- h[5] = int32(h5)
- h[6] = int32(h6)
- h[7] = int32(h7)
- h[8] = int32(h8)
- h[9] = int32(h9)
-}
-
-// FeMul calculates h = f * g
-// Can overlap h with f or g.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-// |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Notes on implementation strategy:
-//
-// Using schoolbook multiplication.
-// Karatsuba would save a little in some cost models.
-//
-// Most multiplications by 2 and 19 are 32-bit precomputations;
-// cheaper than 64-bit postcomputations.
-//
-// There is one remaining multiplication by 19 in the carry chain;
-// one *19 precomputation can be merged into this,
-// but the resulting data flow is considerably less clean.
-//
-// There are 12 carries below.
-// 10 of them are 2-way parallelizable and vectorizable.
-// Can get away with 11 carries, but then data flow is much deeper.
-//
-// With tighter constraints on inputs can squeeze carries into int32.
-func FeMul(h, f, g *FieldElement) {
- f0 := int64(f[0])
- f1 := int64(f[1])
- f2 := int64(f[2])
- f3 := int64(f[3])
- f4 := int64(f[4])
- f5 := int64(f[5])
- f6 := int64(f[6])
- f7 := int64(f[7])
- f8 := int64(f[8])
- f9 := int64(f[9])
-
- f1_2 := int64(2 * f[1])
- f3_2 := int64(2 * f[3])
- f5_2 := int64(2 * f[5])
- f7_2 := int64(2 * f[7])
- f9_2 := int64(2 * f[9])
-
- g0 := int64(g[0])
- g1 := int64(g[1])
- g2 := int64(g[2])
- g3 := int64(g[3])
- g4 := int64(g[4])
- g5 := int64(g[5])
- g6 := int64(g[6])
- g7 := int64(g[7])
- g8 := int64(g[8])
- g9 := int64(g[9])
-
- g1_19 := int64(19 * g[1]) /* 1.4*2^29 */
- g2_19 := int64(19 * g[2]) /* 1.4*2^30; still ok */
- g3_19 := int64(19 * g[3])
- g4_19 := int64(19 * g[4])
- g5_19 := int64(19 * g[5])
- g6_19 := int64(19 * g[6])
- g7_19 := int64(19 * g[7])
- g8_19 := int64(19 * g[8])
- g9_19 := int64(19 * g[9])
-
- h0 := f0*g0 + f1_2*g9_19 + f2*g8_19 + f3_2*g7_19 + f4*g6_19 + f5_2*g5_19 + f6*g4_19 + f7_2*g3_19 + f8*g2_19 + f9_2*g1_19
- h1 := f0*g1 + f1*g0 + f2*g9_19 + f3*g8_19 + f4*g7_19 + f5*g6_19 + f6*g5_19 + f7*g4_19 + f8*g3_19 + f9*g2_19
- h2 := f0*g2 + f1_2*g1 + f2*g0 + f3_2*g9_19 + f4*g8_19 + f5_2*g7_19 + f6*g6_19 + f7_2*g5_19 + f8*g4_19 + f9_2*g3_19
- h3 := f0*g3 + f1*g2 + f2*g1 + f3*g0 + f4*g9_19 + f5*g8_19 + f6*g7_19 + f7*g6_19 + f8*g5_19 + f9*g4_19
- h4 := f0*g4 + f1_2*g3 + f2*g2 + f3_2*g1 + f4*g0 + f5_2*g9_19 + f6*g8_19 + f7_2*g7_19 + f8*g6_19 + f9_2*g5_19
- h5 := f0*g5 + f1*g4 + f2*g3 + f3*g2 + f4*g1 + f5*g0 + f6*g9_19 + f7*g8_19 + f8*g7_19 + f9*g6_19
- h6 := f0*g6 + f1_2*g5 + f2*g4 + f3_2*g3 + f4*g2 + f5_2*g1 + f6*g0 + f7_2*g9_19 + f8*g8_19 + f9_2*g7_19
- h7 := f0*g7 + f1*g6 + f2*g5 + f3*g4 + f4*g3 + f5*g2 + f6*g1 + f7*g0 + f8*g9_19 + f9*g8_19
- h8 := f0*g8 + f1_2*g7 + f2*g6 + f3_2*g5 + f4*g4 + f5_2*g3 + f6*g2 + f7_2*g1 + f8*g0 + f9_2*g9_19
- h9 := f0*g9 + f1*g8 + f2*g7 + f3*g6 + f4*g5 + f5*g4 + f6*g3 + f7*g2 + f8*g1 + f9*g0
-
- FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-func feSquare(f *FieldElement) (h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
- f0 := int64(f[0])
- f1 := int64(f[1])
- f2 := int64(f[2])
- f3 := int64(f[3])
- f4 := int64(f[4])
- f5 := int64(f[5])
- f6 := int64(f[6])
- f7 := int64(f[7])
- f8 := int64(f[8])
- f9 := int64(f[9])
- f0_2 := int64(2 * f[0])
- f1_2 := int64(2 * f[1])
- f2_2 := int64(2 * f[2])
- f3_2 := int64(2 * f[3])
- f4_2 := int64(2 * f[4])
- f5_2 := int64(2 * f[5])
- f6_2 := int64(2 * f[6])
- f7_2 := int64(2 * f[7])
- f5_38 := 38 * f5 // 1.31*2^30
- f6_19 := 19 * f6 // 1.31*2^30
- f7_38 := 38 * f7 // 1.31*2^30
- f8_19 := 19 * f8 // 1.31*2^30
- f9_38 := 38 * f9 // 1.31*2^30
-
- h0 = f0*f0 + f1_2*f9_38 + f2_2*f8_19 + f3_2*f7_38 + f4_2*f6_19 + f5*f5_38
- h1 = f0_2*f1 + f2*f9_38 + f3_2*f8_19 + f4*f7_38 + f5_2*f6_19
- h2 = f0_2*f2 + f1_2*f1 + f3_2*f9_38 + f4_2*f8_19 + f5_2*f7_38 + f6*f6_19
- h3 = f0_2*f3 + f1_2*f2 + f4*f9_38 + f5_2*f8_19 + f6*f7_38
- h4 = f0_2*f4 + f1_2*f3_2 + f2*f2 + f5_2*f9_38 + f6_2*f8_19 + f7*f7_38
- h5 = f0_2*f5 + f1_2*f4 + f2_2*f3 + f6*f9_38 + f7_2*f8_19
- h6 = f0_2*f6 + f1_2*f5_2 + f2_2*f4 + f3_2*f3 + f7_2*f9_38 + f8*f8_19
- h7 = f0_2*f7 + f1_2*f6 + f2_2*f5 + f3_2*f4 + f8*f9_38
- h8 = f0_2*f8 + f1_2*f7_2 + f2_2*f6 + f3_2*f5_2 + f4*f4 + f9*f9_38
- h9 = f0_2*f9 + f1_2*f8 + f2_2*f7 + f3_2*f6 + f4_2*f5
-
- return
-}
-
-// FeSquare calculates h = f*f. Can overlap h with f.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-func FeSquare(h, f *FieldElement) {
- h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
- FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-// FeSquare2 sets 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.
-func FeSquare2(h, f *FieldElement) {
- h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
-
- h0 += h0
- h1 += h1
- h2 += h2
- h3 += h3
- h4 += h4
- h5 += h5
- h6 += h6
- h7 += h7
- h8 += h8
- h9 += h9
-
- FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-func FeInvert(out, z *FieldElement) {
- var t0, t1, t2, t3 FieldElement
- var i int
-
- FeSquare(&t0, z) // 2^1
- FeSquare(&t1, &t0) // 2^2
- for i = 1; i < 2; i++ { // 2^3
- FeSquare(&t1, &t1)
- }
- FeMul(&t1, z, &t1) // 2^3 + 2^0
- FeMul(&t0, &t0, &t1) // 2^3 + 2^1 + 2^0
- FeSquare(&t2, &t0) // 2^4 + 2^2 + 2^1
- FeMul(&t1, &t1, &t2) // 2^4 + 2^3 + 2^2 + 2^1 + 2^0
- FeSquare(&t2, &t1) // 5,4,3,2,1
- for i = 1; i < 5; i++ { // 9,8,7,6,5
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
- FeSquare(&t2, &t1) // 10..1
- for i = 1; i < 10; i++ { // 19..10
- FeSquare(&t2, &t2)
- }
- FeMul(&t2, &t2, &t1) // 19..0
- FeSquare(&t3, &t2) // 20..1
- for i = 1; i < 20; i++ { // 39..20
- FeSquare(&t3, &t3)
- }
- FeMul(&t2, &t3, &t2) // 39..0
- FeSquare(&t2, &t2) // 40..1
- for i = 1; i < 10; i++ { // 49..10
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1) // 49..0
- FeSquare(&t2, &t1) // 50..1
- for i = 1; i < 50; i++ { // 99..50
- FeSquare(&t2, &t2)
- }
- FeMul(&t2, &t2, &t1) // 99..0
- FeSquare(&t3, &t2) // 100..1
- for i = 1; i < 100; i++ { // 199..100
- FeSquare(&t3, &t3)
- }
- FeMul(&t2, &t3, &t2) // 199..0
- FeSquare(&t2, &t2) // 200..1
- for i = 1; i < 50; i++ { // 249..50
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1) // 249..0
- FeSquare(&t1, &t1) // 250..1
- for i = 1; i < 5; i++ { // 254..5
- FeSquare(&t1, &t1)
- }
- FeMul(out, &t1, &t0) // 254..5,3,1,0
-}
-
-func fePow22523(out, z *FieldElement) {
- var t0, t1, t2 FieldElement
- var i int
-
- FeSquare(&t0, z)
- for i = 1; i < 1; i++ {
- FeSquare(&t0, &t0)
- }
- FeSquare(&t1, &t0)
- for i = 1; i < 2; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t1, z, &t1)
- FeMul(&t0, &t0, &t1)
- FeSquare(&t0, &t0)
- for i = 1; i < 1; i++ {
- FeSquare(&t0, &t0)
- }
- FeMul(&t0, &t1, &t0)
- FeSquare(&t1, &t0)
- for i = 1; i < 5; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t0, &t1, &t0)
- FeSquare(&t1, &t0)
- for i = 1; i < 10; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t1, &t1, &t0)
- FeSquare(&t2, &t1)
- for i = 1; i < 20; i++ {
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1)
- FeSquare(&t1, &t1)
- for i = 1; i < 10; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t0, &t1, &t0)
- FeSquare(&t1, &t0)
- for i = 1; i < 50; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t1, &t1, &t0)
- FeSquare(&t2, &t1)
- for i = 1; i < 100; i++ {
- FeSquare(&t2, &t2)
- }
- FeMul(&t1, &t2, &t1)
- FeSquare(&t1, &t1)
- for i = 1; i < 50; i++ {
- FeSquare(&t1, &t1)
- }
- FeMul(&t0, &t1, &t0)
- FeSquare(&t0, &t0)
- for i = 1; i < 2; i++ {
- FeSquare(&t0, &t0)
- }
- FeMul(out, &t0, z)
-}
-
-// Group elements are members of the elliptic curve -x^2 + y^2 = 1 + d * x^2 *
-// y^2 where d = -121665/121666.
-//
-// Several representations are used:
-// ProjectiveGroupElement: (X:Y:Z) satisfying x=X/Z, y=Y/Z
-// ExtendedGroupElement: (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
-// CompletedGroupElement: ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
-// PreComputedGroupElement: (y+x,y-x,2dxy)
-
-type ProjectiveGroupElement struct {
- X, Y, Z FieldElement
-}
-
-type ExtendedGroupElement struct {
- X, Y, Z, T FieldElement
-}
-
-type CompletedGroupElement struct {
- X, Y, Z, T FieldElement
-}
-
-type PreComputedGroupElement struct {
- yPlusX, yMinusX, xy2d FieldElement
-}
-
-type CachedGroupElement struct {
- yPlusX, yMinusX, Z, T2d FieldElement
-}
-
-func (p *ProjectiveGroupElement) Zero() {
- FeZero(&p.X)
- FeOne(&p.Y)
- FeOne(&p.Z)
-}
-
-func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement) {
- var t0 FieldElement
-
- FeSquare(&r.X, &p.X)
- FeSquare(&r.Z, &p.Y)
- FeSquare2(&r.T, &p.Z)
- FeAdd(&r.Y, &p.X, &p.Y)
- FeSquare(&t0, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.X)
- FeSub(&r.Z, &r.Z, &r.X)
- FeSub(&r.X, &t0, &r.Y)
- FeSub(&r.T, &r.T, &r.Z)
-}
-
-func (p *ProjectiveGroupElement) ToBytes(s *[32]byte) {
- var recip, x, y FieldElement
-
- FeInvert(&recip, &p.Z)
- FeMul(&x, &p.X, &recip)
- FeMul(&y, &p.Y, &recip)
- FeToBytes(s, &y)
- s[31] ^= FeIsNegative(&x) << 7
-}
-
-func (p *ExtendedGroupElement) Zero() {
- FeZero(&p.X)
- FeOne(&p.Y)
- FeOne(&p.Z)
- FeZero(&p.T)
-}
-
-func (p *ExtendedGroupElement) Double(r *CompletedGroupElement) {
- var q ProjectiveGroupElement
- p.ToProjective(&q)
- q.Double(r)
-}
-
-func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement) {
- FeAdd(&r.yPlusX, &p.Y, &p.X)
- FeSub(&r.yMinusX, &p.Y, &p.X)
- FeCopy(&r.Z, &p.Z)
- FeMul(&r.T2d, &p.T, &d2)
-}
-
-func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement) {
- FeCopy(&r.X, &p.X)
- FeCopy(&r.Y, &p.Y)
- FeCopy(&r.Z, &p.Z)
-}
-
-func (p *ExtendedGroupElement) ToBytes(s *[32]byte) {
- var recip, x, y FieldElement
-
- FeInvert(&recip, &p.Z)
- FeMul(&x, &p.X, &recip)
- FeMul(&y, &p.Y, &recip)
- FeToBytes(s, &y)
- s[31] ^= FeIsNegative(&x) << 7
-}
-
-func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool {
- var u, v, v3, vxx, check FieldElement
-
- FeFromBytes(&p.Y, s)
- FeOne(&p.Z)
- FeSquare(&u, &p.Y)
- FeMul(&v, &u, &d)
- FeSub(&u, &u, &p.Z) // y = y^2-1
- FeAdd(&v, &v, &p.Z) // v = dy^2+1
-
- FeSquare(&v3, &v)
- FeMul(&v3, &v3, &v) // v3 = v^3
- FeSquare(&p.X, &v3)
- FeMul(&p.X, &p.X, &v)
- FeMul(&p.X, &p.X, &u) // x = uv^7
-
- fePow22523(&p.X, &p.X) // x = (uv^7)^((q-5)/8)
- FeMul(&p.X, &p.X, &v3)
- FeMul(&p.X, &p.X, &u) // x = uv^3(uv^7)^((q-5)/8)
-
- var tmpX, tmp2 [32]byte
-
- FeSquare(&vxx, &p.X)
- FeMul(&vxx, &vxx, &v)
- FeSub(&check, &vxx, &u) // vx^2-u
- if FeIsNonZero(&check) == 1 {
- FeAdd(&check, &vxx, &u) // vx^2+u
- if FeIsNonZero(&check) == 1 {
- return false
- }
- FeMul(&p.X, &p.X, &SqrtM1)
-
- FeToBytes(&tmpX, &p.X)
- for i, v := range tmpX {
- tmp2[31-i] = v
- }
- }
-
- if FeIsNegative(&p.X) != (s[31] >> 7) {
- FeNeg(&p.X, &p.X)
- }
-
- FeMul(&p.T, &p.X, &p.Y)
- return true
-}
-
-func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement) {
- FeMul(&r.X, &p.X, &p.T)
- FeMul(&r.Y, &p.Y, &p.Z)
- FeMul(&r.Z, &p.Z, &p.T)
-}
-
-func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement) {
- FeMul(&r.X, &p.X, &p.T)
- FeMul(&r.Y, &p.Y, &p.Z)
- FeMul(&r.Z, &p.Z, &p.T)
- FeMul(&r.T, &p.X, &p.Y)
-}
-
-func (p *PreComputedGroupElement) Zero() {
- FeOne(&p.yPlusX)
- FeOne(&p.yMinusX)
- FeZero(&p.xy2d)
-}
-
-func geAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
- var t0 FieldElement
-
- FeAdd(&r.X, &p.Y, &p.X)
- FeSub(&r.Y, &p.Y, &p.X)
- FeMul(&r.Z, &r.X, &q.yPlusX)
- FeMul(&r.Y, &r.Y, &q.yMinusX)
- FeMul(&r.T, &q.T2d, &p.T)
- FeMul(&r.X, &p.Z, &q.Z)
- FeAdd(&t0, &r.X, &r.X)
- FeSub(&r.X, &r.Z, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.Y)
- FeAdd(&r.Z, &t0, &r.T)
- FeSub(&r.T, &t0, &r.T)
-}
-
-func geSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
- var t0 FieldElement
-
- FeAdd(&r.X, &p.Y, &p.X)
- FeSub(&r.Y, &p.Y, &p.X)
- FeMul(&r.Z, &r.X, &q.yMinusX)
- FeMul(&r.Y, &r.Y, &q.yPlusX)
- FeMul(&r.T, &q.T2d, &p.T)
- FeMul(&r.X, &p.Z, &q.Z)
- FeAdd(&t0, &r.X, &r.X)
- FeSub(&r.X, &r.Z, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.Y)
- FeSub(&r.Z, &t0, &r.T)
- FeAdd(&r.T, &t0, &r.T)
-}
-
-func geMixedAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
- var t0 FieldElement
-
- FeAdd(&r.X, &p.Y, &p.X)
- FeSub(&r.Y, &p.Y, &p.X)
- FeMul(&r.Z, &r.X, &q.yPlusX)
- FeMul(&r.Y, &r.Y, &q.yMinusX)
- FeMul(&r.T, &q.xy2d, &p.T)
- FeAdd(&t0, &p.Z, &p.Z)
- FeSub(&r.X, &r.Z, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.Y)
- FeAdd(&r.Z, &t0, &r.T)
- FeSub(&r.T, &t0, &r.T)
-}
-
-func geMixedSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
- var t0 FieldElement
-
- FeAdd(&r.X, &p.Y, &p.X)
- FeSub(&r.Y, &p.Y, &p.X)
- FeMul(&r.Z, &r.X, &q.yMinusX)
- FeMul(&r.Y, &r.Y, &q.yPlusX)
- FeMul(&r.T, &q.xy2d, &p.T)
- FeAdd(&t0, &p.Z, &p.Z)
- FeSub(&r.X, &r.Z, &r.Y)
- FeAdd(&r.Y, &r.Z, &r.Y)
- FeSub(&r.Z, &t0, &r.T)
- FeAdd(&r.T, &t0, &r.T)
-}
-
-func slide(r *[256]int8, a *[32]byte) {
- for i := range r {
- r[i] = int8(1 & (a[i>>3] >> uint(i&7)))
- }
-
- for i := range r {
- if r[i] != 0 {
- for b := 1; b <= 6 && i+b < 256; b++ {
- if r[i+b] != 0 {
- if r[i]+(r[i+b]<<uint(b)) <= 15 {
- r[i] += r[i+b] << uint(b)
- r[i+b] = 0
- } else if r[i]-(r[i+b]<<uint(b)) >= -15 {
- r[i] -= r[i+b] << uint(b)
- for k := i + b; k < 256; k++ {
- if r[k] == 0 {
- r[k] = 1
- break
- }
- r[k] = 0
- }
- } else {
- break
- }
- }
- }
- }
- }
-}
-
-// GeDoubleScalarMultVartime sets 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.
-func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte) {
- var aSlide, bSlide [256]int8
- var Ai [8]CachedGroupElement // A,3A,5A,7A,9A,11A,13A,15A
- var t CompletedGroupElement
- var u, A2 ExtendedGroupElement
- var i int
-
- slide(&aSlide, a)
- slide(&bSlide, b)
-
- A.ToCached(&Ai[0])
- A.Double(&t)
- t.ToExtended(&A2)
-
- for i := 0; i < 7; i++ {
- geAdd(&t, &A2, &Ai[i])
- t.ToExtended(&u)
- u.ToCached(&Ai[i+1])
- }
-
- r.Zero()
-
- for i = 255; i >= 0; i-- {
- if aSlide[i] != 0 || bSlide[i] != 0 {
- break
- }
- }
-
- for ; i >= 0; i-- {
- r.Double(&t)
-
- if aSlide[i] > 0 {
- t.ToExtended(&u)
- geAdd(&t, &u, &Ai[aSlide[i]/2])
- } else if aSlide[i] < 0 {
- t.ToExtended(&u)
- geSub(&t, &u, &Ai[(-aSlide[i])/2])
- }
-
- if bSlide[i] > 0 {
- t.ToExtended(&u)
- geMixedAdd(&t, &u, &bi[bSlide[i]/2])
- } else if bSlide[i] < 0 {
- t.ToExtended(&u)
- geMixedSub(&t, &u, &bi[(-bSlide[i])/2])
- }
-
- t.ToProjective(r)
- }
-}
-
-// equal returns 1 if b == c and 0 otherwise.
-func equal(b, c int32) int32 {
- x := uint32(b ^ c)
- x--
- return int32(x >> 31)
-}
-
-// negative returns 1 if b < 0 and 0 otherwise.
-func negative(b int32) int32 {
- return (b >> 31) & 1
-}
-
-func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32) {
- FeCMove(&t.yPlusX, &u.yPlusX, b)
- FeCMove(&t.yMinusX, &u.yMinusX, b)
- FeCMove(&t.xy2d, &u.xy2d, b)
-}
-
-func selectPoint(t *PreComputedGroupElement, pos int32, b int32) {
- var minusT PreComputedGroupElement
- bNegative := negative(b)
- bAbs := b - (((-bNegative) & b) << 1)
-
- t.Zero()
- for i := int32(0); i < 8; i++ {
- PreComputedGroupElementCMove(t, &base[pos][i], equal(bAbs, i+1))
- }
- FeCopy(&minusT.yPlusX, &t.yMinusX)
- FeCopy(&minusT.yMinusX, &t.yPlusX)
- FeNeg(&minusT.xy2d, &t.xy2d)
- PreComputedGroupElementCMove(t, &minusT, bNegative)
-}
-
-// GeScalarMultBase computes 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
-func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte) {
- var e [64]int8
-
- for i, v := range a {
- e[2*i] = int8(v & 15)
- e[2*i+1] = int8((v >> 4) & 15)
- }
-
- // each e[i] is between 0 and 15 and e[63] is between 0 and 7.
-
- carry := int8(0)
- for i := 0; i < 63; i++ {
- e[i] += carry
- carry = (e[i] + 8) >> 4
- e[i] -= carry << 4
- }
- e[63] += carry
- // each e[i] is between -8 and 8.
-
- h.Zero()
- var t PreComputedGroupElement
- var r CompletedGroupElement
- for i := int32(1); i < 64; i += 2 {
- selectPoint(&t, i/2, int32(e[i]))
- geMixedAdd(&r, h, &t)
- r.ToExtended(h)
- }
-
- var s ProjectiveGroupElement
-
- h.Double(&r)
- r.ToProjective(&s)
- s.Double(&r)
- r.ToProjective(&s)
- s.Double(&r)
- r.ToProjective(&s)
- s.Double(&r)
- r.ToExtended(h)
-
- for i := int32(0); i < 64; i += 2 {
- selectPoint(&t, i/2, int32(e[i]))
- geMixedAdd(&r, h, &t)
- r.ToExtended(h)
- }
-}
-
-// The scalars are GF(2^252 + 27742317777372353535851937790883648493).
-
-// 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.
-func ScMulAdd(s, a, b, c *[32]byte) {
- a0 := 2097151 & load3(a[:])
- a1 := 2097151 & (load4(a[2:]) >> 5)
- a2 := 2097151 & (load3(a[5:]) >> 2)
- a3 := 2097151 & (load4(a[7:]) >> 7)
- a4 := 2097151 & (load4(a[10:]) >> 4)
- a5 := 2097151 & (load3(a[13:]) >> 1)
- a6 := 2097151 & (load4(a[15:]) >> 6)
- a7 := 2097151 & (load3(a[18:]) >> 3)
- a8 := 2097151 & load3(a[21:])
- a9 := 2097151 & (load4(a[23:]) >> 5)
- a10 := 2097151 & (load3(a[26:]) >> 2)
- a11 := (load4(a[28:]) >> 7)
- b0 := 2097151 & load3(b[:])
- b1 := 2097151 & (load4(b[2:]) >> 5)
- b2 := 2097151 & (load3(b[5:]) >> 2)
- b3 := 2097151 & (load4(b[7:]) >> 7)
- b4 := 2097151 & (load4(b[10:]) >> 4)
- b5 := 2097151 & (load3(b[13:]) >> 1)
- b6 := 2097151 & (load4(b[15:]) >> 6)
- b7 := 2097151 & (load3(b[18:]) >> 3)
- b8 := 2097151 & load3(b[21:])
- b9 := 2097151 & (load4(b[23:]) >> 5)
- b10 := 2097151 & (load3(b[26:]) >> 2)
- b11 := (load4(b[28:]) >> 7)
- c0 := 2097151 & load3(c[:])
- c1 := 2097151 & (load4(c[2:]) >> 5)
- c2 := 2097151 & (load3(c[5:]) >> 2)
- c3 := 2097151 & (load4(c[7:]) >> 7)
- c4 := 2097151 & (load4(c[10:]) >> 4)
- c5 := 2097151 & (load3(c[13:]) >> 1)
- c6 := 2097151 & (load4(c[15:]) >> 6)
- c7 := 2097151 & (load3(c[18:]) >> 3)
- c8 := 2097151 & load3(c[21:])
- c9 := 2097151 & (load4(c[23:]) >> 5)
- c10 := 2097151 & (load3(c[26:]) >> 2)
- c11 := (load4(c[28:]) >> 7)
- var carry [23]int64
-
- 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 := int64(0)
-
- carry[0] = (s0 + (1 << 20)) >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[2] = (s2 + (1 << 20)) >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[4] = (s4 + (1 << 20)) >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[12] = (s12 + (1 << 20)) >> 21
- s13 += carry[12]
- s12 -= carry[12] << 21
- carry[14] = (s14 + (1 << 20)) >> 21
- s15 += carry[14]
- s14 -= carry[14] << 21
- carry[16] = (s16 + (1 << 20)) >> 21
- s17 += carry[16]
- s16 -= carry[16] << 21
- carry[18] = (s18 + (1 << 20)) >> 21
- s19 += carry[18]
- s18 -= carry[18] << 21
- carry[20] = (s20 + (1 << 20)) >> 21
- s21 += carry[20]
- s20 -= carry[20] << 21
- carry[22] = (s22 + (1 << 20)) >> 21
- s23 += carry[22]
- s22 -= carry[22] << 21
-
- carry[1] = (s1 + (1 << 20)) >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[3] = (s3 + (1 << 20)) >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[5] = (s5 + (1 << 20)) >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
- carry[13] = (s13 + (1 << 20)) >> 21
- s14 += carry[13]
- s13 -= carry[13] << 21
- carry[15] = (s15 + (1 << 20)) >> 21
- s16 += carry[15]
- s15 -= carry[15] << 21
- carry[17] = (s17 + (1 << 20)) >> 21
- s18 += carry[17]
- s17 -= carry[17] << 21
- carry[19] = (s19 + (1 << 20)) >> 21
- s20 += carry[19]
- s19 -= carry[19] << 21
- carry[21] = (s21 + (1 << 20)) >> 21
- s22 += carry[21]
- s21 -= carry[21] << 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
-
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[12] = (s12 + (1 << 20)) >> 21
- s13 += carry[12]
- s12 -= carry[12] << 21
- carry[14] = (s14 + (1 << 20)) >> 21
- s15 += carry[14]
- s14 -= carry[14] << 21
- carry[16] = (s16 + (1 << 20)) >> 21
- s17 += carry[16]
- s16 -= carry[16] << 21
-
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
- carry[13] = (s13 + (1 << 20)) >> 21
- s14 += carry[13]
- s13 -= carry[13] << 21
- carry[15] = (s15 + (1 << 20)) >> 21
- s16 += carry[15]
- s15 -= carry[15] << 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
-
- carry[0] = (s0 + (1 << 20)) >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[2] = (s2 + (1 << 20)) >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[4] = (s4 + (1 << 20)) >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- carry[1] = (s1 + (1 << 20)) >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[3] = (s3 + (1 << 20)) >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[5] = (s5 + (1 << 20)) >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[11] = s11 >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- s[0] = byte(s0 >> 0)
- s[1] = byte(s0 >> 8)
- s[2] = byte((s0 >> 16) | (s1 << 5))
- s[3] = byte(s1 >> 3)
- s[4] = byte(s1 >> 11)
- s[5] = byte((s1 >> 19) | (s2 << 2))
- s[6] = byte(s2 >> 6)
- s[7] = byte((s2 >> 14) | (s3 << 7))
- s[8] = byte(s3 >> 1)
- s[9] = byte(s3 >> 9)
- s[10] = byte((s3 >> 17) | (s4 << 4))
- s[11] = byte(s4 >> 4)
- s[12] = byte(s4 >> 12)
- s[13] = byte((s4 >> 20) | (s5 << 1))
- s[14] = byte(s5 >> 7)
- s[15] = byte((s5 >> 15) | (s6 << 6))
- s[16] = byte(s6 >> 2)
- s[17] = byte(s6 >> 10)
- s[18] = byte((s6 >> 18) | (s7 << 3))
- s[19] = byte(s7 >> 5)
- s[20] = byte(s7 >> 13)
- s[21] = byte(s8 >> 0)
- s[22] = byte(s8 >> 8)
- s[23] = byte((s8 >> 16) | (s9 << 5))
- s[24] = byte(s9 >> 3)
- s[25] = byte(s9 >> 11)
- s[26] = byte((s9 >> 19) | (s10 << 2))
- s[27] = byte(s10 >> 6)
- s[28] = byte((s10 >> 14) | (s11 << 7))
- s[29] = byte(s11 >> 1)
- s[30] = byte(s11 >> 9)
- s[31] = byte(s11 >> 17)
-}
-
-// 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.
-func ScReduce(out *[32]byte, s *[64]byte) {
- s0 := 2097151 & load3(s[:])
- s1 := 2097151 & (load4(s[2:]) >> 5)
- s2 := 2097151 & (load3(s[5:]) >> 2)
- s3 := 2097151 & (load4(s[7:]) >> 7)
- s4 := 2097151 & (load4(s[10:]) >> 4)
- s5 := 2097151 & (load3(s[13:]) >> 1)
- s6 := 2097151 & (load4(s[15:]) >> 6)
- s7 := 2097151 & (load3(s[18:]) >> 3)
- s8 := 2097151 & load3(s[21:])
- s9 := 2097151 & (load4(s[23:]) >> 5)
- s10 := 2097151 & (load3(s[26:]) >> 2)
- s11 := 2097151 & (load4(s[28:]) >> 7)
- s12 := 2097151 & (load4(s[31:]) >> 4)
- s13 := 2097151 & (load3(s[34:]) >> 1)
- s14 := 2097151 & (load4(s[36:]) >> 6)
- s15 := 2097151 & (load3(s[39:]) >> 3)
- s16 := 2097151 & load3(s[42:])
- s17 := 2097151 & (load4(s[44:]) >> 5)
- s18 := 2097151 & (load3(s[47:]) >> 2)
- s19 := 2097151 & (load4(s[49:]) >> 7)
- s20 := 2097151 & (load4(s[52:]) >> 4)
- s21 := 2097151 & (load3(s[55:]) >> 1)
- s22 := 2097151 & (load4(s[57:]) >> 6)
- s23 := (load4(s[60:]) >> 3)
-
- 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
-
- var carry [17]int64
-
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[12] = (s12 + (1 << 20)) >> 21
- s13 += carry[12]
- s12 -= carry[12] << 21
- carry[14] = (s14 + (1 << 20)) >> 21
- s15 += carry[14]
- s14 -= carry[14] << 21
- carry[16] = (s16 + (1 << 20)) >> 21
- s17 += carry[16]
- s16 -= carry[16] << 21
-
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
- carry[13] = (s13 + (1 << 20)) >> 21
- s14 += carry[13]
- s13 -= carry[13] << 21
- carry[15] = (s15 + (1 << 20)) >> 21
- s16 += carry[15]
- s15 -= carry[15] << 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
-
- carry[0] = (s0 + (1 << 20)) >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[2] = (s2 + (1 << 20)) >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[4] = (s4 + (1 << 20)) >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- carry[1] = (s1 + (1 << 20)) >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[3] = (s3 + (1 << 20)) >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[5] = (s5 + (1 << 20)) >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[11] = s11 >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- out[0] = byte(s0 >> 0)
- out[1] = byte(s0 >> 8)
- out[2] = byte((s0 >> 16) | (s1 << 5))
- out[3] = byte(s1 >> 3)
- out[4] = byte(s1 >> 11)
- out[5] = byte((s1 >> 19) | (s2 << 2))
- out[6] = byte(s2 >> 6)
- out[7] = byte((s2 >> 14) | (s3 << 7))
- out[8] = byte(s3 >> 1)
- out[9] = byte(s3 >> 9)
- out[10] = byte((s3 >> 17) | (s4 << 4))
- out[11] = byte(s4 >> 4)
- out[12] = byte(s4 >> 12)
- out[13] = byte((s4 >> 20) | (s5 << 1))
- out[14] = byte(s5 >> 7)
- out[15] = byte((s5 >> 15) | (s6 << 6))
- out[16] = byte(s6 >> 2)
- out[17] = byte(s6 >> 10)
- out[18] = byte((s6 >> 18) | (s7 << 3))
- out[19] = byte(s7 >> 5)
- out[20] = byte(s7 >> 13)
- out[21] = byte(s8 >> 0)
- out[22] = byte(s8 >> 8)
- out[23] = byte((s8 >> 16) | (s9 << 5))
- out[24] = byte(s9 >> 3)
- out[25] = byte(s9 >> 11)
- out[26] = byte((s9 >> 19) | (s10 << 2))
- out[27] = byte(s10 >> 6)
- out[28] = byte((s10 >> 14) | (s11 << 7))
- out[29] = byte(s11 >> 1)
- out[30] = byte(s11 >> 9)
- out[31] = byte(s11 >> 17)
-}
diff --git a/internal/extra25519/extra25519.go b/internal/extra25519/extra25519.go
deleted file mode 100644
index 7e1d227..0000000
--- a/internal/extra25519/extra25519.go
+++ /dev/null
@@ -1,291 +0,0 @@
-// Copyright 2013 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package extra25519
-
-import "gitlab.com/yawning/obfs4.git/internal/edwards25519"
-
-// sqrtMinusAPlus2 is sqrt(-(486662+2))
-var sqrtMinusAPlus2 = edwards25519.FieldElement{
- -12222970, -8312128, -11511410, 9067497, -15300785, -241793, 25456130, 14121551, -12187136, 3972024,
-}
-
-// sqrtMinusHalf is sqrt(-1/2)
-var sqrtMinusHalf = edwards25519.FieldElement{
- -17256545, 3971863, 28865457, -1750208, 27359696, -16640980, 12573105, 1002827, -163343, 11073975,
-}
-
-// halfQMinus1Bytes is (2^255-20)/2 expressed in little endian form.
-var halfQMinus1Bytes = [32]byte{
- 0xf6, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f,
-}
-
-// feBytesLess returns one if a <= b and zero otherwise.
-func feBytesLE(a, b *[32]byte) int32 {
- equalSoFar := int32(-1)
- greater := int32(0)
-
- for i := uint(31); i < 32; i-- {
- x := int32(a[i])
- y := int32(b[i])
-
- greater = (^equalSoFar & greater) | (equalSoFar & ((x - y) >> 31))
- equalSoFar = equalSoFar & (((x ^ y) - 1) >> 31)
- }
-
- return int32(^equalSoFar & 1 & greater)
-}
-
-// UnsafeBrokenScalarBaseMult computes a curve25519 public key from a private
-// key and also a uniform representative for that public key. Note that this
-// function will fail and return false for about half of private keys.
-// See http://elligator.cr.yp.to/elligator-20130828.pdf.
-func UnsafeBrokenScalarBaseMult(publicKey, representative, privateKey *[32]byte) bool {
- var maskedPrivateKey [32]byte
- copy(maskedPrivateKey[:], privateKey[:])
-
- maskedPrivateKey[0] &= 248
- maskedPrivateKey[31] &= 127
- maskedPrivateKey[31] |= 64
-
- var A edwards25519.ExtendedGroupElement
- edwards25519.GeScalarMultBase(&A, &maskedPrivateKey)
-
- var inv1 edwards25519.FieldElement
- edwards25519.FeSub(&inv1, &A.Z, &A.Y)
- edwards25519.FeMul(&inv1, &inv1, &A.X)
- edwards25519.FeInvert(&inv1, &inv1)
-
- var t0, u edwards25519.FieldElement
- edwards25519.FeMul(&u, &inv1, &A.X)
- edwards25519.FeAdd(&t0, &A.Y, &A.Z)
- edwards25519.FeMul(&u, &u, &t0)
-
- var v edwards25519.FieldElement
- edwards25519.FeMul(&v, &t0, &inv1)
- edwards25519.FeMul(&v, &v, &A.Z)
- edwards25519.FeMul(&v, &v, &sqrtMinusAPlus2)
-
- var b edwards25519.FieldElement
- edwards25519.FeAdd(&b, &u, &edwards25519.A)
-
- var c, b3, b7, b8 edwards25519.FieldElement
- edwards25519.FeSquare(&b3, &b) // 2
- edwards25519.FeMul(&b3, &b3, &b) // 3
- edwards25519.FeSquare(&c, &b3) // 6
- edwards25519.FeMul(&b7, &c, &b) // 7
- edwards25519.FeMul(&b8, &b7, &b) // 8
- edwards25519.FeMul(&c, &b7, &u)
- q58(&c, &c)
-
- var chi edwards25519.FieldElement
- edwards25519.FeSquare(&chi, &c)
- edwards25519.FeSquare(&chi, &chi)
-
- edwards25519.FeSquare(&t0, &u)
- edwards25519.FeMul(&chi, &chi, &t0)
-
- edwards25519.FeSquare(&t0, &b7) // 14
- edwards25519.FeMul(&chi, &chi, &t0)
- edwards25519.FeNeg(&chi, &chi)
-
- var chiBytes [32]byte
- edwards25519.FeToBytes(&chiBytes, &chi)
- // chi[1] is either 0 or 0xff
- if chiBytes[1] == 0xff {
- return false
- }
-
- // Calculate r1 = sqrt(-u/(2*(u+A)))
- var r1 edwards25519.FieldElement
- edwards25519.FeMul(&r1, &c, &u)
- edwards25519.FeMul(&r1, &r1, &b3)
- edwards25519.FeMul(&r1, &r1, &sqrtMinusHalf)
-
- var maybeSqrtM1 edwards25519.FieldElement
- edwards25519.FeSquare(&t0, &r1)
- edwards25519.FeMul(&t0, &t0, &b)
- edwards25519.FeAdd(&t0, &t0, &t0)
- edwards25519.FeAdd(&t0, &t0, &u)
-
- edwards25519.FeOne(&maybeSqrtM1)
- edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
- edwards25519.FeMul(&r1, &r1, &maybeSqrtM1)
-
- // Calculate r = sqrt(-(u+A)/(2u))
- var r edwards25519.FieldElement
- edwards25519.FeSquare(&t0, &c) // 2
- edwards25519.FeMul(&t0, &t0, &c) // 3
- edwards25519.FeSquare(&t0, &t0) // 6
- edwards25519.FeMul(&r, &t0, &c) // 7
-
- edwards25519.FeSquare(&t0, &u) // 2
- edwards25519.FeMul(&t0, &t0, &u) // 3
- edwards25519.FeMul(&r, &r, &t0)
-
- edwards25519.FeSquare(&t0, &b8) // 16
- edwards25519.FeMul(&t0, &t0, &b8) // 24
- edwards25519.FeMul(&t0, &t0, &b) // 25
- edwards25519.FeMul(&r, &r, &t0)
- edwards25519.FeMul(&r, &r, &sqrtMinusHalf)
-
- edwards25519.FeSquare(&t0, &r)
- edwards25519.FeMul(&t0, &t0, &u)
- edwards25519.FeAdd(&t0, &t0, &t0)
- edwards25519.FeAdd(&t0, &t0, &b)
- edwards25519.FeOne(&maybeSqrtM1)
- edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
- edwards25519.FeMul(&r, &r, &maybeSqrtM1)
-
- var vBytes [32]byte
- edwards25519.FeToBytes(&vBytes, &v)
- vInSquareRootImage := feBytesLE(&vBytes, &halfQMinus1Bytes)
- edwards25519.FeCMove(&r, &r1, vInSquareRootImage)
-
- edwards25519.FeToBytes(publicKey, &u)
- edwards25519.FeToBytes(representative, &r)
- return true
-}
-
-// q58 calculates out = z^((p-5)/8).
-func q58(out, z *edwards25519.FieldElement) {
- var t1, t2, t3 edwards25519.FieldElement
- var i int
-
- edwards25519.FeSquare(&t1, z) // 2^1
- edwards25519.FeMul(&t1, &t1, z) // 2^1 + 2^0
- edwards25519.FeSquare(&t1, &t1) // 2^2 + 2^1
- edwards25519.FeSquare(&t2, &t1) // 2^3 + 2^2
- edwards25519.FeSquare(&t2, &t2) // 2^4 + 2^3
- edwards25519.FeMul(&t2, &t2, &t1) // 4,3,2,1
- edwards25519.FeMul(&t1, &t2, z) // 4..0
- edwards25519.FeSquare(&t2, &t1) // 5..1
- for i = 1; i < 5; i++ { // 9,8,7,6,5
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
- edwards25519.FeSquare(&t2, &t1) // 10..1
- for i = 1; i < 10; i++ { // 19..10
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t2, &t2, &t1) // 19..0
- edwards25519.FeSquare(&t3, &t2) // 20..1
- for i = 1; i < 20; i++ { // 39..20
- edwards25519.FeSquare(&t3, &t3)
- }
- edwards25519.FeMul(&t2, &t3, &t2) // 39..0
- edwards25519.FeSquare(&t2, &t2) // 40..1
- for i = 1; i < 10; i++ { // 49..10
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 49..0
- edwards25519.FeSquare(&t2, &t1) // 50..1
- for i = 1; i < 50; i++ { // 99..50
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t2, &t2, &t1) // 99..0
- edwards25519.FeSquare(&t3, &t2) // 100..1
- for i = 1; i < 100; i++ { // 199..100
- edwards25519.FeSquare(&t3, &t3)
- }
- edwards25519.FeMul(&t2, &t3, &t2) // 199..0
- edwards25519.FeSquare(&t2, &t2) // 200..1
- for i = 1; i < 50; i++ { // 249..50
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 249..0
- edwards25519.FeSquare(&t1, &t1) // 250..1
- edwards25519.FeSquare(&t1, &t1) // 251..2
- edwards25519.FeMul(out, &t1, z) // 251..2,0
-}
-
-// chi calculates out = z^((p-1)/2). The result is either 1, 0, or -1 depending
-// on whether z is a non-zero square, zero, or a non-square.
-func chi(out, z *edwards25519.FieldElement) {
- var t0, t1, t2, t3 edwards25519.FieldElement
- var i int
-
- edwards25519.FeSquare(&t0, z) // 2^1
- edwards25519.FeMul(&t1, &t0, z) // 2^1 + 2^0
- edwards25519.FeSquare(&t0, &t1) // 2^2 + 2^1
- edwards25519.FeSquare(&t2, &t0) // 2^3 + 2^2
- edwards25519.FeSquare(&t2, &t2) // 4,3
- edwards25519.FeMul(&t2, &t2, &t0) // 4,3,2,1
- edwards25519.FeMul(&t1, &t2, z) // 4..0
- edwards25519.FeSquare(&t2, &t1) // 5..1
- for i = 1; i < 5; i++ { // 9,8,7,6,5
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
- edwards25519.FeSquare(&t2, &t1) // 10..1
- for i = 1; i < 10; i++ { // 19..10
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t2, &t2, &t1) // 19..0
- edwards25519.FeSquare(&t3, &t2) // 20..1
- for i = 1; i < 20; i++ { // 39..20
- edwards25519.FeSquare(&t3, &t3)
- }
- edwards25519.FeMul(&t2, &t3, &t2) // 39..0
- edwards25519.FeSquare(&t2, &t2) // 40..1
- for i = 1; i < 10; i++ { // 49..10
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 49..0
- edwards25519.FeSquare(&t2, &t1) // 50..1
- for i = 1; i < 50; i++ { // 99..50
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t2, &t2, &t1) // 99..0
- edwards25519.FeSquare(&t3, &t2) // 100..1
- for i = 1; i < 100; i++ { // 199..100
- edwards25519.FeSquare(&t3, &t3)
- }
- edwards25519.FeMul(&t2, &t3, &t2) // 199..0
- edwards25519.FeSquare(&t2, &t2) // 200..1
- for i = 1; i < 50; i++ { // 249..50
- edwards25519.FeSquare(&t2, &t2)
- }
- edwards25519.FeMul(&t1, &t2, &t1) // 249..0
- edwards25519.FeSquare(&t1, &t1) // 250..1
- for i = 1; i < 4; i++ { // 253..4
- edwards25519.FeSquare(&t1, &t1)
- }
- edwards25519.FeMul(out, &t1, &t0) // 253..4,2,1
-}
-
-// UnsafeBrokenRepresentativeToPublicKey converts a uniform representative
-// value for a curve25519 public key, as produced by UnsafeBrokenScalarBaseMult,
-// to a curve25519 public key.
-func UnsafeBrokenRepresentativeToPublicKey(publicKey, representative *[32]byte) {
- var rr2, v, e edwards25519.FieldElement
- edwards25519.FeFromBytes(&rr2, representative)
-
- edwards25519.FeSquare2(&rr2, &rr2)
- rr2[0]++
- edwards25519.FeInvert(&rr2, &rr2)
- edwards25519.FeMul(&v, &edwards25519.A, &rr2)
- edwards25519.FeNeg(&v, &v)
-
- var v2, v3 edwards25519.FieldElement
- edwards25519.FeSquare(&v2, &v)
- edwards25519.FeMul(&v3, &v, &v2)
- edwards25519.FeAdd(&e, &v3, &v)
- edwards25519.FeMul(&v2, &v2, &edwards25519.A)
- edwards25519.FeAdd(&e, &v2, &e)
- chi(&e, &e)
- var eBytes [32]byte
- edwards25519.FeToBytes(&eBytes, &e)
- // eBytes[1] is either 0 (for e = 1) or 0xff (for e = -1)
- eIsMinus1 := int32(eBytes[1]) & 1
- var negV edwards25519.FieldElement
- edwards25519.FeNeg(&negV, &v)
- edwards25519.FeCMove(&v, &negV, eIsMinus1)
-
- edwards25519.FeZero(&v2)
- edwards25519.FeCMove(&v2, &edwards25519.A, eIsMinus1)
- edwards25519.FeSub(&v, &v, &v2)
-
- edwards25519.FeToBytes(publicKey, &v)
-}
diff --git a/internal/extra25519/extra25519_test.go b/internal/extra25519/extra25519_test.go
deleted file mode 100644
index 7cf1e97..0000000
--- a/internal/extra25519/extra25519_test.go
+++ /dev/null
@@ -1,61 +0,0 @@
-// Copyright 2013 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package extra25519
-
-import (
- "bytes"
- "crypto/rand"
- "testing"
-
- "golang.org/x/crypto/curve25519"
-)
-
-func TestElligator(t *testing.T) {
- var publicKey, publicKey2, publicKey3, representative, privateKey [32]byte
-
- for i := 0; i < 1000; i++ {
- rand.Reader.Read(privateKey[:])
-
- if !UnsafeBrokenScalarBaseMult(&publicKey, &representative, &privateKey) {
- continue
- }
- UnsafeBrokenRepresentativeToPublicKey(&publicKey2, &representative)
- if !bytes.Equal(publicKey[:], publicKey2[:]) {
- t.Fatal("The resulting public key doesn't match the initial one.")
- }
-
- curve25519.ScalarBaseMult(&publicKey3, &privateKey)
- if !bytes.Equal(publicKey[:], publicKey3[:]) {
- t.Fatal("The public key doesn't match the value that curve25519 produced.")
- }
- }
-}
-
-func BenchmarkKeyGeneration(b *testing.B) {
- var publicKey, representative, privateKey [32]byte
-
- // Find the private key that results in a point that's in the image of the map.
- for {
- rand.Reader.Read(privateKey[:])
- if UnsafeBrokenScalarBaseMult(&publicKey, &representative, &privateKey) {
- break
- }
- }
-
- b.ResetTimer()
- for i := 0; i < b.N; i++ {
- UnsafeBrokenScalarBaseMult(&publicKey, &representative, &privateKey)
- }
-}
-
-func BenchmarkMap(b *testing.B) {
- var publicKey, representative [32]byte
- rand.Reader.Read(representative[:])
-
- b.ResetTimer()
- for i := 0; i < b.N; i++ {
- UnsafeBrokenRepresentativeToPublicKey(&publicKey, &representative)
- }
-}
diff --git a/internal/x25519ell2/x25519ell2.go b/internal/x25519ell2/x25519ell2.go
new file mode 100644
index 0000000..cbf0ad6
--- /dev/null
+++ b/internal/x25519ell2/x25519ell2.go
@@ -0,0 +1,177 @@
+// Copyright (c) 2021 Yawning Angel <yawning at schwanenlied dot me>
+//
+// This program is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program. If not, see <https://www.gnu.org/licenses/>.
+
+// Package x25519ell2 implements obfuscated X25519 ECDH, via the Elligator2
+// mapping.
+package x25519ell2
+
+import (
+ "encoding/binary"
+
+ "filippo.io/edwards25519"
+ "filippo.io/edwards25519/field"
+
+ "gitlab.com/yawning/edwards25519-extra.git/elligator2"
+)
+
+// The corrected version of this that solves the implementation errors
+// present in the historical implementation by agl is derived from
+// Monocypher (CC-0 or BSD-2) by Loup Vaillant. Without their efforts
+// and prodding, this would likely have stayed broken forever.
+
+var (
+ feOne = new(field.Element).One()
+
+ feNegTwo = mustFeFromBytes([]byte{
+ 0xeb, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f,
+ })
+
+ feA = mustFeFromUint64(486662)
+
+ feSqrtM1 = mustFeFromBytes([]byte{
+ 0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4, 0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f,
+ 0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, 0x4d, 0x2b, 0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b,
+ })
+
+ // Low order point Edwards x-coordinate `sqrt((sqrt(d + 1) + 1) / d)`.
+ feLopX = mustFeFromBytes([]byte{
+ 0x4a, 0xd1, 0x45, 0xc5, 0x46, 0x46, 0xa1, 0xde, 0x38, 0xe2, 0xe5, 0x13, 0x70, 0x3c, 0x19, 0x5c,
+ 0xbb, 0x4a, 0xde, 0x38, 0x32, 0x99, 0x33, 0xe9, 0x28, 0x4a, 0x39, 0x06, 0xa0, 0xb9, 0xd5, 0x1f,
+ })
+
+ // Low order point Edwards y-coordinate `-lop_x * sqrtm1`
+ feLopY = mustFeFromBytes([]byte{
+ 0x26, 0xe8, 0x95, 0x8f, 0xc2, 0xb2, 0x27, 0xb0, 0x45, 0xc3, 0xf4, 0x89, 0xf2, 0xef, 0x98, 0xf0,
+ 0xd5, 0xdf, 0xac, 0x05, 0xd3, 0xc6, 0x33, 0x39, 0xb1, 0x38, 0x02, 0x88, 0x6d, 0x53, 0xfc, 0x05,
+ })
+)
+
+func mustFeFromBytes(b []byte) *field.Element {
+ fe, err := new(field.Element).SetBytes(b)
+ if err != nil {
+ panic("internal/x25519ell2: failed to deserialize constant: " + err.Error())
+ }
+ return fe
+}
+
+func mustFeFromUint64(x uint64) *field.Element {
+ var b [32]byte
+ binary.LittleEndian.PutUint64(b[:], x)
+ return mustFeFromBytes(b[:])
+}
+
+func selectLowOrderPoint(out, x, k *field.Element, cofactor uint8) {
+ out.Zero()
+ out.Select(k, out, int((cofactor>>1)&1)) // bit 1
+ out.Select(x, out, int((cofactor>>0)&1)) // bit 1
+ var tmp field.Element
+ tmp.Negate(out)
+ out.Select(&tmp, out, int((cofactor>>2)&1)) // bit 2
+}
+
+func scalarBaseMultDirty(privateKey *[32]byte) *field.Element {
+ // Compute clean scalar multiplication
+ scalar, err := new(edwards25519.Scalar).SetBytesWithClamping(privateKey[:])
+ if err != nil {
+ panic("internal/x25519ell2: failed to deserialize scalar: " + err.Error())
+ }
+ pk := new(edwards25519.Point).ScalarBaseMult(scalar)
+
+ // Compute low order point
+ var lopX, lopY, lopT field.Element
+ selectLowOrderPoint(&lopX, feLopX, feSqrtM1, privateKey[0])
+ selectLowOrderPoint(&lopY, feLopY, feOne, privateKey[0]+2)
+ // Z = one
+ lopT.Multiply(&lopX, &lopY)
+ lop, err := new(edwards25519.Point).SetExtendedCoordinates(&lopX, &lopY, feOne, &lopT)
+ if err != nil {
+ panic("interal/x25519ell2: failed to create edwards point from x, y: " + err.Error())
+ }
+
+ // Add low order point to the public key
+ pk.Add(pk, lop)
+
+ // Convert to Montgomery u coordinate (we ignore the sign)
+ _, yExt, zExt, _ := pk.ExtendedCoordinates()
+ var t1, t2 field.Element
+ t1.Add(zExt, yExt)
+ t2.Subtract(zExt, yExt)
+ t2.Invert(&t2)
+ t1.Multiply(&t1, &t2)
+
+ return &t1
+}
+
+func uToRepresentative(representative *[32]byte, u *field.Element, tweak byte) bool {
+ t1 := new(field.Element).Set(u)
+
+ t2 := new(field.Element).Add(t1, feA)
+ t3 := new(field.Element).Multiply(t1, t2)
+ t3.Multiply(t3, feNegTwo)
+ if _, isSquare := t3.SqrtRatio(feOne, t3); isSquare == 1 {
+ t1.Select(t2, t1, int(tweak&1))
+ t3.Multiply(t1, t3)
+ t1.Mult32(t3, 2)
+ t2.Negate(t3)
+ tmp := t1.Bytes()
+ t3.Select(t2, t3, int(tmp[0]&1))
+ copy(representative[:], t3.Bytes())
+
+ // Pad with two random bits
+ representative[31] |= tweak & 0xc0
+
+ return true
+ }
+
+ return false
+}
+
+// ScalarBaseMult computes a curve25519 public key from a private
+// key and also a uniform representative for that public key.
+// Note that this function will fail and return false for about
+// half of private keys.
+//
+// WARNING: The underlying scalar multiply explicitly does not clear
+// the cofactor, and thus the public keys will be different from
+// those produced by normal implementations.
+func ScalarBaseMult(publicKey, representative, privateKey *[32]byte, tweak byte) bool {
+ u := scalarBaseMultDirty(privateKey)
+ if !uToRepresentative(representative, u, tweak) {
+ // No representative.
+ return false
+ }
+ copy(publicKey[:], u.Bytes())
+ return true
+}
+
+// RepresentativeToPublicKey converts a uniform representative value for
+// a curve25519 public key, as produced by ScalarBaseMult, to a curve25519
+// public key.
+func RepresentativeToPublicKey(publicKey, representative *[32]byte) {
+ // Representatives are encoded in 254 bits.
+ var clamped [32]byte
+ copy(clamped[:], representative[:])
+ clamped[31] &= 63
+
+ var fe field.Element
+ if _, err := fe.SetBytes(clamped[:]); err != nil {
+ // Panic is fine, the only way this fails is if the representative
+ // is not 32-bytes.
+ panic("internal/x25519ell2: failed to deserialize representative: " + err.Error())
+ }
+ u, _ := elligator2.MontgomeryFlavor(&fe)
+ copy(publicKey[:], u.Bytes())
+}
diff --git a/internal/x25519ell2/x25519ell2_test.go b/internal/x25519ell2/x25519ell2_test.go
new file mode 100644
index 0000000..4598538
--- /dev/null
+++ b/internal/x25519ell2/x25519ell2_test.go
@@ -0,0 +1,153 @@
+// Copyright (c) 2021 Yawning Angel <yawning at schwanenlied dot me>
+//
+// This program is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program. If not, see <https://www.gnu.org/licenses/>.
+
+package x25519ell2
+
+import (
+ "bytes"
+ "crypto/rand"
+ "testing"
+
+ "filippo.io/edwards25519/field"
+ "golang.org/x/crypto/curve25519"
+)
+
+func TestX25519Ell2(t *testing.T) {
+ t.Run("Constants", testConstants)
+ t.Run("KeyExchage", testKeyExchange)
+}
+
+func testConstants(t *testing.T) {
+ // While the constants were calculated and serialized with a known
+ // correct implementation of the field arithmetic, re-derive them
+ // to be sure.
+
+ t.Run("NegTwo", func(t *testing.T) {
+ expected := new(field.Element).Add(feOne, feOne)
+ expected.Negate(expected)
+
+ if expected.Equal(feNegTwo) != 1 {
+ t.Fatalf("invalid value for -2: %x", feNegTwo.Bytes())
+ }
+ })
+
+ t.Run("LopX", func(t *testing.T) {
+ // d = -121665/121666
+ d := mustFeFromUint64(121666)
+ d.Invert(d)
+ d.Multiply(d, mustFeFromUint64(121665))
+ d.Negate(d)
+
+ // lop_x = sqrt((sqrt(d + 1) + 1) / d)
+ expected := new(field.Element).Add(d, feOne)
+ expected.Invert(expected)
+ expected.SqrtRatio(feOne, expected)
+ expected.Add(expected, feOne)
+ expected.SqrtRatio(expected, d)
+
+ if expected.Equal(feLopX) != 1 {
+ t.Fatalf("invalid value for low order point X: %x", feLopX.Bytes())
+ }
+ })
+
+ t.Run("LopY", func(t *testing.T) {
+ // lop_y = -lop_x * sqrtm1
+ expected := new(field.Element).Negate(feLopX)
+ expected.Multiply(expected, feSqrtM1)
+
+ if expected.Equal(feLopY) != 1 {
+ t.Fatalf("invalid value for low order point Y: %x", feLopY.Bytes())
+ }
+ })
+}
+
+func testKeyExchange(t *testing.T) {
+ var randSk [32]byte
+ _, _ = rand.Read(randSk[:])
+
+ var good, bad int
+ for i := 0; i < 1000; i++ {
+ var (
+ publicKey, privateKey, representative [32]byte
+ publicKeyClean [32]byte
+ tweak [1]byte
+ )
+ _, _ = rand.Read(privateKey[:])
+ _, _ = rand.Read(tweak[:])
+
+ // This won't match the public key from the Elligator2-ed scalar
+ // basepoint multiply, but we want to ensure that the public keys
+ // we do happen to generate are interoperable (otherwise something
+ // is badly broken).
+ curve25519.ScalarBaseMult(&publicKeyClean, &privateKey)
+
+ if !ScalarBaseMult(&publicKey, &representative, &privateKey, tweak[0]) {
+ t.Logf("bad: %x", privateKey)
+ bad++
+ continue
+ }
+ t.Logf("good: %x", privateKey)
+
+ t.Logf("publicKey: %x, repr: %x", publicKey, representative)
+
+ var shared, sharedRep, sharedClean, pkFromRep [32]byte
+ RepresentativeToPublicKey(&pkFromRep, &representative)
+ if !bytes.Equal(pkFromRep[:], publicKey[:]) {
+ t.Fatalf("public key mismatch(repr): expected %x, actual: %x", publicKey, pkFromRep)
+ }
+
+ curve25519.ScalarMult(&sharedClean, &randSk, &publicKeyClean) //nolint: staticcheck
+ curve25519.ScalarMult(&shared, &randSk, &publicKey) //nolint: staticcheck
+ curve25519.ScalarMult(&sharedRep, &randSk, &pkFromRep) //nolint: staticcheck
+
+ if !bytes.Equal(shared[:], sharedRep[:]) {
+ t.Fatalf("shared secret mismatch: expected %x, actual: %x", shared, sharedRep)
+ }
+ if !bytes.Equal(shared[:], sharedClean[:]) {
+ t.Fatalf("shared secret mismatch(clean): expected %x, actual: %x", shared, sharedClean)
+ }
+
+ good++
+ }
+
+ t.Logf("good: %d, bad: %d", good, bad)
+}
+
+func BenchmarkKeyGeneration(b *testing.B) {
+ var publicKey, representative, privateKey [32]byte
+
+ // Find the private key that results in a point that's in the image of the map.
+ for {
+ _, _ = rand.Reader.Read(privateKey[:])
+ if ScalarBaseMult(&publicKey, &representative, &privateKey, 0) {
+ break
+ }
+ }
+
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ ScalarBaseMult(&publicKey, &representative, &privateKey, 0)
+ }
+}
+
+func BenchmarkMap(b *testing.B) {
+ var publicKey, representative [32]byte
+ _, _ = rand.Reader.Read(representative[:])
+
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ RepresentativeToPublicKey(&publicKey, &representative)
+ }
+}
1
0
[obfs4/master] internal/x25519ell2: Add a canonical import path annotation
by cohosh＠torproject.org 24 Jan '22
by cohosh＠torproject.org 24 Jan '22
24 Jan '22
commit c083c6309aa0aa1e5b33e4b096e627869e09214d
Author: Yawning Angel <yawning(a)schwanenlied.me>
Date: Fri Dec 31 06:33:11 2021 +0000
internal/x25519ell2: Add a canonical import path annotation
---
internal/x25519ell2/x25519ell2.go | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/internal/x25519ell2/x25519ell2.go b/internal/x25519ell2/x25519ell2.go
index cbf0ad6..6247da6 100644
--- a/internal/x25519ell2/x25519ell2.go
+++ b/internal/x25519ell2/x25519ell2.go
@@ -15,7 +15,7 @@
// Package x25519ell2 implements obfuscated X25519 ECDH, via the Elligator2
// mapping.
-package x25519ell2
+package x25519ell2 // import "gitlab.com/yawning/obfs4.git/internal/x25519ell2"
import (
"encoding/binary"
1
0
24 Jan '22
commit 0f7ce7e653ae3a1e615587ab0f160a820186a6f2
Author: Yawning Angel <yawning(a)schwanenlied.me>
Date: Sat Jan 1 09:29:44 2022 +0000
fixup! internal/x25519ell2: Initial import
Fix a comment, no functional changes.
---
internal/x25519ell2/x25519ell2.go | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/internal/x25519ell2/x25519ell2.go b/internal/x25519ell2/x25519ell2.go
index 6247da6..c3676ed 100644
--- a/internal/x25519ell2/x25519ell2.go
+++ b/internal/x25519ell2/x25519ell2.go
@@ -76,7 +76,7 @@ func mustFeFromUint64(x uint64) *field.Element {
func selectLowOrderPoint(out, x, k *field.Element, cofactor uint8) {
out.Zero()
out.Select(k, out, int((cofactor>>1)&1)) // bit 1
- out.Select(x, out, int((cofactor>>0)&1)) // bit 1
+ out.Select(x, out, int((cofactor>>0)&1)) // bit 0
var tmp field.Element
tmp.Negate(out)
out.Select(&tmp, out, int((cofactor>>2)&1)) // bit 2
1
0