diff options
| author | Lokesh Mandvekar <lsm5@fedoraproject.org> | 2022-04-12 09:29:36 -0400 |
|---|---|---|
| committer | Lokesh Mandvekar <lsm5@fedoraproject.org> | 2022-04-12 10:24:32 -0400 |
| commit | 5e680d54e9e8b849b90047d2d87bc7664edaaa1d (patch) | |
| tree | 4f9b314d7211bd04d030f6aa6563ddd8628a60b8 /vendor/golang.org/x/crypto | |
| parent | 9822c46981226c3296b5ad7833d8937cfc3ece49 (diff) | |
| download | podman-5e680d54e9e8b849b90047d2d87bc7664edaaa1d.tar.gz podman-5e680d54e9e8b849b90047d2d87bc7664edaaa1d.tar.bz2 podman-5e680d54e9e8b849b90047d2d87bc7664edaaa1d.zip | |
Bump golang.org/x/crypto to 7b82a4e
Resolves: GHSA-8c26-wmh5-6g9v - CVE-2022-27191
Podman doesn't seem to be directly affected as the logic in question
is not called.
golang.org/x/crypto@1baeb1ce contains the actual CVE fix. Using the
latest upstream commit to also include support for SHA-2.
Signed-off-by: Lokesh Mandvekar <lsm5@fedoraproject.org>
Diffstat (limited to 'vendor/golang.org/x/crypto')
27 files changed, 567 insertions, 3837 deletions
diff --git a/vendor/golang.org/x/crypto/chacha20/chacha_s390x.go b/vendor/golang.org/x/crypto/chacha20/chacha_s390x.go index c5898db46..4652247b8 100644 --- a/vendor/golang.org/x/crypto/chacha20/chacha_s390x.go +++ b/vendor/golang.org/x/crypto/chacha20/chacha_s390x.go @@ -15,6 +15,7 @@ const bufSize = 256 // xorKeyStreamVX is an assembly implementation of XORKeyStream. It must only // be called when the vector facility is available. Implementation in asm_s390x.s. +// //go:noescape func xorKeyStreamVX(dst, src []byte, key *[8]uint32, nonce *[3]uint32, counter *uint32) diff --git a/vendor/golang.org/x/crypto/curve25519/internal/field/fe_amd64.go b/vendor/golang.org/x/crypto/curve25519/internal/field/fe_amd64.go index 44dc8e8ca..edcf163c4 100644 --- a/vendor/golang.org/x/crypto/curve25519/internal/field/fe_amd64.go +++ b/vendor/golang.org/x/crypto/curve25519/internal/field/fe_amd64.go @@ -1,13 +1,16 @@ // Code generated by command: go run fe_amd64_asm.go -out ../fe_amd64.s -stubs ../fe_amd64.go -pkg field. DO NOT EDIT. +//go:build amd64 && gc && !purego // +build amd64,gc,!purego package field // feMul sets out = a * b. It works like feMulGeneric. +// //go:noescape func feMul(out *Element, a *Element, b *Element) // feSquare sets out = a * a. It works like feSquareGeneric. +// //go:noescape func feSquare(out *Element, a *Element) diff --git a/vendor/golang.org/x/crypto/ed25519/ed25519.go b/vendor/golang.org/x/crypto/ed25519/ed25519.go index 71ad917da..a7828345f 100644 --- a/vendor/golang.org/x/crypto/ed25519/ed25519.go +++ b/vendor/golang.org/x/crypto/ed25519/ed25519.go @@ -1,13 +1,7 @@ -// Copyright 2016 The Go Authors. All rights reserved. +// Copyright 2019 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. -// In Go 1.13, the ed25519 package was promoted to the standard library as -// crypto/ed25519, and this package became a wrapper for the standard library one. -// -//go:build !go1.13 -// +build !go1.13 - // Package ed25519 implements the Ed25519 signature algorithm. See // https://ed25519.cr.yp.to/. // @@ -16,21 +10,15 @@ // representation includes a public key suffix to make multiple signing // operations with the same key more efficient. This package refers to the RFC // 8032 private key as the “seed”. +// +// Beginning with Go 1.13, the functionality of this package was moved to the +// standard library as crypto/ed25519. This package only acts as a compatibility +// wrapper. package ed25519 -// This code is a port of the public domain, “ref10” implementation of ed25519 -// from SUPERCOP. - import ( - "bytes" - "crypto" - cryptorand "crypto/rand" - "crypto/sha512" - "errors" + "crypto/ed25519" "io" - "strconv" - - "golang.org/x/crypto/ed25519/internal/edwards25519" ) const ( @@ -45,57 +33,21 @@ const ( ) // PublicKey is the type of Ed25519 public keys. -type PublicKey []byte +// +// This type is an alias for crypto/ed25519's PublicKey type. +// See the crypto/ed25519 package for the methods on this type. +type PublicKey = ed25519.PublicKey // PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer. -type PrivateKey []byte - -// Public returns the PublicKey corresponding to priv. -func (priv PrivateKey) Public() crypto.PublicKey { - publicKey := make([]byte, PublicKeySize) - copy(publicKey, priv[32:]) - return PublicKey(publicKey) -} - -// Seed returns the private key seed corresponding to priv. It is provided for -// interoperability with RFC 8032. RFC 8032's private keys correspond to seeds -// in this package. -func (priv PrivateKey) Seed() []byte { - seed := make([]byte, SeedSize) - copy(seed, priv[:32]) - return seed -} - -// Sign signs the given message with priv. -// Ed25519 performs two passes over messages to be signed and therefore cannot -// handle pre-hashed messages. Thus opts.HashFunc() must return zero to -// indicate the message hasn't been hashed. This can be achieved by passing -// crypto.Hash(0) as the value for opts. -func (priv PrivateKey) Sign(rand io.Reader, message []byte, opts crypto.SignerOpts) (signature []byte, err error) { - if opts.HashFunc() != crypto.Hash(0) { - return nil, errors.New("ed25519: cannot sign hashed message") - } - - return Sign(priv, message), nil -} +// +// This type is an alias for crypto/ed25519's PrivateKey type. +// See the crypto/ed25519 package for the methods on this type. +type PrivateKey = ed25519.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { - if rand == nil { - rand = cryptorand.Reader - } - - seed := make([]byte, SeedSize) - if _, err := io.ReadFull(rand, seed); err != nil { - return nil, nil, err - } - - privateKey := NewKeyFromSeed(seed) - publicKey := make([]byte, PublicKeySize) - copy(publicKey, privateKey[32:]) - - return publicKey, privateKey, nil + return ed25519.GenerateKey(rand) } // NewKeyFromSeed calculates a private key from a seed. It will panic if @@ -103,121 +55,17 @@ func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { // with RFC 8032. RFC 8032's private keys correspond to seeds in this // package. func NewKeyFromSeed(seed []byte) PrivateKey { - if l := len(seed); l != SeedSize { - panic("ed25519: bad seed length: " + strconv.Itoa(l)) - } - - digest := sha512.Sum512(seed) - digest[0] &= 248 - digest[31] &= 127 - digest[31] |= 64 - - var A edwards25519.ExtendedGroupElement - var hBytes [32]byte - copy(hBytes[:], digest[:]) - edwards25519.GeScalarMultBase(&A, &hBytes) - var publicKeyBytes [32]byte - A.ToBytes(&publicKeyBytes) - - privateKey := make([]byte, PrivateKeySize) - copy(privateKey, seed) - copy(privateKey[32:], publicKeyBytes[:]) - - return privateKey + return ed25519.NewKeyFromSeed(seed) } // Sign signs the message with privateKey and returns a signature. It will // panic if len(privateKey) is not PrivateKeySize. func Sign(privateKey PrivateKey, message []byte) []byte { - if l := len(privateKey); l != PrivateKeySize { - panic("ed25519: bad private key length: " + strconv.Itoa(l)) - } - - h := sha512.New() - h.Write(privateKey[:32]) - - var digest1, messageDigest, hramDigest [64]byte - var expandedSecretKey [32]byte - h.Sum(digest1[:0]) - copy(expandedSecretKey[:], digest1[:]) - expandedSecretKey[0] &= 248 - expandedSecretKey[31] &= 63 - expandedSecretKey[31] |= 64 - - h.Reset() - h.Write(digest1[32:]) - h.Write(message) - h.Sum(messageDigest[:0]) - - var messageDigestReduced [32]byte - edwards25519.ScReduce(&messageDigestReduced, &messageDigest) - var R edwards25519.ExtendedGroupElement - edwards25519.GeScalarMultBase(&R, &messageDigestReduced) - - var encodedR [32]byte - R.ToBytes(&encodedR) - - h.Reset() - h.Write(encodedR[:]) - h.Write(privateKey[32:]) - h.Write(message) - h.Sum(hramDigest[:0]) - var hramDigestReduced [32]byte - edwards25519.ScReduce(&hramDigestReduced, &hramDigest) - - var s [32]byte - edwards25519.ScMulAdd(&s, &hramDigestReduced, &expandedSecretKey, &messageDigestReduced) - - signature := make([]byte, SignatureSize) - copy(signature[:], encodedR[:]) - copy(signature[32:], s[:]) - - return signature + return ed25519.Sign(privateKey, message) } // Verify reports whether sig is a valid signature of message by publicKey. It // will panic if len(publicKey) is not PublicKeySize. func Verify(publicKey PublicKey, message, sig []byte) bool { - if l := len(publicKey); l != PublicKeySize { - panic("ed25519: bad public key length: " + strconv.Itoa(l)) - } - - if len(sig) != SignatureSize || sig[63]&224 != 0 { - return false - } - - var A edwards25519.ExtendedGroupElement - var publicKeyBytes [32]byte - copy(publicKeyBytes[:], publicKey) - if !A.FromBytes(&publicKeyBytes) { - return false - } - edwards25519.FeNeg(&A.X, &A.X) - edwards25519.FeNeg(&A.T, &A.T) - - h := sha512.New() - h.Write(sig[:32]) - h.Write(publicKey[:]) - h.Write(message) - var digest [64]byte - h.Sum(digest[:0]) - - var hReduced [32]byte - edwards25519.ScReduce(&hReduced, &digest) - - var R edwards25519.ProjectiveGroupElement - var s [32]byte - copy(s[:], sig[32:]) - - // https://tools.ietf.org/html/rfc8032#section-5.1.7 requires that s be in - // the range [0, order) in order to prevent signature malleability. - if !edwards25519.ScMinimal(&s) { - return false - } - - edwards25519.GeDoubleScalarMultVartime(&R, &hReduced, &A, &s) - - var checkR [32]byte - R.ToBytes(&checkR) - return bytes.Equal(sig[:32], checkR[:]) + return ed25519.Verify(publicKey, message, sig) } diff --git a/vendor/golang.org/x/crypto/ed25519/ed25519_go113.go b/vendor/golang.org/x/crypto/ed25519/ed25519_go113.go deleted file mode 100644 index b5974dc8b..000000000 --- a/vendor/golang.org/x/crypto/ed25519/ed25519_go113.go +++ /dev/null @@ -1,74 +0,0 @@ -// Copyright 2019 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. - -//go:build go1.13 -// +build go1.13 - -// Package ed25519 implements the Ed25519 signature algorithm. See -// https://ed25519.cr.yp.to/. -// -// These functions are also compatible with the “Ed25519” function defined in -// RFC 8032. However, unlike RFC 8032's formulation, this package's private key -// representation includes a public key suffix to make multiple signing -// operations with the same key more efficient. This package refers to the RFC -// 8032 private key as the “seed”. -// -// Beginning with Go 1.13, the functionality of this package was moved to the -// standard library as crypto/ed25519. This package only acts as a compatibility -// wrapper. -package ed25519 - -import ( - "crypto/ed25519" - "io" -) - -const ( - // PublicKeySize is the size, in bytes, of public keys as used in this package. - PublicKeySize = 32 - // PrivateKeySize is the size, in bytes, of private keys as used in this package. - PrivateKeySize = 64 - // SignatureSize is the size, in bytes, of signatures generated and verified by this package. - SignatureSize = 64 - // SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032. - SeedSize = 32 -) - -// PublicKey is the type of Ed25519 public keys. -// -// This type is an alias for crypto/ed25519's PublicKey type. -// See the crypto/ed25519 package for the methods on this type. -type PublicKey = ed25519.PublicKey - -// PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer. -// -// This type is an alias for crypto/ed25519's PrivateKey type. -// See the crypto/ed25519 package for the methods on this type. -type PrivateKey = ed25519.PrivateKey - -// GenerateKey generates a public/private key pair using entropy from rand. -// If rand is nil, crypto/rand.Reader will be used. -func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { - return ed25519.GenerateKey(rand) -} - -// NewKeyFromSeed calculates a private key from a seed. It will panic if -// len(seed) is not SeedSize. This function is provided for interoperability -// with RFC 8032. RFC 8032's private keys correspond to seeds in this -// package. -func NewKeyFromSeed(seed []byte) PrivateKey { - return ed25519.NewKeyFromSeed(seed) -} - -// Sign signs the message with privateKey and returns a signature. It will -// panic if len(privateKey) is not PrivateKeySize. -func Sign(privateKey PrivateKey, message []byte) []byte { - return ed25519.Sign(privateKey, message) -} - -// Verify reports whether sig is a valid signature of message by publicKey. It -// will panic if len(publicKey) is not PublicKeySize. -func Verify(publicKey PublicKey, message, sig []byte) bool { - return ed25519.Verify(publicKey, message, sig) -} diff --git a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go b/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go deleted file mode 100644 index e39f086c1..000000000 --- a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go +++ /dev/null @@ -1,1422 +0,0 @@ -// Copyright 2016 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 - -// These values are from the public domain, “ref10” implementation of ed25519 -// from SUPERCOP. - -// d is a constant in the Edwards curve equation. -var d = FieldElement{ - -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116, -} - -// d2 is 2*d. -var d2 = FieldElement{ - -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199, -} - -// SqrtM1 is the square-root of -1 in the field. -var SqrtM1 = FieldElement{ - -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482, -} - -// A is a constant in the Montgomery-form of curve25519. -var A = FieldElement{ - 486662, 0, 0, 0, 0, 0, 0, 0, 0, 0, -} - -// bi contains precomputed multiples of the base-point. See the Ed25519 paper -// for a discussion about how these values are used. -var bi = [8]PreComputedGroupElement{ - { - FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605}, - FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378}, - FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546}, - }, - { - FieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024}, - FieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574}, - FieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357}, - }, - { - FieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380}, - FieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306}, - FieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942}, - }, - { - FieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766}, - FieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701}, - FieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300}, - }, - { - FieldElement{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877}, - FieldElement{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951}, - FieldElement{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784}, - }, - { - FieldElement{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436}, - FieldElement{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918}, - FieldElement{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877}, - }, - { - FieldElement{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800}, - FieldElement{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305}, - FieldElement{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300}, - }, - { - FieldElement{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876}, - FieldElement{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619}, - FieldElement{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683}, - }, -} - -// base contains precomputed multiples of the base-point. See the Ed25519 paper -// for a discussion about how these values are used. -var base = [32][8]PreComputedGroupElement{ - { - { - FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605}, - FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378}, - FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546}, - }, - { - FieldElement{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303}, - FieldElement{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081}, - FieldElement{26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697}, - }, - { - FieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024}, - FieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574}, - FieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357}, - }, - { - FieldElement{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540}, - FieldElement{23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397}, - FieldElement{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325}, - }, - { - FieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380}, - FieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306}, - FieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942}, - }, - { - FieldElement{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777}, - FieldElement{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737}, - FieldElement{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652}, - }, - { - FieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766}, - FieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701}, - FieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300}, - }, - { - FieldElement{14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726}, - FieldElement{-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955}, - FieldElement{27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425}, - }, - }, - { - { - FieldElement{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171}, - FieldElement{27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510}, - FieldElement{17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660}, - }, - { - FieldElement{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639}, - FieldElement{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963}, - FieldElement{5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950}, - }, - { - FieldElement{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568}, - FieldElement{12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335}, - FieldElement{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628}, - }, - { - FieldElement{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007}, - FieldElement{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772}, - FieldElement{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653}, - }, - { - FieldElement{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567}, - FieldElement{13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686}, - FieldElement{21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372}, - }, - { - FieldElement{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887}, - FieldElement{-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954}, - FieldElement{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953}, - }, - { - FieldElement{24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833}, - FieldElement{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532}, - FieldElement{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876}, - }, - { - FieldElement{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268}, - FieldElement{33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214}, - FieldElement{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038}, - }, - }, - { - { - FieldElement{6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800}, - FieldElement{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645}, - FieldElement{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664}, - }, - { - FieldElement{1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933}, - FieldElement{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182}, - FieldElement{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222}, - }, - { - FieldElement{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991}, - FieldElement{20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880}, - FieldElement{9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092}, - }, - { - FieldElement{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295}, - FieldElement{19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788}, - FieldElement{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553}, - }, - { - FieldElement{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026}, - FieldElement{11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347}, - FieldElement{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033}, - }, - { - FieldElement{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395}, - FieldElement{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278}, - FieldElement{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890}, - }, - { - FieldElement{32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995}, - FieldElement{-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596}, - FieldElement{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891}, - }, - { - FieldElement{31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060}, - FieldElement{11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608}, - FieldElement{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606}, - }, - }, - { - { - FieldElement{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389}, - FieldElement{-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016}, - FieldElement{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341}, - }, - { - FieldElement{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505}, - FieldElement{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553}, - FieldElement{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655}, - }, - { - FieldElement{15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220}, - FieldElement{12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631}, - FieldElement{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099}, - }, - { - FieldElement{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556}, - FieldElement{14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749}, - FieldElement{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930}, - }, - { - FieldElement{1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391}, - FieldElement{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253}, - FieldElement{20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066}, - }, - { - FieldElement{24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958}, - FieldElement{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082}, - FieldElement{-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383}, - }, - { - FieldElement{-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521}, - FieldElement{-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807}, - FieldElement{23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948}, - }, - { - FieldElement{9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134}, - FieldElement{-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455}, - FieldElement{27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629}, - }, - }, - { - { - FieldElement{-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069}, - FieldElement{-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746}, - FieldElement{24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919}, - }, - { - FieldElement{11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837}, - FieldElement{8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906}, - FieldElement{-28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771}, - }, - { - FieldElement{-25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817}, - FieldElement{10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098}, - FieldElement{10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409}, - }, - { - FieldElement{-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504}, - FieldElement{-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727}, - FieldElement{28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420}, - }, - { - FieldElement{-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003}, - FieldElement{-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605}, - FieldElement{-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384}, - }, - { - FieldElement{-26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701}, - FieldElement{-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683}, - FieldElement{29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708}, - }, - { - FieldElement{-3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -21284170, 8971513, -28539189, 15326563}, - FieldElement{-19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -15523050, 15300988, -20514118, 9168260}, - FieldElement{-5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -28948358, 9601605, 33087103, -9011387}, - }, - { - FieldElement{-19443170, -15512900, -20797467, -12445323, -29824447, 10229461, -27444329, -15000531, -5996870, 15664672}, - FieldElement{23294591, -16632613, -22650781, -8470978, 27844204, 11461195, 13099750, -2460356, 18151676, 13417686}, - FieldElement{-24722913, -4176517, -31150679, 5988919, -26858785, 6685065, 1661597, -12551441, 15271676, -15452665}, - }, - }, - { - { - FieldElement{11433042, -13228665, 8239631, -5279517, -1985436, -725718, -18698764, 2167544, -6921301, -13440182}, - FieldElement{-31436171, 15575146, 30436815, 12192228, -22463353, 9395379, -9917708, -8638997, 12215110, 12028277}, - FieldElement{14098400, 6555944, 23007258, 5757252, -15427832, -12950502, 30123440, 4617780, -16900089, -655628}, - }, - { - FieldElement{-4026201, -15240835, 11893168, 13718664, -14809462, 1847385, -15819999, 10154009, 23973261, -12684474}, - FieldElement{-26531820, -3695990, -1908898, 2534301, -31870557, -16550355, 18341390, -11419951, 32013174, -10103539}, - FieldElement{-25479301, 10876443, -11771086, -14625140, -12369567, 1838104, 21911214, 6354752, 4425632, -837822}, - }, - { - FieldElement{-10433389, -14612966, 22229858, -3091047, -13191166, 776729, -17415375, -12020462, 4725005, 14044970}, - FieldElement{19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, -1411784, -19522291, -16109756}, - FieldElement{-24864089, 12986008, -10898878, -5558584, -11312371, -148526, 19541418, 8180106, 9282262, 10282508}, - }, - { - FieldElement{-26205082, 4428547, -8661196, -13194263, 4098402, -14165257, 15522535, 8372215, 5542595, -10702683}, - FieldElement{-10562541, 14895633, 26814552, -16673850, -17480754, -2489360, -2781891, 6993761, -18093885, 10114655}, - FieldElement{-20107055, -929418, 31422704, 10427861, -7110749, 6150669, -29091755, -11529146, 25953725, -106158}, - }, - { - FieldElement{-4234397, -8039292, -9119125, 3046000, 2101609, -12607294, 19390020, 6094296, -3315279, 12831125}, - FieldElement{-15998678, 7578152, 5310217, 14408357, -33548620, -224739, 31575954, 6326196, 7381791, -2421839}, - FieldElement{-20902779, 3296811, 24736065, -16328389, 18374254, 7318640, 6295303, 8082724, -15362489, 12339664}, - }, - { - FieldElement{27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414, 15768922, 25091167, 14856294}, - FieldElement{-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, -12695493, -22182473, -9012899}, - FieldElement{-11423429, -5421590, 11632845, 3405020, 30536730, -11674039, -27260765, 13866390, 30146206, 9142070}, - }, - { - FieldElement{3924129, -15307516, -13817122, -10054960, 12291820, -668366, -27702774, 9326384, -8237858, 4171294}, - FieldElement{-15921940, 16037937, 6713787, 16606682, -21612135, 2790944, 26396185, 3731949, 345228, -5462949}, - FieldElement{-21327538, 13448259, 25284571, 1143661, 20614966, -8849387, 2031539, -12391231, -16253183, -13582083}, - }, - { - FieldElement{31016211, -16722429, 26371392, -14451233, -5027349, 14854137, 17477601, 3842657, 28012650, -16405420}, - FieldElement{-5075835, 9368966, -8562079, -4600902, -15249953, 6970560, -9189873, 16292057, -8867157, 3507940}, - FieldElement{29439664, 3537914, 23333589, 6997794, -17555561, -11018068, -15209202, -15051267, -9164929, 6580396}, - }, - }, - { - { - FieldElement{-12185861, -7679788, 16438269, 10826160, -8696817, -6235611, 17860444, -9273846, -2095802, 9304567}, - FieldElement{20714564, -4336911, 29088195, 7406487, 11426967, -5095705, 14792667, -14608617, 5289421, -477127}, - FieldElement{-16665533, -10650790, -6160345, -13305760, 9192020, -1802462, 17271490, 12349094, 26939669, -3752294}, - }, - { - FieldElement{-12889898, 9373458, 31595848, 16374215, 21471720, 13221525, -27283495, -12348559, -3698806, 117887}, - FieldElement{22263325, -6560050, 3984570, -11174646, -15114008, -566785, 28311253, 5358056, -23319780, 541964}, - FieldElement{16259219, 3261970, 2309254, -15534474, -16885711, -4581916, 24134070, -16705829, -13337066, -13552195}, - }, - { - FieldElement{9378160, -13140186, -22845982, -12745264, 28198281, -7244098, -2399684, -717351, 690426, 14876244}, - FieldElement{24977353, -314384, -8223969, -13465086, 28432343, -1176353, -13068804, -12297348, -22380984, 6618999}, - FieldElement{-1538174, 11685646, 12944378, 13682314, -24389511, -14413193, 8044829, -13817328, 32239829, -5652762}, - }, - { - FieldElement{-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647, -10350059, 32779359, 5095274}, - FieldElement{-33008130, -5214506, -32264887, -3685216, 9460461, -9327423, -24601656, 14506724, 21639561, -2630236}, - FieldElement{-16400943, -13112215, 25239338, 15531969, 3987758, -4499318, -1289502, -6863535, 17874574, 558605}, - }, - { - FieldElement{-13600129, 10240081, 9171883, 16131053, -20869254, 9599700, 33499487, 5080151, 2085892, 5119761}, - FieldElement{-22205145, -2519528, -16381601, 414691, -25019550, 2170430, 30634760, -8363614, -31999993, -5759884}, - FieldElement{-6845704, 15791202, 8550074, -1312654, 29928809, -12092256, 27534430, -7192145, -22351378, 12961482}, - }, - { - FieldElement{-24492060, -9570771, 10368194, 11582341, -23397293, -2245287, 16533930, 8206996, -30194652, -5159638}, - FieldElement{-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, 7031275, 7589640, 8945490}, - FieldElement{-32152748, 8917967, 6661220, -11677616, -1192060, -15793393, 7251489, -11182180, 24099109, -14456170}, - }, - { - FieldElement{5019558, -7907470, 4244127, -14714356, -26933272, 6453165, -19118182, -13289025, -6231896, -10280736}, - FieldElement{10853594, 10721687, 26480089, 5861829, -22995819, 1972175, -1866647, -10557898, -3363451, -6441124}, - FieldElement{-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, -2008168, -13866408, 7421392}, - }, - { - FieldElement{8139927, -6546497, 32257646, -5890546, 30375719, 1886181, -21175108, 15441252, 28826358, -4123029}, - FieldElement{6267086, 9695052, 7709135, -16603597, -32869068, -1886135, 14795160, -7840124, 13746021, -1742048}, - FieldElement{28584902, 7787108, -6732942, -15050729, 22846041, -7571236, -3181936, -363524, 4771362, -8419958}, - }, - }, - { - { - FieldElement{24949256, 6376279, -27466481, -8174608, -18646154, -9930606, 33543569, -12141695, 3569627, 11342593}, - FieldElement{26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, 4608608, 7325975, -14801071}, - FieldElement{-11618399, -14554430, -24321212, 7655128, -1369274, 5214312, -27400540, 10258390, -17646694, -8186692}, - }, - { - FieldElement{11431204, 15823007, 26570245, 14329124, 18029990, 4796082, -31446179, 15580664, 9280358, -3973687}, - FieldElement{-160783, -10326257, -22855316, -4304997, -20861367, -13621002, -32810901, -11181622, -15545091, 4387441}, - FieldElement{-20799378, 12194512, 3937617, -5805892, -27154820, 9340370, -24513992, 8548137, 20617071, -7482001}, - }, - { - FieldElement{-938825, -3930586, -8714311, 16124718, 24603125, -6225393, -13775352, -11875822, 24345683, 10325460}, - FieldElement{-19855277, -1568885, -22202708, 8714034, 14007766, 6928528, 16318175, -1010689, 4766743, 3552007}, - FieldElement{-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, 14481909, 10988822, -3994762}, - }, - { - FieldElement{15564307, -14311570, 3101243, 5684148, 30446780, -8051356, 12677127, -6505343, -8295852, 13296005}, - FieldElement{-9442290, 6624296, -30298964, -11913677, -4670981, -2057379, 31521204, 9614054, -30000824, 12074674}, - FieldElement{4771191, -135239, 14290749, -13089852, 27992298, 14998318, -1413936, -1556716, 29832613, -16391035}, - }, - { - FieldElement{7064884, -7541174, -19161962, -5067537, -18891269, -2912736, 25825242, 5293297, -27122660, 13101590}, - FieldElement{-2298563, 2439670, -7466610, 1719965, -27267541, -16328445, 32512469, -5317593, -30356070, -4190957}, - FieldElement{-30006540, 10162316, -33180176, 3981723, -16482138, -13070044, 14413974, 9515896, 19568978, 9628812}, - }, - { - FieldElement{33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, -6106839, -6291786, 3437740}, - FieldElement{-18978877, 3884493, 19469877, 12726490, 15913552, 13614290, -22961733, 70104, 7463304, 4176122}, - FieldElement{-27124001, 10659917, 11482427, -16070381, 12771467, -6635117, -32719404, -5322751, 24216882, 5944158}, - }, - { - FieldElement{8894125, 7450974, -2664149, -9765752, -28080517, -12389115, 19345746, 14680796, 11632993, 5847885}, - FieldElement{26942781, -2315317, 9129564, -4906607, 26024105, 11769399, -11518837, 6367194, -9727230, 4782140}, - FieldElement{19916461, -4828410, -22910704, -11414391, 25606324, -5972441, 33253853, 8220911, 6358847, -1873857}, - }, - { - FieldElement{801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, -4480480, -13538503, 1387155}, - FieldElement{19646058, 5720633, -11416706, 12814209, 11607948, 12749789, 14147075, 15156355, -21866831, 11835260}, - FieldElement{19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, 15467869, -26560550, 5052483}, - }, - }, - { - { - FieldElement{-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, -12618185, 12228557, -7003677}, - FieldElement{32944382, 14922211, -22844894, 5188528, 21913450, -8719943, 4001465, 13238564, -6114803, 8653815}, - FieldElement{22865569, -4652735, 27603668, -12545395, 14348958, 8234005, 24808405, 5719875, 28483275, 2841751}, - }, - { - FieldElement{-16420968, -1113305, -327719, -12107856, 21886282, -15552774, -1887966, -315658, 19932058, -12739203}, - FieldElement{-11656086, 10087521, -8864888, -5536143, -19278573, -3055912, 3999228, 13239134, -4777469, -13910208}, - FieldElement{1382174, -11694719, 17266790, 9194690, -13324356, 9720081, 20403944, 11284705, -14013818, 3093230}, - }, - { - FieldElement{16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, 16271225, -24049421, -6691850}, - FieldElement{-21911077, -5927941, -4611316, -5560156, -31744103, -10785293, 24123614, 15193618, -21652117, -16739389}, - FieldElement{-9935934, -4289447, -25279823, 4372842, 2087473, 10399484, 31870908, 14690798, 17361620, 11864968}, - }, - { - FieldElement{-11307610, 6210372, 13206574, 5806320, -29017692, -13967200, -12331205, -7486601, -25578460, -16240689}, - FieldElement{14668462, -12270235, 26039039, 15305210, 25515617, 4542480, 10453892, 6577524, 9145645, -6443880}, - FieldElement{5974874, 3053895, -9433049, -10385191, -31865124, 3225009, -7972642, 3936128, -5652273, -3050304}, - }, - { - FieldElement{30625386, -4729400, -25555961, -12792866, -20484575, 7695099, 17097188, -16303496, -27999779, 1803632}, - FieldElement{-3553091, 9865099, -5228566, 4272701, -5673832, -16689700, 14911344, 12196514, -21405489, 7047412}, - FieldElement{20093277, 9920966, -11138194, -5343857, 13161587, 12044805, -32856851, 4124601, -32343828, -10257566}, - }, - { - FieldElement{-20788824, 14084654, -13531713, 7842147, 19119038, -13822605, 4752377, -8714640, -21679658, 2288038}, - FieldElement{-26819236, -3283715, 29965059, 3039786, -14473765, 2540457, 29457502, 14625692, -24819617, 12570232}, - FieldElement{-1063558, -11551823, 16920318, 12494842, 1278292, -5869109, -21159943, -3498680, -11974704, 4724943}, - }, - { - FieldElement{17960970, -11775534, -4140968, -9702530, -8876562, -1410617, -12907383, -8659932, -29576300, 1903856}, - FieldElement{23134274, -14279132, -10681997, -1611936, 20684485, 15770816, -12989750, 3190296, 26955097, 14109738}, - FieldElement{15308788, 5320727, -30113809, -14318877, 22902008, 7767164, 29425325, -11277562, 31960942, 11934971}, - }, - { - FieldElement{-27395711, 8435796, 4109644, 12222639, -24627868, 14818669, 20638173, 4875028, 10491392, 1379718}, - FieldElement{-13159415, 9197841, 3875503, -8936108, -1383712, -5879801, 33518459, 16176658, 21432314, 12180697}, - FieldElement{-11787308, 11500838, 13787581, -13832590, -22430679, 10140205, 1465425, 12689540, -10301319, -13872883}, - }, - }, - { - { - FieldElement{5414091, -15386041, -21007664, 9643570, 12834970, 1186149, -2622916, -1342231, 26128231, 6032912}, - FieldElement{-26337395, -13766162, 32496025, -13653919, 17847801, -12669156, 3604025, 8316894, -25875034, -10437358}, - FieldElement{3296484, 6223048, 24680646, -12246460, -23052020, 5903205, -8862297, -4639164, 12376617, 3188849}, - }, - { - FieldElement{29190488, -14659046, 27549113, -1183516, 3520066, -10697301, 32049515, -7309113, -16109234, -9852307}, - FieldElement{-14744486, -9309156, 735818, -598978, -20407687, -5057904, 25246078, -15795669, 18640741, -960977}, - FieldElement{-6928835, -16430795, 10361374, 5642961, 4910474, 12345252, -31638386, -494430, 10530747, 1053335}, - }, - { - FieldElement{-29265967, -14186805, -13538216, -12117373, -19457059, -10655384, -31462369, -2948985, 24018831, 15026644}, - FieldElement{-22592535, -3145277, -2289276, 5953843, -13440189, 9425631, 25310643, 13003497, -2314791, -15145616}, - FieldElement{-27419985, -603321, -8043984, -1669117, -26092265, 13987819, -27297622, 187899, -23166419, -2531735}, - }, - { - FieldElement{-21744398, -13810475, 1844840, 5021428, -10434399, -15911473, 9716667, 16266922, -5070217, 726099}, - FieldElement{29370922, -6053998, 7334071, -15342259, 9385287, 2247707, -13661962, -4839461, 30007388, -15823341}, - FieldElement{-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, 730663, 9835848, 4555336}, - }, - { - FieldElement{-23376435, 1410446, -22253753, -12899614, 30867635, 15826977, 17693930, 544696, -11985298, 12422646}, - FieldElement{31117226, -12215734, -13502838, 6561947, -9876867, -12757670, -5118685, -4096706, 29120153, 13924425}, - FieldElement{-17400879, -14233209, 19675799, -2734756, -11006962, -5858820, -9383939, -11317700, 7240931, -237388}, - }, - { - FieldElement{-31361739, -11346780, -15007447, -5856218, -22453340, -12152771, 1222336, 4389483, 3293637, -15551743}, - FieldElement{-16684801, -14444245, 11038544, 11054958, -13801175, -3338533, -24319580, 7733547, 12796905, -6335822}, - FieldElement{-8759414, -10817836, -25418864, 10783769, -30615557, -9746811, -28253339, 3647836, 3222231, -11160462}, - }, - { - FieldElement{18606113, 1693100, -25448386, -15170272, 4112353, 10045021, 23603893, -2048234, -7550776, 2484985}, - FieldElement{9255317, -3131197, -12156162, -1004256, 13098013, -9214866, 16377220, -2102812, -19802075, -3034702}, - FieldElement{-22729289, 7496160, -5742199, 11329249, 19991973, -3347502, -31718148, 9936966, -30097688, -10618797}, - }, - { - FieldElement{21878590, -5001297, 4338336, 13643897, -3036865, 13160960, 19708896, 5415497, -7360503, -4109293}, - FieldElement{27736861, 10103576, 12500508, 8502413, -3413016, -9633558, 10436918, -1550276, -23659143, -8132100}, - FieldElement{19492550, -12104365, -29681976, -852630, -3208171, 12403437, 30066266, 8367329, 13243957, 8709688}, - }, - }, - { - { - FieldElement{12015105, 2801261, 28198131, 10151021, 24818120, -4743133, -11194191, -5645734, 5150968, 7274186}, - FieldElement{2831366, -12492146, 1478975, 6122054, 23825128, -12733586, 31097299, 6083058, 31021603, -9793610}, - FieldElement{-2529932, -2229646, 445613, 10720828, -13849527, -11505937, -23507731, 16354465, 15067285, -14147707}, - }, - { - FieldElement{7840942, 14037873, -33364863, 15934016, -728213, -3642706, 21403988, 1057586, -19379462, -12403220}, - FieldElement{915865, -16469274, 15608285, -8789130, -24357026, 6060030, -17371319, 8410997, -7220461, 16527025}, - FieldElement{32922597, -556987, 20336074, -16184568, 10903705, -5384487, 16957574, 52992, 23834301, 6588044}, - }, - { - FieldElement{32752030, 11232950, 3381995, -8714866, 22652988, -10744103, 17159699, 16689107, -20314580, -1305992}, - FieldElement{-4689649, 9166776, -25710296, -10847306, 11576752, 12733943, 7924251, -2752281, 1976123, -7249027}, - FieldElement{21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, -3371252, 12331345, -8237197}, - }, - { - FieldElement{8651614, -4477032, -16085636, -4996994, 13002507, 2950805, 29054427, -5106970, 10008136, -4667901}, - FieldElement{31486080, 15114593, -14261250, 12951354, 14369431, -7387845, 16347321, -13662089, 8684155, -10532952}, - FieldElement{19443825, 11385320, 24468943, -9659068, -23919258, 2187569, -26263207, -6086921, 31316348, 14219878}, - }, - { - FieldElement{-28594490, 1193785, 32245219, 11392485, 31092169, 15722801, 27146014, 6992409, 29126555, 9207390}, - FieldElement{32382935, 1110093, 18477781, 11028262, -27411763, -7548111, -4980517, 10843782, -7957600, -14435730}, - FieldElement{2814918, 7836403, 27519878, -7868156, -20894015, -11553689, -21494559, 8550130, 28346258, 1994730}, - }, - { - FieldElement{-19578299, 8085545, -14000519, -3948622, 2785838, -16231307, -19516951, 7174894, 22628102, 8115180}, - FieldElement{-30405132, 955511, -11133838, -15078069, -32447087, -13278079, -25651578, 3317160, -9943017, 930272}, - FieldElement{-15303681, -6833769, 28856490, 1357446, 23421993, 1057177, 24091212, -1388970, -22765376, -10650715}, - }, - { - FieldElement{-22751231, -5303997, -12907607, -12768866, -15811511, -7797053, -14839018, -16554220, -1867018, 8398970}, - FieldElement{-31969310, 2106403, -4736360, 1362501, 12813763, 16200670, 22981545, -6291273, 18009408, -15772772}, - FieldElement{-17220923, -9545221, -27784654, 14166835, 29815394, 7444469, 29551787, -3727419, 19288549, 1325865}, - }, - { - FieldElement{15100157, -15835752, -23923978, -1005098, -26450192, 15509408, 12376730, -3479146, 33166107, -8042750}, - FieldElement{20909231, 13023121, -9209752, 16251778, -5778415, -8094914, 12412151, 10018715, 2213263, -13878373}, - FieldElement{32529814, -11074689, 30361439, -16689753, -9135940, 1513226, 22922121, 6382134, -5766928, 8371348}, - }, - }, - { - { - FieldElement{9923462, 11271500, 12616794, 3544722, -29998368, -1721626, 12891687, -8193132, -26442943, 10486144}, - FieldElement{-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, 2610596, -23921530, -11455195}, - FieldElement{5408411, -1136691, -4969122, 10561668, 24145918, 14240566, 31319731, -4235541, 19985175, -3436086}, - }, - { - FieldElement{-13994457, 16616821, 14549246, 3341099, 32155958, 13648976, -17577068, 8849297, 65030, 8370684}, - FieldElement{-8320926, -12049626, 31204563, 5839400, -20627288, -1057277, -19442942, 6922164, 12743482, -9800518}, - FieldElement{-2361371, 12678785, 28815050, 4759974, -23893047, 4884717, 23783145, 11038569, 18800704, 255233}, - }, - { - FieldElement{-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, 9066957, 19258688, -14753793}, - FieldElement{-2936654, -10827535, -10432089, 14516793, -3640786, 4372541, -31934921, 2209390, -1524053, 2055794}, - FieldElement{580882, 16705327, 5468415, -2683018, -30926419, -14696000, -7203346, -8994389, -30021019, 7394435}, - }, - { - FieldElement{23838809, 1822728, -15738443, 15242727, 8318092, -3733104, -21672180, -3492205, -4821741, 14799921}, - FieldElement{13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, 13496856, -9056018, 7402518}, - FieldElement{2286874, -4435931, -20042458, -2008336, -13696227, 5038122, 11006906, -15760352, 8205061, 1607563}, - }, - { - FieldElement{14414086, -8002132, 3331830, -3208217, 22249151, -5594188, 18364661, -2906958, 30019587, -9029278}, - FieldElement{-27688051, 1585953, -10775053, 931069, -29120221, -11002319, -14410829, 12029093, 9944378, 8024}, - FieldElement{4368715, -3709630, 29874200, -15022983, -20230386, -11410704, -16114594, -999085, -8142388, 5640030}, - }, - { - FieldElement{10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, -16694564, 15219798, -14327783}, - FieldElement{27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, -1173195, -18342183, 9742717}, - FieldElement{6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, 7406442, 12420155, 1994844}, - }, - { - FieldElement{14012521, -5024720, -18384453, -9578469, -26485342, -3936439, -13033478, -10909803, 24319929, -6446333}, - FieldElement{16412690, -4507367, 10772641, 15929391, -17068788, -4658621, 10555945, -10484049, -30102368, -4739048}, - FieldElement{22397382, -7767684, -9293161, -12792868, 17166287, -9755136, -27333065, 6199366, 21880021, -12250760}, - }, - { - FieldElement{-4283307, 5368523, -31117018, 8163389, -30323063, 3209128, 16557151, 8890729, 8840445, 4957760}, - FieldElement{-15447727, 709327, -6919446, -10870178, -29777922, 6522332, -21720181, 12130072, -14796503, 5005757}, - FieldElement{-2114751, -14308128, 23019042, 15765735, -25269683, 6002752, 10183197, -13239326, -16395286, -2176112}, - }, - }, - { - { - FieldElement{-19025756, 1632005, 13466291, -7995100, -23640451, 16573537, -32013908, -3057104, 22208662, 2000468}, - FieldElement{3065073, -1412761, -25598674, -361432, -17683065, -5703415, -8164212, 11248527, -3691214, -7414184}, - FieldElement{10379208, -6045554, 8877319, 1473647, -29291284, -12507580, 16690915, 2553332, -3132688, 16400289}, - }, - { - FieldElement{15716668, 1254266, -18472690, 7446274, -8448918, 6344164, -22097271, -7285580, 26894937, 9132066}, - FieldElement{24158887, 12938817, 11085297, -8177598, -28063478, -4457083, -30576463, 64452, -6817084, -2692882}, - FieldElement{13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, -3418511, -4688006, 2364226}, - }, - { - FieldElement{16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024, -11697457, 15445875, -7798101}, - FieldElement{29004207, -7867081, 28661402, -640412, -12794003, -7943086, 31863255, -4135540, -278050, -15759279}, - FieldElement{-6122061, -14866665, -28614905, 14569919, -10857999, -3591829, 10343412, -6976290, -29828287, -10815811}, - }, - { - FieldElement{27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636, 15372179, 17293797, 960709}, - FieldElement{20263915, 11434237, -5765435, 11236810, 13505955, -10857102, -16111345, 6493122, -19384511, 7639714}, - FieldElement{-2830798, -14839232, 25403038, -8215196, -8317012, -16173699, 18006287, -16043750, 29994677, -15808121}, - }, - { - FieldElement{9769828, 5202651, -24157398, -13631392, -28051003, -11561624, -24613141, -13860782, -31184575, 709464}, - FieldElement{12286395, 13076066, -21775189, -1176622, -25003198, 4057652, -32018128, -8890874, 16102007, 13205847}, - FieldElement{13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, 8525972, 10151379, 10394400}, - }, - { - FieldElement{4024660, -16137551, 22436262, 12276534, -9099015, -2686099, 19698229, 11743039, -33302334, 8934414}, - FieldElement{-15879800, -4525240, -8580747, -2934061, 14634845, -698278, -9449077, 3137094, -11536886, 11721158}, - FieldElement{17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, 8835153, -9205489, -1280045}, - }, - { - FieldElement{-461409, -7830014, 20614118, 16688288, -7514766, -4807119, 22300304, 505429, 6108462, -6183415}, - FieldElement{-5070281, 12367917, -30663534, 3234473, 32617080, -8422642, 29880583, -13483331, -26898490, -7867459}, - FieldElement{-31975283, 5726539, 26934134, 10237677, -3173717, -605053, 24199304, 3795095, 7592688, -14992079}, - }, - { - FieldElement{21594432, -14964228, 17466408, -4077222, 32537084, 2739898, 6407723, 12018833, -28256052, 4298412}, - FieldElement{-20650503, -11961496, -27236275, 570498, 3767144, -1717540, 13891942, -1569194, 13717174, 10805743}, - FieldElement{-14676630, -15644296, 15287174, 11927123, 24177847, -8175568, -796431, 14860609, -26938930, -5863836}, - }, - }, - { - { - FieldElement{12962541, 5311799, -10060768, 11658280, 18855286, -7954201, 13286263, -12808704, -4381056, 9882022}, - FieldElement{18512079, 11319350, -20123124, 15090309, 18818594, 5271736, -22727904, 3666879, -23967430, -3299429}, - FieldElement{-6789020, -3146043, 16192429, 13241070, 15898607, -14206114, -10084880, -6661110, -2403099, 5276065}, - }, - { - FieldElement{30169808, -5317648, 26306206, -11750859, 27814964, 7069267, 7152851, 3684982, 1449224, 13082861}, - FieldElement{10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, 15056736, -21016438, -8202000}, - FieldElement{-33150110, 3261608, 22745853, 7948688, 19370557, -15177665, -26171976, 6482814, -10300080, -11060101}, - }, - { - FieldElement{32869458, -5408545, 25609743, 15678670, -10687769, -15471071, 26112421, 2521008, -22664288, 6904815}, - FieldElement{29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737, 3841096, -29003639, -6657642}, - FieldElement{10340844, -6630377, -18656632, -2278430, 12621151, -13339055, 30878497, -11824370, -25584551, 5181966}, - }, - { - FieldElement{25940115, -12658025, 17324188, -10307374, -8671468, 15029094, 24396252, -16450922, -2322852, -12388574}, - FieldElement{-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390, 12641087, 20603771, -6561742}, - FieldElement{-18882287, -11673380, 24849422, 11501709, 13161720, -4768874, 1925523, 11914390, 4662781, 7820689}, - }, - { - FieldElement{12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456, 12172924, 16136752, 15264020}, - FieldElement{-10349955, -14680563, -8211979, 2330220, -17662549, -14545780, 10658213, 6671822, 19012087, 3772772}, - FieldElement{3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732, -15762884, 20527771, 12988982}, - }, - { - FieldElement{-14822485, -5797269, -3707987, 12689773, -898983, -10914866, -24183046, -10564943, 3299665, -12424953}, - FieldElement{-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197, 6461331, -25583147, 8991218}, - FieldElement{-17226263, 1816362, -1673288, -6086439, 31783888, -8175991, -32948145, 7417950, -30242287, 1507265}, - }, - { - FieldElement{29692663, 6829891, -10498800, 4334896, 20945975, -11906496, -28887608, 8209391, 14606362, -10647073}, - FieldElement{-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695, 9761487, 4170404, -2085325}, - FieldElement{-11587470, 14855945, -4127778, -1531857, -26649089, 15084046, 22186522, 16002000, -14276837, -8400798}, - }, - { - FieldElement{-4811456, 13761029, -31703877, -2483919, -3312471, 7869047, -7113572, -9620092, 13240845, 10965870}, - FieldElement{-7742563, -8256762, -14768334, -13656260, -23232383, 12387166, 4498947, 14147411, 29514390, 4302863}, - FieldElement{-13413405, -12407859, 20757302, -13801832, 14785143, 8976368, -5061276, -2144373, 17846988, -13971927}, - }, - }, - { - { - FieldElement{-2244452, -754728, -4597030, -1066309, -6247172, 1455299, -21647728, -9214789, -5222701, 12650267}, - FieldElement{-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813, 13770293, -19134326, 10958663}, - FieldElement{22470984, 12369526, 23446014, -5441109, -21520802, -9698723, -11772496, -11574455, -25083830, 4271862}, - }, - { - FieldElement{-25169565, -10053642, -19909332, 15361595, -5984358, 2159192, 75375, -4278529, -32526221, 8469673}, - FieldElement{15854970, 4148314, -8893890, 7259002, 11666551, 13824734, -30531198, 2697372, 24154791, -9460943}, - FieldElement{15446137, -15806644, 29759747, 14019369, 30811221, -9610191, -31582008, 12840104, 24913809, 9815020}, - }, - { - FieldElement{-4709286, -5614269, -31841498, -12288893, -14443537, 10799414, -9103676, 13438769, 18735128, 9466238}, - FieldElement{11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821, -10896103, -22728655, 16199064}, - FieldElement{14576810, 379472, -26786533, -8317236, -29426508, -10812974, -102766, 1876699, 30801119, 2164795}, - }, - { - FieldElement{15995086, 3199873, 13672555, 13712240, -19378835, -4647646, -13081610, -15496269, -13492807, 1268052}, - FieldElement{-10290614, -3659039, -3286592, 10948818, 23037027, 3794475, -3470338, -12600221, -17055369, 3565904}, - FieldElement{29210088, -9419337, -5919792, -4952785, 10834811, -13327726, -16512102, -10820713, -27162222, -14030531}, - }, - { - FieldElement{-13161890, 15508588, 16663704, -8156150, -28349942, 9019123, -29183421, -3769423, 2244111, -14001979}, - FieldElement{-5152875, -3800936, -9306475, -6071583, 16243069, 14684434, -25673088, -16180800, 13491506, 4641841}, - FieldElement{10813417, 643330, -19188515, -728916, 30292062, -16600078, 27548447, -7721242, 14476989, -12767431}, - }, - { - FieldElement{10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937, -1644259, -27912810, 12651324}, - FieldElement{-31185513, -813383, 22271204, 11835308, 10201545, 15351028, 17099662, 3988035, 21721536, -3148940}, - FieldElement{10202177, -6545839, -31373232, -9574638, -32150642, -8119683, -12906320, 3852694, 13216206, 14842320}, - }, - { - FieldElement{-15815640, -10601066, -6538952, -7258995, -6984659, -6581778, -31500847, 13765824, -27434397, 9900184}, - FieldElement{14465505, -13833331, -32133984, -14738873, -27443187, 12990492, 33046193, 15796406, -7051866, -8040114}, - FieldElement{30924417, -8279620, 6359016, -12816335, 16508377, 9071735, -25488601, 15413635, 9524356, -7018878}, - }, - { - FieldElement{12274201, -13175547, 32627641, -1785326, 6736625, 13267305, 5237659, -5109483, 15663516, 4035784}, - FieldElement{-2951309, 8903985, 17349946, 601635, -16432815, -4612556, -13732739, -15889334, -22258478, 4659091}, - FieldElement{-16916263, -4952973, -30393711, -15158821, 20774812, 15897498, 5736189, 15026997, -2178256, -13455585}, - }, - }, - { - { - FieldElement{-8858980, -2219056, 28571666, -10155518, -474467, -10105698, -3801496, 278095, 23440562, -290208}, - FieldElement{10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275, 11551483, -16571960, -7442864}, - FieldElement{17932739, -12437276, -24039557, 10749060, 11316803, 7535897, 22503767, 5561594, -3646624, 3898661}, - }, - { - FieldElement{7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531, 7152530, 21831162, 1245233}, - FieldElement{26958459, -14658026, 4314586, 8346991, -5677764, 11960072, -32589295, -620035, -30402091, -16716212}, - FieldElement{-12165896, 9166947, 33491384, 13673479, 29787085, 13096535, 6280834, 14587357, -22338025, 13987525}, - }, - { - FieldElement{-24349909, 7778775, 21116000, 15572597, -4833266, -5357778, -4300898, -5124639, -7469781, -2858068}, - FieldElement{9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781, 6439245, -14581012, 4091397}, - FieldElement{-8426427, 1470727, -28109679, -1596990, 3978627, -5123623, -19622683, 12092163, 29077877, -14741988}, - }, - { - FieldElement{5269168, -6859726, -13230211, -8020715, 25932563, 1763552, -5606110, -5505881, -20017847, 2357889}, - FieldElement{32264008, -15407652, -5387735, -1160093, -2091322, -3946900, 23104804, -12869908, 5727338, 189038}, - FieldElement{14609123, -8954470, -6000566, -16622781, -14577387, -7743898, -26745169, 10942115, -25888931, -14884697}, - }, - { - FieldElement{20513500, 5557931, -15604613, 7829531, 26413943, -2019404, -21378968, 7471781, 13913677, -5137875}, - FieldElement{-25574376, 11967826, 29233242, 12948236, -6754465, 4713227, -8940970, 14059180, 12878652, 8511905}, - FieldElement{-25656801, 3393631, -2955415, -7075526, -2250709, 9366908, -30223418, 6812974, 5568676, -3127656}, - }, - { - FieldElement{11630004, 12144454, 2116339, 13606037, 27378885, 15676917, -17408753, -13504373, -14395196, 8070818}, - FieldElement{27117696, -10007378, -31282771, -5570088, 1127282, 12772488, -29845906, 10483306, -11552749, -1028714}, - FieldElement{10637467, -5688064, 5674781, 1072708, -26343588, -6982302, -1683975, 9177853, -27493162, 15431203}, - }, - { - FieldElement{20525145, 10892566, -12742472, 12779443, -29493034, 16150075, -28240519, 14943142, -15056790, -7935931}, - FieldElement{-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767, -3239766, -3356550, 9594024}, - FieldElement{-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683, -6492290, 13352335, -10977084}, - }, - { - FieldElement{-1931799, -5407458, 3304649, -12884869, 17015806, -4877091, -29783850, -7752482, -13215537, -319204}, - FieldElement{20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742, 15077870, -22750759, 14523817}, - FieldElement{27406042, -6041657, 27423596, -4497394, 4996214, 10002360, -28842031, -4545494, -30172742, -4805667}, - }, - }, - { - { - FieldElement{11374242, 12660715, 17861383, -12540833, 10935568, 1099227, -13886076, -9091740, -27727044, 11358504}, - FieldElement{-12730809, 10311867, 1510375, 10778093, -2119455, -9145702, 32676003, 11149336, -26123651, 4985768}, - FieldElement{-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043, 13794114, -19414307, -15621255}, - }, - { - FieldElement{6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603, 6970005, -1691065, -9004790}, - FieldElement{1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622, -5475723, -16796596, -5031438}, - FieldElement{-22273315, -13524424, -64685, -4334223, -18605636, -10921968, -20571065, -7007978, -99853, -10237333}, - }, - { - FieldElement{17747465, 10039260, 19368299, -4050591, -20630635, -16041286, 31992683, -15857976, -29260363, -5511971}, - FieldElement{31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999, -3744247, 4882242, -10626905}, - FieldElement{29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198, 3272828, -5190932, -4162409}, - }, - { - FieldElement{12501286, 4044383, -8612957, -13392385, -32430052, 5136599, -19230378, -3529697, 330070, -3659409}, - FieldElement{6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522, -8573892, -271295, 12071499}, - FieldElement{-8365515, -4042521, 25133448, -4517355, -6211027, 2265927, -32769618, 1936675, -5159697, 3829363}, - }, - { - FieldElement{28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550, -6567787, 26333140, 14267664}, - FieldElement{-11067219, 11871231, 27385719, -10559544, -4585914, -11189312, 10004786, -8709488, -21761224, 8930324}, - FieldElement{-21197785, -16396035, 25654216, -1725397, 12282012, 11008919, 1541940, 4757911, -26491501, -16408940}, - }, - { - FieldElement{13537262, -7759490, -20604840, 10961927, -5922820, -13218065, -13156584, 6217254, -15943699, 13814990}, - FieldElement{-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681, 9257833, -1956526, -1776914}, - FieldElement{-25045300, -10191966, 15366585, 15166509, -13105086, 8423556, -29171540, 12361135, -18685978, 4578290}, - }, - { - FieldElement{24579768, 3711570, 1342322, -11180126, -27005135, 14124956, -22544529, 14074919, 21964432, 8235257}, - FieldElement{-6528613, -2411497, 9442966, -5925588, 12025640, -1487420, -2981514, -1669206, 13006806, 2355433}, - FieldElement{-16304899, -13605259, -6632427, -5142349, 16974359, -10911083, 27202044, 1719366, 1141648, -12796236}, - }, - { - FieldElement{-12863944, -13219986, -8318266, -11018091, -6810145, -4843894, 13475066, -3133972, 32674895, 13715045}, - FieldElement{11423335, -5468059, 32344216, 8962751, 24989809, 9241752, -13265253, 16086212, -28740881, -15642093}, - FieldElement{-1409668, 12530728, -6368726, 10847387, 19531186, -14132160, -11709148, 7791794, -27245943, 4383347}, - }, - }, - { - { - FieldElement{-28970898, 5271447, -1266009, -9736989, -12455236, 16732599, -4862407, -4906449, 27193557, 6245191}, - FieldElement{-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898, 3260492, 22510453, 8577507}, - FieldElement{-12632451, 11257346, -32692994, 13548177, -721004, 10879011, 31168030, 13952092, -29571492, -3635906}, - }, - { - FieldElement{3877321, -9572739, 32416692, 5405324, -11004407, -13656635, 3759769, 11935320, 5611860, 8164018}, - FieldElement{-16275802, 14667797, 15906460, 12155291, -22111149, -9039718, 32003002, -8832289, 5773085, -8422109}, - FieldElement{-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725, 12376320, 31632953, 190926}, - }, - { - FieldElement{-24593607, -16138885, -8423991, 13378746, 14162407, 6901328, -8288749, 4508564, -25341555, -3627528}, - FieldElement{8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941, -14786005, -1672488, 827625}, - FieldElement{-32720583, -16289296, -32503547, 7101210, 13354605, 2659080, -1800575, -14108036, -24878478, 1541286}, - }, - { - FieldElement{2901347, -1117687, 3880376, -10059388, -17620940, -3612781, -21802117, -3567481, 20456845, -1885033}, - FieldElement{27019610, 12299467, -13658288, -1603234, -12861660, -4861471, -19540150, -5016058, 29439641, 15138866}, - FieldElement{21536104, -6626420, -32447818, -10690208, -22408077, 5175814, -5420040, -16361163, 7779328, 109896}, - }, - { - FieldElement{30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390, 12180118, 23177719, -554075}, - FieldElement{26572847, 3405927, -31701700, 12890905, -19265668, 5335866, -6493768, 2378492, 4439158, -13279347}, - FieldElement{-22716706, 3489070, -9225266, -332753, 18875722, -1140095, 14819434, -12731527, -17717757, -5461437}, - }, - { - FieldElement{-5056483, 16566551, 15953661, 3767752, -10436499, 15627060, -820954, 2177225, 8550082, -15114165}, - FieldElement{-18473302, 16596775, -381660, 15663611, 22860960, 15585581, -27844109, -3582739, -23260460, -8428588}, - FieldElement{-32480551, 15707275, -8205912, -5652081, 29464558, 2713815, -22725137, 15860482, -21902570, 1494193}, - }, - { - FieldElement{-19562091, -14087393, -25583872, -9299552, 13127842, 759709, 21923482, 16529112, 8742704, 12967017}, - FieldElement{-28464899, 1553205, 32536856, -10473729, -24691605, -406174, -8914625, -2933896, -29903758, 15553883}, - FieldElement{21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572, 14513274, 19375923, -12647961}, - }, - { - FieldElement{8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818, -6222716, 2862653, 9455043}, - FieldElement{29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124, -2990080, 15511449, 4789663}, - FieldElement{-20679756, 7004547, 8824831, -9434977, -4045704, -3750736, -5754762, 108893, 23513200, 16652362}, - }, - }, - { - { - FieldElement{-33256173, 4144782, -4476029, -6579123, 10770039, -7155542, -6650416, -12936300, -18319198, 10212860}, - FieldElement{2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801, 2600940, -9988298, -12506466}, - FieldElement{-24645692, 13317462, -30449259, -15653928, 21365574, -10869657, 11344424, 864440, -2499677, -16710063}, - }, - { - FieldElement{-26432803, 6148329, -17184412, -14474154, 18782929, -275997, -22561534, 211300, 2719757, 4940997}, - FieldElement{-1323882, 3911313, -6948744, 14759765, -30027150, 7851207, 21690126, 8518463, 26699843, 5276295}, - FieldElement{-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586, 149635, -15452774, 7159369}, - }, - { - FieldElement{9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009, 8312176, 22477218, -8403385}, - FieldElement{18155857, -16504990, 19744716, 9006923, 15154154, -10538976, 24256460, -4864995, -22548173, 9334109}, - FieldElement{2986088, -4911893, 10776628, -3473844, 10620590, -7083203, -21413845, 14253545, -22587149, 536906}, - }, - { - FieldElement{4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551, 10589625, 10838060, -15420424}, - FieldElement{-19342404, 867880, 9277171, -3218459, -14431572, -1986443, 19295826, -15796950, 6378260, 699185}, - FieldElement{7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039, 15693155, -5045064, -13373962}, - }, - { - FieldElement{-7737563, -5869402, -14566319, -7406919, 11385654, 13201616, 31730678, -10962840, -3918636, -9669325}, - FieldElement{10188286, -15770834, -7336361, 13427543, 22223443, 14896287, 30743455, 7116568, -21786507, 5427593}, - FieldElement{696102, 13206899, 27047647, -10632082, 15285305, -9853179, 10798490, -4578720, 19236243, 12477404}, - }, - { - FieldElement{-11229439, 11243796, -17054270, -8040865, -788228, -8167967, -3897669, 11180504, -23169516, 7733644}, - FieldElement{17800790, -14036179, -27000429, -11766671, 23887827, 3149671, 23466177, -10538171, 10322027, 15313801}, - FieldElement{26246234, 11968874, 32263343, -5468728, 6830755, -13323031, -15794704, -101982, -24449242, 10890804}, - }, - { - FieldElement{-31365647, 10271363, -12660625, -6267268, 16690207, -13062544, -14982212, 16484931, 25180797, -5334884}, - FieldElement{-586574, 10376444, -32586414, -11286356, 19801893, 10997610, 2276632, 9482883, 316878, 13820577}, - FieldElement{-9882808, -4510367, -2115506, 16457136, -11100081, 11674996, 30756178, -7515054, 30696930, -3712849}, - }, - { - FieldElement{32988917, -9603412, 12499366, 7910787, -10617257, -11931514, -7342816, -9985397, -32349517, 7392473}, - FieldElement{-8855661, 15927861, 9866406, -3649411, -2396914, -16655781, -30409476, -9134995, 25112947, -2926644}, - FieldElement{-2504044, -436966, 25621774, -5678772, 15085042, -5479877, -24884878, -13526194, 5537438, -13914319}, - }, - }, - { - { - FieldElement{-11225584, 2320285, -9584280, 10149187, -33444663, 5808648, -14876251, -1729667, 31234590, 6090599}, - FieldElement{-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721, 15878753, -6970405, -9034768}, - FieldElement{-27757857, 247744, -15194774, -9002551, 23288161, -10011936, -23869595, 6503646, 20650474, 1804084}, - }, - { - FieldElement{-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995, -10329713, 27842616, -202328}, - FieldElement{-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656, 5031932, -11375082, 12714369}, - FieldElement{20807691, -7270825, 29286141, 11421711, -27876523, -13868230, -21227475, 1035546, -19733229, 12796920}, - }, - { - FieldElement{12076899, -14301286, -8785001, -11848922, -25012791, 16400684, -17591495, -12899438, 3480665, -15182815}, - FieldElement{-32361549, 5457597, 28548107, 7833186, 7303070, -11953545, -24363064, -15921875, -33374054, 2771025}, - FieldElement{-21389266, 421932, 26597266, 6860826, 22486084, -6737172, -17137485, -4210226, -24552282, 15673397}, - }, - { - FieldElement{-20184622, 2338216, 19788685, -9620956, -4001265, -8740893, -20271184, 4733254, 3727144, -12934448}, - FieldElement{6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594, 7975683, 31123697, -10958981}, - FieldElement{30069250, -11435332, 30434654, 2958439, 18399564, -976289, 12296869, 9204260, -16432438, 9648165}, - }, - { - FieldElement{32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266, 5248604, -26008332, -11377501}, - FieldElement{17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711, 15298639, 2662509, -16297073}, - FieldElement{-1172927, -7558695, -4366770, -4287744, -21346413, -8434326, 32087529, -1222777, 32247248, -14389861}, - }, - { - FieldElement{14312628, 1221556, 17395390, -8700143, -4945741, -8684635, -28197744, -9637817, -16027623, -13378845}, - FieldElement{-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502, 9803137, 17597934, 2346211}, - FieldElement{18510800, 15337574, 26171504, 981392, -22241552, 7827556, -23491134, -11323352, 3059833, -11782870}, - }, - { - FieldElement{10141598, 6082907, 17829293, -1947643, 9830092, 13613136, -25556636, -5544586, -33502212, 3592096}, - FieldElement{33114168, -15889352, -26525686, -13343397, 33076705, 8716171, 1151462, 1521897, -982665, -6837803}, - FieldElement{-32939165, -4255815, 23947181, -324178, -33072974, -12305637, -16637686, 3891704, 26353178, 693168}, - }, - { - FieldElement{30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294, -400668, 31375464, 14369965}, - FieldElement{-14370654, -7772529, 1510301, 6434173, -18784789, -6262728, 32732230, -13108839, 17901441, 16011505}, - FieldElement{18171223, -11934626, -12500402, 15197122, -11038147, -15230035, -19172240, -16046376, 8764035, 12309598}, - }, - }, - { - { - FieldElement{5975908, -5243188, -19459362, -9681747, -11541277, 14015782, -23665757, 1228319, 17544096, -10593782}, - FieldElement{5811932, -1715293, 3442887, -2269310, -18367348, -8359541, -18044043, -15410127, -5565381, 12348900}, - FieldElement{-31399660, 11407555, 25755363, 6891399, -3256938, 14872274, -24849353, 8141295, -10632534, -585479}, - }, - { - FieldElement{-12675304, 694026, -5076145, 13300344, 14015258, -14451394, -9698672, -11329050, 30944593, 1130208}, - FieldElement{8247766, -6710942, -26562381, -7709309, -14401939, -14648910, 4652152, 2488540, 23550156, -271232}, - FieldElement{17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737, -5908146, -408818, -137719}, - }, - { - FieldElement{16091085, -16253926, 18599252, 7340678, 2137637, -1221657, -3364161, 14550936, 3260525, -7166271}, - FieldElement{-4910104, -13332887, 18550887, 10864893, -16459325, -7291596, -23028869, -13204905, -12748722, 2701326}, - FieldElement{-8574695, 16099415, 4629974, -16340524, -20786213, -6005432, -10018363, 9276971, 11329923, 1862132}, - }, - { - FieldElement{14763076, -15903608, -30918270, 3689867, 3511892, 10313526, -21951088, 12219231, -9037963, -940300}, - FieldElement{8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216, -2909717, -15438168, 11595570}, - FieldElement{15214962, 3537601, -26238722, -14058872, 4418657, -15230761, 13947276, 10730794, -13489462, -4363670}, - }, - { - FieldElement{-2538306, 7682793, 32759013, 263109, -29984731, -7955452, -22332124, -10188635, 977108, 699994}, - FieldElement{-12466472, 4195084, -9211532, 550904, -15565337, 12917920, 19118110, -439841, -30534533, -14337913}, - FieldElement{31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237, -10051775, 12493932, -5409317}, - }, - { - FieldElement{-25680606, 5260744, -19235809, -6284470, -3695942, 16566087, 27218280, 2607121, 29375955, 6024730}, - FieldElement{842132, -2794693, -4763381, -8722815, 26332018, -12405641, 11831880, 6985184, -9940361, 2854096}, - FieldElement{-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645, 960770, 12121869, 16648078}, - }, - { - FieldElement{-15218652, 14667096, -13336229, 2013717, 30598287, -464137, -31504922, -7882064, 20237806, 2838411}, - FieldElement{-19288047, 4453152, 15298546, -16178388, 22115043, -15972604, 12544294, -13470457, 1068881, -12499905}, - FieldElement{-9558883, -16518835, 33238498, 13506958, 30505848, -1114596, -8486907, -2630053, 12521378, 4845654}, - }, - { - FieldElement{-28198521, 10744108, -2958380, 10199664, 7759311, -13088600, 3409348, -873400, -6482306, -12885870}, - FieldElement{-23561822, 6230156, -20382013, 10655314, -24040585, -11621172, 10477734, -1240216, -3113227, 13974498}, - FieldElement{12966261, 15550616, -32038948, -1615346, 21025980, -629444, 5642325, 7188737, 18895762, 12629579}, - }, - }, - { - { - FieldElement{14741879, -14946887, 22177208, -11721237, 1279741, 8058600, 11758140, 789443, 32195181, 3895677}, - FieldElement{10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575, -3566119, -8982069, 4429647}, - FieldElement{-2453894, 15725973, -20436342, -10410672, -5803908, -11040220, -7135870, -11642895, 18047436, -15281743}, - }, - { - FieldElement{-25173001, -11307165, 29759956, 11776784, -22262383, -15820455, 10993114, -12850837, -17620701, -9408468}, - FieldElement{21987233, 700364, -24505048, 14972008, -7774265, -5718395, 32155026, 2581431, -29958985, 8773375}, - FieldElement{-25568350, 454463, -13211935, 16126715, 25240068, 8594567, 20656846, 12017935, -7874389, -13920155}, - }, - { - FieldElement{6028182, 6263078, -31011806, -11301710, -818919, 2461772, -31841174, -5468042, -1721788, -2776725}, - FieldElement{-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845, -4166698, 28408820, 6816612}, - FieldElement{-10358094, -8237829, 19549651, -12169222, 22082623, 16147817, 20613181, 13982702, -10339570, 5067943}, - }, - { - FieldElement{-30505967, -3821767, 12074681, 13582412, -19877972, 2443951, -19719286, 12746132, 5331210, -10105944}, - FieldElement{30528811, 3601899, -1957090, 4619785, -27361822, -15436388, 24180793, -12570394, 27679908, -1648928}, - FieldElement{9402404, -13957065, 32834043, 10838634, -26580150, -13237195, 26653274, -8685565, 22611444, -12715406}, - }, - { - FieldElement{22190590, 1118029, 22736441, 15130463, -30460692, -5991321, 19189625, -4648942, 4854859, 6622139}, - FieldElement{-8310738, -2953450, -8262579, -3388049, -10401731, -271929, 13424426, -3567227, 26404409, 13001963}, - FieldElement{-31241838, -15415700, -2994250, 8939346, 11562230, -12840670, -26064365, -11621720, -15405155, 11020693}, - }, - { - FieldElement{1866042, -7949489, -7898649, -10301010, 12483315, 13477547, 3175636, -12424163, 28761762, 1406734}, - FieldElement{-448555, -1777666, 13018551, 3194501, -9580420, -11161737, 24760585, -4347088, 25577411, -13378680}, - FieldElement{-24290378, 4759345, -690653, -1852816, 2066747, 10693769, -29595790, 9884936, -9368926, 4745410}, - }, - { - FieldElement{-9141284, 6049714, -19531061, -4341411, -31260798, 9944276, -15462008, -11311852, 10931924, -11931931}, - FieldElement{-16561513, 14112680, -8012645, 4817318, -8040464, -11414606, -22853429, 10856641, -20470770, 13434654}, - FieldElement{22759489, -10073434, -16766264, -1871422, 13637442, -10168091, 1765144, -12654326, 28445307, -5364710}, - }, - { - FieldElement{29875063, 12493613, 2795536, -3786330, 1710620, 15181182, -10195717, -8788675, 9074234, 1167180}, - FieldElement{-26205683, 11014233, -9842651, -2635485, -26908120, 7532294, -18716888, -9535498, 3843903, 9367684}, - FieldElement{-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123, 8601684, -139197, 4242895}, - }, - }, - { - { - FieldElement{22092954, -13191123, -2042793, -11968512, 32186753, -11517388, -6574341, 2470660, -27417366, 16625501}, - FieldElement{-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857, 2602725, -27351616, 14247413}, - FieldElement{6314175, -10264892, -32772502, 15957557, -10157730, 168750, -8618807, 14290061, 27108877, -1180880}, - }, - { - FieldElement{-8586597, -7170966, 13241782, 10960156, -32991015, -13794596, 33547976, -11058889, -27148451, 981874}, - FieldElement{22833440, 9293594, -32649448, -13618667, -9136966, 14756819, -22928859, -13970780, -10479804, -16197962}, - FieldElement{-7768587, 3326786, -28111797, 10783824, 19178761, 14905060, 22680049, 13906969, -15933690, 3797899}, - }, - { - FieldElement{21721356, -4212746, -12206123, 9310182, -3882239, -13653110, 23740224, -2709232, 20491983, -8042152}, - FieldElement{9209270, -15135055, -13256557, -6167798, -731016, 15289673, 25947805, 15286587, 30997318, -6703063}, - FieldElement{7392032, 16618386, 23946583, -8039892, -13265164, -1533858, -14197445, -2321576, 17649998, -250080}, - }, - { - FieldElement{-9301088, -14193827, 30609526, -3049543, -25175069, -1283752, -15241566, -9525724, -2233253, 7662146}, - FieldElement{-17558673, 1763594, -33114336, 15908610, -30040870, -12174295, 7335080, -8472199, -3174674, 3440183}, - FieldElement{-19889700, -5977008, -24111293, -9688870, 10799743, -16571957, 40450, -4431835, 4862400, 1133}, - }, - { - FieldElement{-32856209, -7873957, -5422389, 14860950, -16319031, 7956142, 7258061, 311861, -30594991, -7379421}, - FieldElement{-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763, 16527196, 18278453, 15405622}, - FieldElement{-4381906, 8508652, -19898366, -3674424, -5984453, 15149970, -13313598, 843523, -21875062, 13626197}, - }, - { - FieldElement{2281448, -13487055, -10915418, -2609910, 1879358, 16164207, -10783882, 3953792, 13340839, 15928663}, - FieldElement{31727126, -7179855, -18437503, -8283652, 2875793, -16390330, -25269894, -7014826, -23452306, 5964753}, - FieldElement{4100420, -5959452, -17179337, 6017714, -18705837, 12227141, -26684835, 11344144, 2538215, -7570755}, - }, - { - FieldElement{-9433605, 6123113, 11159803, -2156608, 30016280, 14966241, -20474983, 1485421, -629256, -15958862}, - FieldElement{-26804558, 4260919, 11851389, 9658551, -32017107, 16367492, -20205425, -13191288, 11659922, -11115118}, - FieldElement{26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568, -10170080, 33100372, -1306171}, - }, - { - FieldElement{15121113, -5201871, -10389905, 15427821, -27509937, -15992507, 21670947, 4486675, -5931810, -14466380}, - FieldElement{16166486, -9483733, -11104130, 6023908, -31926798, -1364923, 2340060, -16254968, -10735770, -10039824}, - FieldElement{28042865, -3557089, -12126526, 12259706, -3717498, -6945899, 6766453, -8689599, 18036436, 5803270}, - }, - }, - { - { - FieldElement{-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391, 4598332, -6159431, -14117438}, - FieldElement{-31031306, -14256194, 17332029, -2383520, 31312682, -5967183, 696309, 50292, -20095739, 11763584}, - FieldElement{-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117, -12613632, -19773211, -10713562}, - }, - { - FieldElement{30464590, -11262872, -4127476, -12734478, 19835327, -7105613, -24396175, 2075773, -17020157, 992471}, - FieldElement{18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841, 8080033, -11574335, -10601610}, - FieldElement{19598397, 10334610, 12555054, 2555664, 18821899, -10339780, 21873263, 16014234, 26224780, 16452269}, - }, - { - FieldElement{-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804, -7618186, -20533829, 3698650}, - FieldElement{14187449, 3448569, -10636236, -10810935, -22663880, -3433596, 7268410, -10890444, 27394301, 12015369}, - FieldElement{19695761, 16087646, 28032085, 12999827, 6817792, 11427614, 20244189, -1312777, -13259127, -3402461}, - }, - { - FieldElement{30860103, 12735208, -1888245, -4699734, -16974906, 2256940, -8166013, 12298312, -8550524, -10393462}, - FieldElement{-5719826, -11245325, -1910649, 15569035, 26642876, -7587760, -5789354, -15118654, -4976164, 12651793}, - FieldElement{-2848395, 9953421, 11531313, -5282879, 26895123, -12697089, -13118820, -16517902, 9768698, -2533218}, - }, - { - FieldElement{-24719459, 1894651, -287698, -4704085, 15348719, -8156530, 32767513, 12765450, 4940095, 10678226}, - FieldElement{18860224, 15980149, -18987240, -1562570, -26233012, -11071856, -7843882, 13944024, -24372348, 16582019}, - FieldElement{-15504260, 4970268, -29893044, 4175593, -20993212, -2199756, -11704054, 15444560, -11003761, 7989037}, - }, - { - FieldElement{31490452, 5568061, -2412803, 2182383, -32336847, 4531686, -32078269, 6200206, -19686113, -14800171}, - FieldElement{-17308668, -15879940, -31522777, -2831, -32887382, 16375549, 8680158, -16371713, 28550068, -6857132}, - FieldElement{-28126887, -5688091, 16837845, -1820458, -6850681, 12700016, -30039981, 4364038, 1155602, 5988841}, - }, - { - FieldElement{21890435, -13272907, -12624011, 12154349, -7831873, 15300496, 23148983, -4470481, 24618407, 8283181}, - FieldElement{-33136107, -10512751, 9975416, 6841041, -31559793, 16356536, 3070187, -7025928, 1466169, 10740210}, - FieldElement{-1509399, -15488185, -13503385, -10655916, 32799044, 909394, -13938903, -5779719, -32164649, -15327040}, - }, - { - FieldElement{3960823, -14267803, -28026090, -15918051, -19404858, 13146868, 15567327, 951507, -3260321, -573935}, - FieldElement{24740841, 5052253, -30094131, 8961361, 25877428, 6165135, -24368180, 14397372, -7380369, -6144105}, - FieldElement{-28888365, 3510803, -28103278, -1158478, -11238128, -10631454, -15441463, -14453128, -1625486, -6494814}, - }, - }, - { - { - FieldElement{793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843, -4885251, -9906200, -621852}, - FieldElement{5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374, 1468826, -6171428, -15186581}, - FieldElement{-4859255, -3779343, -2917758, -6748019, 7778750, 11688288, -30404353, -9871238, -1558923, -9863646}, - }, - { - FieldElement{10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958, 14783338, -30581476, -15757844}, - FieldElement{10566929, 12612572, -31944212, 11118703, -12633376, 12362879, 21752402, 8822496, 24003793, 14264025}, - FieldElement{27713862, -7355973, -11008240, 9227530, 27050101, 2504721, 23886875, -13117525, 13958495, -5732453}, - }, - { - FieldElement{-23481610, 4867226, -27247128, 3900521, 29838369, -8212291, -31889399, -10041781, 7340521, -15410068}, - FieldElement{4646514, -8011124, -22766023, -11532654, 23184553, 8566613, 31366726, -1381061, -15066784, -10375192}, - FieldElement{-17270517, 12723032, -16993061, 14878794, 21619651, -6197576, 27584817, 3093888, -8843694, 3849921}, - }, - { - FieldElement{-9064912, 2103172, 25561640, -15125738, -5239824, 9582958, 32477045, -9017955, 5002294, -15550259}, - FieldElement{-12057553, -11177906, 21115585, -13365155, 8808712, -12030708, 16489530, 13378448, -25845716, 12741426}, - FieldElement{-5946367, 10645103, -30911586, 15390284, -3286982, -7118677, 24306472, 15852464, 28834118, -7646072}, - }, - { - FieldElement{-17335748, -9107057, -24531279, 9434953, -8472084, -583362, -13090771, 455841, 20461858, 5491305}, - FieldElement{13669248, -16095482, -12481974, -10203039, -14569770, -11893198, -24995986, 11293807, -28588204, -9421832}, - FieldElement{28497928, 6272777, -33022994, 14470570, 8906179, -1225630, 18504674, -14165166, 29867745, -8795943}, - }, - { - FieldElement{-16207023, 13517196, -27799630, -13697798, 24009064, -6373891, -6367600, -13175392, 22853429, -4012011}, - FieldElement{24191378, 16712145, -13931797, 15217831, 14542237, 1646131, 18603514, -11037887, 12876623, -2112447}, - FieldElement{17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753, 608397, 16031844, 3723494}, - }, - { - FieldElement{-28632773, 12763728, -20446446, 7577504, 33001348, -13017745, 17558842, -7872890, 23896954, -4314245}, - FieldElement{-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064, 7229064, -9919646, -8826859}, - FieldElement{28816045, 298879, -28165016, -15920938, 19000928, -1665890, -12680833, -2949325, -18051778, -2082915}, - }, - { - FieldElement{16000882, -344896, 3493092, -11447198, -29504595, -13159789, 12577740, 16041268, -19715240, 7847707}, - FieldElement{10151868, 10572098, 27312476, 7922682, 14825339, 4723128, -32855931, -6519018, -10020567, 3852848}, - FieldElement{-11430470, 15697596, -21121557, -4420647, 5386314, 15063598, 16514493, -15932110, 29330899, -15076224}, - }, - }, - { - { - FieldElement{-25499735, -4378794, -15222908, -6901211, 16615731, 2051784, 3303702, 15490, -27548796, 12314391}, - FieldElement{15683520, -6003043, 18109120, -9980648, 15337968, -5997823, -16717435, 15921866, 16103996, -3731215}, - FieldElement{-23169824, -10781249, 13588192, -1628807, -3798557, -1074929, -19273607, 5402699, -29815713, -9841101}, - }, - { - FieldElement{23190676, 2384583, -32714340, 3462154, -29903655, -1529132, -11266856, 8911517, -25205859, 2739713}, - FieldElement{21374101, -3554250, -33524649, 9874411, 15377179, 11831242, -33529904, 6134907, 4931255, 11987849}, - FieldElement{-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539, 13861388, -30076310, 10117930}, - }, - { - FieldElement{-29501170, -10744872, -26163768, 13051539, -25625564, 5089643, -6325503, 6704079, 12890019, 15728940}, - FieldElement{-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376, -10428139, 12885167, 8311031}, - FieldElement{-17516482, 5352194, 10384213, -13811658, 7506451, 13453191, 26423267, 4384730, 1888765, -5435404}, - }, - { - FieldElement{-25817338, -3107312, -13494599, -3182506, 30896459, -13921729, -32251644, -12707869, -19464434, -3340243}, - FieldElement{-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245, 14845197, 17151279, -9854116}, - FieldElement{-24830458, -12733720, -15165978, 10367250, -29530908, -265356, 22825805, -7087279, -16866484, 16176525}, - }, - { - FieldElement{-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182, -10363426, -28746253, -10197509}, - FieldElement{-10626600, -4486402, -13320562, -5125317, 3432136, -6393229, 23632037, -1940610, 32808310, 1099883}, - FieldElement{15030977, 5768825, -27451236, -2887299, -6427378, -15361371, -15277896, -6809350, 2051441, -15225865}, - }, - { - FieldElement{-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398, -14154188, -22686354, 16633660}, - FieldElement{4577086, -16752288, 13249841, -15304328, 19958763, -14537274, 18559670, -10759549, 8402478, -9864273}, - FieldElement{-28406330, -1051581, -26790155, -907698, -17212414, -11030789, 9453451, -14980072, 17983010, 9967138}, - }, - { - FieldElement{-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990, 7806337, 17507396, 3651560}, - FieldElement{-10420457, -4118111, 14584639, 15971087, -15768321, 8861010, 26556809, -5574557, -18553322, -11357135}, - FieldElement{2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121, 8459447, -5605463, -7621941}, - }, - { - FieldElement{-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813, -849066, 17258084, -7977739}, - FieldElement{18164541, -10595176, -17154882, -1542417, 19237078, -9745295, 23357533, -15217008, 26908270, 12150756}, - FieldElement{-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168, -5537701, -32302074, 16215819}, - }, - }, - { - { - FieldElement{-6898905, 9824394, -12304779, -4401089, -31397141, -6276835, 32574489, 12532905, -7503072, -8675347}, - FieldElement{-27343522, -16515468, -27151524, -10722951, 946346, 16291093, 254968, 7168080, 21676107, -1943028}, - FieldElement{21260961, -8424752, -16831886, -11920822, -23677961, 3968121, -3651949, -6215466, -3556191, -7913075}, - }, - { - FieldElement{16544754, 13250366, -16804428, 15546242, -4583003, 12757258, -2462308, -8680336, -18907032, -9662799}, - FieldElement{-2415239, -15577728, 18312303, 4964443, -15272530, -12653564, 26820651, 16690659, 25459437, -4564609}, - FieldElement{-25144690, 11425020, 28423002, -11020557, -6144921, -15826224, 9142795, -2391602, -6432418, -1644817}, - }, - { - FieldElement{-23104652, 6253476, 16964147, -3768872, -25113972, -12296437, -27457225, -16344658, 6335692, 7249989}, - FieldElement{-30333227, 13979675, 7503222, -12368314, -11956721, -4621693, -30272269, 2682242, 25993170, -12478523}, - FieldElement{4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278}, - }, - { - FieldElement{31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045}, - FieldElement{19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377}, - FieldElement{24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480}, - }, - { - FieldElement{17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016}, - FieldElement{510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426}, - FieldElement{18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525}, - }, - { - FieldElement{13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396}, - FieldElement{9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080}, - FieldElement{12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892}, - }, - { - FieldElement{15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275}, - FieldElement{11038231, -11582396, -27310482, -7316562, -10498527, -16307831, -23479533, -9371869, -21393143, 2465074}, - FieldElement{20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140}, - }, - { - FieldElement{-16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717}, - FieldElement{-1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101}, - FieldElement{24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127}, - }, - }, - { - { - FieldElement{-12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632}, - FieldElement{-26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415}, - FieldElement{-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160}, - }, - { - FieldElement{31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876}, - FieldElement{22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625}, - FieldElement{-15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478}, - }, - { - FieldElement{27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164}, - FieldElement{26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595}, - FieldElement{-7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248}, - }, - { - FieldElement{-16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858}, - FieldElement{15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193}, - FieldElement{8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184}, - }, - { - FieldElement{-18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942}, - FieldElement{-1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635}, - FieldElement{21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948}, - }, - { - FieldElement{11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935}, - FieldElement{-25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415}, - FieldElement{-15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416}, - }, - { - FieldElement{-7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018}, - FieldElement{4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778}, - FieldElement{366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659}, - }, - { - FieldElement{-24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385}, - FieldElement{18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503}, - FieldElement{476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329}, - }, - }, - { - { - FieldElement{20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056}, - FieldElement{-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838}, - FieldElement{24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948}, - }, - { - FieldElement{-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691}, - FieldElement{-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118}, - FieldElement{-23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517}, - }, - { - FieldElement{-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269}, - FieldElement{-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904}, - FieldElement{-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589}, - }, - { - FieldElement{-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193}, - FieldElement{-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910}, - FieldElement{-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930}, - }, - { - FieldElement{-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667}, - FieldElement{25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481}, - FieldElement{-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876}, - }, - { - FieldElement{22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640}, - FieldElement{-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278}, - FieldElement{-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112}, - }, - { - FieldElement{26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272}, - FieldElement{17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012}, - 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/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go b/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go deleted file mode 100644 index fd03c252a..000000000 --- a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go +++ /dev/null @@ -1,1793 +0,0 @@ -// Copyright 2016 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 - -import "encoding/binary" - -// 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, assuming that b and c are -// non-negative. -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) -} - -// order is the order of Curve25519 in little-endian form. -var order = [4]uint64{0x5812631a5cf5d3ed, 0x14def9dea2f79cd6, 0, 0x1000000000000000} - -// ScMinimal returns true if the given scalar is less than the order of the -// curve. -func ScMinimal(scalar *[32]byte) bool { - for i := 3; ; i-- { - v := binary.LittleEndian.Uint64(scalar[i*8:]) - if v > order[i] { - return false - } else if v < order[i] { - break - } else if i == 0 { - return false - } - } - - return true -} diff --git a/vendor/golang.org/x/crypto/internal/poly1305/sum_generic.go b/vendor/golang.org/x/crypto/internal/poly1305/sum_generic.go index c942a6590..e041da5ea 100644 --- a/vendor/golang.org/x/crypto/internal/poly1305/sum_generic.go +++ b/vendor/golang.org/x/crypto/internal/poly1305/sum_generic.go @@ -136,7 +136,7 @@ func shiftRightBy2(a uint128) uint128 { // updateGeneric absorbs msg into the state.h accumulator. For each chunk m of // 128 bits of message, it computes // -// h₊ = (h + m) * r mod 2¹³⁰ - 5 +// h₊ = (h + m) * r mod 2¹³⁰ - 5 // // If the msg length is not a multiple of TagSize, it assumes the last // incomplete chunk is the final one. @@ -278,8 +278,7 @@ const ( // finalize completes the modular reduction of h and computes // -// out = h + s mod 2¹²⁸ -// +// out = h + s mod 2¹²⁸ func finalize(out *[TagSize]byte, h *[3]uint64, s *[2]uint64) { h0, h1, h2 := h[0], h[1], h[2] diff --git a/vendor/golang.org/x/crypto/internal/poly1305/sum_s390x.go b/vendor/golang.org/x/crypto/internal/poly1305/sum_s390x.go index 62cc9f847..ec9596688 100644 --- a/vendor/golang.org/x/crypto/internal/poly1305/sum_s390x.go +++ b/vendor/golang.org/x/crypto/internal/poly1305/sum_s390x.go @@ -14,6 +14,7 @@ import ( // updateVX is an assembly implementation of Poly1305 that uses vector // instructions. It must only be called if the vector facility (vx) is // available. +// //go:noescape func updateVX(state *macState, msg []byte) diff --git a/vendor/golang.org/x/crypto/openpgp/armor/armor.go b/vendor/golang.org/x/crypto/openpgp/armor/armor.go index ebc87876e..be342ad47 100644 --- a/vendor/golang.org/x/crypto/openpgp/armor/armor.go +++ b/vendor/golang.org/x/crypto/openpgp/armor/armor.go @@ -23,12 +23,14 @@ import ( // A Block represents an OpenPGP armored structure. // // The encoded form is: -// -----BEGIN Type----- -// Headers // -// base64-encoded Bytes -// '=' base64 encoded checksum -// -----END Type----- +// -----BEGIN Type----- +// Headers +// +// base64-encoded Bytes +// '=' base64 encoded checksum +// -----END Type----- +// // where Headers is a possibly empty sequence of Key: Value lines. // // Since the armored data can be very large, this package presents a streaming diff --git a/vendor/golang.org/x/crypto/openpgp/armor/encode.go b/vendor/golang.org/x/crypto/openpgp/armor/encode.go index 6f07582c3..5b6e16c19 100644 --- a/vendor/golang.org/x/crypto/openpgp/armor/encode.go +++ b/vendor/golang.org/x/crypto/openpgp/armor/encode.go @@ -96,7 +96,8 @@ func (l *lineBreaker) Close() (err error) { // trailer. // // It's built into a stack of io.Writers: -// encoding -> base64 encoder -> lineBreaker -> out +// +// encoding -> base64 encoder -> lineBreaker -> out type encoding struct { out io.Writer breaker *lineBreaker diff --git a/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go b/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go index 84396a089..743b35a12 100644 --- a/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go +++ b/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go @@ -77,8 +77,8 @@ func Encrypt(random io.Reader, pub *PublicKey, msg []byte) (c1, c2 *big.Int, err // returns the plaintext of the message. An error can result only if the // ciphertext is invalid. Users should keep in mind that this is a padding // oracle and thus, if exposed to an adaptive chosen ciphertext attack, can -// be used to break the cryptosystem. See ``Chosen Ciphertext Attacks -// Against Protocols Based on the RSA Encryption Standard PKCS #1'', Daniel +// be used to break the cryptosystem. See “Chosen Ciphertext Attacks +// Against Protocols Based on the RSA Encryption Standard PKCS #1”, Daniel // Bleichenbacher, Advances in Cryptology (Crypto '98), func Decrypt(priv *PrivateKey, c1, c2 *big.Int) (msg []byte, err error) { s := new(big.Int).Exp(c1, priv.X, priv.P) diff --git a/vendor/golang.org/x/crypto/pbkdf2/pbkdf2.go b/vendor/golang.org/x/crypto/pbkdf2/pbkdf2.go index 593f65300..904b57e01 100644 --- a/vendor/golang.org/x/crypto/pbkdf2/pbkdf2.go +++ b/vendor/golang.org/x/crypto/pbkdf2/pbkdf2.go @@ -32,7 +32,7 @@ import ( // can get a derived key for e.g. AES-256 (which needs a 32-byte key) by // doing: // -// dk := pbkdf2.Key([]byte("some password"), salt, 4096, 32, sha1.New) +// dk := pbkdf2.Key([]byte("some password"), salt, 4096, 32, sha1.New) // // Remember to get a good random salt. At least 8 bytes is recommended by the // RFC. diff --git a/vendor/golang.org/x/crypto/ssh/agent/client.go b/vendor/golang.org/x/crypto/ssh/agent/client.go index b909471cc..dbc79d583 100644 --- a/vendor/golang.org/x/crypto/ssh/agent/client.go +++ b/vendor/golang.org/x/crypto/ssh/agent/client.go @@ -8,7 +8,8 @@ // ssh-agent process using the sample server. // // References: -// [PROTOCOL.agent]: https://tools.ietf.org/html/draft-miller-ssh-agent-00 +// +// [PROTOCOL.agent]: https://tools.ietf.org/html/draft-miller-ssh-agent-00 package agent // import "golang.org/x/crypto/ssh/agent" import ( @@ -25,7 +26,6 @@ import ( "math/big" "sync" - "crypto" "golang.org/x/crypto/ed25519" "golang.org/x/crypto/ssh" ) @@ -771,19 +771,26 @@ func (s *agentKeyringSigner) Sign(rand io.Reader, data []byte) (*ssh.Signature, return s.agent.Sign(s.pub, data) } -func (s *agentKeyringSigner) SignWithOpts(rand io.Reader, data []byte, opts crypto.SignerOpts) (*ssh.Signature, error) { +func (s *agentKeyringSigner) SignWithAlgorithm(rand io.Reader, data []byte, algorithm string) (*ssh.Signature, error) { + if algorithm == "" || algorithm == s.pub.Type() { + return s.Sign(rand, data) + } + var flags SignatureFlags - if opts != nil { - switch opts.HashFunc() { - case crypto.SHA256: - flags = SignatureFlagRsaSha256 - case crypto.SHA512: - flags = SignatureFlagRsaSha512 - } + switch algorithm { + case ssh.KeyAlgoRSASHA256: + flags = SignatureFlagRsaSha256 + case ssh.KeyAlgoRSASHA512: + flags = SignatureFlagRsaSha512 + default: + return nil, fmt.Errorf("agent: unsupported algorithm %q", algorithm) } + return s.agent.SignWithFlags(s.pub, data, flags) } +var _ ssh.AlgorithmSigner = &agentKeyringSigner{} + // Calls an extension method. It is up to the agent implementation as to whether or not // any particular extension is supported and may always return an error. Because the // type of the response is up to the implementation, this returns the bytes of the diff --git a/vendor/golang.org/x/crypto/ssh/agent/keyring.go b/vendor/golang.org/x/crypto/ssh/agent/keyring.go index c9d979430..21bfa870f 100644 --- a/vendor/golang.org/x/crypto/ssh/agent/keyring.go +++ b/vendor/golang.org/x/crypto/ssh/agent/keyring.go @@ -113,7 +113,7 @@ func (r *keyring) Unlock(passphrase []byte) error { // expireKeysLocked removes expired keys from the keyring. If a key was added // with a lifetimesecs contraint and seconds >= lifetimesecs seconds have -// ellapsed, it is removed. The caller *must* be holding the keyring mutex. +// elapsed, it is removed. The caller *must* be holding the keyring mutex. func (r *keyring) expireKeysLocked() { for _, k := range r.keys { if k.expire != nil && time.Now().After(*k.expire) { @@ -205,9 +205,9 @@ func (r *keyring) SignWithFlags(key ssh.PublicKey, data []byte, flags SignatureF var algorithm string switch flags { case SignatureFlagRsaSha256: - algorithm = ssh.SigAlgoRSASHA2256 + algorithm = ssh.KeyAlgoRSASHA256 case SignatureFlagRsaSha512: - algorithm = ssh.SigAlgoRSASHA2512 + algorithm = ssh.KeyAlgoRSASHA512 default: return nil, fmt.Errorf("agent: unsupported signature flags: %d", flags) } diff --git a/vendor/golang.org/x/crypto/ssh/certs.go b/vendor/golang.org/x/crypto/ssh/certs.go index 6605bf644..a69e22491 100644 --- a/vendor/golang.org/x/crypto/ssh/certs.go +++ b/vendor/golang.org/x/crypto/ssh/certs.go @@ -14,8 +14,10 @@ import ( "time" ) -// These constants from [PROTOCOL.certkeys] represent the key algorithm names -// for certificate types supported by this package. +// Certificate algorithm names from [PROTOCOL.certkeys]. These values can appear +// in Certificate.Type, PublicKey.Type, and ClientConfig.HostKeyAlgorithms. +// Unlike key algorithm names, these are not passed to AlgorithmSigner and don't +// appear in the Signature.Format field. const ( CertAlgoRSAv01 = "ssh-rsa-cert-v01@openssh.com" CertAlgoDSAv01 = "ssh-dss-cert-v01@openssh.com" @@ -25,14 +27,21 @@ const ( CertAlgoSKECDSA256v01 = "sk-ecdsa-sha2-nistp256-cert-v01@openssh.com" CertAlgoED25519v01 = "ssh-ed25519-cert-v01@openssh.com" CertAlgoSKED25519v01 = "sk-ssh-ed25519-cert-v01@openssh.com" + + // CertAlgoRSASHA256v01 and CertAlgoRSASHA512v01 can't appear as a + // Certificate.Type (or PublicKey.Type), but only in + // ClientConfig.HostKeyAlgorithms. + CertAlgoRSASHA256v01 = "rsa-sha2-256-cert-v01@openssh.com" + CertAlgoRSASHA512v01 = "rsa-sha2-512-cert-v01@openssh.com" ) -// These constants from [PROTOCOL.certkeys] represent additional signature -// algorithm names for certificate types supported by this package. const ( - CertSigAlgoRSAv01 = "ssh-rsa-cert-v01@openssh.com" - CertSigAlgoRSASHA2256v01 = "rsa-sha2-256-cert-v01@openssh.com" - CertSigAlgoRSASHA2512v01 = "rsa-sha2-512-cert-v01@openssh.com" + // Deprecated: use CertAlgoRSAv01. + CertSigAlgoRSAv01 = CertAlgoRSAv01 + // Deprecated: use CertAlgoRSASHA256v01. + CertSigAlgoRSASHA2256v01 = CertAlgoRSASHA256v01 + // Deprecated: use CertAlgoRSASHA512v01. + CertSigAlgoRSASHA2512v01 = CertAlgoRSASHA512v01 ) // Certificate types distinguish between host and user @@ -431,10 +440,14 @@ func (c *Certificate) SignCert(rand io.Reader, authority Signer) error { } c.SignatureKey = authority.PublicKey() - if v, ok := authority.(AlgorithmSigner); ok { - if v.PublicKey().Type() == KeyAlgoRSA { - authority = &rsaSigner{v, SigAlgoRSASHA2512} + // Default to KeyAlgoRSASHA512 for ssh-rsa signers. + if v, ok := authority.(AlgorithmSigner); ok && v.PublicKey().Type() == KeyAlgoRSA { + sig, err := v.SignWithAlgorithm(rand, c.bytesForSigning(), KeyAlgoRSASHA512) + if err != nil { + return err } + c.Signature = sig + return nil } sig, err := authority.Sign(rand, c.bytesForSigning()) @@ -445,32 +458,40 @@ func (c *Certificate) SignCert(rand io.Reader, authority Signer) error { return nil } -// certAlgoNames includes a mapping from signature algorithms to the -// corresponding certificate signature algorithm. When a key type (such -// as ED25516) is associated with only one algorithm, the KeyAlgo -// constant is used instead of the SigAlgo. -var certAlgoNames = map[string]string{ - SigAlgoRSA: CertSigAlgoRSAv01, - SigAlgoRSASHA2256: CertSigAlgoRSASHA2256v01, - SigAlgoRSASHA2512: CertSigAlgoRSASHA2512v01, - KeyAlgoDSA: CertAlgoDSAv01, - KeyAlgoECDSA256: CertAlgoECDSA256v01, - KeyAlgoECDSA384: CertAlgoECDSA384v01, - KeyAlgoECDSA521: CertAlgoECDSA521v01, - KeyAlgoSKECDSA256: CertAlgoSKECDSA256v01, - KeyAlgoED25519: CertAlgoED25519v01, - KeyAlgoSKED25519: CertAlgoSKED25519v01, +// certKeyAlgoNames is a mapping from known certificate algorithm names to the +// corresponding public key signature algorithm. +var certKeyAlgoNames = map[string]string{ + CertAlgoRSAv01: KeyAlgoRSA, + CertAlgoRSASHA256v01: KeyAlgoRSASHA256, + CertAlgoRSASHA512v01: KeyAlgoRSASHA512, + CertAlgoDSAv01: KeyAlgoDSA, + CertAlgoECDSA256v01: KeyAlgoECDSA256, + CertAlgoECDSA384v01: KeyAlgoECDSA384, + CertAlgoECDSA521v01: KeyAlgoECDSA521, + CertAlgoSKECDSA256v01: KeyAlgoSKECDSA256, + CertAlgoED25519v01: KeyAlgoED25519, + CertAlgoSKED25519v01: KeyAlgoSKED25519, +} + +// underlyingAlgo returns the signature algorithm associated with algo (which is +// an advertised or negotiated public key or host key algorithm). These are +// usually the same, except for certificate algorithms. +func underlyingAlgo(algo string) string { + if a, ok := certKeyAlgoNames[algo]; ok { + return a + } + return algo } -// certToPrivAlgo returns the underlying algorithm for a certificate algorithm. -// Panics if a non-certificate algorithm is passed. -func certToPrivAlgo(algo string) string { - for privAlgo, pubAlgo := range certAlgoNames { - if pubAlgo == algo { - return privAlgo +// certificateAlgo returns the certificate algorithms that uses the provided +// underlying signature algorithm. +func certificateAlgo(algo string) (certAlgo string, ok bool) { + for certName, algoName := range certKeyAlgoNames { + if algoName == algo { + return certName, true } } - panic("unknown cert algorithm") + return "", false } func (cert *Certificate) bytesForSigning() []byte { @@ -514,13 +535,13 @@ func (c *Certificate) Marshal() []byte { return result } -// Type returns the key name. It is part of the PublicKey interface. +// Type returns the certificate algorithm name. It is part of the PublicKey interface. func (c *Certificate) Type() string { - algo, ok := certAlgoNames[c.Key.Type()] + certName, ok := certificateAlgo(c.Key.Type()) if !ok { - panic("unknown cert key type " + c.Key.Type()) + panic("unknown certificate type for key type " + c.Key.Type()) } - return algo + return certName } // Verify verifies a signature against the certificate's public diff --git a/vendor/golang.org/x/crypto/ssh/cipher.go b/vendor/golang.org/x/crypto/ssh/cipher.go index f8bdf4984..770e8a663 100644 --- a/vendor/golang.org/x/crypto/ssh/cipher.go +++ b/vendor/golang.org/x/crypto/ssh/cipher.go @@ -640,7 +640,7 @@ const chacha20Poly1305ID = "chacha20-poly1305@openssh.com" // chacha20Poly1305Cipher implements the chacha20-poly1305@openssh.com // AEAD, which is described here: // -// https://tools.ietf.org/html/draft-josefsson-ssh-chacha20-poly1305-openssh-00 +// https://tools.ietf.org/html/draft-josefsson-ssh-chacha20-poly1305-openssh-00 // // the methods here also implement padding, which RFC4253 Section 6 // also requires of stream ciphers. diff --git a/vendor/golang.org/x/crypto/ssh/client.go b/vendor/golang.org/x/crypto/ssh/client.go index ba8621a89..bdc356cbd 100644 --- a/vendor/golang.org/x/crypto/ssh/client.go +++ b/vendor/golang.org/x/crypto/ssh/client.go @@ -113,25 +113,16 @@ func (c *connection) clientHandshake(dialAddress string, config *ClientConfig) e return c.clientAuthenticate(config) } -// verifyHostKeySignature verifies the host key obtained in the key -// exchange. +// verifyHostKeySignature verifies the host key obtained in the key exchange. +// algo is the negotiated algorithm, and may be a certificate type. func verifyHostKeySignature(hostKey PublicKey, algo string, result *kexResult) error { sig, rest, ok := parseSignatureBody(result.Signature) if len(rest) > 0 || !ok { return errors.New("ssh: signature parse error") } - // For keys, underlyingAlgo is exactly algo. For certificates, - // we have to look up the underlying key algorithm that SSH - // uses to evaluate signatures. - underlyingAlgo := algo - for sigAlgo, certAlgo := range certAlgoNames { - if certAlgo == algo { - underlyingAlgo = sigAlgo - } - } - if sig.Format != underlyingAlgo { - return fmt.Errorf("ssh: invalid signature algorithm %q, expected %q", sig.Format, underlyingAlgo) + if a := underlyingAlgo(algo); sig.Format != a { + return fmt.Errorf("ssh: invalid signature algorithm %q, expected %q", sig.Format, a) } return hostKey.Verify(result.H, sig) @@ -237,11 +228,11 @@ type ClientConfig struct { // be used for the connection. If empty, a reasonable default is used. ClientVersion string - // HostKeyAlgorithms lists the key types that the client will - // accept from the server as host key, in order of + // HostKeyAlgorithms lists the public key algorithms that the client will + // accept from the server for host key authentication, in order of // preference. If empty, a reasonable default is used. Any - // string returned from PublicKey.Type method may be used, or - // any of the CertAlgoXxxx and KeyAlgoXxxx constants. + // string returned from a PublicKey.Type method may be used, or + // any of the CertAlgo and KeyAlgo constants. HostKeyAlgorithms []string // Timeout is the maximum amount of time for the TCP connection to establish. diff --git a/vendor/golang.org/x/crypto/ssh/client_auth.go b/vendor/golang.org/x/crypto/ssh/client_auth.go index c611aeb68..409b5ea1d 100644 --- a/vendor/golang.org/x/crypto/ssh/client_auth.go +++ b/vendor/golang.org/x/crypto/ssh/client_auth.go @@ -9,6 +9,7 @@ import ( "errors" "fmt" "io" + "strings" ) type authResult int @@ -29,6 +30,33 @@ func (c *connection) clientAuthenticate(config *ClientConfig) error { if err != nil { return err } + // The server may choose to send a SSH_MSG_EXT_INFO at this point (if we + // advertised willingness to receive one, which we always do) or not. See + // RFC 8308, Section 2.4. + extensions := make(map[string][]byte) + if len(packet) > 0 && packet[0] == msgExtInfo { + var extInfo extInfoMsg + if err := Unmarshal(packet, &extInfo); err != nil { + return err + } + payload := extInfo.Payload + for i := uint32(0); i < extInfo.NumExtensions; i++ { + name, rest, ok := parseString(payload) + if !ok { + return parseError(msgExtInfo) + } + value, rest, ok := parseString(rest) + if !ok { + return parseError(msgExtInfo) + } + extensions[string(name)] = value + payload = rest + } + packet, err = c.transport.readPacket() + if err != nil { + return err + } + } var serviceAccept serviceAcceptMsg if err := Unmarshal(packet, &serviceAccept); err != nil { return err @@ -41,7 +69,7 @@ func (c *connection) clientAuthenticate(config *ClientConfig) error { sessionID := c.transport.getSessionID() for auth := AuthMethod(new(noneAuth)); auth != nil; { - ok, methods, err := auth.auth(sessionID, config.User, c.transport, config.Rand) + ok, methods, err := auth.auth(sessionID, config.User, c.transport, config.Rand, extensions) if err != nil { return err } @@ -93,7 +121,7 @@ type AuthMethod interface { // If authentication is not successful, a []string of alternative // method names is returned. If the slice is nil, it will be ignored // and the previous set of possible methods will be reused. - auth(session []byte, user string, p packetConn, rand io.Reader) (authResult, []string, error) + auth(session []byte, user string, p packetConn, rand io.Reader, extensions map[string][]byte) (authResult, []string, error) // method returns the RFC 4252 method name. method() string @@ -102,7 +130,7 @@ type AuthMethod interface { // "none" authentication, RFC 4252 section 5.2. type noneAuth int -func (n *noneAuth) auth(session []byte, user string, c packetConn, rand io.Reader) (authResult, []string, error) { +func (n *noneAuth) auth(session []byte, user string, c packetConn, rand io.Reader, _ map[string][]byte) (authResult, []string, error) { if err := c.writePacket(Marshal(&userAuthRequestMsg{ User: user, Service: serviceSSH, @@ -122,7 +150,7 @@ func (n *noneAuth) method() string { // a function call, e.g. by prompting the user. type passwordCallback func() (password string, err error) -func (cb passwordCallback) auth(session []byte, user string, c packetConn, rand io.Reader) (authResult, []string, error) { +func (cb passwordCallback) auth(session []byte, user string, c packetConn, rand io.Reader, _ map[string][]byte) (authResult, []string, error) { type passwordAuthMsg struct { User string `sshtype:"50"` Service string @@ -189,7 +217,46 @@ func (cb publicKeyCallback) method() string { return "publickey" } -func (cb publicKeyCallback) auth(session []byte, user string, c packetConn, rand io.Reader) (authResult, []string, error) { +func pickSignatureAlgorithm(signer Signer, extensions map[string][]byte) (as AlgorithmSigner, algo string) { + keyFormat := signer.PublicKey().Type() + + // Like in sendKexInit, if the public key implements AlgorithmSigner we + // assume it supports all algorithms, otherwise only the key format one. + as, ok := signer.(AlgorithmSigner) + if !ok { + return algorithmSignerWrapper{signer}, keyFormat + } + + extPayload, ok := extensions["server-sig-algs"] + if !ok { + // If there is no "server-sig-algs" extension, fall back to the key + // format algorithm. + return as, keyFormat + } + + // The server-sig-algs extension only carries underlying signature + // algorithm, but we are trying to select a protocol-level public key + // algorithm, which might be a certificate type. Extend the list of server + // supported algorithms to include the corresponding certificate algorithms. + serverAlgos := strings.Split(string(extPayload), ",") + for _, algo := range serverAlgos { + if certAlgo, ok := certificateAlgo(algo); ok { + serverAlgos = append(serverAlgos, certAlgo) + } + } + + keyAlgos := algorithmsForKeyFormat(keyFormat) + algo, err := findCommon("public key signature algorithm", keyAlgos, serverAlgos) + if err != nil { + // If there is no overlap, try the key anyway with the key format + // algorithm, to support servers that fail to list all supported + // algorithms. + return as, keyFormat + } + return as, algo +} + +func (cb publicKeyCallback) auth(session []byte, user string, c packetConn, rand io.Reader, extensions map[string][]byte) (authResult, []string, error) { // Authentication is performed by sending an enquiry to test if a key is // acceptable to the remote. If the key is acceptable, the client will // attempt to authenticate with the valid key. If not the client will repeat @@ -201,7 +268,10 @@ func (cb publicKeyCallback) auth(session []byte, user string, c packetConn, rand } var methods []string for _, signer := range signers { - ok, err := validateKey(signer.PublicKey(), user, c) + pub := signer.PublicKey() + as, algo := pickSignatureAlgorithm(signer, extensions) + + ok, err := validateKey(pub, algo, user, c) if err != nil { return authFailure, nil, err } @@ -209,13 +279,13 @@ func (cb publicKeyCallback) auth(session []byte, user string, c packetConn, rand continue } - pub := signer.PublicKey() pubKey := pub.Marshal() - sign, err := signer.Sign(rand, buildDataSignedForAuth(session, userAuthRequestMsg{ + data := buildDataSignedForAuth(session, userAuthRequestMsg{ User: user, Service: serviceSSH, Method: cb.method(), - }, []byte(pub.Type()), pubKey)) + }, algo, pubKey) + sign, err := as.SignWithAlgorithm(rand, data, underlyingAlgo(algo)) if err != nil { return authFailure, nil, err } @@ -229,7 +299,7 @@ func (cb publicKeyCallback) auth(session []byte, user string, c packetConn, rand Service: serviceSSH, Method: cb.method(), HasSig: true, - Algoname: pub.Type(), + Algoname: algo, PubKey: pubKey, Sig: sig, } @@ -266,26 +336,25 @@ func containsMethod(methods []string, method string) bool { } // validateKey validates the key provided is acceptable to the server. -func validateKey(key PublicKey, user string, c packetConn) (bool, error) { +func validateKey(key PublicKey, algo string, user string, c packetConn) (bool, error) { pubKey := key.Marshal() msg := publickeyAuthMsg{ User: user, Service: serviceSSH, Method: "publickey", HasSig: false, - Algoname: key.Type(), + Algoname: algo, PubKey: pubKey, } if err := c.writePacket(Marshal(&msg)); err != nil { return false, err } - return confirmKeyAck(key, c) + return confirmKeyAck(key, algo, c) } -func confirmKeyAck(key PublicKey, c packetConn) (bool, error) { +func confirmKeyAck(key PublicKey, algo string, c packetConn) (bool, error) { pubKey := key.Marshal() - algoname := key.Type() for { packet, err := c.readPacket() @@ -302,14 +371,14 @@ func confirmKeyAck(key PublicKey, c packetConn) (bool, error) { if err := Unmarshal(packet, &msg); err != nil { return false, err } - if msg.Algo != algoname || !bytes.Equal(msg.PubKey, pubKey) { + if msg.Algo != algo || !bytes.Equal(msg.PubKey, pubKey) { return false, nil } return true, nil case msgUserAuthFailure: return false, nil default: - return false, unexpectedMessageError(msgUserAuthSuccess, packet[0]) + return false, unexpectedMessageError(msgUserAuthPubKeyOk, packet[0]) } } } @@ -330,6 +399,7 @@ func PublicKeysCallback(getSigners func() (signers []Signer, err error)) AuthMet // along with a list of remaining authentication methods to try next and // an error if an unexpected response was received. func handleAuthResponse(c packetConn) (authResult, []string, error) { + gotMsgExtInfo := false for { packet, err := c.readPacket() if err != nil { @@ -341,6 +411,12 @@ func handleAuthResponse(c packetConn) (authResult, []string, error) { if err := handleBannerResponse(c, packet); err != nil { return authFailure, nil, err } + case msgExtInfo: + // Ignore post-authentication RFC 8308 extensions, once. + if gotMsgExtInfo { + return authFailure, nil, unexpectedMessageError(msgUserAuthSuccess, packet[0]) + } + gotMsgExtInfo = true case msgUserAuthFailure: var msg userAuthFailureMsg if err := Unmarshal(packet, &msg); err != nil { @@ -380,10 +456,10 @@ func handleBannerResponse(c packetConn, packet []byte) error { // disabling echoing (e.g. for passwords), and return all the answers. // Challenge may be called multiple times in a single session. After // successful authentication, the server may send a challenge with no -// questions, for which the user and instruction messages should be +// questions, for which the name and instruction messages should be // printed. RFC 4256 section 3.3 details how the UI should behave for // both CLI and GUI environments. -type KeyboardInteractiveChallenge func(user, instruction string, questions []string, echos []bool) (answers []string, err error) +type KeyboardInteractiveChallenge func(name, instruction string, questions []string, echos []bool) (answers []string, err error) // KeyboardInteractive returns an AuthMethod using a prompt/response // sequence controlled by the server. @@ -395,7 +471,7 @@ func (cb KeyboardInteractiveChallenge) method() string { return "keyboard-interactive" } -func (cb KeyboardInteractiveChallenge) auth(session []byte, user string, c packetConn, rand io.Reader) (authResult, []string, error) { +func (cb KeyboardInteractiveChallenge) auth(session []byte, user string, c packetConn, rand io.Reader, _ map[string][]byte) (authResult, []string, error) { type initiateMsg struct { User string `sshtype:"50"` Service string @@ -412,6 +488,7 @@ func (cb KeyboardInteractiveChallenge) auth(session []byte, user string, c packe return authFailure, nil, err } + gotMsgExtInfo := false for { packet, err := c.readPacket() if err != nil { @@ -425,6 +502,13 @@ func (cb KeyboardInteractiveChallenge) auth(session []byte, user string, c packe return authFailure, nil, err } continue + case msgExtInfo: + // Ignore post-authentication RFC 8308 extensions, once. + if gotMsgExtInfo { + return authFailure, nil, unexpectedMessageError(msgUserAuthInfoRequest, packet[0]) + } + gotMsgExtInfo = true + continue case msgUserAuthInfoRequest: // OK case msgUserAuthFailure: @@ -465,7 +549,7 @@ func (cb KeyboardInteractiveChallenge) auth(session []byte, user string, c packe return authFailure, nil, errors.New("ssh: extra data following keyboard-interactive pairs") } - answers, err := cb(msg.User, msg.Instruction, prompts, echos) + answers, err := cb(msg.Name, msg.Instruction, prompts, echos) if err != nil { return authFailure, nil, err } @@ -497,9 +581,9 @@ type retryableAuthMethod struct { maxTries int } -func (r *retryableAuthMethod) auth(session []byte, user string, c packetConn, rand io.Reader) (ok authResult, methods []string, err error) { +func (r *retryableAuthMethod) auth(session []byte, user string, c packetConn, rand io.Reader, extensions map[string][]byte) (ok authResult, methods []string, err error) { for i := 0; r.maxTries <= 0 || i < r.maxTries; i++ { - ok, methods, err = r.authMethod.auth(session, user, c, rand) + ok, methods, err = r.authMethod.auth(session, user, c, rand, extensions) if ok != authFailure || err != nil { // either success, partial success or error terminate return ok, methods, err } @@ -542,7 +626,7 @@ type gssAPIWithMICCallback struct { target string } -func (g *gssAPIWithMICCallback) auth(session []byte, user string, c packetConn, rand io.Reader) (authResult, []string, error) { +func (g *gssAPIWithMICCallback) auth(session []byte, user string, c packetConn, rand io.Reader, _ map[string][]byte) (authResult, []string, error) { m := &userAuthRequestMsg{ User: user, Service: serviceSSH, diff --git a/vendor/golang.org/x/crypto/ssh/common.go b/vendor/golang.org/x/crypto/ssh/common.go index 5ae227574..2a47a61de 100644 --- a/vendor/golang.org/x/crypto/ssh/common.go +++ b/vendor/golang.org/x/crypto/ssh/common.go @@ -44,11 +44,11 @@ var preferredCiphers = []string{ // supportedKexAlgos specifies the supported key-exchange algorithms in // preference order. var supportedKexAlgos = []string{ - kexAlgoCurve25519SHA256, + kexAlgoCurve25519SHA256, kexAlgoCurve25519SHA256LibSSH, // P384 and P521 are not constant-time yet, but since we don't // reuse ephemeral keys, using them for ECDH should be OK. kexAlgoECDH256, kexAlgoECDH384, kexAlgoECDH521, - kexAlgoDH14SHA1, kexAlgoDH1SHA1, + kexAlgoDH14SHA256, kexAlgoDH14SHA1, kexAlgoDH1SHA1, } // serverForbiddenKexAlgos contains key exchange algorithms, that are forbidden @@ -61,21 +61,21 @@ var serverForbiddenKexAlgos = map[string]struct{}{ // preferredKexAlgos specifies the default preference for key-exchange algorithms // in preference order. var preferredKexAlgos = []string{ - kexAlgoCurve25519SHA256, + kexAlgoCurve25519SHA256, kexAlgoCurve25519SHA256LibSSH, kexAlgoECDH256, kexAlgoECDH384, kexAlgoECDH521, - kexAlgoDH14SHA1, + kexAlgoDH14SHA256, kexAlgoDH14SHA1, } // supportedHostKeyAlgos specifies the supported host-key algorithms (i.e. methods // of authenticating servers) in preference order. var supportedHostKeyAlgos = []string{ - CertSigAlgoRSASHA2512v01, CertSigAlgoRSASHA2256v01, - CertSigAlgoRSAv01, CertAlgoDSAv01, CertAlgoECDSA256v01, + CertAlgoRSASHA512v01, CertAlgoRSASHA256v01, + CertAlgoRSAv01, CertAlgoDSAv01, CertAlgoECDSA256v01, CertAlgoECDSA384v01, CertAlgoECDSA521v01, CertAlgoED25519v01, KeyAlgoECDSA256, KeyAlgoECDSA384, KeyAlgoECDSA521, - SigAlgoRSASHA2512, SigAlgoRSASHA2256, - SigAlgoRSA, KeyAlgoDSA, + KeyAlgoRSASHA512, KeyAlgoRSASHA256, + KeyAlgoRSA, KeyAlgoDSA, KeyAlgoED25519, } @@ -89,23 +89,33 @@ var supportedMACs = []string{ var supportedCompressions = []string{compressionNone} -// hashFuncs keeps the mapping of supported algorithms to their respective -// hashes needed for signature verification. +// hashFuncs keeps the mapping of supported signature algorithms to their +// respective hashes needed for signing and verification. var hashFuncs = map[string]crypto.Hash{ - SigAlgoRSA: crypto.SHA1, - SigAlgoRSASHA2256: crypto.SHA256, - SigAlgoRSASHA2512: crypto.SHA512, - KeyAlgoDSA: crypto.SHA1, - KeyAlgoECDSA256: crypto.SHA256, - KeyAlgoECDSA384: crypto.SHA384, - KeyAlgoECDSA521: crypto.SHA512, - CertSigAlgoRSAv01: crypto.SHA1, - CertSigAlgoRSASHA2256v01: crypto.SHA256, - CertSigAlgoRSASHA2512v01: crypto.SHA512, - CertAlgoDSAv01: crypto.SHA1, - CertAlgoECDSA256v01: crypto.SHA256, - CertAlgoECDSA384v01: crypto.SHA384, - CertAlgoECDSA521v01: crypto.SHA512, + KeyAlgoRSA: crypto.SHA1, + KeyAlgoRSASHA256: crypto.SHA256, + KeyAlgoRSASHA512: crypto.SHA512, + KeyAlgoDSA: crypto.SHA1, + KeyAlgoECDSA256: crypto.SHA256, + KeyAlgoECDSA384: crypto.SHA384, + KeyAlgoECDSA521: crypto.SHA512, + // KeyAlgoED25519 doesn't pre-hash. + KeyAlgoSKECDSA256: crypto.SHA256, + KeyAlgoSKED25519: crypto.SHA256, +} + +// algorithmsForKeyFormat returns the supported signature algorithms for a given +// public key format (PublicKey.Type), in order of preference. See RFC 8332, +// Section 2. See also the note in sendKexInit on backwards compatibility. +func algorithmsForKeyFormat(keyFormat string) []string { + switch keyFormat { + case KeyAlgoRSA: + return []string{KeyAlgoRSASHA256, KeyAlgoRSASHA512, KeyAlgoRSA} + case CertAlgoRSAv01: + return []string{CertAlgoRSASHA256v01, CertAlgoRSASHA512v01, CertAlgoRSAv01} + default: + return []string{keyFormat} + } } // unexpectedMessageError results when the SSH message that we received didn't @@ -152,6 +162,11 @@ func (a *directionAlgorithms) rekeyBytes() int64 { return 1 << 30 } +var aeadCiphers = map[string]bool{ + gcmCipherID: true, + chacha20Poly1305ID: true, +} + type algorithms struct { kex string hostKey string @@ -187,14 +202,18 @@ func findAgreedAlgorithms(isClient bool, clientKexInit, serverKexInit *kexInitMs return } - ctos.MAC, err = findCommon("client to server MAC", clientKexInit.MACsClientServer, serverKexInit.MACsClientServer) - if err != nil { - return + if !aeadCiphers[ctos.Cipher] { + ctos.MAC, err = findCommon("client to server MAC", clientKexInit.MACsClientServer, serverKexInit.MACsClientServer) + if err != nil { + return + } } - stoc.MAC, err = findCommon("server to client MAC", clientKexInit.MACsServerClient, serverKexInit.MACsServerClient) - if err != nil { - return + if !aeadCiphers[stoc.Cipher] { + stoc.MAC, err = findCommon("server to client MAC", clientKexInit.MACsServerClient, serverKexInit.MACsServerClient) + if err != nil { + return + } } ctos.Compression, err = findCommon("client to server compression", clientKexInit.CompressionClientServer, serverKexInit.CompressionClientServer) @@ -278,8 +297,9 @@ func (c *Config) SetDefaults() { } // buildDataSignedForAuth returns the data that is signed in order to prove -// possession of a private key. See RFC 4252, section 7. -func buildDataSignedForAuth(sessionID []byte, req userAuthRequestMsg, algo, pubKey []byte) []byte { +// possession of a private key. See RFC 4252, section 7. algo is the advertised +// algorithm, and may be a certificate type. +func buildDataSignedForAuth(sessionID []byte, req userAuthRequestMsg, algo string, pubKey []byte) []byte { data := struct { Session []byte Type byte @@ -287,7 +307,7 @@ func buildDataSignedForAuth(sessionID []byte, req userAuthRequestMsg, algo, pubK Service string Method string Sign bool - Algo []byte + Algo string PubKey []byte }{ sessionID, diff --git a/vendor/golang.org/x/crypto/ssh/doc.go b/vendor/golang.org/x/crypto/ssh/doc.go index 67b7322c0..f6bff60dc 100644 --- a/vendor/golang.org/x/crypto/ssh/doc.go +++ b/vendor/golang.org/x/crypto/ssh/doc.go @@ -12,8 +12,9 @@ the multiplexed nature of SSH is exposed to users that wish to support others. References: - [PROTOCOL.certkeys]: http://cvsweb.openbsd.org/cgi-bin/cvsweb/src/usr.bin/ssh/PROTOCOL.certkeys?rev=HEAD - [SSH-PARAMETERS]: http://www.iana.org/assignments/ssh-parameters/ssh-parameters.xml#ssh-parameters-1 + + [PROTOCOL.certkeys]: http://cvsweb.openbsd.org/cgi-bin/cvsweb/src/usr.bin/ssh/PROTOCOL.certkeys?rev=HEAD + [SSH-PARAMETERS]: http://www.iana.org/assignments/ssh-parameters/ssh-parameters.xml#ssh-parameters-1 This package does not fall under the stability promise of the Go language itself, so its API may be changed when pressing needs arise. diff --git a/vendor/golang.org/x/crypto/ssh/handshake.go b/vendor/golang.org/x/crypto/ssh/handshake.go index 05ad49c36..653dc4d2c 100644 --- a/vendor/golang.org/x/crypto/ssh/handshake.go +++ b/vendor/golang.org/x/crypto/ssh/handshake.go @@ -455,21 +455,38 @@ func (t *handshakeTransport) sendKexInit() error { } io.ReadFull(rand.Reader, msg.Cookie[:]) - if len(t.hostKeys) > 0 { + isServer := len(t.hostKeys) > 0 + if isServer { for _, k := range t.hostKeys { - algo := k.PublicKey().Type() - switch algo { - case KeyAlgoRSA: - msg.ServerHostKeyAlgos = append(msg.ServerHostKeyAlgos, []string{SigAlgoRSASHA2512, SigAlgoRSASHA2256, SigAlgoRSA}...) - case CertAlgoRSAv01: - msg.ServerHostKeyAlgos = append(msg.ServerHostKeyAlgos, []string{CertSigAlgoRSASHA2512v01, CertSigAlgoRSASHA2256v01, CertSigAlgoRSAv01}...) - default: - msg.ServerHostKeyAlgos = append(msg.ServerHostKeyAlgos, algo) + // If k is an AlgorithmSigner, presume it supports all signature algorithms + // associated with the key format. (Ideally AlgorithmSigner would have a + // method to advertise supported algorithms, but it doesn't. This means that + // adding support for a new algorithm is a breaking change, as we will + // immediately negotiate it even if existing implementations don't support + // it. If that ever happens, we'll have to figure something out.) + // If k is not an AlgorithmSigner, we can only assume it only supports the + // algorithms that matches the key format. (This means that Sign can't pick + // a different default.) + keyFormat := k.PublicKey().Type() + if _, ok := k.(AlgorithmSigner); ok { + msg.ServerHostKeyAlgos = append(msg.ServerHostKeyAlgos, algorithmsForKeyFormat(keyFormat)...) + } else { + msg.ServerHostKeyAlgos = append(msg.ServerHostKeyAlgos, keyFormat) } } } else { msg.ServerHostKeyAlgos = t.hostKeyAlgorithms + + // As a client we opt in to receiving SSH_MSG_EXT_INFO so we know what + // algorithms the server supports for public key authentication. See RFC + // 8308, Section 2.1. + if firstKeyExchange := t.sessionID == nil; firstKeyExchange { + msg.KexAlgos = make([]string, 0, len(t.config.KeyExchanges)+1) + msg.KexAlgos = append(msg.KexAlgos, t.config.KeyExchanges...) + msg.KexAlgos = append(msg.KexAlgos, "ext-info-c") + } } + packet := Marshal(msg) // writePacket destroys the contents, so save a copy. @@ -589,9 +606,9 @@ func (t *handshakeTransport) enterKeyExchange(otherInitPacket []byte) error { var result *kexResult if len(t.hostKeys) > 0 { - result, err = t.server(kex, t.algorithms, &magics) + result, err = t.server(kex, &magics) } else { - result, err = t.client(kex, t.algorithms, &magics) + result, err = t.client(kex, &magics) } if err != nil { @@ -618,33 +635,52 @@ func (t *handshakeTransport) enterKeyExchange(otherInitPacket []byte) error { return nil } -func (t *handshakeTransport) server(kex kexAlgorithm, algs *algorithms, magics *handshakeMagics) (*kexResult, error) { - var hostKey Signer - for _, k := range t.hostKeys { - kt := k.PublicKey().Type() - if kt == algs.hostKey { - hostKey = k - } else if signer, ok := k.(AlgorithmSigner); ok { - // Some signature algorithms don't show up as key types - // so we have to manually check for a compatible host key. - switch kt { - case KeyAlgoRSA: - if algs.hostKey == SigAlgoRSASHA2256 || algs.hostKey == SigAlgoRSASHA2512 { - hostKey = &rsaSigner{signer, algs.hostKey} - } - case CertAlgoRSAv01: - if algs.hostKey == CertSigAlgoRSASHA2256v01 || algs.hostKey == CertSigAlgoRSASHA2512v01 { - hostKey = &rsaSigner{signer, certToPrivAlgo(algs.hostKey)} - } +// algorithmSignerWrapper is an AlgorithmSigner that only supports the default +// key format algorithm. +// +// This is technically a violation of the AlgorithmSigner interface, but it +// should be unreachable given where we use this. Anyway, at least it returns an +// error instead of panicing or producing an incorrect signature. +type algorithmSignerWrapper struct { + Signer +} + +func (a algorithmSignerWrapper) SignWithAlgorithm(rand io.Reader, data []byte, algorithm string) (*Signature, error) { + if algorithm != underlyingAlgo(a.PublicKey().Type()) { + return nil, errors.New("ssh: internal error: algorithmSignerWrapper invoked with non-default algorithm") + } + return a.Sign(rand, data) +} + +func pickHostKey(hostKeys []Signer, algo string) AlgorithmSigner { + for _, k := range hostKeys { + if algo == k.PublicKey().Type() { + return algorithmSignerWrapper{k} + } + k, ok := k.(AlgorithmSigner) + if !ok { + continue + } + for _, a := range algorithmsForKeyFormat(k.PublicKey().Type()) { + if algo == a { + return k } } } + return nil +} + +func (t *handshakeTransport) server(kex kexAlgorithm, magics *handshakeMagics) (*kexResult, error) { + hostKey := pickHostKey(t.hostKeys, t.algorithms.hostKey) + if hostKey == nil { + return nil, errors.New("ssh: internal error: negotiated unsupported signature type") + } - r, err := kex.Server(t.conn, t.config.Rand, magics, hostKey) + r, err := kex.Server(t.conn, t.config.Rand, magics, hostKey, t.algorithms.hostKey) return r, err } -func (t *handshakeTransport) client(kex kexAlgorithm, algs *algorithms, magics *handshakeMagics) (*kexResult, error) { +func (t *handshakeTransport) client(kex kexAlgorithm, magics *handshakeMagics) (*kexResult, error) { result, err := kex.Client(t.conn, t.config.Rand, magics) if err != nil { return nil, err @@ -655,7 +691,7 @@ func (t *handshakeTransport) client(kex kexAlgorithm, algs *algorithms, magics * return nil, err } - if err := verifyHostKeySignature(hostKey, algs.hostKey, result); err != nil { + if err := verifyHostKeySignature(hostKey, t.algorithms.hostKey, result); err != nil { return nil, err } diff --git a/vendor/golang.org/x/crypto/ssh/kex.go b/vendor/golang.org/x/crypto/ssh/kex.go index 766e92939..927a90cd4 100644 --- a/vendor/golang.org/x/crypto/ssh/kex.go +++ b/vendor/golang.org/x/crypto/ssh/kex.go @@ -20,12 +20,14 @@ import ( ) const ( - kexAlgoDH1SHA1 = "diffie-hellman-group1-sha1" - kexAlgoDH14SHA1 = "diffie-hellman-group14-sha1" - kexAlgoECDH256 = "ecdh-sha2-nistp256" - kexAlgoECDH384 = "ecdh-sha2-nistp384" - kexAlgoECDH521 = "ecdh-sha2-nistp521" - kexAlgoCurve25519SHA256 = "curve25519-sha256@libssh.org" + kexAlgoDH1SHA1 = "diffie-hellman-group1-sha1" + kexAlgoDH14SHA1 = "diffie-hellman-group14-sha1" + kexAlgoDH14SHA256 = "diffie-hellman-group14-sha256" + kexAlgoECDH256 = "ecdh-sha2-nistp256" + kexAlgoECDH384 = "ecdh-sha2-nistp384" + kexAlgoECDH521 = "ecdh-sha2-nistp521" + kexAlgoCurve25519SHA256LibSSH = "curve25519-sha256@libssh.org" + kexAlgoCurve25519SHA256 = "curve25519-sha256" // For the following kex only the client half contains a production // ready implementation. The server half only consists of a minimal @@ -75,8 +77,9 @@ func (m *handshakeMagics) write(w io.Writer) { // kexAlgorithm abstracts different key exchange algorithms. type kexAlgorithm interface { // Server runs server-side key agreement, signing the result - // with a hostkey. - Server(p packetConn, rand io.Reader, magics *handshakeMagics, s Signer) (*kexResult, error) + // with a hostkey. algo is the negotiated algorithm, and may + // be a certificate type. + Server(p packetConn, rand io.Reader, magics *handshakeMagics, s AlgorithmSigner, algo string) (*kexResult, error) // Client runs the client-side key agreement. Caller is // responsible for verifying the host key signature. @@ -86,6 +89,7 @@ type kexAlgorithm interface { // dhGroup is a multiplicative group suitable for implementing Diffie-Hellman key agreement. type dhGroup struct { g, p, pMinus1 *big.Int + hashFunc crypto.Hash } func (group *dhGroup) diffieHellman(theirPublic, myPrivate *big.Int) (*big.Int, error) { @@ -96,8 +100,6 @@ func (group *dhGroup) diffieHellman(theirPublic, myPrivate *big.Int) (*big.Int, } func (group *dhGroup) Client(c packetConn, randSource io.Reader, magics *handshakeMagics) (*kexResult, error) { - hashFunc := crypto.SHA1 - var x *big.Int for { var err error @@ -132,7 +134,7 @@ func (group *dhGroup) Client(c packetConn, randSource io.Reader, magics *handsha return nil, err } - h := hashFunc.New() + h := group.hashFunc.New() magics.write(h) writeString(h, kexDHReply.HostKey) writeInt(h, X) @@ -146,12 +148,11 @@ func (group *dhGroup) Client(c packetConn, randSource io.Reader, magics *handsha K: K, HostKey: kexDHReply.HostKey, Signature: kexDHReply.Signature, - Hash: crypto.SHA1, + Hash: group.hashFunc, }, nil } -func (group *dhGroup) Server(c packetConn, randSource io.Reader, magics *handshakeMagics, priv Signer) (result *kexResult, err error) { - hashFunc := crypto.SHA1 +func (group *dhGroup) Server(c packetConn, randSource io.Reader, magics *handshakeMagics, priv AlgorithmSigner, algo string) (result *kexResult, err error) { packet, err := c.readPacket() if err != nil { return @@ -179,7 +180,7 @@ func (group *dhGroup) Server(c packetConn, randSource io.Reader, magics *handsha hostKeyBytes := priv.PublicKey().Marshal() - h := hashFunc.New() + h := group.hashFunc.New() magics.write(h) writeString(h, hostKeyBytes) writeInt(h, kexDHInit.X) @@ -193,7 +194,7 @@ func (group *dhGroup) Server(c packetConn, randSource io.Reader, magics *handsha // H is already a hash, but the hostkey signing will apply its // own key-specific hash algorithm. - sig, err := signAndMarshal(priv, randSource, H) + sig, err := signAndMarshal(priv, randSource, H, algo) if err != nil { return nil, err } @@ -211,7 +212,7 @@ func (group *dhGroup) Server(c packetConn, randSource io.Reader, magics *handsha K: K, HostKey: hostKeyBytes, Signature: sig, - Hash: crypto.SHA1, + Hash: group.hashFunc, }, err } @@ -314,7 +315,7 @@ func validateECPublicKey(curve elliptic.Curve, x, y *big.Int) bool { return true } -func (kex *ecdh) Server(c packetConn, rand io.Reader, magics *handshakeMagics, priv Signer) (result *kexResult, err error) { +func (kex *ecdh) Server(c packetConn, rand io.Reader, magics *handshakeMagics, priv AlgorithmSigner, algo string) (result *kexResult, err error) { packet, err := c.readPacket() if err != nil { return nil, err @@ -359,7 +360,7 @@ func (kex *ecdh) Server(c packetConn, rand io.Reader, magics *handshakeMagics, p // H is already a hash, but the hostkey signing will apply its // own key-specific hash algorithm. - sig, err := signAndMarshal(priv, rand, H) + sig, err := signAndMarshal(priv, rand, H, algo) if err != nil { return nil, err } @@ -384,39 +385,62 @@ func (kex *ecdh) Server(c packetConn, rand io.Reader, magics *handshakeMagics, p }, nil } +// ecHash returns the hash to match the given elliptic curve, see RFC +// 5656, section 6.2.1 +func ecHash(curve elliptic.Curve) crypto.Hash { + bitSize := curve.Params().BitSize + switch { + case bitSize <= 256: + return crypto.SHA256 + case bitSize <= 384: + return crypto.SHA384 + } + return crypto.SHA512 +} + var kexAlgoMap = map[string]kexAlgorithm{} func init() { - // This is the group called diffie-hellman-group1-sha1 in RFC - // 4253 and Oakley Group 2 in RFC 2409. + // This is the group called diffie-hellman-group1-sha1 in + // RFC 4253 and Oakley Group 2 in RFC 2409. p, _ := new(big.Int).SetString("FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE649286651ECE65381FFFFFFFFFFFFFFFF", 16) kexAlgoMap[kexAlgoDH1SHA1] = &dhGroup{ - g: new(big.Int).SetInt64(2), - p: p, - pMinus1: new(big.Int).Sub(p, bigOne), + g: new(big.Int).SetInt64(2), + p: p, + pMinus1: new(big.Int).Sub(p, bigOne), + hashFunc: crypto.SHA1, } - // This is the group called diffie-hellman-group14-sha1 in RFC - // 4253 and Oakley Group 14 in RFC 3526. + // This are the groups called diffie-hellman-group14-sha1 and + // diffie-hellman-group14-sha256 in RFC 4253 and RFC 8268, + // and Oakley Group 14 in RFC 3526. p, _ = new(big.Int).SetString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kexAlgoMap[kexAlgoDH14SHA1] = &dhGroup{ + group14 := &dhGroup{ g: new(big.Int).SetInt64(2), p: p, pMinus1: new(big.Int).Sub(p, bigOne), } + kexAlgoMap[kexAlgoDH14SHA1] = &dhGroup{ + g: group14.g, p: group14.p, pMinus1: group14.pMinus1, + hashFunc: crypto.SHA1, + } + kexAlgoMap[kexAlgoDH14SHA256] = &dhGroup{ + g: group14.g, p: group14.p, pMinus1: group14.pMinus1, + hashFunc: crypto.SHA256, + } + kexAlgoMap[kexAlgoECDH521] = &ecdh{elliptic.P521()} kexAlgoMap[kexAlgoECDH384] = &ecdh{elliptic.P384()} kexAlgoMap[kexAlgoECDH256] = &ecdh{elliptic.P256()} kexAlgoMap[kexAlgoCurve25519SHA256] = &curve25519sha256{} + kexAlgoMap[kexAlgoCurve25519SHA256LibSSH] = &curve25519sha256{} kexAlgoMap[kexAlgoDHGEXSHA1] = &dhGEXSHA{hashFunc: crypto.SHA1} kexAlgoMap[kexAlgoDHGEXSHA256] = &dhGEXSHA{hashFunc: crypto.SHA256} } -// curve25519sha256 implements the curve25519-sha256@libssh.org key -// agreement protocol, as described in -// https://git.libssh.org/projects/libssh.git/tree/doc/curve25519-sha256@libssh.org.txt +// curve25519sha256 implements the curve25519-sha256 (formerly known as +// curve25519-sha256@libssh.org) key exchange method, as described in RFC 8731. type curve25519sha256 struct{} type curve25519KeyPair struct { @@ -486,7 +510,7 @@ func (kex *curve25519sha256) Client(c packetConn, rand io.Reader, magics *handsh }, nil } -func (kex *curve25519sha256) Server(c packetConn, rand io.Reader, magics *handshakeMagics, priv Signer) (result *kexResult, err error) { +func (kex *curve25519sha256) Server(c packetConn, rand io.Reader, magics *handshakeMagics, priv AlgorithmSigner, algo string) (result *kexResult, err error) { packet, err := c.readPacket() if err != nil { return @@ -527,7 +551,7 @@ func (kex *curve25519sha256) Server(c packetConn, rand io.Reader, magics *handsh H := h.Sum(nil) - sig, err := signAndMarshal(priv, rand, H) + sig, err := signAndMarshal(priv, rand, H, algo) if err != nil { return nil, err } @@ -553,7 +577,6 @@ func (kex *curve25519sha256) Server(c packetConn, rand io.Reader, magics *handsh // diffie-hellman-group-exchange-sha256 key agreement protocols, // as described in RFC 4419 type dhGEXSHA struct { - g, p *big.Int hashFunc crypto.Hash } @@ -563,14 +586,7 @@ const ( dhGroupExchangeMaximumBits = 8192 ) -func (gex *dhGEXSHA) diffieHellman(theirPublic, myPrivate *big.Int) (*big.Int, error) { - if theirPublic.Sign() <= 0 || theirPublic.Cmp(gex.p) >= 0 { - return nil, fmt.Errorf("ssh: DH parameter out of bounds") - } - return new(big.Int).Exp(theirPublic, myPrivate, gex.p), nil -} - -func (gex dhGEXSHA) Client(c packetConn, randSource io.Reader, magics *handshakeMagics) (*kexResult, error) { +func (gex *dhGEXSHA) Client(c packetConn, randSource io.Reader, magics *handshakeMagics) (*kexResult, error) { // Send GexRequest kexDHGexRequest := kexDHGexRequestMsg{ MinBits: dhGroupExchangeMinimumBits, @@ -587,35 +603,29 @@ func (gex dhGEXSHA) Client(c packetConn, randSource io.Reader, magics *handshake return nil, err } - var kexDHGexGroup kexDHGexGroupMsg - if err = Unmarshal(packet, &kexDHGexGroup); err != nil { + var msg kexDHGexGroupMsg + if err = Unmarshal(packet, &msg); err != nil { return nil, err } // reject if p's bit length < dhGroupExchangeMinimumBits or > dhGroupExchangeMaximumBits - if kexDHGexGroup.P.BitLen() < dhGroupExchangeMinimumBits || kexDHGexGroup.P.BitLen() > dhGroupExchangeMaximumBits { - return nil, fmt.Errorf("ssh: server-generated gex p is out of range (%d bits)", kexDHGexGroup.P.BitLen()) + if msg.P.BitLen() < dhGroupExchangeMinimumBits || msg.P.BitLen() > dhGroupExchangeMaximumBits { + return nil, fmt.Errorf("ssh: server-generated gex p is out of range (%d bits)", msg.P.BitLen()) } - gex.p = kexDHGexGroup.P - gex.g = kexDHGexGroup.G - - // Check if g is safe by verifing that g > 1 and g < p - 1 - one := big.NewInt(1) - var pMinusOne = &big.Int{} - pMinusOne.Sub(gex.p, one) - if gex.g.Cmp(one) != 1 && gex.g.Cmp(pMinusOne) != -1 { + // Check if g is safe by verifying that 1 < g < p-1 + pMinusOne := new(big.Int).Sub(msg.P, bigOne) + if msg.G.Cmp(bigOne) <= 0 || msg.G.Cmp(pMinusOne) >= 0 { return nil, fmt.Errorf("ssh: server provided gex g is not safe") } // Send GexInit - var pHalf = &big.Int{} - pHalf.Rsh(gex.p, 1) + pHalf := new(big.Int).Rsh(msg.P, 1) x, err := rand.Int(randSource, pHalf) if err != nil { return nil, err } - X := new(big.Int).Exp(gex.g, x, gex.p) + X := new(big.Int).Exp(msg.G, x, msg.P) kexDHGexInit := kexDHGexInitMsg{ X: X, } @@ -634,13 +644,13 @@ func (gex dhGEXSHA) Client(c packetConn, randSource io.Reader, magics *handshake return nil, err } - kInt, err := gex.diffieHellman(kexDHGexReply.Y, x) - if err != nil { - return nil, err + if kexDHGexReply.Y.Cmp(bigOne) <= 0 || kexDHGexReply.Y.Cmp(pMinusOne) >= 0 { + return nil, errors.New("ssh: DH parameter out of bounds") } + kInt := new(big.Int).Exp(kexDHGexReply.Y, x, msg.P) - // Check if k is safe by verifing that k > 1 and k < p - 1 - if kInt.Cmp(one) != 1 && kInt.Cmp(pMinusOne) != -1 { + // Check if k is safe by verifying that k > 1 and k < p - 1 + if kInt.Cmp(bigOne) <= 0 || kInt.Cmp(pMinusOne) >= 0 { return nil, fmt.Errorf("ssh: derived k is not safe") } @@ -650,8 +660,8 @@ func (gex dhGEXSHA) Client(c packetConn, randSource io.Reader, magics *handshake binary.Write(h, binary.BigEndian, uint32(dhGroupExchangeMinimumBits)) binary.Write(h, binary.BigEndian, uint32(dhGroupExchangePreferredBits)) binary.Write(h, binary.BigEndian, uint32(dhGroupExchangeMaximumBits)) - writeInt(h, gex.p) - writeInt(h, gex.g) + writeInt(h, msg.P) + writeInt(h, msg.G) writeInt(h, X) writeInt(h, kexDHGexReply.Y) K := make([]byte, intLength(kInt)) @@ -670,7 +680,7 @@ func (gex dhGEXSHA) Client(c packetConn, randSource io.Reader, magics *handshake // Server half implementation of the Diffie Hellman Key Exchange with SHA1 and SHA256. // // This is a minimal implementation to satisfy the automated tests. -func (gex dhGEXSHA) Server(c packetConn, randSource io.Reader, magics *handshakeMagics, priv Signer) (result *kexResult, err error) { +func (gex dhGEXSHA) Server(c packetConn, randSource io.Reader, magics *handshakeMagics, priv AlgorithmSigner, algo string) (result *kexResult, err error) { // Receive GexRequest packet, err := c.readPacket() if err != nil { @@ -681,35 +691,17 @@ func (gex dhGEXSHA) Server(c packetConn, randSource io.Reader, magics *handshake return } - // smoosh the user's preferred size into our own limits - if kexDHGexRequest.PreferedBits > dhGroupExchangeMaximumBits { - kexDHGexRequest.PreferedBits = dhGroupExchangeMaximumBits - } - if kexDHGexRequest.PreferedBits < dhGroupExchangeMinimumBits { - kexDHGexRequest.PreferedBits = dhGroupExchangeMinimumBits - } - // fix min/max if they're inconsistent. technically, we could just pout - // and hang up, but there's no harm in giving them the benefit of the - // doubt and just picking a bitsize for them. - if kexDHGexRequest.MinBits > kexDHGexRequest.PreferedBits { - kexDHGexRequest.MinBits = kexDHGexRequest.PreferedBits - } - if kexDHGexRequest.MaxBits < kexDHGexRequest.PreferedBits { - kexDHGexRequest.MaxBits = kexDHGexRequest.PreferedBits - } - // Send GexGroup // This is the group called diffie-hellman-group14-sha1 in RFC // 4253 and Oakley Group 14 in RFC 3526. p, _ := new(big.Int).SetString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gex.p = p - gex.g = big.NewInt(2) + g := big.NewInt(2) - kexDHGexGroup := kexDHGexGroupMsg{ - P: gex.p, - G: gex.g, + msg := &kexDHGexGroupMsg{ + P: p, + G: g, } - if err := c.writePacket(Marshal(&kexDHGexGroup)); err != nil { + if err := c.writePacket(Marshal(msg)); err != nil { return nil, err } @@ -723,19 +715,19 @@ func (gex dhGEXSHA) Server(c packetConn, randSource io.Reader, magics *handshake return } - var pHalf = &big.Int{} - pHalf.Rsh(gex.p, 1) + pHalf := new(big.Int).Rsh(p, 1) y, err := rand.Int(randSource, pHalf) if err != nil { return } + Y := new(big.Int).Exp(g, y, p) - Y := new(big.Int).Exp(gex.g, y, gex.p) - kInt, err := gex.diffieHellman(kexDHGexInit.X, y) - if err != nil { - return nil, err + pMinusOne := new(big.Int).Sub(p, bigOne) + if kexDHGexInit.X.Cmp(bigOne) <= 0 || kexDHGexInit.X.Cmp(pMinusOne) >= 0 { + return nil, errors.New("ssh: DH parameter out of bounds") } + kInt := new(big.Int).Exp(kexDHGexInit.X, y, p) hostKeyBytes := priv.PublicKey().Marshal() @@ -745,8 +737,8 @@ func (gex dhGEXSHA) Server(c packetConn, randSource io.Reader, magics *handshake binary.Write(h, binary.BigEndian, uint32(dhGroupExchangeMinimumBits)) binary.Write(h, binary.BigEndian, uint32(dhGroupExchangePreferredBits)) binary.Write(h, binary.BigEndian, uint32(dhGroupExchangeMaximumBits)) - writeInt(h, gex.p) - writeInt(h, gex.g) + writeInt(h, p) + writeInt(h, g) writeInt(h, kexDHGexInit.X) writeInt(h, Y) @@ -758,7 +750,7 @@ func (gex dhGEXSHA) Server(c packetConn, randSource io.Reader, magics *handshake // H is already a hash, but the hostkey signing will apply its // own key-specific hash algorithm. - sig, err := signAndMarshal(priv, randSource, H) + sig, err := signAndMarshal(priv, randSource, H, algo) if err != nil { return nil, err } diff --git a/vendor/golang.org/x/crypto/ssh/keys.go b/vendor/golang.org/x/crypto/ssh/keys.go index c67d3a31c..1c7de1a6d 100644 --- a/vendor/golang.org/x/crypto/ssh/keys.go +++ b/vendor/golang.org/x/crypto/ssh/keys.go @@ -30,8 +30,9 @@ import ( "golang.org/x/crypto/ssh/internal/bcrypt_pbkdf" ) -// These constants represent the algorithm names for key types supported by this -// package. +// Public key algorithms names. These values can appear in PublicKey.Type, +// ClientConfig.HostKeyAlgorithms, Signature.Format, or as AlgorithmSigner +// arguments. const ( KeyAlgoRSA = "ssh-rsa" KeyAlgoDSA = "ssh-dss" @@ -41,16 +42,21 @@ const ( KeyAlgoECDSA521 = "ecdsa-sha2-nistp521" KeyAlgoED25519 = "ssh-ed25519" KeyAlgoSKED25519 = "sk-ssh-ed25519@openssh.com" + + // KeyAlgoRSASHA256 and KeyAlgoRSASHA512 are only public key algorithms, not + // public key formats, so they can't appear as a PublicKey.Type. The + // corresponding PublicKey.Type is KeyAlgoRSA. See RFC 8332, Section 2. + KeyAlgoRSASHA256 = "rsa-sha2-256" + KeyAlgoRSASHA512 = "rsa-sha2-512" ) -// These constants represent non-default signature algorithms that are supported -// as algorithm parameters to AlgorithmSigner.SignWithAlgorithm methods. See -// [PROTOCOL.agent] section 4.5.1 and -// https://tools.ietf.org/html/draft-ietf-curdle-rsa-sha2-10 const ( - SigAlgoRSA = "ssh-rsa" - SigAlgoRSASHA2256 = "rsa-sha2-256" - SigAlgoRSASHA2512 = "rsa-sha2-512" + // Deprecated: use KeyAlgoRSA. + SigAlgoRSA = KeyAlgoRSA + // Deprecated: use KeyAlgoRSASHA256. + SigAlgoRSASHA2256 = KeyAlgoRSASHA256 + // Deprecated: use KeyAlgoRSASHA512. + SigAlgoRSASHA2512 = KeyAlgoRSASHA512 ) // parsePubKey parses a public key of the given algorithm. @@ -70,7 +76,7 @@ func parsePubKey(in []byte, algo string) (pubKey PublicKey, rest []byte, err err case KeyAlgoSKED25519: return parseSKEd25519(in) case CertAlgoRSAv01, CertAlgoDSAv01, CertAlgoECDSA256v01, CertAlgoECDSA384v01, CertAlgoECDSA521v01, CertAlgoSKECDSA256v01, CertAlgoED25519v01, CertAlgoSKED25519v01: - cert, err := parseCert(in, certToPrivAlgo(algo)) + cert, err := parseCert(in, certKeyAlgoNames[algo]) if err != nil { return nil, nil, err } @@ -289,18 +295,21 @@ func MarshalAuthorizedKey(key PublicKey) []byte { return b.Bytes() } -// PublicKey is an abstraction of different types of public keys. +// PublicKey represents a public key using an unspecified algorithm. +// +// Some PublicKeys provided by this package also implement CryptoPublicKey. type PublicKey interface { - // Type returns the key's type, e.g. "ssh-rsa". + // Type returns the key format name, e.g. "ssh-rsa". Type() string - // Marshal returns the serialized key data in SSH wire format, - // with the name prefix. To unmarshal the returned data, use - // the ParsePublicKey function. + // Marshal returns the serialized key data in SSH wire format, with the name + // prefix. To unmarshal the returned data, use the ParsePublicKey function. Marshal() []byte - // Verify that sig is a signature on the given data using this - // key. This function will hash the data appropriately first. + // Verify that sig is a signature on the given data using this key. This + // method will hash the data appropriately first. sig.Format is allowed to + // be any signature algorithm compatible with the key type, the caller + // should check if it has more stringent requirements. Verify(data []byte, sig *Signature) error } @@ -311,25 +320,32 @@ type CryptoPublicKey interface { } // A Signer can create signatures that verify against a public key. +// +// Some Signers provided by this package also implement AlgorithmSigner. type Signer interface { - // PublicKey returns an associated PublicKey instance. + // PublicKey returns the associated PublicKey. PublicKey() PublicKey - // Sign returns raw signature for the given data. This method - // will apply the hash specified for the keytype to the data. + // Sign returns a signature for the given data. This method will hash the + // data appropriately first. The signature algorithm is expected to match + // the key format returned by the PublicKey.Type method (and not to be any + // alternative algorithm supported by the key format). Sign(rand io.Reader, data []byte) (*Signature, error) } -// A AlgorithmSigner is a Signer that also supports specifying a specific -// algorithm to use for signing. +// An AlgorithmSigner is a Signer that also supports specifying an algorithm to +// use for signing. +// +// An AlgorithmSigner can't advertise the algorithms it supports, so it should +// be prepared to be invoked with every algorithm supported by the public key +// format. type AlgorithmSigner interface { Signer - // SignWithAlgorithm is like Signer.Sign, but allows specification of a - // non-default signing algorithm. See the SigAlgo* constants in this - // package for signature algorithms supported by this package. Callers may - // pass an empty string for the algorithm in which case the AlgorithmSigner - // will use its default algorithm. + // SignWithAlgorithm is like Signer.Sign, but allows specifying a desired + // signing algorithm. Callers may pass an empty string for the algorithm in + // which case the AlgorithmSigner will use a default algorithm. This default + // doesn't currently control any behavior in this package. SignWithAlgorithm(rand io.Reader, data []byte, algorithm string) (*Signature, error) } @@ -381,17 +397,11 @@ func (r *rsaPublicKey) Marshal() []byte { } func (r *rsaPublicKey) Verify(data []byte, sig *Signature) error { - var hash crypto.Hash - switch sig.Format { - case SigAlgoRSA: - hash = crypto.SHA1 - case SigAlgoRSASHA2256: - hash = crypto.SHA256 - case SigAlgoRSASHA2512: - hash = crypto.SHA512 - default: + supportedAlgos := algorithmsForKeyFormat(r.Type()) + if !contains(supportedAlgos, sig.Format) { return fmt.Errorf("ssh: signature type %s for key type %s", sig.Format, r.Type()) } + hash := hashFuncs[sig.Format] h := hash.New() h.Write(data) digest := h.Sum(nil) @@ -466,7 +476,7 @@ func (k *dsaPublicKey) Verify(data []byte, sig *Signature) error { if sig.Format != k.Type() { return fmt.Errorf("ssh: signature type %s for key type %s", sig.Format, k.Type()) } - h := crypto.SHA1.New() + h := hashFuncs[sig.Format].New() h.Write(data) digest := h.Sum(nil) @@ -499,7 +509,7 @@ func (k *dsaPrivateKey) PublicKey() PublicKey { } func (k *dsaPrivateKey) Sign(rand io.Reader, data []byte) (*Signature, error) { - return k.SignWithAlgorithm(rand, data, "") + return k.SignWithAlgorithm(rand, data, k.PublicKey().Type()) } func (k *dsaPrivateKey) SignWithAlgorithm(rand io.Reader, data []byte, algorithm string) (*Signature, error) { @@ -507,7 +517,7 @@ func (k *dsaPrivateKey) SignWithAlgorithm(rand io.Reader, data []byte, algorithm return nil, fmt.Errorf("ssh: unsupported signature algorithm %s", algorithm) } - h := crypto.SHA1.New() + h := hashFuncs[k.PublicKey().Type()].New() h.Write(data) digest := h.Sum(nil) r, s, err := dsa.Sign(rand, k.PrivateKey, digest) @@ -603,19 +613,6 @@ func supportedEllipticCurve(curve elliptic.Curve) bool { return curve == elliptic.P256() || curve == elliptic.P384() || curve == elliptic.P521() } -// ecHash returns the hash to match the given elliptic curve, see RFC -// 5656, section 6.2.1 -func ecHash(curve elliptic.Curve) crypto.Hash { - bitSize := curve.Params().BitSize - switch { - case bitSize <= 256: - return crypto.SHA256 - case bitSize <= 384: - return crypto.SHA384 - } - return crypto.SHA512 -} - // parseECDSA parses an ECDSA key according to RFC 5656, section 3.1. func parseECDSA(in []byte) (out PublicKey, rest []byte, err error) { var w struct { @@ -671,7 +668,7 @@ func (k *ecdsaPublicKey) Verify(data []byte, sig *Signature) error { return fmt.Errorf("ssh: signature type %s for key type %s", sig.Format, k.Type()) } - h := ecHash(k.Curve).New() + h := hashFuncs[sig.Format].New() h.Write(data) digest := h.Sum(nil) @@ -775,7 +772,7 @@ func (k *skECDSAPublicKey) Verify(data []byte, sig *Signature) error { return fmt.Errorf("ssh: signature type %s for key type %s", sig.Format, k.Type()) } - h := ecHash(k.Curve).New() + h := hashFuncs[sig.Format].New() h.Write([]byte(k.application)) appDigest := h.Sum(nil) @@ -874,7 +871,7 @@ func (k *skEd25519PublicKey) Verify(data []byte, sig *Signature) error { return fmt.Errorf("invalid size %d for Ed25519 public key", l) } - h := sha256.New() + h := hashFuncs[sig.Format].New() h.Write([]byte(k.application)) appDigest := h.Sum(nil) @@ -939,15 +936,6 @@ func newDSAPrivateKey(key *dsa.PrivateKey) (Signer, error) { return &dsaPrivateKey{key}, nil } -type rsaSigner struct { - AlgorithmSigner - defaultAlgorithm string -} - -func (s *rsaSigner) Sign(rand io.Reader, data []byte) (*Signature, error) { - return s.AlgorithmSigner.SignWithAlgorithm(rand, data, s.defaultAlgorithm) -} - type wrappedSigner struct { signer crypto.Signer pubKey PublicKey @@ -970,44 +958,20 @@ func (s *wrappedSigner) PublicKey() PublicKey { } func (s *wrappedSigner) Sign(rand io.Reader, data []byte) (*Signature, error) { - return s.SignWithAlgorithm(rand, data, "") + return s.SignWithAlgorithm(rand, data, s.pubKey.Type()) } func (s *wrappedSigner) SignWithAlgorithm(rand io.Reader, data []byte, algorithm string) (*Signature, error) { - var hashFunc crypto.Hash - - if _, ok := s.pubKey.(*rsaPublicKey); ok { - // RSA keys support a few hash functions determined by the requested signature algorithm - switch algorithm { - case "", SigAlgoRSA: - algorithm = SigAlgoRSA - hashFunc = crypto.SHA1 - case SigAlgoRSASHA2256: - hashFunc = crypto.SHA256 - case SigAlgoRSASHA2512: - hashFunc = crypto.SHA512 - default: - return nil, fmt.Errorf("ssh: unsupported signature algorithm %s", algorithm) - } - } else { - // The only supported algorithm for all other key types is the same as the type of the key - if algorithm == "" { - algorithm = s.pubKey.Type() - } else if algorithm != s.pubKey.Type() { - return nil, fmt.Errorf("ssh: unsupported signature algorithm %s", algorithm) - } + if algorithm == "" { + algorithm = s.pubKey.Type() + } - switch key := s.pubKey.(type) { - case *dsaPublicKey: - hashFunc = crypto.SHA1 - case *ecdsaPublicKey: - hashFunc = ecHash(key.Curve) - case ed25519PublicKey: - default: - return nil, fmt.Errorf("ssh: unsupported key type %T", key) - } + supportedAlgos := algorithmsForKeyFormat(s.pubKey.Type()) + if !contains(supportedAlgos, algorithm) { + return nil, fmt.Errorf("ssh: unsupported signature algorithm %q for key format %q", algorithm, s.pubKey.Type()) } + hashFunc := hashFuncs[algorithm] var digest []byte if hashFunc != 0 { h := hashFunc.New() diff --git a/vendor/golang.org/x/crypto/ssh/messages.go b/vendor/golang.org/x/crypto/ssh/messages.go index ac41a4168..19bc67c46 100644 --- a/vendor/golang.org/x/crypto/ssh/messages.go +++ b/vendor/golang.org/x/crypto/ssh/messages.go @@ -141,6 +141,14 @@ type serviceAcceptMsg struct { Service string `sshtype:"6"` } +// See RFC 8308, section 2.3 +const msgExtInfo = 7 + +type extInfoMsg struct { + NumExtensions uint32 `sshtype:"7"` + Payload []byte `ssh:"rest"` +} + // See RFC 4252, section 5. const msgUserAuthRequest = 50 @@ -180,11 +188,11 @@ const msgUserAuthInfoRequest = 60 const msgUserAuthInfoResponse = 61 type userAuthInfoRequestMsg struct { - User string `sshtype:"60"` - Instruction string - DeprecatedLanguage string - NumPrompts uint32 - Prompts []byte `ssh:"rest"` + Name string `sshtype:"60"` + Instruction string + Language string + NumPrompts uint32 + Prompts []byte `ssh:"rest"` } // See RFC 4254, section 5.1. @@ -782,6 +790,8 @@ func decode(packet []byte) (interface{}, error) { msg = new(serviceRequestMsg) case msgServiceAccept: msg = new(serviceAcceptMsg) + case msgExtInfo: + msg = new(extInfoMsg) case msgKexInit: msg = new(kexInitMsg) case msgKexDHInit: @@ -843,6 +853,7 @@ var packetTypeNames = map[byte]string{ msgDisconnect: "disconnectMsg", msgServiceRequest: "serviceRequestMsg", msgServiceAccept: "serviceAcceptMsg", + msgExtInfo: "extInfoMsg", msgKexInit: "kexInitMsg", msgKexDHInit: "kexDHInitMsg", msgKexDHReply: "kexDHReplyMsg", diff --git a/vendor/golang.org/x/crypto/ssh/server.go b/vendor/golang.org/x/crypto/ssh/server.go index 6a58e1208..70045bdfd 100644 --- a/vendor/golang.org/x/crypto/ssh/server.go +++ b/vendor/golang.org/x/crypto/ssh/server.go @@ -120,7 +120,7 @@ type ServerConfig struct { } // AddHostKey adds a private key as a host key. If an existing host -// key exists with the same algorithm, it is overwritten. Each server +// key exists with the same public key format, it is replaced. Each server // config must have at least one host key. func (s *ServerConfig) AddHostKey(key Signer) { for i, k := range s.hostKeys { @@ -212,9 +212,10 @@ func NewServerConn(c net.Conn, config *ServerConfig) (*ServerConn, <-chan NewCha } // signAndMarshal signs the data with the appropriate algorithm, -// and serializes the result in SSH wire format. -func signAndMarshal(k Signer, rand io.Reader, data []byte) ([]byte, error) { - sig, err := k.Sign(rand, data) +// and serializes the result in SSH wire format. algo is the negotiate +// algorithm and may be a certificate type. +func signAndMarshal(k AlgorithmSigner, rand io.Reader, data []byte, algo string) ([]byte, error) { + sig, err := k.SignWithAlgorithm(rand, data, underlyingAlgo(algo)) if err != nil { return nil, err } @@ -284,7 +285,7 @@ func (s *connection) serverHandshake(config *ServerConfig) (*Permissions, error) func isAcceptableAlgo(algo string) bool { switch algo { - case SigAlgoRSA, SigAlgoRSASHA2256, SigAlgoRSASHA2512, KeyAlgoDSA, KeyAlgoECDSA256, KeyAlgoECDSA384, KeyAlgoECDSA521, KeyAlgoSKECDSA256, KeyAlgoED25519, KeyAlgoSKED25519, + case KeyAlgoRSA, KeyAlgoRSASHA256, KeyAlgoRSASHA512, KeyAlgoDSA, KeyAlgoECDSA256, KeyAlgoECDSA384, KeyAlgoECDSA521, KeyAlgoSKECDSA256, KeyAlgoED25519, KeyAlgoSKED25519, CertAlgoRSAv01, CertAlgoDSAv01, CertAlgoECDSA256v01, CertAlgoECDSA384v01, CertAlgoECDSA521v01, CertAlgoSKECDSA256v01, CertAlgoED25519v01, CertAlgoSKED25519v01: return true } @@ -553,6 +554,7 @@ userAuthLoop: if !ok || len(payload) > 0 { return nil, parseError(msgUserAuthRequest) } + // Ensure the public key algo and signature algo // are supported. Compare the private key // algorithm name that corresponds to algo with @@ -562,7 +564,12 @@ userAuthLoop: authErr = fmt.Errorf("ssh: algorithm %q not accepted", sig.Format) break } - signedData := buildDataSignedForAuth(sessionID, userAuthReq, algoBytes, pubKeyData) + if underlyingAlgo(algo) != sig.Format { + authErr = fmt.Errorf("ssh: signature %q not compatible with selected algorithm %q", sig.Format, algo) + break + } + + signedData := buildDataSignedForAuth(sessionID, userAuthReq, algo, pubKeyData) if err := pubKey.Verify(signedData, sig); err != nil { return nil, err @@ -633,6 +640,30 @@ userAuthLoop: } authFailures++ + if config.MaxAuthTries > 0 && authFailures >= config.MaxAuthTries { + // If we have hit the max attempts, don't bother sending the + // final SSH_MSG_USERAUTH_FAILURE message, since there are + // no more authentication methods which can be attempted, + // and this message may cause the client to re-attempt + // authentication while we send the disconnect message. + // Continue, and trigger the disconnect at the start of + // the loop. + // + // The SSH specification is somewhat confusing about this, + // RFC 4252 Section 5.1 requires each authentication failure + // be responded to with a respective SSH_MSG_USERAUTH_FAILURE + // message, but Section 4 says the server should disconnect + // after some number of attempts, but it isn't explicit which + // message should take precedence (i.e. should there be a failure + // message than a disconnect message, or if we are going to + // disconnect, should we only send that message.) + // + // Either way, OpenSSH disconnects immediately after the last + // failed authnetication attempt, and given they are typically + // considered the golden implementation it seems reasonable + // to match that behavior. + continue + } var failureMsg userAuthFailureMsg if config.PasswordCallback != nil { @@ -670,7 +701,7 @@ type sshClientKeyboardInteractive struct { *connection } -func (c *sshClientKeyboardInteractive) Challenge(user, instruction string, questions []string, echos []bool) (answers []string, err error) { +func (c *sshClientKeyboardInteractive) Challenge(name, instruction string, questions []string, echos []bool) (answers []string, err error) { if len(questions) != len(echos) { return nil, errors.New("ssh: echos and questions must have equal length") } @@ -682,6 +713,7 @@ func (c *sshClientKeyboardInteractive) Challenge(user, instruction string, quest } if err := c.transport.writePacket(Marshal(&userAuthInfoRequestMsg{ + Name: name, Instruction: instruction, NumPrompts: uint32(len(questions)), Prompts: prompts, diff --git a/vendor/golang.org/x/crypto/ssh/session.go b/vendor/golang.org/x/crypto/ssh/session.go index d3321f6b7..eca31a22d 100644 --- a/vendor/golang.org/x/crypto/ssh/session.go +++ b/vendor/golang.org/x/crypto/ssh/session.go @@ -85,6 +85,7 @@ const ( IXANY = 39 IXOFF = 40 IMAXBEL = 41 + IUTF8 = 42 // RFC 8160 ISIG = 50 ICANON = 51 XCASE = 52 diff --git a/vendor/golang.org/x/crypto/ssh/transport.go b/vendor/golang.org/x/crypto/ssh/transport.go index 49ddc2e7d..acf5a21bb 100644 --- a/vendor/golang.org/x/crypto/ssh/transport.go +++ b/vendor/golang.org/x/crypto/ssh/transport.go @@ -238,15 +238,19 @@ var ( // (to setup server->client keys) or clientKeys (for client->server keys). func newPacketCipher(d direction, algs directionAlgorithms, kex *kexResult) (packetCipher, error) { cipherMode := cipherModes[algs.Cipher] - macMode := macModes[algs.MAC] iv := make([]byte, cipherMode.ivSize) key := make([]byte, cipherMode.keySize) - macKey := make([]byte, macMode.keySize) generateKeyMaterial(iv, d.ivTag, kex) generateKeyMaterial(key, d.keyTag, kex) - generateKeyMaterial(macKey, d.macKeyTag, kex) + + var macKey []byte + if !aeadCiphers[algs.Cipher] { + macMode := macModes[algs.MAC] + macKey = make([]byte, macMode.keySize) + generateKeyMaterial(macKey, d.macKeyTag, kex) + } return cipherModes[algs.Cipher].create(key, iv, macKey, algs) } |