From 1cdab66b94c35334de1b64d3299c9c4f558be3a8 Mon Sep 17 00:00:00 2001 From: ChihYunChuang Date: Wed, 25 Aug 2021 15:19:57 +0800 Subject: [PATCH 01/10] crypto/ecpointgrouplaw: support Ed25519 --- .DS_Store | Bin 0 -> 6148 bytes crypto/.DS_Store | Bin 0 -> 6148 bytes crypto/binaryfield/message.pb.go | 2 +- crypto/binaryquadraticform/message.pb.go | 2 +- crypto/bip32/child/message.pb.go | 2 +- crypto/bip32/master/message.pb.go | 2 +- crypto/birkhoffinterpolation/bk.pb.go | 2 +- crypto/circuit/message.pb.go | 2 +- crypto/commitment/message.pb.go | 2 +- .../ecpointgrouplaw/ecpointgrouplaw_test.go | 3 +- crypto/ecpointgrouplaw/point.go | 34 +- crypto/ecpointgrouplaw/point.pb.go | 36 +- crypto/ecpointgrouplaw/point.proto | 1 + crypto/ecpointgrouplaw/point_test.go | 2 +- crypto/homo/cl/message.pb.go | 2 +- crypto/homo/paillier/message.pb.go | 2 +- crypto/ot/message.pb.go | 2 +- crypto/schnorrsignature/.DS_Store | Bin 0 -> 6148 bytes crypto/schnorrsignature/edwards25519/const.go | 1411 +++++++++++++ .../edwards25519/edwards25519.go | 1773 +++++++++++++++++ crypto/schnorrsignature/message.pb.go | 280 +++ crypto/schnorrsignature/message.proto | 34 + crypto/schnorrsignature/sign.go | 359 ++++ crypto/schnorrsignature/sign_test.go | 82 + crypto/tss/addshare/message.pb.go | 2 +- crypto/tss/dkg/message.pb.go | 2 +- crypto/tss/reshare/message.pb.go | 2 +- crypto/tss/signer/message.pb.go | 2 +- crypto/utils/message.pb.go | 12 +- crypto/zkproof/message.pb.go | 2 +- go.mod | 3 + go.sum | 8 + 32 files changed, 4021 insertions(+), 47 deletions(-) create mode 100644 .DS_Store create mode 100644 crypto/.DS_Store create mode 100644 crypto/schnorrsignature/.DS_Store create mode 100644 crypto/schnorrsignature/edwards25519/const.go create mode 100644 crypto/schnorrsignature/edwards25519/edwards25519.go create mode 100644 crypto/schnorrsignature/message.pb.go create mode 100644 crypto/schnorrsignature/message.proto create mode 100644 crypto/schnorrsignature/sign.go create mode 100644 crypto/schnorrsignature/sign_test.go diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..127d581db8b26245c687958d8fd531c013efee83 GIT binary patch literal 6148 zcmeHK!Ab)$5KY>uyNI|4!5(w*)GAwXW=M=pXq7 z{*E(AS}4_n7ZE!HlQ)^nB;@UqNf=|iG3vOCIgBw26tQ4K^M&9z>XHgUt|Ek-8#Et12$oOw)p+t!+snM(`xmD7mB5|^$p9mEqlwp^?P#cr$IUz zHiE%5_RfQ}7aIFQ%6M)E;bqhvx1605nWRCKbO$Oq>U1IG<|;}$a@>%kq%&0W_ga$5ua7uh zLPP-@-x7$zpl2}G2qPd|rvmC!Zk`xir-NUZIL~0NQKvJmR)%@Z%G|tAxLO_jLWMK# zX{44IAO;p0DC(|*_5bwy_y1xN^@sst;9oJoOHIGofGwHYy0kg0wF0yaih^;u#(4@D isuV*kmf|v~67UN&06l}bM(}{pML^L&4KeVm415B%JW{Lx literal 0 HcmV?d00001 diff --git a/crypto/.DS_Store b/crypto/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..5d897fb36f0f188d0489e9ee3939c99ad9b4baf5 GIT binary patch literal 6148 zcmeHK&2G~`5T0!V*dWv#km%6|xJ5WARYea-CWHeLs*nuj0I0PSE3xW$jeoF02+AXH zg(GjkjXMX#6Yx5G`=hEQphO%higu*kZ)SI9cV{x=%@PsoR)Y>vlZY%dfsM=PenVnj zv;|tzBQ}u9HDXGsq#@&xd)uihVhy|;jV*__lwz(nATA|SpG4w^tu<6NQqbfA+@0AK^dlE90%gs^cmdK%{n zF#}@C6sSy@equ0Xj&Vopc^c;ml{qo}_+WZxre7#b?vC{xsZPvOXnGR?6M@qaSXW|G z-2V^${Qf^}WF!*-6M_FK0<6*VdtJDs@74w9#9iy49ij;mdUJ)+1f9N)B_polO*BcE Za|8qQG|m-b1Z4gQ$S|1BMBq##@Dqso&fNe2 literal 0 HcmV?d00001 diff --git a/crypto/binaryfield/message.pb.go b/crypto/binaryfield/message.pb.go index f9bf83ba..369fa5e2 100644 --- a/crypto/binaryfield/message.pb.go +++ b/crypto/binaryfield/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/binaryfield/message.proto package binaryfield diff --git a/crypto/binaryquadraticform/message.pb.go b/crypto/binaryquadraticform/message.pb.go index 279f2ad2..f44dd705 100644 --- a/crypto/binaryquadraticform/message.pb.go +++ b/crypto/binaryquadraticform/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/binaryquadraticform/message.proto package binaryquadraticform diff --git a/crypto/bip32/child/message.pb.go b/crypto/bip32/child/message.pb.go index 1e8741de..bb52f5f7 100644 --- a/crypto/bip32/child/message.pb.go +++ b/crypto/bip32/child/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/bip32/child/message.proto package child diff --git a/crypto/bip32/master/message.pb.go b/crypto/bip32/master/message.pb.go index 77f2e7f9..144ab6f4 100644 --- a/crypto/bip32/master/message.pb.go +++ b/crypto/bip32/master/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/bip32/master/message.proto package master diff --git a/crypto/birkhoffinterpolation/bk.pb.go b/crypto/birkhoffinterpolation/bk.pb.go index 6decd069..c816a3fb 100644 --- a/crypto/birkhoffinterpolation/bk.pb.go +++ b/crypto/birkhoffinterpolation/bk.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/birkhoffinterpolation/bk.proto package birkhoffinterpolation diff --git a/crypto/circuit/message.pb.go b/crypto/circuit/message.pb.go index 843be9d0..408a88ff 100644 --- a/crypto/circuit/message.pb.go +++ b/crypto/circuit/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/circuit/message.proto package circuit diff --git a/crypto/commitment/message.pb.go b/crypto/commitment/message.pb.go index eede3dce..808a6237 100644 --- a/crypto/commitment/message.pb.go +++ b/crypto/commitment/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/commitment/message.proto package commitment diff --git a/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go b/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go index 2fa4f775..3d125e9d 100644 --- a/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go +++ b/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go @@ -19,6 +19,7 @@ import ( "testing" "github.com/btcsuite/btcd/btcec" + "github.com/decred/dcrd/dcrec/edwards/v2" . "github.com/onsi/ginkgo" . "github.com/onsi/gomega" @@ -30,7 +31,7 @@ func TestEllipticcurve(t *testing.T) { } var ( - curveList = []elliptic.Curve{elliptic.P224(), elliptic.P256(), elliptic.P384(), btcec.S256()} + curveList = []elliptic.Curve{elliptic.P224(), elliptic.P256(), elliptic.P384(), btcec.S256(), edwards.Edwards()} ) var _ = Describe("Elliptic curves", func() { diff --git a/crypto/ecpointgrouplaw/point.go b/crypto/ecpointgrouplaw/point.go index 52cf108f..963deec1 100644 --- a/crypto/ecpointgrouplaw/point.go +++ b/crypto/ecpointgrouplaw/point.go @@ -22,6 +22,7 @@ import ( "reflect" "github.com/btcsuite/btcd/btcec" + "github.com/decred/dcrd/dcrec/edwards" ) var ( @@ -103,13 +104,10 @@ func (p *ECPoint) Add(p1 *ECPoint) (*ECPoint, error) { return p.Copy(), nil } - // The case : aG+(-a)G. Assume that the coordinate of aG = (x,y). Then (-a)G = (x,-y). Then aG + (-a)G = identity = (nil, nil). - if p1.x.Cmp(p.x) == 0 { - tempNegative := new(big.Int).Neg(p1.y) - tempNegative.Mod(tempNegative, p.curve.Params().P) - if tempNegative.Cmp(p.y) == 0 { - return NewIdentity(p.curve), nil - } + // The case : aG+(-a)G. + minusP1 := p1.Neg() + if minusP1.Equal(p) { + return NewIdentity(p.curve), nil } // The case : aG + aG = 2aG. if p1.x.Cmp(p.x) == 0 && p1.y.Cmp(p.y) == 0 { @@ -138,6 +136,17 @@ func (p *ECPoint) Neg() *ECPoint { if p.IsIdentity() { return NewIdentity(p.curve) } + + // TODO: Not compare cofactor terms + if isSameCurve(p.curve, edwards.Edwards()) { + negativeX := new(big.Int).Neg(p.x) + negativeX = negativeX.Mod(negativeX, p.curve.Params().P) + return &ECPoint{ + curve: p.curve, + x: negativeX, + y: new(big.Int).Set(p.y), + } + } negativeY := new(big.Int).Neg(p.y) negativeY = negativeY.Mod(negativeY, p.curve.Params().P) return &ECPoint{ @@ -233,7 +242,10 @@ func isIdentity(x *big.Int, y *big.Int) bool { } func isSameCurve(curve1 elliptic.Curve, curve2 elliptic.Curve) bool { - return reflect.DeepEqual(curve1, curve2) + if curve1 == nil || curve2 == nil { + return false + } + return reflect.DeepEqual(curve1.Params(), curve2.Params()) } func isOnCurve(curve elliptic.Curve, x, y *big.Int) bool { @@ -257,6 +269,8 @@ func (c EcPointMessage_Curve) GetEllipticCurve() (elliptic.Curve, error) { return elliptic.P384(), nil case EcPointMessage_S256: return btcec.S256(), nil + case EcPointMessage_EDWARD25519: + return edwards.Edwards(), nil } return nil, ErrInvalidCurve } @@ -272,5 +286,9 @@ func ToCurve(c elliptic.Curve) (EcPointMessage_Curve, error) { case btcec.S256(): return EcPointMessage_S256, nil } + // TODO: Rewrite it to be a switch case. + if isSameCurve(c, edwards.Edwards()) { + return EcPointMessage_EDWARD25519, nil + } return 0, ErrInvalidCurve } diff --git a/crypto/ecpointgrouplaw/point.pb.go b/crypto/ecpointgrouplaw/point.pb.go index 30d6a589..b832594b 100644 --- a/crypto/ecpointgrouplaw/point.pb.go +++ b/crypto/ecpointgrouplaw/point.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/ecpointgrouplaw/point.proto package ecpointgrouplaw @@ -37,10 +37,11 @@ const ( type EcPointMessage_Curve int32 const ( - EcPointMessage_P224 EcPointMessage_Curve = 0 - EcPointMessage_P256 EcPointMessage_Curve = 1 - EcPointMessage_P384 EcPointMessage_Curve = 2 - EcPointMessage_S256 EcPointMessage_Curve = 3 + EcPointMessage_P224 EcPointMessage_Curve = 0 + EcPointMessage_P256 EcPointMessage_Curve = 1 + EcPointMessage_P384 EcPointMessage_Curve = 2 + EcPointMessage_S256 EcPointMessage_Curve = 3 + EcPointMessage_EDWARD25519 EcPointMessage_Curve = 4 ) // Enum value maps for EcPointMessage_Curve. @@ -50,12 +51,14 @@ var ( 1: "P256", 2: "P384", 3: "S256", + 4: "EDWARD25519", } EcPointMessage_Curve_value = map[string]int32{ - "P224": 0, - "P256": 1, - "P384": 2, - "S256": 3, + "P224": 0, + "P256": 1, + "P384": 2, + "S256": 3, + "EDWARD25519": 4, } ) @@ -156,21 +159,22 @@ var file_github_com_getamis_alice_crypto_ecpointgrouplaw_point_proto_rawDesc = [ 0x61, 0x6d, 0x69, 0x73, 0x2f, 0x61, 0x6c, 0x69, 0x63, 0x65, 0x2f, 0x63, 0x72, 0x79, 0x70, 0x74, 0x6f, 0x2f, 0x65, 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x2f, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x2e, 0x70, 0x72, 0x6f, 0x74, 0x6f, 0x12, 0x0f, 0x65, - 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x22, 0x9a, + 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x22, 0xab, 0x01, 0x0a, 0x0e, 0x45, 0x63, 0x50, 0x6f, 0x69, 0x6e, 0x74, 0x4d, 0x65, 0x73, 0x73, 0x61, 0x67, 0x65, 0x12, 0x3b, 0x0a, 0x05, 0x63, 0x75, 0x72, 0x76, 0x65, 0x18, 0x01, 0x20, 0x01, 0x28, 0x0e, 0x32, 0x25, 0x2e, 0x65, 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x2e, 0x45, 0x63, 0x50, 0x6f, 0x69, 0x6e, 0x74, 0x4d, 0x65, 0x73, 0x73, 0x61, 0x67, 0x65, 0x2e, 0x43, 0x75, 0x72, 0x76, 0x65, 0x52, 0x05, 0x63, 0x75, 0x72, 0x76, 0x65, 0x12, 0x0c, 0x0a, 0x01, 0x78, 0x18, 0x02, 0x20, 0x01, 0x28, 0x0c, 0x52, 0x01, 0x78, 0x12, 0x0c, 0x0a, 0x01, - 0x79, 0x18, 0x03, 0x20, 0x01, 0x28, 0x0c, 0x52, 0x01, 0x79, 0x22, 0x2f, 0x0a, 0x05, 0x43, 0x75, + 0x79, 0x18, 0x03, 0x20, 0x01, 0x28, 0x0c, 0x52, 0x01, 0x79, 0x22, 0x40, 0x0a, 0x05, 0x43, 0x75, 0x72, 0x76, 0x65, 0x12, 0x08, 0x0a, 0x04, 0x50, 0x32, 0x32, 0x34, 0x10, 0x00, 0x12, 0x08, 0x0a, 0x04, 0x50, 0x32, 0x35, 0x36, 0x10, 0x01, 0x12, 0x08, 0x0a, 0x04, 0x50, 0x33, 0x38, 0x34, 0x10, - 0x02, 0x12, 0x08, 0x0a, 0x04, 0x53, 0x32, 0x35, 0x36, 0x10, 0x03, 0x42, 0x31, 0x5a, 0x2f, 0x67, - 0x69, 0x74, 0x68, 0x75, 0x62, 0x2e, 0x63, 0x6f, 0x6d, 0x2f, 0x67, 0x65, 0x74, 0x61, 0x6d, 0x69, - 0x73, 0x2f, 0x61, 0x6c, 0x69, 0x63, 0x65, 0x2f, 0x63, 0x72, 0x79, 0x70, 0x74, 0x6f, 0x2f, 0x65, - 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x62, 0x06, - 0x70, 0x72, 0x6f, 0x74, 0x6f, 0x33, + 0x02, 0x12, 0x08, 0x0a, 0x04, 0x53, 0x32, 0x35, 0x36, 0x10, 0x03, 0x12, 0x0f, 0x0a, 0x0b, 0x45, + 0x44, 0x57, 0x41, 0x52, 0x44, 0x32, 0x35, 0x35, 0x31, 0x39, 0x10, 0x04, 0x42, 0x31, 0x5a, 0x2f, + 0x67, 0x69, 0x74, 0x68, 0x75, 0x62, 0x2e, 0x63, 0x6f, 0x6d, 0x2f, 0x67, 0x65, 0x74, 0x61, 0x6d, + 0x69, 0x73, 0x2f, 0x61, 0x6c, 0x69, 0x63, 0x65, 0x2f, 0x63, 0x72, 0x79, 0x70, 0x74, 0x6f, 0x2f, + 0x65, 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x62, + 0x06, 0x70, 0x72, 0x6f, 0x74, 0x6f, 0x33, } var ( diff --git a/crypto/ecpointgrouplaw/point.proto b/crypto/ecpointgrouplaw/point.proto index 2e0b5989..00432532 100644 --- a/crypto/ecpointgrouplaw/point.proto +++ b/crypto/ecpointgrouplaw/point.proto @@ -24,6 +24,7 @@ message EcPointMessage { P256 = 1; P384 = 2; S256 = 3; + EDWARD25519 = 4; } Curve curve = 1; bytes x = 2; diff --git a/crypto/ecpointgrouplaw/point_test.go b/crypto/ecpointgrouplaw/point_test.go index 3fcb5749..e139c00e 100644 --- a/crypto/ecpointgrouplaw/point_test.go +++ b/crypto/ecpointgrouplaw/point_test.go @@ -457,7 +457,7 @@ var _ = Describe("Point", func() { }) It("ToPoint()", func() { - const UnSupportedEcPointMessage EcPointMessage_Curve = 4 + const UnSupportedEcPointMessage EcPointMessage_Curve = 100 msg := &EcPointMessage{ Curve: UnSupportedEcPointMessage, } diff --git a/crypto/homo/cl/message.pb.go b/crypto/homo/cl/message.pb.go index 0413a4e1..d964274c 100644 --- a/crypto/homo/cl/message.pb.go +++ b/crypto/homo/cl/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/homo/cl/message.proto package cl diff --git a/crypto/homo/paillier/message.pb.go b/crypto/homo/paillier/message.pb.go index 85bf385d..41f83348 100644 --- a/crypto/homo/paillier/message.pb.go +++ b/crypto/homo/paillier/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/homo/paillier/message.proto package paillier diff --git a/crypto/ot/message.pb.go b/crypto/ot/message.pb.go index dc30c226..7549722d 100644 --- a/crypto/ot/message.pb.go +++ b/crypto/ot/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/ot/message.proto package ot diff --git a/crypto/schnorrsignature/.DS_Store b/crypto/schnorrsignature/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..b439b88e53351353778b8a3a3c619b2bcba29f53 GIT binary patch literal 6148 zcmeHK!AiqG5S^`66IAR$(Bodb_0WbY<{*Sx58i}`9#m{XiUw*TO={3u$#3W%`33%t zGrQYjQEwtxX3FfFot@cb-%z(OUg*w}m{G*0?OD#k-7)EondAOi<> z@W=8W7@)ITg&v+;0RenIzb3e0k==#;G{l&<@U9{iE*f!{g{_{QRO>7x;%%vTkq! zuW0vciOlmQ(M1mj%uw$?V^%U oT&Z!If`%%^7)zyi3snjFB^ijG!BQi7Q20YY(ZCHe@TUxX05C&S3jhEB literal 0 HcmV?d00001 diff --git a/crypto/schnorrsignature/edwards25519/const.go b/crypto/schnorrsignature/edwards25519/const.go new file mode 100644 index 00000000..ea5b77a7 --- /dev/null +++ b/crypto/schnorrsignature/edwards25519/const.go @@ -0,0 +1,1411 @@ +// Copyright 2013 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package edwards25519 + +var d = FieldElement{ + -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116, +} + +var d2 = FieldElement{ + -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199, +} + +var SqrtM1 = FieldElement{ + -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482, +} + +var A = FieldElement{ + 486662, 0, 0, 0, 0, 0, 0, 0, 0, 0, +} + +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}, + }, +} + +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/crypto/schnorrsignature/edwards25519/edwards25519.go b/crypto/schnorrsignature/edwards25519/edwards25519.go new file mode 100644 index 00000000..90798185 --- /dev/null +++ b/crypto/schnorrsignature/edwards25519/edwards25519.go @@ -0,0 +1,1773 @@ +// Copyright 2013 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package edwards25519 implements operations in GF(2**255-19) and on an +// Edwards curve that is isomorphic to curve25519. See +// http://ed25519.cr.yp.to/. +package edwards25519 + +// This code is a port of the public domain, "ref10" implementation of ed25519 +// from SUPERCOP. + +// FieldElement represents an element of the field GF(2^255 - 19). An element +// t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 +// t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on +// context. +type FieldElement [10]int32 + +var zero FieldElement + +func FeZero(fe *FieldElement) { + copy(fe[:], zero[:]) +} + +func FeOne(fe *FieldElement) { + FeZero(fe) + fe[0] = 1 +} + +func FeAdd(dst, a, b *FieldElement) { + dst[0] = a[0] + b[0] + dst[1] = a[1] + b[1] + dst[2] = a[2] + b[2] + dst[3] = a[3] + b[3] + dst[4] = a[4] + b[4] + dst[5] = a[5] + b[5] + dst[6] = a[6] + b[6] + dst[7] = a[7] + b[7] + dst[8] = a[8] + b[8] + dst[9] = a[9] + b[9] +} + +func FeSub(dst, a, b *FieldElement) { + dst[0] = a[0] - b[0] + dst[1] = a[1] - b[1] + dst[2] = a[2] - b[2] + dst[3] = a[3] - b[3] + dst[4] = a[4] - b[4] + dst[5] = a[5] - b[5] + dst[6] = a[6] - b[6] + dst[7] = a[7] - b[7] + dst[8] = a[8] - b[8] + dst[9] = a[9] - b[9] +} + +func FeCopy(dst, src *FieldElement) { + copy(dst[:], src[:]) +} + +// Replace (f,g) with (g,g) if b == 1; +// replace (f,g) with (f,g) if b == 0. +// +// Preconditions: b in {0,1}. +func FeCMove(f, g *FieldElement, b int32) { + b = -b + f[0] ^= b & (f[0] ^ g[0]) + f[1] ^= b & (f[1] ^ g[1]) + f[2] ^= b & (f[2] ^ g[2]) + f[3] ^= b & (f[3] ^ g[3]) + f[4] ^= b & (f[4] ^ g[4]) + f[5] ^= b & (f[5] ^ g[5]) + f[6] ^= b & (f[6] ^ g[6]) + f[7] ^= b & (f[7] ^ g[7]) + f[8] ^= b & (f[8] ^ g[8]) + f[9] ^= b & (f[9] ^ g[9]) +} + +func load3(in []byte) int64 { + var r int64 + r = int64(in[0]) + r |= int64(in[1]) << 8 + r |= int64(in[2]) << 16 + return r +} + +func load4(in []byte) int64 { + var r int64 + r = int64(in[0]) + r |= int64(in[1]) << 8 + r |= int64(in[2]) << 16 + r |= int64(in[3]) << 24 + return r +} + +func FeFromBytes(dst *FieldElement, src *[32]byte) { + h0 := load4(src[:]) + h1 := load3(src[4:]) << 6 + h2 := load3(src[7:]) << 5 + h3 := load3(src[10:]) << 3 + h4 := load3(src[13:]) << 2 + h5 := load4(src[16:]) + h6 := load3(src[20:]) << 7 + h7 := load3(src[23:]) << 5 + h8 := load3(src[26:]) << 4 + h9 := (load3(src[29:]) & 8388607) << 2 + + FeCombine(dst, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9) +} + +// FeToBytes marshals h to s. +// Preconditions: +// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +// +// Write p=2^255-19; q=floor(h/p). +// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). +// +// Proof: +// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. +// Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4. +// +// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). +// Then 0> 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]<= -15 { + r[i] -= r[i+b] << uint(b) + for k := i + b; k < 256; k++ { + if r[k] == 0 { + r[k] = 1 + break + } + r[k] = 0 + } + } else { + break + } + } + } + } + } +} + +// GeDoubleScalarMultVartime sets r = a*A + b*B +// where a = a[0]+256*a[1]+...+256^31 a[31]. +// and b = b[0]+256*b[1]+...+256^31 b[31]. +// B is the Ed25519 base point (x,4/5) with x positive. +func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte) { + var aSlide, bSlide [256]int8 + var Ai [8]CachedGroupElement // A,3A,5A,7A,9A,11A,13A,15A + var t CompletedGroupElement + var u, A2 ExtendedGroupElement + var i int + + slide(&aSlide, a) + slide(&bSlide, b) + + A.ToCached(&Ai[0]) + A.Double(&t) + t.ToExtended(&A2) + + for i := 0; i < 7; i++ { + geAdd(&t, &A2, &Ai[i]) + t.ToExtended(&u) + u.ToCached(&Ai[i+1]) + } + + r.Zero() + + for i = 255; i >= 0; i-- { + if aSlide[i] != 0 || bSlide[i] != 0 { + break + } + } + + for ; i >= 0; i-- { + r.Double(&t) + + if aSlide[i] > 0 { + t.ToExtended(&u) + geAdd(&t, &u, &Ai[aSlide[i]/2]) + } else if aSlide[i] < 0 { + t.ToExtended(&u) + geSub(&t, &u, &Ai[(-aSlide[i])/2]) + } + + if bSlide[i] > 0 { + t.ToExtended(&u) + geMixedAdd(&t, &u, &bi[bSlide[i]/2]) + } else if bSlide[i] < 0 { + t.ToExtended(&u) + geMixedSub(&t, &u, &bi[(-bSlide[i])/2]) + } + + t.ToProjective(r) + } +} + +// equal returns 1 if b == c and 0 otherwise. +func equal(b, c int32) int32 { + x := uint32(b ^ c) + x-- + return int32(x >> 31) +} + +// negative returns 1 if b < 0 and 0 otherwise. +func negative(b int32) int32 { + return (b >> 31) & 1 +} + +func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32) { + FeCMove(&t.yPlusX, &u.yPlusX, b) + FeCMove(&t.yMinusX, &u.yMinusX, b) + FeCMove(&t.xy2d, &u.xy2d, b) +} + +func selectPoint(t *PreComputedGroupElement, pos int32, b int32) { + var minusT PreComputedGroupElement + bNegative := negative(b) + bAbs := b - (((-bNegative) & b) << 1) + + t.Zero() + for i := int32(0); i < 8; i++ { + PreComputedGroupElementCMove(t, &base[pos][i], equal(bAbs, i+1)) + } + FeCopy(&minusT.yPlusX, &t.yMinusX) + FeCopy(&minusT.yMinusX, &t.yPlusX) + FeNeg(&minusT.xy2d, &t.xy2d) + PreComputedGroupElementCMove(t, &minusT, bNegative) +} + +// GeScalarMultBase computes h = a*B, where +// a = a[0]+256*a[1]+...+256^31 a[31] +// B is the Ed25519 base point (x,4/5) with x positive. +// +// Preconditions: +// a[31] <= 127 +func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte) { + var e [64]int8 + + for i, v := range a { + e[2*i] = int8(v & 15) + e[2*i+1] = int8((v >> 4) & 15) + } + + // each e[i] is between 0 and 15 and e[63] is between 0 and 7. + + carry := int8(0) + for i := 0; i < 63; i++ { + e[i] += carry + carry = (e[i] + 8) >> 4 + e[i] -= carry << 4 + } + e[63] += carry + // each e[i] is between -8 and 8. + + h.Zero() + var t PreComputedGroupElement + var r CompletedGroupElement + for i := int32(1); i < 64; i += 2 { + selectPoint(&t, i/2, int32(e[i])) + geMixedAdd(&r, h, &t) + r.ToExtended(h) + } + + var s ProjectiveGroupElement + + h.Double(&r) + r.ToProjective(&s) + s.Double(&r) + r.ToProjective(&s) + s.Double(&r) + r.ToProjective(&s) + s.Double(&r) + r.ToExtended(h) + + for i := int32(0); i < 64; i += 2 { + selectPoint(&t, i/2, int32(e[i])) + geMixedAdd(&r, h, &t) + r.ToExtended(h) + } +} + +// The scalars are GF(2^252 + 27742317777372353535851937790883648493). + +// Input: +// a[0]+256*a[1]+...+256^31*a[31] = a +// b[0]+256*b[1]+...+256^31*b[31] = b +// c[0]+256*c[1]+...+256^31*c[31] = c +// +// Output: +// s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l +// where l = 2^252 + 27742317777372353535851937790883648493. +func ScMulAdd(s, a, b, c *[32]byte) { + a0 := 2097151 & load3(a[:]) + a1 := 2097151 & (load4(a[2:]) >> 5) + a2 := 2097151 & (load3(a[5:]) >> 2) + a3 := 2097151 & (load4(a[7:]) >> 7) + a4 := 2097151 & (load4(a[10:]) >> 4) + a5 := 2097151 & (load3(a[13:]) >> 1) + a6 := 2097151 & (load4(a[15:]) >> 6) + a7 := 2097151 & (load3(a[18:]) >> 3) + a8 := 2097151 & load3(a[21:]) + a9 := 2097151 & (load4(a[23:]) >> 5) + a10 := 2097151 & (load3(a[26:]) >> 2) + a11 := (load4(a[28:]) >> 7) + b0 := 2097151 & load3(b[:]) + b1 := 2097151 & (load4(b[2:]) >> 5) + b2 := 2097151 & (load3(b[5:]) >> 2) + b3 := 2097151 & (load4(b[7:]) >> 7) + b4 := 2097151 & (load4(b[10:]) >> 4) + b5 := 2097151 & (load3(b[13:]) >> 1) + b6 := 2097151 & (load4(b[15:]) >> 6) + b7 := 2097151 & (load3(b[18:]) >> 3) + b8 := 2097151 & load3(b[21:]) + b9 := 2097151 & (load4(b[23:]) >> 5) + b10 := 2097151 & (load3(b[26:]) >> 2) + b11 := (load4(b[28:]) >> 7) + c0 := 2097151 & load3(c[:]) + c1 := 2097151 & (load4(c[2:]) >> 5) + c2 := 2097151 & (load3(c[5:]) >> 2) + c3 := 2097151 & (load4(c[7:]) >> 7) + c4 := 2097151 & (load4(c[10:]) >> 4) + c5 := 2097151 & (load3(c[13:]) >> 1) + c6 := 2097151 & (load4(c[15:]) >> 6) + c7 := 2097151 & (load3(c[18:]) >> 3) + c8 := 2097151 & load3(c[21:]) + c9 := 2097151 & (load4(c[23:]) >> 5) + c10 := 2097151 & (load3(c[26:]) >> 2) + c11 := (load4(c[28:]) >> 7) + var carry [23]int64 + + s0 := c0 + a0*b0 + s1 := c1 + a0*b1 + a1*b0 + s2 := c2 + a0*b2 + a1*b1 + a2*b0 + s3 := c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0 + s4 := c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0 + s5 := c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0 + s6 := c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0 + s7 := c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0 + s8 := c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0 + s9 := c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0 + s10 := c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0 + s11 := c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0 + s12 := a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1 + s13 := a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2 + s14 := a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3 + s15 := a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4 + s16 := a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5 + s17 := a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6 + s18 := a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7 + s19 := a8*b11 + a9*b10 + a10*b9 + a11*b8 + s20 := a9*b11 + a10*b10 + a11*b9 + s21 := a10*b11 + a11*b10 + s22 := a11 * b11 + s23 := int64(0) + + carry[0] = (s0 + (1 << 20)) >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[2] = (s2 + (1 << 20)) >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[4] = (s4 + (1 << 20)) >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[12] = (s12 + (1 << 20)) >> 21 + s13 += carry[12] + s12 -= carry[12] << 21 + carry[14] = (s14 + (1 << 20)) >> 21 + s15 += carry[14] + s14 -= carry[14] << 21 + carry[16] = (s16 + (1 << 20)) >> 21 + s17 += carry[16] + s16 -= carry[16] << 21 + carry[18] = (s18 + (1 << 20)) >> 21 + s19 += carry[18] + s18 -= carry[18] << 21 + carry[20] = (s20 + (1 << 20)) >> 21 + s21 += carry[20] + s20 -= carry[20] << 21 + carry[22] = (s22 + (1 << 20)) >> 21 + s23 += carry[22] + s22 -= carry[22] << 21 + + carry[1] = (s1 + (1 << 20)) >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[3] = (s3 + (1 << 20)) >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[5] = (s5 + (1 << 20)) >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + carry[13] = (s13 + (1 << 20)) >> 21 + s14 += carry[13] + s13 -= carry[13] << 21 + carry[15] = (s15 + (1 << 20)) >> 21 + s16 += carry[15] + s15 -= carry[15] << 21 + carry[17] = (s17 + (1 << 20)) >> 21 + s18 += carry[17] + s17 -= carry[17] << 21 + carry[19] = (s19 + (1 << 20)) >> 21 + s20 += carry[19] + s19 -= carry[19] << 21 + carry[21] = (s21 + (1 << 20)) >> 21 + s22 += carry[21] + s21 -= carry[21] << 21 + + s11 += s23 * 666643 + s12 += s23 * 470296 + s13 += s23 * 654183 + s14 -= s23 * 997805 + s15 += s23 * 136657 + s16 -= s23 * 683901 + s23 = 0 + + s10 += s22 * 666643 + s11 += s22 * 470296 + s12 += s22 * 654183 + s13 -= s22 * 997805 + s14 += s22 * 136657 + s15 -= s22 * 683901 + s22 = 0 + + s9 += s21 * 666643 + s10 += s21 * 470296 + s11 += s21 * 654183 + s12 -= s21 * 997805 + s13 += s21 * 136657 + s14 -= s21 * 683901 + s21 = 0 + + s8 += s20 * 666643 + s9 += s20 * 470296 + s10 += s20 * 654183 + s11 -= s20 * 997805 + s12 += s20 * 136657 + s13 -= s20 * 683901 + s20 = 0 + + s7 += s19 * 666643 + s8 += s19 * 470296 + s9 += s19 * 654183 + s10 -= s19 * 997805 + s11 += s19 * 136657 + s12 -= s19 * 683901 + s19 = 0 + + s6 += s18 * 666643 + s7 += s18 * 470296 + s8 += s18 * 654183 + s9 -= s18 * 997805 + s10 += s18 * 136657 + s11 -= s18 * 683901 + s18 = 0 + + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[12] = (s12 + (1 << 20)) >> 21 + s13 += carry[12] + s12 -= carry[12] << 21 + carry[14] = (s14 + (1 << 20)) >> 21 + s15 += carry[14] + s14 -= carry[14] << 21 + carry[16] = (s16 + (1 << 20)) >> 21 + s17 += carry[16] + s16 -= carry[16] << 21 + + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + carry[13] = (s13 + (1 << 20)) >> 21 + s14 += carry[13] + s13 -= carry[13] << 21 + carry[15] = (s15 + (1 << 20)) >> 21 + s16 += carry[15] + s15 -= carry[15] << 21 + + s5 += s17 * 666643 + s6 += s17 * 470296 + s7 += s17 * 654183 + s8 -= s17 * 997805 + s9 += s17 * 136657 + s10 -= s17 * 683901 + s17 = 0 + + s4 += s16 * 666643 + s5 += s16 * 470296 + s6 += s16 * 654183 + s7 -= s16 * 997805 + s8 += s16 * 136657 + s9 -= s16 * 683901 + s16 = 0 + + s3 += s15 * 666643 + s4 += s15 * 470296 + s5 += s15 * 654183 + s6 -= s15 * 997805 + s7 += s15 * 136657 + s8 -= s15 * 683901 + s15 = 0 + + s2 += s14 * 666643 + s3 += s14 * 470296 + s4 += s14 * 654183 + s5 -= s14 * 997805 + s6 += s14 * 136657 + s7 -= s14 * 683901 + s14 = 0 + + s1 += s13 * 666643 + s2 += s13 * 470296 + s3 += s13 * 654183 + s4 -= s13 * 997805 + s5 += s13 * 136657 + s6 -= s13 * 683901 + s13 = 0 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = (s0 + (1 << 20)) >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[2] = (s2 + (1 << 20)) >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[4] = (s4 + (1 << 20)) >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + + carry[1] = (s1 + (1 << 20)) >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[3] = (s3 + (1 << 20)) >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[5] = (s5 + (1 << 20)) >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = s0 >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[1] = s1 >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[2] = s2 >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[3] = s3 >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[4] = s4 >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[5] = s5 >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[6] = s6 >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[7] = s7 >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[8] = s8 >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[9] = s9 >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[10] = s10 >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[11] = s11 >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = s0 >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[1] = s1 >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[2] = s2 >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[3] = s3 >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[4] = s4 >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[5] = s5 >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[6] = s6 >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[7] = s7 >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[8] = s8 >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[9] = s9 >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[10] = s10 >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + + s[0] = byte(s0 >> 0) + s[1] = byte(s0 >> 8) + s[2] = byte((s0 >> 16) | (s1 << 5)) + s[3] = byte(s1 >> 3) + s[4] = byte(s1 >> 11) + s[5] = byte((s1 >> 19) | (s2 << 2)) + s[6] = byte(s2 >> 6) + s[7] = byte((s2 >> 14) | (s3 << 7)) + s[8] = byte(s3 >> 1) + s[9] = byte(s3 >> 9) + s[10] = byte((s3 >> 17) | (s4 << 4)) + s[11] = byte(s4 >> 4) + s[12] = byte(s4 >> 12) + s[13] = byte((s4 >> 20) | (s5 << 1)) + s[14] = byte(s5 >> 7) + s[15] = byte((s5 >> 15) | (s6 << 6)) + s[16] = byte(s6 >> 2) + s[17] = byte(s6 >> 10) + s[18] = byte((s6 >> 18) | (s7 << 3)) + s[19] = byte(s7 >> 5) + s[20] = byte(s7 >> 13) + s[21] = byte(s8 >> 0) + s[22] = byte(s8 >> 8) + s[23] = byte((s8 >> 16) | (s9 << 5)) + s[24] = byte(s9 >> 3) + s[25] = byte(s9 >> 11) + s[26] = byte((s9 >> 19) | (s10 << 2)) + s[27] = byte(s10 >> 6) + s[28] = byte((s10 >> 14) | (s11 << 7)) + s[29] = byte(s11 >> 1) + s[30] = byte(s11 >> 9) + s[31] = byte(s11 >> 17) +} + +// Input: +// s[0]+256*s[1]+...+256^63*s[63] = s +// +// Output: +// s[0]+256*s[1]+...+256^31*s[31] = s mod l +// where l = 2^252 + 27742317777372353535851937790883648493. +func ScReduce(out *[32]byte, s *[64]byte) { + s0 := 2097151 & load3(s[:]) + s1 := 2097151 & (load4(s[2:]) >> 5) + s2 := 2097151 & (load3(s[5:]) >> 2) + s3 := 2097151 & (load4(s[7:]) >> 7) + s4 := 2097151 & (load4(s[10:]) >> 4) + s5 := 2097151 & (load3(s[13:]) >> 1) + s6 := 2097151 & (load4(s[15:]) >> 6) + s7 := 2097151 & (load3(s[18:]) >> 3) + s8 := 2097151 & load3(s[21:]) + s9 := 2097151 & (load4(s[23:]) >> 5) + s10 := 2097151 & (load3(s[26:]) >> 2) + s11 := 2097151 & (load4(s[28:]) >> 7) + s12 := 2097151 & (load4(s[31:]) >> 4) + s13 := 2097151 & (load3(s[34:]) >> 1) + s14 := 2097151 & (load4(s[36:]) >> 6) + s15 := 2097151 & (load3(s[39:]) >> 3) + s16 := 2097151 & load3(s[42:]) + s17 := 2097151 & (load4(s[44:]) >> 5) + s18 := 2097151 & (load3(s[47:]) >> 2) + s19 := 2097151 & (load4(s[49:]) >> 7) + s20 := 2097151 & (load4(s[52:]) >> 4) + s21 := 2097151 & (load3(s[55:]) >> 1) + s22 := 2097151 & (load4(s[57:]) >> 6) + s23 := (load4(s[60:]) >> 3) + + s11 += s23 * 666643 + s12 += s23 * 470296 + s13 += s23 * 654183 + s14 -= s23 * 997805 + s15 += s23 * 136657 + s16 -= s23 * 683901 + s23 = 0 + + s10 += s22 * 666643 + s11 += s22 * 470296 + s12 += s22 * 654183 + s13 -= s22 * 997805 + s14 += s22 * 136657 + s15 -= s22 * 683901 + s22 = 0 + + s9 += s21 * 666643 + s10 += s21 * 470296 + s11 += s21 * 654183 + s12 -= s21 * 997805 + s13 += s21 * 136657 + s14 -= s21 * 683901 + s21 = 0 + + s8 += s20 * 666643 + s9 += s20 * 470296 + s10 += s20 * 654183 + s11 -= s20 * 997805 + s12 += s20 * 136657 + s13 -= s20 * 683901 + s20 = 0 + + s7 += s19 * 666643 + s8 += s19 * 470296 + s9 += s19 * 654183 + s10 -= s19 * 997805 + s11 += s19 * 136657 + s12 -= s19 * 683901 + s19 = 0 + + s6 += s18 * 666643 + s7 += s18 * 470296 + s8 += s18 * 654183 + s9 -= s18 * 997805 + s10 += s18 * 136657 + s11 -= s18 * 683901 + s18 = 0 + + var carry [17]int64 + + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[12] = (s12 + (1 << 20)) >> 21 + s13 += carry[12] + s12 -= carry[12] << 21 + carry[14] = (s14 + (1 << 20)) >> 21 + s15 += carry[14] + s14 -= carry[14] << 21 + carry[16] = (s16 + (1 << 20)) >> 21 + s17 += carry[16] + s16 -= carry[16] << 21 + + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + carry[13] = (s13 + (1 << 20)) >> 21 + s14 += carry[13] + s13 -= carry[13] << 21 + carry[15] = (s15 + (1 << 20)) >> 21 + s16 += carry[15] + s15 -= carry[15] << 21 + + s5 += s17 * 666643 + s6 += s17 * 470296 + s7 += s17 * 654183 + s8 -= s17 * 997805 + s9 += s17 * 136657 + s10 -= s17 * 683901 + s17 = 0 + + s4 += s16 * 666643 + s5 += s16 * 470296 + s6 += s16 * 654183 + s7 -= s16 * 997805 + s8 += s16 * 136657 + s9 -= s16 * 683901 + s16 = 0 + + s3 += s15 * 666643 + s4 += s15 * 470296 + s5 += s15 * 654183 + s6 -= s15 * 997805 + s7 += s15 * 136657 + s8 -= s15 * 683901 + s15 = 0 + + s2 += s14 * 666643 + s3 += s14 * 470296 + s4 += s14 * 654183 + s5 -= s14 * 997805 + s6 += s14 * 136657 + s7 -= s14 * 683901 + s14 = 0 + + s1 += s13 * 666643 + s2 += s13 * 470296 + s3 += s13 * 654183 + s4 -= s13 * 997805 + s5 += s13 * 136657 + s6 -= s13 * 683901 + s13 = 0 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = (s0 + (1 << 20)) >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[2] = (s2 + (1 << 20)) >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[4] = (s4 + (1 << 20)) >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + + carry[1] = (s1 + (1 << 20)) >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[3] = (s3 + (1 << 20)) >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[5] = (s5 + (1 << 20)) >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = s0 >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[1] = s1 >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[2] = s2 >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[3] = s3 >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[4] = s4 >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[5] = s5 >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[6] = s6 >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[7] = s7 >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[8] = s8 >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[9] = s9 >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[10] = s10 >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[11] = s11 >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = s0 >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[1] = s1 >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[2] = s2 >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[3] = s3 >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[4] = s4 >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[5] = s5 >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[6] = s6 >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[7] = s7 >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[8] = s8 >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[9] = s9 >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[10] = s10 >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + + out[0] = byte(s0 >> 0) + out[1] = byte(s0 >> 8) + out[2] = byte((s0 >> 16) | (s1 << 5)) + out[3] = byte(s1 >> 3) + out[4] = byte(s1 >> 11) + out[5] = byte((s1 >> 19) | (s2 << 2)) + out[6] = byte(s2 >> 6) + out[7] = byte((s2 >> 14) | (s3 << 7)) + out[8] = byte(s3 >> 1) + out[9] = byte(s3 >> 9) + out[10] = byte((s3 >> 17) | (s4 << 4)) + out[11] = byte(s4 >> 4) + out[12] = byte(s4 >> 12) + out[13] = byte((s4 >> 20) | (s5 << 1)) + out[14] = byte(s5 >> 7) + out[15] = byte((s5 >> 15) | (s6 << 6)) + out[16] = byte(s6 >> 2) + out[17] = byte(s6 >> 10) + out[18] = byte((s6 >> 18) | (s7 << 3)) + out[19] = byte(s7 >> 5) + out[20] = byte(s7 >> 13) + out[21] = byte(s8 >> 0) + out[22] = byte(s8 >> 8) + out[23] = byte((s8 >> 16) | (s9 << 5)) + out[24] = byte(s9 >> 3) + out[25] = byte(s9 >> 11) + out[26] = byte((s9 >> 19) | (s10 << 2)) + out[27] = byte(s10 >> 6) + out[28] = byte((s10 >> 14) | (s11 << 7)) + out[29] = byte(s11 >> 1) + out[30] = byte(s11 >> 9) + out[31] = byte(s11 >> 17) +} diff --git a/crypto/schnorrsignature/message.pb.go b/crypto/schnorrsignature/message.pb.go new file mode 100644 index 00000000..29670992 --- /dev/null +++ b/crypto/schnorrsignature/message.pb.go @@ -0,0 +1,280 @@ +// Copyright © 2021 AMIS Technologies +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by protoc-gen-go. DO NOT EDIT. +// versions: +// protoc-gen-go v1.26.0 +// protoc v3.14.0 +// source: github.com/getamis/alice/crypto/schnorrsignature/message.proto + +package schnorrsignature + +import ( + ecpointgrouplaw "github.com/getamis/alice/crypto/ecpointgrouplaw" + zkproof "github.com/getamis/alice/crypto/zkproof" + protoreflect "google.golang.org/protobuf/reflect/protoreflect" + protoimpl "google.golang.org/protobuf/runtime/protoimpl" + reflect "reflect" + sync "sync" +) + +const ( + // Verify that this generated code is sufficiently up-to-date. + _ = protoimpl.EnforceVersion(20 - protoimpl.MinVersion) + // Verify that runtime/protoimpl is sufficiently up-to-date. + _ = protoimpl.EnforceVersion(protoimpl.MaxVersion - 20) +) + +type CommitmentMsg struct { + state protoimpl.MessageState + sizeCache protoimpl.SizeCache + unknownFields protoimpl.UnknownFields + + X []byte `protobuf:"bytes,1,opt,name=x,proto3" json:"x,omitempty"` + D *ecpointgrouplaw.EcPointMessage `protobuf:"bytes,2,opt,name=D,proto3" json:"D,omitempty"` + E *ecpointgrouplaw.EcPointMessage `protobuf:"bytes,3,opt,name=E,proto3" json:"E,omitempty"` + SG *zkproof.SchnorrProofMessage `protobuf:"bytes,4,opt,name=sG,proto3" json:"sG,omitempty"` +} + +func (x *CommitmentMsg) Reset() { + *x = CommitmentMsg{} + if protoimpl.UnsafeEnabled { + mi := &file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_msgTypes[0] + ms := protoimpl.X.MessageStateOf(protoimpl.Pointer(x)) + ms.StoreMessageInfo(mi) + } +} + +func (x *CommitmentMsg) String() string { + return protoimpl.X.MessageStringOf(x) +} + +func (*CommitmentMsg) ProtoMessage() {} + +func (x *CommitmentMsg) ProtoReflect() protoreflect.Message { + mi := &file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_msgTypes[0] + if protoimpl.UnsafeEnabled && x != nil { + ms := protoimpl.X.MessageStateOf(protoimpl.Pointer(x)) + if ms.LoadMessageInfo() == nil { + ms.StoreMessageInfo(mi) + } + return ms + } + return mi.MessageOf(x) +} + +// Deprecated: Use CommitmentMsg.ProtoReflect.Descriptor instead. +func (*CommitmentMsg) Descriptor() ([]byte, []int) { + return file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDescGZIP(), []int{0} +} + +func (x *CommitmentMsg) GetX() []byte { + if x != nil { + return x.X + } + return nil +} + +func (x *CommitmentMsg) GetD() *ecpointgrouplaw.EcPointMessage { + if x != nil { + return x.D + } + return nil +} + +func (x *CommitmentMsg) GetE() *ecpointgrouplaw.EcPointMessage { + if x != nil { + return x.E + } + return nil +} + +func (x *CommitmentMsg) GetSG() *zkproof.SchnorrProofMessage { + if x != nil { + return x.SG + } + return nil +} + +type PartialSignatureMsg struct { + state protoimpl.MessageState + sizeCache protoimpl.SizeCache + unknownFields protoimpl.UnknownFields + + X []byte `protobuf:"bytes,1,opt,name=x,proto3" json:"x,omitempty"` + Si []byte `protobuf:"bytes,2,opt,name=si,proto3" json:"si,omitempty"` +} + +func (x *PartialSignatureMsg) Reset() { + *x = PartialSignatureMsg{} + if protoimpl.UnsafeEnabled { + mi := &file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_msgTypes[1] + ms := protoimpl.X.MessageStateOf(protoimpl.Pointer(x)) + ms.StoreMessageInfo(mi) + } +} + +func (x *PartialSignatureMsg) String() string { + return protoimpl.X.MessageStringOf(x) +} + +func (*PartialSignatureMsg) ProtoMessage() {} + +func (x *PartialSignatureMsg) ProtoReflect() protoreflect.Message { + mi := &file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_msgTypes[1] + if protoimpl.UnsafeEnabled && x != nil { + ms := protoimpl.X.MessageStateOf(protoimpl.Pointer(x)) + if ms.LoadMessageInfo() == nil { + ms.StoreMessageInfo(mi) + } + return ms + } + return mi.MessageOf(x) +} + +// Deprecated: Use PartialSignatureMsg.ProtoReflect.Descriptor instead. +func (*PartialSignatureMsg) Descriptor() ([]byte, []int) { + return file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDescGZIP(), []int{1} +} + +func (x *PartialSignatureMsg) GetX() []byte { + if x != nil { + return x.X + } + return nil +} + +func (x *PartialSignatureMsg) GetSi() []byte { + if x != nil { + return x.Si + } + return nil +} + +var File_github_com_getamis_alice_crypto_schnorrsignature_message_proto protoreflect.FileDescriptor + +var file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDesc = []byte{ + 0x0a, 0x3e, 0x67, 0x69, 0x74, 0x68, 0x75, 0x62, 0x2e, 0x63, 0x6f, 0x6d, 0x2f, 0x67, 0x65, 0x74, + 0x61, 0x6d, 0x69, 0x73, 0x2f, 0x61, 0x6c, 0x69, 0x63, 0x65, 0x2f, 0x63, 0x72, 0x79, 0x70, 0x74, + 0x6f, 0x2f, 0x73, 0x63, 0x68, 0x6e, 0x6f, 0x72, 0x72, 0x73, 0x69, 0x67, 0x6e, 0x61, 0x74, 0x75, + 0x72, 0x65, 0x2f, 0x6d, 0x65, 0x73, 0x73, 0x61, 0x67, 0x65, 0x2e, 0x70, 0x72, 0x6f, 0x74, 0x6f, + 0x12, 0x10, 0x73, 0x63, 0x68, 0x6e, 0x6f, 0x72, 0x72, 0x73, 0x69, 0x67, 0x6e, 0x61, 0x74, 0x75, + 0x72, 0x65, 0x1a, 0x35, 0x67, 0x69, 0x74, 0x68, 0x75, 0x62, 0x2e, 0x63, 0x6f, 0x6d, 0x2f, 0x67, + 0x65, 0x74, 0x61, 0x6d, 0x69, 0x73, 0x2f, 0x61, 0x6c, 0x69, 0x63, 0x65, 0x2f, 0x63, 0x72, 0x79, + 0x70, 0x74, 0x6f, 0x2f, 0x7a, 0x6b, 0x70, 0x72, 0x6f, 0x6f, 0x66, 0x2f, 0x6d, 0x65, 0x73, 0x73, + 0x61, 0x67, 0x65, 0x2e, 0x70, 0x72, 0x6f, 0x74, 0x6f, 0x1a, 0x3b, 0x67, 0x69, 0x74, 0x68, 0x75, + 0x62, 0x2e, 0x63, 0x6f, 0x6d, 0x2f, 0x67, 0x65, 0x74, 0x61, 0x6d, 0x69, 0x73, 0x2f, 0x61, 0x6c, + 0x69, 0x63, 0x65, 0x2f, 0x63, 0x72, 0x79, 0x70, 0x74, 0x6f, 0x2f, 0x65, 0x63, 0x70, 0x6f, 0x69, + 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x2f, 0x70, 0x6f, 0x69, 0x6e, 0x74, + 0x2e, 0x70, 0x72, 0x6f, 0x74, 0x6f, 0x22, 0xa9, 0x01, 0x0a, 0x0d, 0x43, 0x6f, 0x6d, 0x6d, 0x69, + 0x74, 0x6d, 0x65, 0x6e, 0x74, 0x4d, 0x73, 0x67, 0x12, 0x0c, 0x0a, 0x01, 0x78, 0x18, 0x01, 0x20, + 0x01, 0x28, 0x0c, 0x52, 0x01, 0x78, 0x12, 0x2d, 0x0a, 0x01, 0x44, 0x18, 0x02, 0x20, 0x01, 0x28, + 0x0b, 0x32, 0x1f, 0x2e, 0x65, 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, + 0x6c, 0x61, 0x77, 0x2e, 0x45, 0x63, 0x50, 0x6f, 0x69, 0x6e, 0x74, 0x4d, 0x65, 0x73, 0x73, 0x61, + 0x67, 0x65, 0x52, 0x01, 0x44, 0x12, 0x2d, 0x0a, 0x01, 0x45, 0x18, 0x03, 0x20, 0x01, 0x28, 0x0b, + 0x32, 0x1f, 0x2e, 0x65, 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, + 0x61, 0x77, 0x2e, 0x45, 0x63, 0x50, 0x6f, 0x69, 0x6e, 0x74, 0x4d, 0x65, 0x73, 0x73, 0x61, 0x67, + 0x65, 0x52, 0x01, 0x45, 0x12, 0x2c, 0x0a, 0x02, 0x73, 0x47, 0x18, 0x04, 0x20, 0x01, 0x28, 0x0b, + 0x32, 0x1c, 0x2e, 0x7a, 0x6b, 0x70, 0x72, 0x6f, 0x6f, 0x66, 0x2e, 0x53, 0x63, 0x68, 0x6e, 0x6f, + 0x72, 0x72, 0x50, 0x72, 0x6f, 0x6f, 0x66, 0x4d, 0x65, 0x73, 0x73, 0x61, 0x67, 0x65, 0x52, 0x02, + 0x73, 0x47, 0x22, 0x33, 0x0a, 0x13, 0x50, 0x61, 0x72, 0x74, 0x69, 0x61, 0x6c, 0x53, 0x69, 0x67, + 0x6e, 0x61, 0x74, 0x75, 0x72, 0x65, 0x4d, 0x73, 0x67, 0x12, 0x0c, 0x0a, 0x01, 0x78, 0x18, 0x01, + 0x20, 0x01, 0x28, 0x0c, 0x52, 0x01, 0x78, 0x12, 0x0e, 0x0a, 0x02, 0x73, 0x69, 0x18, 0x02, 0x20, + 0x01, 0x28, 0x0c, 0x52, 0x02, 0x73, 0x69, 0x42, 0x32, 0x5a, 0x30, 0x67, 0x69, 0x74, 0x68, 0x75, + 0x62, 0x2e, 0x63, 0x6f, 0x6d, 0x2f, 0x67, 0x65, 0x74, 0x61, 0x6d, 0x69, 0x73, 0x2f, 0x61, 0x6c, + 0x69, 0x63, 0x65, 0x2f, 0x63, 0x72, 0x79, 0x70, 0x74, 0x6f, 0x2f, 0x73, 0x63, 0x68, 0x6e, 0x6f, + 0x72, 0x72, 0x73, 0x69, 0x67, 0x6e, 0x61, 0x74, 0x75, 0x72, 0x65, 0x62, 0x06, 0x70, 0x72, 0x6f, + 0x74, 0x6f, 0x33, +} + +var ( + file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDescOnce sync.Once + file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDescData = file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDesc +) + +func file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDescGZIP() []byte { + file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDescOnce.Do(func() { + file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDescData = protoimpl.X.CompressGZIP(file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDescData) + }) + return file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDescData +} + +var file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_msgTypes = make([]protoimpl.MessageInfo, 2) +var file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_goTypes = []interface{}{ + (*CommitmentMsg)(nil), // 0: schnorrsignature.CommitmentMsg + (*PartialSignatureMsg)(nil), // 1: schnorrsignature.PartialSignatureMsg + (*ecpointgrouplaw.EcPointMessage)(nil), // 2: ecpointgrouplaw.EcPointMessage + (*zkproof.SchnorrProofMessage)(nil), // 3: zkproof.SchnorrProofMessage +} +var file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_depIdxs = []int32{ + 2, // 0: schnorrsignature.CommitmentMsg.D:type_name -> ecpointgrouplaw.EcPointMessage + 2, // 1: schnorrsignature.CommitmentMsg.E:type_name -> ecpointgrouplaw.EcPointMessage + 3, // 2: schnorrsignature.CommitmentMsg.sG:type_name -> zkproof.SchnorrProofMessage + 3, // [3:3] is the sub-list for method output_type + 3, // [3:3] is the sub-list for method input_type + 3, // [3:3] is the sub-list for extension type_name + 3, // [3:3] is the sub-list for extension extendee + 0, // [0:3] is the sub-list for field type_name +} + +func init() { file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_init() } +func file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_init() { + if File_github_com_getamis_alice_crypto_schnorrsignature_message_proto != nil { + return + } + if !protoimpl.UnsafeEnabled { + file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_msgTypes[0].Exporter = func(v interface{}, i int) interface{} { + switch v := v.(*CommitmentMsg); i { + case 0: + return &v.state + case 1: + return &v.sizeCache + case 2: + return &v.unknownFields + default: + return nil + } + } + file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_msgTypes[1].Exporter = func(v interface{}, i int) interface{} { + switch v := v.(*PartialSignatureMsg); i { + case 0: + return &v.state + case 1: + return &v.sizeCache + case 2: + return &v.unknownFields + default: + return nil + } + } + } + type x struct{} + out := protoimpl.TypeBuilder{ + File: protoimpl.DescBuilder{ + GoPackagePath: reflect.TypeOf(x{}).PkgPath(), + RawDescriptor: file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDesc, + NumEnums: 0, + NumMessages: 2, + NumExtensions: 0, + NumServices: 0, + }, + GoTypes: file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_goTypes, + DependencyIndexes: file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_depIdxs, + MessageInfos: file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_msgTypes, + }.Build() + File_github_com_getamis_alice_crypto_schnorrsignature_message_proto = out.File + file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_rawDesc = nil + file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_goTypes = nil + file_github_com_getamis_alice_crypto_schnorrsignature_message_proto_depIdxs = nil +} diff --git a/crypto/schnorrsignature/message.proto b/crypto/schnorrsignature/message.proto new file mode 100644 index 00000000..6d701ee0 --- /dev/null +++ b/crypto/schnorrsignature/message.proto @@ -0,0 +1,34 @@ +// Copyright © 2021 AMIS Technologies +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +syntax = "proto3"; + +package schnorrsignature; + +option go_package = "github.com/getamis/alice/crypto/schnorrsignature"; + +import "github.com/getamis/alice/crypto/zkproof/message.proto"; +import "github.com/getamis/alice/crypto/ecpointgrouplaw/point.proto"; + +message CommitmentMsg { + bytes x = 1; + ecpointgrouplaw.EcPointMessage D = 2; + ecpointgrouplaw.EcPointMessage E = 3; + zkproof.SchnorrProofMessage sG = 4; +} + +message PartialSignatureMsg { + bytes x = 1; + bytes si = 2; +} diff --git a/crypto/schnorrsignature/sign.go b/crypto/schnorrsignature/sign.go new file mode 100644 index 00000000..7f7a2c90 --- /dev/null +++ b/crypto/schnorrsignature/sign.go @@ -0,0 +1,359 @@ +// Copyright © 2021 AMIS Technologies +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package schnorrsignature + +import ( + "errors" + //"crypto/elliptic" + "crypto/sha512" + "math/big" + + "github.com/getamis/alice/crypto/birkhoffinterpolation" + "github.com/getamis/alice/crypto/ecpointgrouplaw" + "github.com/getamis/alice/crypto/schnorrsignature/edwards25519" + "github.com/getamis/alice/crypto/utils" + "github.com/getamis/alice/crypto/zkproof" + "github.com/golang/protobuf/ptypes/any" +) + +const ( + // maxRetry defines the max retries to generate proof + maxRetry = 100 +) + +var ( + bit254 = new(big.Int).Lsh(big.NewInt(1), 253) + + //ErrExceedMaxRetry is returned if we retried over times + ErrExceedMaxRetry = errors.New("exceed max retries") + //ErrVerifyFailure is returned if the verification is failure. + ErrVerifyFailure = errors.New("the verification is failure") +) + +// ECPoint is the struct for an elliptic curve point. +type Participant struct { + threshold uint32 + message []byte + share *big.Int + bk *birkhoffinterpolation.BkParameter + pubKey *ecpointgrouplaw.ECPoint + + Y *ecpointgrouplaw.ECPoint + YList map[*big.Int]*ecpointgrouplaw.ECPoint + + allbks birkhoffinterpolation.BkParameters + allbksCoefficient map[*big.Int]*big.Int + + e *big.Int + d *big.Int + + ellList map[*big.Int]*big.Int + riList map[*big.Int]*ecpointgrouplaw.ECPoint + r *ecpointgrouplaw.ECPoint + + c *big.Int +} + +func NewParticipant(threshold uint32, share *big.Int, message []byte, ownbk *birkhoffinterpolation.BkParameter, pubKey *ecpointgrouplaw.ECPoint, allbks birkhoffinterpolation.BkParameters) *Participant { + return &Participant{ + threshold: threshold, + message: message, + share: share, + bk: ownbk, + pubKey: pubKey, + allbks: allbks, + } +} + +func (p *Participant) Round0() (*CommitmentMsg, error) { + curve := p.pubKey.GetCurve() + e, err := utils.RandomPositiveInt(curve.Params().N) + if err != nil { + return nil, err + } + d, err := utils.RandomPositiveInt(curve.Params().N) + if err != nil { + return nil, err + } + D := ecpointgrouplaw.ScalarBaseMult(curve, d) + msgD, err := D.ToEcPointMessage() + if err != nil { + return nil, err + } + E := ecpointgrouplaw.ScalarBaseMult(curve, e) + msgE, err := E.ToEcPointMessage() + if err != nil { + return nil, err + } + Y, err := zkproof.NewBaseSchorrMessage(curve, p.share) + if err != nil { + return nil, err + } + p.Y, err = Y.V.ToPoint() + if err != nil { + return nil, err + } + p.e = e + p.d = d + return &CommitmentMsg{ + // TODO: Should Replace x to bk or any identifier. + X: p.bk.GetX().Bytes(), + D: msgD, + E: msgE, + SG: Y, + }, nil +} + +func (p *Participant) Round1(allMsg0s []*CommitmentMsg) (*PartialSignatureMsg, error) { + identify := ecpointgrouplaw.NewIdentity(p.pubKey.GetCurve()) + curveN := identify.GetCurve().Params().N + bk, err := p.allbks.ComputeBkCoefficient(p.threshold, curveN) + if err != nil { + return nil, err + } + + // Establish the list of Di, Ei, Yi, Bk-Coefficient + DList := make(map[*big.Int]*ecpointgrouplaw.ECPoint) + EList := make(map[*big.Int]*ecpointgrouplaw.ECPoint) + sGList := make(map[*big.Int]*ecpointgrouplaw.ECPoint) + allBkCoefficient := make(map[*big.Int]*big.Int) + G := ecpointgrouplaw.NewBase(p.pubKey.GetCurve()) + for i := 0; i < len(allMsg0s); i++ { + x := new(big.Int).SetBytes(allMsg0s[i].X) + tempD, err := allMsg0s[i].D.ToPoint() + if err != nil { + return nil, err + } + DList[x] = tempD + tempE, err := allMsg0s[i].E.ToPoint() + if err != nil { + return nil, err + } + EList[x] = tempE + err = allMsg0s[i].SG.Verify(G) + if err != nil { + return nil, err + } + tempsG, err := allMsg0s[i].SG.GetV().ToPoint() + if err != nil { + return nil, err + } + sGList[x] = tempsG + for i := 0; i < len(p.allbks); i++ { + if p.allbks[i].GetX().Cmp(x) == 0 { + allBkCoefficient[x] = bk[i] + break + } + } + } + p.allbksCoefficient = allBkCoefficient + p.YList = sGList + + B := computeBList(p.allbks, DList, EList) + ellList, err := computeElli(EList, p.message, B, curveN) + if err != nil { + return nil, err + } + // Compute ell_i*E_i+D_i + RiList, err := computeRiList(DList, EList, ellList) + if err != nil { + return nil, err + } + + R := identify.Copy() + for k, _ := range RiList { + //fmt.Println(" RiList:", RiList[k]) + R, err = R.Add(RiList[k]) + if err != nil { + return nil, err + } + } + + //fmt.Println(" R:", R) + + c := SHAPoints(p.pubKey, R, p.message) + + // Compute own si = di+ ei*li + c bi xi + xCoord := p.bk.GetX() + var s *big.Int + for x, _ := range ellList { + if x.Cmp(xCoord) == 0 { + s = new(big.Int).Mul(p.e, ellList[x]) + temp := new(big.Int).Mul(c, p.allbksCoefficient[x]) + temp = temp.Mul(temp, p.share) + s.Add(s, temp) + s.Add(s, p.d) + s.Mod(s, curveN) + break + } + } + + p.ellList = ellList + p.riList = RiList + p.c = c + p.r = R + return &PartialSignatureMsg{ + X: xCoord.Bytes(), + Si: s.Bytes(), + }, nil +} + +// TODO: This part can be an aggregator. +func (p *Participant) Round2(parSigMsg []*PartialSignatureMsg) (*ecpointgrouplaw.ECPoint, *big.Int, error) { + siList := make(map[*big.Int]*big.Int) + s := big.NewInt(0) + + for x, _ := range p.riList { + for i := 0; i < len(parSigMsg); i++ { + if x.Cmp(new(big.Int).SetBytes(parSigMsg[i].X)) == 0 { + si := new(big.Int).SetBytes(parSigMsg[i].Si) + siList[x] = si + s.Add(s, si) + break + } + } + } + + G := ecpointgrouplaw.NewBase(p.pubKey.GetCurve()) + + for x, _ := range siList { + siG := G.ScalarMult(siList[x]) + ri := p.riList[x] + cbi := new(big.Int).Mul(p.allbksCoefficient[x], p.c) + cbi.Mod(cbi, p.pubKey.GetCurve().Params().N) + + comparePart, err := p.YList[x].ScalarMult(cbi).Add(ri) + if err != nil { + return nil, nil, err + } + if !comparePart.Equal(siG) { + // fmt.Println("p.allbksCoefficient[x]:", p.allbksCoefficient[x]) + // fmt.Println("siList[x]:", siList[x]) + // fmt.Println("p.riList[[x]:", p.riList[x]) + + return nil, nil, ErrVerifyFailure + } + } + return p.r, s, nil +} + +func SHAPoints(pubKey, R *ecpointgrouplaw.ECPoint, message []byte) *big.Int { + encodedR := ecpointEncoding(R) + encodedPubKey := ecpointEncoding(pubKey) + h := sha512.New() + h.Write(encodedR[:]) + + h.Write(encodedPubKey[:]) + h.Write(message) + digest := h.Sum(nil) + result := new(big.Int).SetBytes(utils.ReverseByte(digest)) + return result.Mod(result, R.GetCurve().Params().N) +} + +func ecpointEncoding(pt *ecpointgrouplaw.ECPoint) *[32]byte { + var result, X, Y [32]byte + var x, y edwards25519.FieldElement + if pt.Equal(ecpointgrouplaw.NewIdentity(pt.GetCurve())) { + // TODO: We need to check this + Y[0] = 1 + } else { + tempX := pt.GetX().Bytes() + tempY := pt.GetY().Bytes() + + for i := 0; i < len(tempX); i++ { + index := len(tempX) - 1 - i + X[index] = tempX[i] + Y[index] = tempY[i] + } + } + edwards25519.FeFromBytes(&x, &X) + edwards25519.FeFromBytes(&y, &Y) + edwards25519.FeToBytes(&result, &y) + result[31] ^= edwards25519.FeIsNegative(&x) << 7 + return &result +} + +// Get xi,Di,Ei,....... +func computeBList(bks birkhoffinterpolation.BkParameters, DList, EList map[*big.Int]*ecpointgrouplaw.ECPoint) []byte { + result := make([]byte, len(DList)) + separationSign := []byte(",") + for i := 0; i < len(bks); i++ { + for x, _ := range EList { + if bks[i].GetX().Cmp(x) == 0 { + result = append(result, x.Bytes()...) + result = append(result, separationSign...) + result = append(result, DList[x].GetX().Bytes()...) + result = append(result, separationSign...) + result = append(result, DList[x].GetY().Bytes()...) + result = append(result, separationSign...) + break + } + } + } + return result +} + +func computeRiList(DList, EList map[*big.Int]*ecpointgrouplaw.ECPoint, ellList map[*big.Int]*big.Int) (map[*big.Int]*ecpointgrouplaw.ECPoint, error) { + var err error + result := make(map[*big.Int]*ecpointgrouplaw.ECPoint) + // Compute ell_i*E_i+D_i + for k, _ := range EList { + temp := EList[k].ScalarMult(ellList[k]) + temp, err = temp.Add(DList[k]) + if err != nil { + return nil, err + } + result[k] = temp + } + return result, nil +} + +func computeElli(EList map[*big.Int]*ecpointgrouplaw.ECPoint, message []byte, B []byte, fieldOrder *big.Int) (map[*big.Int]*big.Int, error) { + result := make(map[*big.Int]*big.Int, len(EList)) + for x, _ := range EList { + temp, err := utils.HashProtosToInt(x.Bytes(), &any.Any{ + Value: message, + }, &any.Any{ + Value: B, + }) + if err != nil { + return nil, err + } + tempMod := new(big.Int).Mod(temp, bit254) + if tempMod.Cmp(fieldOrder) > 0 { + for j := 0; j < maxRetry; j++ { + if j == maxRetry { + return nil, ErrExceedMaxRetry + } + temp, err = utils.HashProtosToInt(temp.Bytes(), &any.Any{ + Value: temp.Bytes(), + }, &any.Any{ + Value: B, + }) + tempMod = new(big.Int).Mod(temp, bit254) + if err != nil { + return nil, err + } + if tempMod.Cmp(fieldOrder) < 0 { + result[x] = temp + break + } + } + continue + } + result[x] = temp + } + return result, nil +} diff --git a/crypto/schnorrsignature/sign_test.go b/crypto/schnorrsignature/sign_test.go new file mode 100644 index 00000000..6e358802 --- /dev/null +++ b/crypto/schnorrsignature/sign_test.go @@ -0,0 +1,82 @@ +// Copyright © 2021 AMIS Technologies +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package schnorrsignature + +import ( + "fmt" + "math/big" + "testing" + + "github.com/getamis/alice/crypto/birkhoffinterpolation" + "github.com/getamis/alice/crypto/ecpointgrouplaw" + "github.com/getamis/alice/crypto/utils" + + edwards "github.com/decred/dcrd/dcrec/edwards" + + . "github.com/onsi/ginkgo" + + //. "github.com/onsi/ginkgo/extensions/table" + . "github.com/onsi/gomega" +) + +var _ = Describe("Sign test", func() { + It("Correct case", func() { + nthreshold := uint32(2) + bk1 := birkhoffinterpolation.NewBkParameter(big.NewInt(1), 0) + bk2 := birkhoffinterpolation.NewBkParameter(big.NewInt(2), 0) + allbk := birkhoffinterpolation.BkParameters{bk1, bk2} + privateKey := big.NewInt(100) + share1 := big.NewInt(102) + share2 := big.NewInt(104) + message := []byte("8077818") + pubKey := ecpointgrouplaw.ScalarBaseMult(edwards.Edwards(), privateKey) + + p1 := NewParticipant(nthreshold, share1, message, bk1, pubKey, allbk) + p2 := NewParticipant(nthreshold, share2, message, bk2, pubKey, allbk) + + p1round0Msg, err := p1.Round0() + Expect(err).Should(BeNil()) + p2round0Msg, err := p2.Round0() + Expect(err).Should(BeNil()) + round0Msg := []*CommitmentMsg{p1round0Msg, p2round0Msg} + p1round1Msg, err := p1.Round1(round0Msg) + Expect(err).Should(BeNil()) + p2round1Msg, err := p2.Round1(round0Msg) + Expect(err).Should(BeNil()) + round1Msg := []*PartialSignatureMsg{p1round1Msg, p2round1Msg} + R1, s1, err := p1.Round2(round1Msg) + Expect(err).Should(BeNil()) + R2, s2, err := p2.Round2(round1Msg) + Expect(err).Should(BeNil()) + Expect(R1.Equal(R2)).Should(BeTrue()) + Expect(s1.Cmp(s2) == 0).Should(BeTrue()) + + edwardPubKey := edwards.NewPublicKey(edwards.Edwards(), pubKey.GetX(), pubKey.GetY()) + + test1 := ecpointEncoding(R1) + test2 := *test1 + r := new(big.Int).SetBytes(utils.ReverseByte(test2[:])) + fmt.Println("tse", ecpointEncoding(R1)) + + //edward25519.Verify() + got := edwards.Verify(edwardPubKey, message, r, s1) + Expect(got).Should(BeTrue()) + }) +}) + +func TestSchnorrsignature(t *testing.T) { + RegisterFailHandler(Fail) + RunSpecs(t, "Schnorrsignature Test") +} diff --git a/crypto/tss/addshare/message.pb.go b/crypto/tss/addshare/message.pb.go index b65b453f..6bbdb8af 100644 --- a/crypto/tss/addshare/message.pb.go +++ b/crypto/tss/addshare/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/tss/addshare/message.proto package addshare diff --git a/crypto/tss/dkg/message.pb.go b/crypto/tss/dkg/message.pb.go index c44ded0c..ce1b3041 100644 --- a/crypto/tss/dkg/message.pb.go +++ b/crypto/tss/dkg/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/tss/dkg/message.proto package dkg diff --git a/crypto/tss/reshare/message.pb.go b/crypto/tss/reshare/message.pb.go index 526cb701..b70b47e5 100644 --- a/crypto/tss/reshare/message.pb.go +++ b/crypto/tss/reshare/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/tss/reshare/message.proto package reshare diff --git a/crypto/tss/signer/message.pb.go b/crypto/tss/signer/message.pb.go index 4bf7d74a..f82f58d0 100644 --- a/crypto/tss/signer/message.pb.go +++ b/crypto/tss/signer/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/tss/signer/message.proto package signer diff --git a/crypto/utils/message.pb.go b/crypto/utils/message.pb.go index a8e33127..0962bf62 100644 --- a/crypto/utils/message.pb.go +++ b/crypto/utils/message.pb.go @@ -15,15 +15,15 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/utils/message.proto package utils import ( - any "github.com/golang/protobuf/ptypes/any" protoreflect "google.golang.org/protobuf/reflect/protoreflect" protoimpl "google.golang.org/protobuf/runtime/protoimpl" + anypb "google.golang.org/protobuf/types/known/anypb" reflect "reflect" sync "sync" ) @@ -40,7 +40,7 @@ type Hash struct { sizeCache protoimpl.SizeCache unknownFields protoimpl.UnknownFields - Msgs []*any.Any `protobuf:"bytes,1,rep,name=msgs,proto3" json:"msgs,omitempty"` + Msgs []*anypb.Any `protobuf:"bytes,1,rep,name=msgs,proto3" json:"msgs,omitempty"` } func (x *Hash) Reset() { @@ -75,7 +75,7 @@ func (*Hash) Descriptor() ([]byte, []int) { return file_github_com_getamis_alice_crypto_utils_message_proto_rawDescGZIP(), []int{0} } -func (x *Hash) GetMsgs() []*any.Any { +func (x *Hash) GetMsgs() []*anypb.Any { if x != nil { return x.Msgs } @@ -113,8 +113,8 @@ func file_github_com_getamis_alice_crypto_utils_message_proto_rawDescGZIP() []by var file_github_com_getamis_alice_crypto_utils_message_proto_msgTypes = make([]protoimpl.MessageInfo, 1) var file_github_com_getamis_alice_crypto_utils_message_proto_goTypes = []interface{}{ - (*Hash)(nil), // 0: utils.Hash - (*any.Any)(nil), // 1: google.protobuf.Any + (*Hash)(nil), // 0: utils.Hash + (*anypb.Any)(nil), // 1: google.protobuf.Any } var file_github_com_getamis_alice_crypto_utils_message_proto_depIdxs = []int32{ 1, // 0: utils.Hash.msgs:type_name -> google.protobuf.Any diff --git a/crypto/zkproof/message.pb.go b/crypto/zkproof/message.pb.go index ebf768a6..7f94bce1 100644 --- a/crypto/zkproof/message.pb.go +++ b/crypto/zkproof/message.pb.go @@ -15,7 +15,7 @@ // Code generated by protoc-gen-go. DO NOT EDIT. // versions: // protoc-gen-go v1.26.0 -// protoc v3.6.1 +// protoc v3.14.0 // source: github.com/getamis/alice/crypto/zkproof/message.proto package zkproof diff --git a/go.mod b/go.mod index d550de6a..51acff3b 100644 --- a/go.mod +++ b/go.mod @@ -3,7 +3,10 @@ module github.com/getamis/alice go 1.13 require ( + github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412 github.com/btcsuite/btcd v0.20.1-beta + github.com/decred/dcrd/dcrec/edwards v1.0.0 + github.com/decred/dcrd/dcrec/edwards/v2 v2.0.1 github.com/getamis/sirius v1.1.7 github.com/go-stack/stack v1.8.0 // indirect github.com/gogo/protobuf v1.3.1 diff --git a/go.sum b/go.sum index 56dadc72..69566966 100644 --- a/go.sum +++ b/go.sum @@ -5,6 +5,8 @@ github.com/BurntSushi/toml v0.3.1 h1:WXkYYl6Yr3qBf1K79EBnL4mak0OimBfB0XUf9Vl28OQ github.com/BurntSushi/toml v0.3.1/go.mod h1:xHWCNGjB5oqiDr8zfno3MHue2Ht5sIBksp03qcyfWMU= github.com/Kubuxu/go-os-helper v0.0.1/go.mod h1:N8B+I7vPCT80IcP58r50u4+gEEcsZETFUpAzWW2ep1Y= github.com/aead/siphash v1.0.1/go.mod h1:Nywa3cDsYNNK3gaciGTWPwHt0wlpNV15vwmswBAUSII= +github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412 h1:w1UutsfOrms1J05zt7ISrnJIXKzwaspym5BTKGx93EI= +github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412/go.mod h1:WPjqKcmVOxf0XSf3YxCJs6N6AOSrOx3obionmG7T0y0= github.com/ajstarks/svgo v0.0.0-20180226025133-644b8db467af/go.mod h1:K08gAheRH3/J6wwsYMMT4xOr94bZjxIelGM0+d/wbFw= github.com/armon/consul-api v0.0.0-20180202201655-eb2c6b5be1b6/go.mod h1:grANhF5doyWs3UAsr3K4I6qtAmlQcZDesFNEHPZAzj8= github.com/btcsuite/btcd v0.0.0-20190213025234-306aecffea32/go.mod h1:DrZx5ec/dmnfpw9KyYoQyYo7d0KEvTkk/5M/vbZjAr8= @@ -33,6 +35,12 @@ github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38= github.com/davidlazar/go-crypto v0.0.0-20170701192655-dcfb0a7ac018 h1:6xT9KW8zLC5IlbaIF5Q7JNieBoACT7iW0YTxQHR0in0= github.com/davidlazar/go-crypto v0.0.0-20170701192655-dcfb0a7ac018/go.mod h1:rQYf4tfk5sSwFsnDg3qYaBxSjsD9S8+59vW0dKUgme4= +github.com/decred/dcrd v1.3.0 h1:EEXm7BdiROfazDtuFsOu9mfotnyy00bgCuVwUqaszFo= +github.com/decred/dcrd/dcrec v1.0.0 h1:W+z6Es+Rai3MXYVoPAxYr5U1DGis0Co33scJ6uH2J6o= +github.com/decred/dcrd/dcrec/edwards v1.0.0 h1:UDcPNzclKiJlWqV3x1Fl8xMCJrolo4PB4X9t8LwKDWU= +github.com/decred/dcrd/dcrec/edwards v1.0.0/go.mod h1:HblVh1OfMt7xSxUL1ufjToaEvpbjpWvvTAUx4yem8BI= +github.com/decred/dcrd/dcrec/edwards/v2 v2.0.1 h1:V6eqU1crZzuoFT4KG2LhaU5xDSdkHuvLQsj25wd7Wb4= +github.com/decred/dcrd/dcrec/edwards/v2 v2.0.1/go.mod h1:d0H8xGMWbiIQP7gN3v2rByWUcuZPm9YsgmnfoxgbINc= github.com/dgraph-io/badger v1.5.5-0.20190226225317-8115aed38f8f/go.mod h1:VZxzAIRPHRVNRKRo6AXrX9BJegn6il06VMTZVJYCIjQ= github.com/dgraph-io/badger v1.6.0-rc1/go.mod h1:zwt7syl517jmP8s94KqSxTlM6IMsdhYy6psNgSztDR4= github.com/dgraph-io/badger v1.6.0/go.mod h1:zwt7syl517jmP8s94KqSxTlM6IMsdhYy6psNgSztDR4= From 688ebc23fd9d3360cbf0e8e83c27f44e11dc7c9c Mon Sep 17 00:00:00 2001 From: ChihYunChuang Date: Mon, 18 Oct 2021 10:58:24 +0800 Subject: [PATCH 02/10] refactor elliptic curve --- crypto/.DS_Store | Bin 6148 -> 6148 bytes crypto/bip32/child/0_initial_handler.go | 6 +- crypto/bip32/child/child_test.go | 10 +-- crypto/bip32/master/0_initial_handler.go | 6 +- .../birkhoffinterpolation_test.go | 9 ++- crypto/commitment/feldman.go | 4 +- crypto/commitment/feldman_test.go | 48 ++++++------- crypto/commitment/hash_test.go | 3 +- crypto/commitment/message_test.go | 15 ++-- crypto/commitment/pedersen_test.go | 34 +++++----- crypto/ecpointgrouplaw/ecpointgrouplaw.go | 3 +- .../ecpointgrouplaw/ecpointgrouplaw_test.go | 7 +- crypto/ecpointgrouplaw/point.go | 53 +++++---------- crypto/ecpointgrouplaw/point_test.go | 35 +++++----- crypto/elliptic/.DS_Store | Bin 0 -> 6148 bytes crypto/elliptic/ed25519.go | 64 ++++++++++++++++++ crypto/elliptic/ed25519_test.go | 34 ++++++++++ crypto/elliptic/interface.go | 26 +++++++ crypto/elliptic/secp256k1.go | 64 ++++++++++++++++++ crypto/elliptic/secp256k1_test.go | 39 +++++++++++ crypto/homo/cl/cl.go | 2 +- crypto/homo/cl/cl_test.go | 4 +- crypto/homo/interface.go | 3 +- crypto/homo/mocks/Crypto.go | 2 +- crypto/homo/paillier/paillier.go | 3 +- crypto/homo/paillier/paillier_test.go | 4 +- crypto/mta/interface.go | 5 +- crypto/mta/mocks/Mta.go | 4 +- crypto/mta/mta.go | 3 +- crypto/mta/mta_test.go | 11 +-- crypto/oprf/hasher/secp256k1.go | 6 +- crypto/oprf/hasher/secp256k1_test.go | 6 +- crypto/schnorrsignature/sign_test.go | 7 +- .../addshare/newpeer/0_peer_handler_test.go | 10 +-- .../addshare/newpeer/1_result_handler_test.go | 4 +- crypto/tss/addshare/newpeer/addshare_test.go | 4 +- .../addshare/oldpeer/0_peer_handler_test.go | 7 +- .../oldpeer/1_compute_handler_test.go | 8 +-- .../addshare/oldpeer/2_verify_handler_test.go | 12 ++-- crypto/tss/addshare/oldpeer/addshare_test.go | 5 +- crypto/tss/dkg/0_peer_handler.go | 2 +- crypto/tss/dkg/0_peer_handler_test.go | 4 +- crypto/tss/dkg/1_decommit_handler_test.go | 4 +- crypto/tss/dkg/2_verify_handler_test.go | 7 +- crypto/tss/dkg/3_result_handler_test.go | 9 ++- crypto/tss/dkg/dkg.go | 2 +- crypto/tss/dkg/dkg_test.go | 5 +- crypto/tss/integration/tss_test.go | 11 ++- crypto/tss/reshare/0_commit_handler_test.go | 6 +- crypto/tss/reshare/2_result_handler_test.go | 9 ++- crypto/tss/reshare/reshare_test.go | 5 +- crypto/tss/signer/0_pukkey_handler.go | 2 +- crypto/tss/signer/0_pukkey_handler_test.go | 10 ++- crypto/tss/signer/2_mta_handler_test.go | 7 +- crypto/tss/signer/4_proof_ai_handler.go | 2 +- crypto/tss/signer/4_proof_ai_handler_test.go | 9 ++- .../signer/6_decommit_vi_ai_handler_test.go | 6 +- .../signer/8_decommit_ui_ti_handler_test.go | 6 +- crypto/tss/signer/signer_test.go | 5 +- crypto/zkproof/schnorr.go | 3 +- crypto/zkproof/schnorr_test.go | 31 +++++---- example/utils/utils.go | 5 +- 62 files changed, 469 insertions(+), 251 deletions(-) create mode 100644 crypto/elliptic/.DS_Store create mode 100644 crypto/elliptic/ed25519.go create mode 100644 crypto/elliptic/ed25519_test.go create mode 100644 crypto/elliptic/interface.go create mode 100644 crypto/elliptic/secp256k1.go create mode 100644 crypto/elliptic/secp256k1_test.go diff --git a/crypto/.DS_Store b/crypto/.DS_Store index 5d897fb36f0f188d0489e9ee3939c99ad9b4baf5..4424216cefc4ef145825ce21f883345a01908fdf 100644 GIT binary patch delta 257 zcmZoMXfc@J&&aVcU^g=($7CKBrO9zD{TxPS209AHhL)4RvN%rWXVDYnU`S=i0m4j% z0)`SGnG8{8VX32FWN83WR*#`1C*3eOIX}060Rb@7dPtZhi^@by^U26=V>$bh0=5o{0^uo7p-3@&f>PY(A?1 delta 620 zcmZoMXfc@J&&atkU^g=(=VTrhrOB$S{E7k$#SF;|84P(0`3yxsSj>>gkPhS}GL$fs z0{N+v^;r5jj14Vx6pYLaC*NUptS6`?C*3eOIX}060Sr`*11W-fa`RnWl5+BsfND8* zY+O`0A^Wf+c764z?#s+uQBJ9Y5k|dwf`r?uzpkhCUV1`OyaFsBm zGUPJoGlT&HFb5c9xj=p~knaKx!bBh|6v$5n2dzFhs561VT?tf~2j-Om)#U-5rq56g zj)H8U>H?rxGEk2`kX;01=>z36fi`6TbtTm^=mCZD!ImZht;~cfO$I8h1Zph-%IOp7 b8^2PBX9z|Ql6jK2lgcr+J)7A%{_+C=dT5EH diff --git a/crypto/bip32/child/0_initial_handler.go b/crypto/bip32/child/0_initial_handler.go index f4c2c1c8..896cd31f 100644 --- a/crypto/bip32/child/0_initial_handler.go +++ b/crypto/bip32/child/0_initial_handler.go @@ -18,11 +18,11 @@ import ( "errors" "math/big" - "github.com/btcsuite/btcd/btcec" "github.com/getamis/alice/crypto/bip32" "github.com/getamis/alice/crypto/birkhoffinterpolation" "github.com/getamis/alice/crypto/circuit" ecpointgrouplaw "github.com/getamis/alice/crypto/ecpointgrouplaw" + "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/homo/paillier" "github.com/getamis/alice/crypto/ot" "github.com/getamis/alice/crypto/zkproof" @@ -60,8 +60,8 @@ type initial struct { } var ( - curve = btcec.S256() - secp256k1N = curve.N + curve = elliptic.NewSecp256k1() + secp256k1N = curve.Params().N // alice aliceParseFunc = func(initialBody *BodyInitial, ownResult [][]byte) [][]byte { diff --git a/crypto/bip32/child/child_test.go b/crypto/bip32/child/child_test.go index 17571cdf..1cd10da6 100644 --- a/crypto/bip32/child/child_test.go +++ b/crypto/bip32/child/child_test.go @@ -50,9 +50,9 @@ var _ = Describe("Child test", func() { pubKey := ecpointgrouplaw.ScalarBaseMult(curve, privateKey) // share1: x = 1 rank and share2: x = 2 rank 0 share1 := new(big.Int).Add(privateKey, big.NewInt(1)) - share1.Mod(share1, curve.N) + share1.Mod(share1, secp256k1N) share2 := new(big.Int).Add(privateKey, big.NewInt(2)) - share2.Mod(share2, curve.N) + share2.Mod(share2, secp256k1N) // curve := btcec.S256() childIndex := uint32(2147483648) @@ -101,9 +101,9 @@ var _ = Describe("Child test", func() { } childPrivateKey := new(big.Int).Add(childShares[0].share, childShares[1].share) - childPrivateKey.Mod(childPrivateKey, curve.N) + childPrivateKey.Mod(childPrivateKey, secp256k1N) anotherMethodChildParivateKey := new(big.Int).Add(privateKey, childTranslate) - anotherMethodChildParivateKey.Mod(anotherMethodChildParivateKey, curve.N) + anotherMethodChildParivateKey.Mod(anotherMethodChildParivateKey, secp256k1N) Expect(anotherMethodChildParivateKey).Should(Equal(anotherMethodChildParivateKey)) Expect(hex.EncodeToString(childPrivateKey.Bytes())).Should(Equal(expectedPrivate1)) Expect(hex.EncodeToString(childPrivateKey.Bytes())).Should(Equal(expectedPrivate1)) @@ -113,7 +113,7 @@ var _ = Describe("Child test", func() { grandChildManager, err := childShares[0].ComputeNonHardenedChildShare(1) Expect(err).Should(BeNil()) grandChildPrivateKey := new(big.Int).Add(grandChildManager.share, childShares[1].share) - grandChildPrivateKey.Mod(grandChildPrivateKey, curve.N) + grandChildPrivateKey.Mod(grandChildPrivateKey, secp256k1N) Expect(hex.EncodeToString(grandChildPrivateKey.Bytes())).Should(Equal(expectedPrivate2)) Expect(hex.EncodeToString(grandChildManager.chainCode)).Should(Equal(expectedChaincode2)) }, diff --git a/crypto/bip32/master/0_initial_handler.go b/crypto/bip32/master/0_initial_handler.go index bfcc2e5f..0a94d618 100644 --- a/crypto/bip32/master/0_initial_handler.go +++ b/crypto/bip32/master/0_initial_handler.go @@ -19,10 +19,10 @@ import ( "errors" "math/big" - "github.com/btcsuite/btcd/btcec" "github.com/getamis/alice/crypto/bip32" "github.com/getamis/alice/crypto/birkhoffinterpolation" "github.com/getamis/alice/crypto/circuit" + "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/ot" "github.com/getamis/alice/crypto/utils" "github.com/getamis/alice/internal/message/types" @@ -63,8 +63,8 @@ type initial struct { var ( otherInfoBit, _ = hex.DecodeString(otherInfoBitStr) - curve = btcec.S256() - secp256k1N = curve.N + curve = elliptic.NewSecp256k1() + secp256k1N = curve.Params().N big2Inver, _ = new(big.Int).SetString("57896044618658097711785492504343953926418782139537452191302581570759080747169", 10) // alice diff --git a/crypto/birkhoffinterpolation/birkhoffinterpolation_test.go b/crypto/birkhoffinterpolation/birkhoffinterpolation_test.go index 7bb24c80..632960e3 100644 --- a/crypto/birkhoffinterpolation/birkhoffinterpolation_test.go +++ b/crypto/birkhoffinterpolation/birkhoffinterpolation_test.go @@ -14,11 +14,10 @@ package birkhoffinterpolation import ( - "crypto/elliptic" "math/big" "testing" - "github.com/btcsuite/btcd/btcec" + "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/ecpointgrouplaw" pt "github.com/getamis/alice/crypto/ecpointgrouplaw" "github.com/getamis/alice/crypto/matrix" @@ -29,6 +28,10 @@ import ( . "github.com/onsi/gomega" ) +var ( + secp256k1 = elliptic.NewSecp256k1() +) + func TestBirkhoffinterpolation(t *testing.T) { RegisterFailHandler(Fail) RunSpecs(t, "Birkhoffinterpolation Suite") @@ -274,7 +277,7 @@ var _ = Describe("Birkhoff Interpolation", func() { ) BeforeEach(func() { - curve = btcec.S256() + curve = secp256k1 fieldOrder := curve.Params().N threshold = uint32(3) poly, err = polynomial.RandomPolynomial(fieldOrder, threshold-1) diff --git a/crypto/commitment/feldman.go b/crypto/commitment/feldman.go index b33339fc..60ea174e 100644 --- a/crypto/commitment/feldman.go +++ b/crypto/commitment/feldman.go @@ -15,13 +15,13 @@ package commitment import ( - "crypto/elliptic" "errors" "math/big" bkhoff "github.com/getamis/alice/crypto/birkhoffinterpolation" "github.com/getamis/alice/crypto/ecpointgrouplaw" pt "github.com/getamis/alice/crypto/ecpointgrouplaw" + "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/polynomial" ) @@ -59,8 +59,8 @@ func buildFeldmanCommitMessage(curve elliptic.Curve, secrets *polynomial.Polynom Points: make([]*ecpointgrouplaw.EcPointMessage, lens), } for i := 0; i < lens; i++ { - var err error pt := ecpointgrouplaw.ScalarBaseMult(curve, secrets.Get(i)) + var err error msg.Points[i], err = pt.ToEcPointMessage() if err != nil { return nil, err diff --git a/crypto/commitment/feldman_test.go b/crypto/commitment/feldman_test.go index 5f22439e..1be748a4 100644 --- a/crypto/commitment/feldman_test.go +++ b/crypto/commitment/feldman_test.go @@ -15,10 +15,10 @@ package commitment import ( - "crypto/elliptic" "math/big" - "github.com/btcsuite/btcd/btcec" + "github.com/getamis/alice/crypto/elliptic" + bkhoff "github.com/getamis/alice/crypto/birkhoffinterpolation" pt "github.com/getamis/alice/crypto/ecpointgrouplaw" "github.com/getamis/alice/crypto/polynomial" @@ -42,10 +42,10 @@ var _ = Describe("Feldman commitment test", func() { expected.Points[2], _ = pt.ScalarBaseMult(curve, big.NewInt(100)).ToEcPointMessage() Expect(got).Should(Equal(expected)) }, - Entry("P224", elliptic.P224()), - Entry("P256", elliptic.P256()), - Entry("P384", elliptic.P384()), - Entry("S256", btcec.S256()), + // Entry("P224", elliptic.P224()), + // Entry("P256", elliptic.P256()), + // Entry("P384", elliptic.P384()), + Entry("S256", secp256k1), ) DescribeTable("should be ok", func(x *big.Int, rank, threshold uint32, curve elliptic.Curve) { @@ -65,13 +65,13 @@ var _ = Describe("Feldman commitment test", func() { Expect(err).Should(BeNil()) }, Entry("should be OK", - big.NewInt(225), uint32(1), uint32(3), elliptic.P224()), + big.NewInt(225), uint32(1), uint32(3), secp256k1), Entry("should be OK", - big.NewInt(2290), uint32(0), uint32(2), elliptic.P256()), + big.NewInt(2290), uint32(0), uint32(2), secp256k1), Entry("zero point case", - big.NewInt(2290), uint32(2), uint32(2), elliptic.P224()), + big.NewInt(2290), uint32(2), uint32(2), secp256k1), Entry("should be OK", - big.NewInt(2291), uint32(2), uint32(5), elliptic.P256()), + big.NewInt(2291), uint32(2), uint32(5), secp256k1), ) DescribeTable("failed to verify due to wrong rank", func(x *big.Int, rank, threshold uint32, curve elliptic.Curve) { @@ -92,11 +92,11 @@ var _ = Describe("Feldman commitment test", func() { Expect(err).Should(Equal(ErrFailedVerify)) }, Entry("case #0", - big.NewInt(225), uint32(1), uint32(3), elliptic.P224()), + big.NewInt(225), uint32(1), uint32(3), secp256k1), Entry("case #1", - big.NewInt(2290), uint32(0), uint32(2), elliptic.P256()), + big.NewInt(2290), uint32(0), uint32(2), secp256k1), Entry("case #2", - big.NewInt(2291), uint32(2), uint32(5), elliptic.P256()), + big.NewInt(2291), uint32(2), uint32(5), secp256k1), ) DescribeTable("failed to verify due to wrong x", func(x *big.Int, rank, threshold uint32, curve elliptic.Curve) { @@ -117,11 +117,11 @@ var _ = Describe("Feldman commitment test", func() { Expect(err).Should(Equal(ErrFailedVerify)) }, Entry("case #0", - big.NewInt(225), uint32(1), uint32(3), elliptic.P224()), + big.NewInt(225), uint32(1), uint32(3), secp256k1), Entry("case #1", - big.NewInt(2290), uint32(0), uint32(2), elliptic.P256()), + big.NewInt(2290), uint32(0), uint32(2), secp256k1), Entry("case #2", - big.NewInt(2291), uint32(2), uint32(5), elliptic.P256()), + big.NewInt(2291), uint32(2), uint32(5), secp256k1), ) DescribeTable("invalid commitment message", func(x *big.Int, rank, threshold uint32, curve elliptic.Curve) { @@ -147,13 +147,13 @@ var _ = Describe("Feldman commitment test", func() { Expect(err).Should(Equal(pt.ErrDifferentLength)) }, Entry("should be OK", - big.NewInt(225), uint32(1), uint32(3), elliptic.P224()), + big.NewInt(225), uint32(1), uint32(3), secp256k1), Entry("should be OK", - big.NewInt(2290), uint32(0), uint32(2), elliptic.P256()), + big.NewInt(2290), uint32(0), uint32(2), secp256k1), Entry("zero point case", - big.NewInt(2290), uint32(2), uint32(2), elliptic.P224()), + big.NewInt(2290), uint32(2), uint32(2), secp256k1), Entry("should be OK", - big.NewInt(2291), uint32(2), uint32(5), elliptic.P256()), + big.NewInt(2291), uint32(2), uint32(5), secp256k1), ) DescribeTable("empty points in commitment message", func(x *big.Int, rank, threshold uint32, curve elliptic.Curve) { @@ -175,12 +175,12 @@ var _ = Describe("Feldman commitment test", func() { Expect(err).Should(Equal(pt.ErrDifferentLength)) }, Entry("should be OK", - big.NewInt(225), uint32(1), uint32(3), elliptic.P224()), + big.NewInt(225), uint32(1), uint32(3), secp256k1), Entry("should be OK", - big.NewInt(2290), uint32(0), uint32(2), elliptic.P256()), + big.NewInt(2290), uint32(0), uint32(2), secp256k1), Entry("zero point case", - big.NewInt(2290), uint32(2), uint32(2), elliptic.P224()), + big.NewInt(2290), uint32(2), uint32(2), secp256k1), Entry("should be OK", - big.NewInt(2291), uint32(2), uint32(5), elliptic.P256()), + big.NewInt(2291), uint32(2), uint32(5), secp256k1), ) }) diff --git a/crypto/commitment/hash_test.go b/crypto/commitment/hash_test.go index d7d3b22c..d5900fc7 100644 --- a/crypto/commitment/hash_test.go +++ b/crypto/commitment/hash_test.go @@ -17,7 +17,6 @@ import ( "bytes" "testing" - "github.com/btcsuite/btcd/btcec" pt "github.com/getamis/alice/crypto/ecpointgrouplaw" "github.com/getamis/alice/crypto/utils" . "github.com/onsi/ginkgo" @@ -147,7 +146,7 @@ var _ = Describe("hash", func() { Context("NewCommitterByPoint/GetPointFromHashCommitment", func() { It("should be ok", func() { - p := pt.NewIdentity(btcec.S256()) + p := pt.NewIdentity(secp256k1) c, err := NewCommitterByPoint(p) Expect(err).Should(BeNil()) Expect(c).ShouldNot(BeNil()) diff --git a/crypto/commitment/message_test.go b/crypto/commitment/message_test.go index 9b338ab2..f40d5cd2 100644 --- a/crypto/commitment/message_test.go +++ b/crypto/commitment/message_test.go @@ -15,10 +15,9 @@ package commitment import ( - "crypto/elliptic" "math/big" - "github.com/btcsuite/btcd/btcec" + "github.com/getamis/alice/crypto/elliptic" . "github.com/onsi/ginkgo" . "github.com/onsi/ginkgo/extensions/table" . "github.com/onsi/gomega" @@ -26,6 +25,10 @@ import ( pt "github.com/getamis/alice/crypto/ecpointgrouplaw" ) +var( + secp256k1 = elliptic.NewSecp256k1() +) + var _ = Describe("message test", func() { DescribeTable("EcPoints()", func(curveType pt.EcPointMessage_Curve, curve elliptic.Curve) { var err error @@ -45,10 +48,10 @@ var _ = Describe("message test", func() { Expect(p).Should(Equal(expected[i])) } }, - Entry("P224", pt.EcPointMessage_P224, elliptic.P224()), - Entry("P256", pt.EcPointMessage_P256, elliptic.P256()), - Entry("P384", pt.EcPointMessage_P384, elliptic.P384()), - Entry("S256", pt.EcPointMessage_S256, btcec.S256()), + // Entry("P224", pt.EcPointMessage_P224, elliptic.P224()), + // Entry("P256", pt.EcPointMessage_P256, elliptic.P256()), + // Entry("P384", pt.EcPointMessage_P384, elliptic.P384()), + Entry("S256", pt.EcPointMessage_S256, secp256k1), ) It("invalid point", func() { diff --git a/crypto/commitment/pedersen_test.go b/crypto/commitment/pedersen_test.go index 1d8f4db0..f0cfa6af 100644 --- a/crypto/commitment/pedersen_test.go +++ b/crypto/commitment/pedersen_test.go @@ -15,10 +15,10 @@ package commitment import ( - "crypto/elliptic" "math/big" - "github.com/btcsuite/btcd/btcec" + "github.com/getamis/alice/crypto/elliptic" + bkhoff "github.com/getamis/alice/crypto/birkhoffinterpolation" pt "github.com/getamis/alice/crypto/ecpointgrouplaw" "github.com/getamis/alice/crypto/polynomial" @@ -45,14 +45,14 @@ var _ = Describe("Pedersen commitment test", func() { expected.Points[2], _ = pt.ScalarBaseMult(curve, big.NewInt(1765)).ToEcPointMessage() Expect(got).Should(Equal(expected)) }, - Entry("P224", elliptic.P224()), - Entry("P256", elliptic.P256()), - Entry("P384", elliptic.P384()), - Entry("S256", btcec.S256()), + // Entry("P224", elliptic.P224()), + // Entry("P256", elliptic.P256()), + // Entry("P384", elliptic.P384()), + Entry("S256", secp256k1), ) Context("buildPedersenCommitMessage()", func() { - curve := elliptic.P256() + curve := secp256k1 N := curve.Params().N It("different length", func() { hiddingPoint := pt.ScalarBaseMult(curve, big.NewInt(15)) @@ -86,13 +86,13 @@ var _ = Describe("Pedersen commitment test", func() { Expect(err).Should(BeNil()) }, Entry("should be OK", - big.NewInt(225), big.NewInt(113), uint32(1), uint32(3), elliptic.P224()), + big.NewInt(225), big.NewInt(113), uint32(1), uint32(3), secp256k1), Entry("should be OK", - big.NewInt(2290), big.NewInt(112), uint32(0), uint32(2), elliptic.P256()), + big.NewInt(2290), big.NewInt(112), uint32(0), uint32(2), secp256k1), Entry("zero point case", - big.NewInt(2290), big.NewInt(112), uint32(2), uint32(2), elliptic.P224()), + big.NewInt(2290), big.NewInt(112), uint32(2), uint32(2), secp256k1), Entry("should be OK", - big.NewInt(2291), big.NewInt(114), uint32(2), uint32(5), elliptic.P256()), + big.NewInt(2291), big.NewInt(114), uint32(2), uint32(5), secp256k1), ) DescribeTable("failed to verify due to wrong rank", func(x, hValue *big.Int, rank, threshold uint32, curve elliptic.Curve) { @@ -116,11 +116,11 @@ var _ = Describe("Pedersen commitment test", func() { Expect(err).Should(Equal(ErrFailedVerify)) }, Entry("case #0", - big.NewInt(225), big.NewInt(113), uint32(1), uint32(3), elliptic.P224()), + big.NewInt(225), big.NewInt(113), uint32(1), uint32(3), secp256k1), Entry("case #1", - big.NewInt(2290), big.NewInt(112), uint32(0), uint32(2), elliptic.P256()), + big.NewInt(2290), big.NewInt(112), uint32(0), uint32(2), secp256k1), Entry("case #2", - big.NewInt(2291), big.NewInt(114), uint32(2), uint32(5), elliptic.P256()), + big.NewInt(2291), big.NewInt(114), uint32(2), uint32(5), secp256k1), ) DescribeTable("failed to verify due to wrong x", func(x, hValue *big.Int, rank, threshold uint32, curve elliptic.Curve) { @@ -144,10 +144,10 @@ var _ = Describe("Pedersen commitment test", func() { Expect(err).Should(Equal(ErrFailedVerify)) }, Entry("case #0", - big.NewInt(225), big.NewInt(113), uint32(1), uint32(3), elliptic.P224()), + big.NewInt(225), big.NewInt(113), uint32(1), uint32(3), secp256k1), Entry("case #1", - big.NewInt(2290), big.NewInt(112), uint32(0), uint32(2), elliptic.P256()), + big.NewInt(2290), big.NewInt(112), uint32(0), uint32(2), secp256k1), Entry("case #2", - big.NewInt(2291), big.NewInt(114), uint32(2), uint32(5), elliptic.P256()), + big.NewInt(2291), big.NewInt(114), uint32(2), uint32(5), secp256k1), ) }) diff --git a/crypto/ecpointgrouplaw/ecpointgrouplaw.go b/crypto/ecpointgrouplaw/ecpointgrouplaw.go index 80c20b95..2d612d7e 100644 --- a/crypto/ecpointgrouplaw/ecpointgrouplaw.go +++ b/crypto/ecpointgrouplaw/ecpointgrouplaw.go @@ -15,9 +15,10 @@ package ecpointgrouplaw import ( - "crypto/elliptic" "errors" "math/big" + + "github.com/getamis/alice/crypto/elliptic" ) var ( diff --git a/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go b/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go index 3d125e9d..b3ec3426 100644 --- a/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go +++ b/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go @@ -14,13 +14,10 @@ package ecpointgrouplaw import ( - "crypto/elliptic" + "github.com/getamis/alice/crypto/elliptic" "math/big" "testing" - "github.com/btcsuite/btcd/btcec" - "github.com/decred/dcrd/dcrec/edwards/v2" - . "github.com/onsi/ginkgo" . "github.com/onsi/gomega" ) @@ -31,7 +28,7 @@ func TestEllipticcurve(t *testing.T) { } var ( - curveList = []elliptic.Curve{elliptic.P224(), elliptic.P256(), elliptic.P384(), btcec.S256(), edwards.Edwards()} + curveList = []elliptic.Curve{Ed25519, Secp256k1} ) var _ = Describe("Elliptic curves", func() { diff --git a/crypto/ecpointgrouplaw/point.go b/crypto/ecpointgrouplaw/point.go index 963deec1..4782ed94 100644 --- a/crypto/ecpointgrouplaw/point.go +++ b/crypto/ecpointgrouplaw/point.go @@ -15,14 +15,12 @@ package ecpointgrouplaw import ( - "crypto/elliptic" "errors" "fmt" "math/big" "reflect" - "github.com/btcsuite/btcd/btcec" - "github.com/decred/dcrd/dcrec/edwards" + "github.com/getamis/alice/crypto/elliptic" ) var ( @@ -32,6 +30,9 @@ var ( ErrDifferentCurve = errors.New("different elliptic curves") // ErrInvalidCurve is returned if the curve is invalid. ErrInvalidCurve = errors.New("invalid curve") + + Ed25519 = elliptic.NewEd25519() + Secp256k1 = elliptic.NewSecp256k1() ) // ECPoint is the struct for an elliptic curve point. @@ -136,23 +137,11 @@ func (p *ECPoint) Neg() *ECPoint { if p.IsIdentity() { return NewIdentity(p.curve) } - - // TODO: Not compare cofactor terms - if isSameCurve(p.curve, edwards.Edwards()) { - negativeX := new(big.Int).Neg(p.x) - negativeX = negativeX.Mod(negativeX, p.curve.Params().P) - return &ECPoint{ - curve: p.curve, - x: negativeX, - y: new(big.Int).Set(p.y), - } - } - negativeY := new(big.Int).Neg(p.y) - negativeY = negativeY.Mod(negativeY, p.curve.Params().P) + negX, negY := p.curve.Neg(p.x, p.y) return &ECPoint{ curve: p.curve, - x: new(big.Int).Set(p.x), - y: negativeY, + x: negX, + y: negY, } } @@ -261,33 +250,25 @@ func isOnCurve(curve elliptic.Curve, x, y *big.Int) bool { func (c EcPointMessage_Curve) GetEllipticCurve() (elliptic.Curve, error) { switch c { - case EcPointMessage_P224: - return elliptic.P224(), nil - case EcPointMessage_P256: - return elliptic.P256(), nil - case EcPointMessage_P384: - return elliptic.P384(), nil + // case EcPointMessage_P224: + // return elliptic.P224(), nil + // case EcPointMessage_P256: + // return elliptic.P256(), nil + // case EcPointMessage_P384: + // return elliptic.P384(), nil case EcPointMessage_S256: - return btcec.S256(), nil + return Secp256k1, nil case EcPointMessage_EDWARD25519: - return edwards.Edwards(), nil + return Ed25519, nil } return nil, ErrInvalidCurve } func ToCurve(c elliptic.Curve) (EcPointMessage_Curve, error) { - switch c { - case elliptic.P224(): - return EcPointMessage_P224, nil - case elliptic.P256(): - return EcPointMessage_P256, nil - case elliptic.P384(): - return EcPointMessage_P384, nil - case btcec.S256(): + if isSameCurve(c, Secp256k1) { return EcPointMessage_S256, nil } - // TODO: Rewrite it to be a switch case. - if isSameCurve(c, edwards.Edwards()) { + if isSameCurve(c, Ed25519) { return EcPointMessage_EDWARD25519, nil } return 0, ErrInvalidCurve diff --git a/crypto/ecpointgrouplaw/point_test.go b/crypto/ecpointgrouplaw/point_test.go index e139c00e..8c5297c9 100644 --- a/crypto/ecpointgrouplaw/point_test.go +++ b/crypto/ecpointgrouplaw/point_test.go @@ -14,11 +14,10 @@ package ecpointgrouplaw import ( - "crypto/elliptic" + "github.com/getamis/alice/crypto/elliptic" "fmt" "math/big" - "github.com/btcsuite/btcd/btcec" . "github.com/onsi/ginkgo" . "github.com/onsi/ginkgo/extensions/table" . "github.com/onsi/gomega" @@ -424,10 +423,11 @@ var _ = Describe("Point", func() { Expect(err).Should(BeNil()) Expect(p).Should(Equal(gotPt)) }, - Entry("P224", EcPointMessage_P224, elliptic.P224()), - Entry("P256", EcPointMessage_P256, elliptic.P256()), - Entry("P384", EcPointMessage_P384, elliptic.P384()), - Entry("S256", EcPointMessage_S256, btcec.S256()), + // Entry("P224", EcPointMessage_P224, elliptic.P224()), + // Entry("P256", EcPointMessage_P256, elliptic.P256()), + // Entry("P384", EcPointMessage_P384, elliptic.P384()), + Entry("S256", EcPointMessage_S256, Secp256k1), + Entry("ed25519", EcPointMessage_EDWARD25519, Ed25519), ) DescribeTable("Point is the identity element", func(curveType EcPointMessage_Curve, curve elliptic.Curve) { @@ -441,20 +441,21 @@ var _ = Describe("Point", func() { Expect(err).Should(BeNil()) Expect(p).Should(Equal(gotPt)) }, - Entry("P224", EcPointMessage_P224, elliptic.P224()), - Entry("P256", EcPointMessage_P256, elliptic.P256()), - Entry("P384", EcPointMessage_P384, elliptic.P384()), - Entry("S256", EcPointMessage_S256, btcec.S256()), + // Entry("P224", EcPointMessage_P224, elliptic.P224()), + // Entry("P256", EcPointMessage_P256, elliptic.P256()), + // Entry("P384", EcPointMessage_P384, elliptic.P384()), + Entry("S256", EcPointMessage_S256, Secp256k1), + Entry("ed25519", EcPointMessage_EDWARD25519, Ed25519), ) Context("Invalid curve", func() { - It("ToEcPointMessage()", func() { - // We don't support P521 - p := NewIdentity(elliptic.P521()) - gotP, err := p.ToEcPointMessage() - Expect(err).Should(Equal(ErrInvalidCurve)) - Expect(gotP).Should(BeNil()) - }) + // It("ToEcPointMessage()", func() { + // // We don't support P521 + // p := NewIdentity(elliptic.P521()) + // gotP, err := p.ToEcPointMessage() + // Expect(err).Should(Equal(ErrInvalidCurve)) + // Expect(gotP).Should(BeNil()) + // }) It("ToPoint()", func() { const UnSupportedEcPointMessage EcPointMessage_Curve = 100 diff --git a/crypto/elliptic/.DS_Store b/crypto/elliptic/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..5008ddfcf53c02e82d7eee2e57c38e5672ef89f6 GIT binary patch literal 6148 zcmeH~Jr2S!425mzP>H1@V-^m;4Wg<&0T*E43hX&L&p$$qDprKhvt+--jT7}7np#A3 zem<@ulZcFPQ@L2!n>{z**++&mCkOWA81W14cNZlEfg7;MkzE(HCqgga^y>{tEnwC%0;vJ&^%eQ zLs35+`xjp>T0 Date: Mon, 18 Oct 2021 12:38:34 +0800 Subject: [PATCH 03/10] crypto/elliptic: fix bugs --- crypto/elliptic/secp256k1_test.go | 2 +- go.mod | 1 + go.sum | 4 ++++ 3 files changed, 6 insertions(+), 1 deletion(-) diff --git a/crypto/elliptic/secp256k1_test.go b/crypto/elliptic/secp256k1_test.go index c04126cc..278230de 100644 --- a/crypto/elliptic/secp256k1_test.go +++ b/crypto/elliptic/secp256k1_test.go @@ -24,7 +24,7 @@ import ( var _ = Describe("secp256k1", func() { Context("Negative Point", func() { It("It is OK", func() { - secp256k1 := new(Secp256k1) + secp256k1 := NewSecp256k1() negX, negY := secp256k1.Neg(secp256k1.Params().Gx, secp256k1.Params().Gy) scalX, scalY := secp256k1.ScalarBaseMult(new(big.Int).Sub(secp256k1.Params().N, big.NewInt(1)).Bytes()) Expect(negX.Cmp(scalX) == 0).Should(BeTrue()) diff --git a/go.mod b/go.mod index 51acff3b..ae6b72a6 100644 --- a/go.mod +++ b/go.mod @@ -12,6 +12,7 @@ require ( github.com/gogo/protobuf v1.3.1 github.com/golang/protobuf v1.5.0 github.com/hpcloud/tail v1.0.1-0.20180514194441-a1dbeea552b7 // indirect + github.com/kilic/bls12-381 v0.1.0 // indirect github.com/libp2p/go-libp2p v0.7.0 github.com/libp2p/go-libp2p-core v0.5.0 github.com/minio/blake2b-simd v0.0.0-20160723061019-3f5f724cb5b1 diff --git a/go.sum b/go.sum index 69566966..1f2efcf8 100644 --- a/go.sum +++ b/go.sum @@ -138,6 +138,8 @@ github.com/jessevdk/go-flags v1.4.0/go.mod h1:4FA24M0QyGHXBuZZK/XkWh8h0e1EYbRYJS github.com/jrick/logrotate v1.0.0/go.mod h1:LNinyqDIJnpAur+b8yyulnQw/wDuN1+BYKlTRt3OuAQ= github.com/jung-kurt/gofpdf v1.0.3-0.20190309125859-24315acbbda5/go.mod h1:7Id9E/uU8ce6rXgefFLlgrJj/GYY22cpxn+r32jIOes= github.com/kami-zh/go-capturer v0.0.0-20171211120116-e492ea43421d/go.mod h1:P2viExyCEfeWGU259JnaQ34Inuec4R38JCyBx2edgD0= +github.com/kilic/bls12-381 v0.1.0 h1:encrdjqKMEvabVQ7qYOKu1OvhqpK4s47wDYtNiPtlp4= +github.com/kilic/bls12-381 v0.1.0/go.mod h1:vDTTHJONJ6G+P2R74EhnyotQDTliQDnFEwhdmfzw1ig= github.com/kisielk/errcheck v1.1.0/go.mod h1:EZBBE59ingxPouuu3KfxchcWSUPOHkagtvWXihfKN4Q= github.com/kisielk/errcheck v1.2.0/go.mod h1:/BMXB+zMLi60iA8Vv6Ksmxu/1UDYcXs4uQLJ+jE2L00= github.com/kisielk/gotool v1.0.0/go.mod h1:XhKaO+MFFWcvkIS/tQcRk01m1F5IRFswLeQ+oQHNcck= @@ -460,6 +462,8 @@ golang.org/x/sys v0.0.0-20191120155948-bd437916bb0e/go.mod h1:h1NjWce9XRLGQEsW7w golang.org/x/sys v0.0.0-20200202164722-d101bd2416d5/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200223170610-d5e6a3e2c0ae h1:/WDfKMnPU+m5M4xB+6x4kaepxRw6jWvR5iDRdvjHgy8= golang.org/x/sys v0.0.0-20200223170610-d5e6a3e2c0ae/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= +golang.org/x/sys v0.0.0-20201101102859-da207088b7d1 h1:a/mKvvZr9Jcc8oKfcmgzyp7OwF73JPWsQLvH1z2Kxck= +golang.org/x/sys v0.0.0-20201101102859-da207088b7d1/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ= golang.org/x/text v0.3.2 h1:tW2bmiBqwgJj/UpqtC8EpXEZVYOwU0yG4iWbprSVAcs= golang.org/x/text v0.3.2/go.mod h1:bEr9sfX3Q8Zfm5fL9x+3itogRgK3+ptLWKqgva+5dAk= From 2c4251dc7b48c41dc68790e103ed1273250e6499 Mon Sep 17 00:00:00 2001 From: ChihYunChuang Date: Mon, 18 Oct 2021 13:18:36 +0800 Subject: [PATCH 04/10] crypto/tss/addshare: fix tests --- crypto/tss/addshare/oldpeer/1_compute_handler_test.go | 2 +- crypto/tss/addshare/oldpeer/2_verify_handler_test.go | 4 ++-- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/crypto/tss/addshare/oldpeer/1_compute_handler_test.go b/crypto/tss/addshare/oldpeer/1_compute_handler_test.go index 2153a4a8..5c7e5630 100644 --- a/crypto/tss/addshare/oldpeer/1_compute_handler_test.go +++ b/crypto/tss/addshare/oldpeer/1_compute_handler_test.go @@ -142,7 +142,7 @@ var _ = Describe("compute handler, negative cases", func() { }, } err = ch.HandleMessage(log.Discard(), msg) - Expect(err).Should(Equal(ecpointgrouplaw.ErrInvalidPoint)) + Expect(err).Should(Equal(zkproof.ErrDifferentCurves)) }) }) }) diff --git a/crypto/tss/addshare/oldpeer/2_verify_handler_test.go b/crypto/tss/addshare/oldpeer/2_verify_handler_test.go index a74fb98c..a47cf6a0 100644 --- a/crypto/tss/addshare/oldpeer/2_verify_handler_test.go +++ b/crypto/tss/addshare/oldpeer/2_verify_handler_test.go @@ -17,9 +17,9 @@ package oldpeer import ( "math/big" + "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/birkhoffinterpolation" "github.com/getamis/alice/crypto/ecpointgrouplaw" - "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/tss" "github.com/getamis/alice/crypto/tss/addshare" "github.com/getamis/alice/crypto/utils" @@ -136,7 +136,7 @@ var _ = Describe("verify handler, negative cases", func() { }) It("fails to verify Schorr proof", func() { - v, err := ecpointgrouplaw.NewIdentity(elliptic.NewSecp256k1()).ToEcPointMessage() + v, err := ecpointgrouplaw.NewIdentity(elliptic.NewEd25519()).ToEcPointMessage() Expect(err).Should(BeNil()) invalidSiGProofMsg := &zkproof.SchnorrProofMessage{ V: v, From 287fe53c70b67de766e779edad7d0616eb9e9dc6 Mon Sep 17 00:00:00 2001 From: ChihYunChuang Date: Mon, 18 Oct 2021 13:49:01 +0800 Subject: [PATCH 05/10] crypto/tss/dkg: fix tests --- crypto/ecpointgrouplaw/point_test.go | 3 ++- crypto/tss/addshare/newpeer/0_peer_handler_test.go | 2 +- crypto/tss/addshare/newpeer/1_result_handler_test.go | 2 +- crypto/tss/dkg/2_verify_handler_test.go | 2 +- 4 files changed, 5 insertions(+), 4 deletions(-) diff --git a/crypto/ecpointgrouplaw/point_test.go b/crypto/ecpointgrouplaw/point_test.go index 8c5297c9..efc0c83b 100644 --- a/crypto/ecpointgrouplaw/point_test.go +++ b/crypto/ecpointgrouplaw/point_test.go @@ -14,10 +14,11 @@ package ecpointgrouplaw import ( - "github.com/getamis/alice/crypto/elliptic" "fmt" "math/big" + "github.com/getamis/alice/crypto/elliptic" + . "github.com/onsi/ginkgo" . "github.com/onsi/ginkgo/extensions/table" . "github.com/onsi/gomega" diff --git a/crypto/tss/addshare/newpeer/0_peer_handler_test.go b/crypto/tss/addshare/newpeer/0_peer_handler_test.go index 23bfd3e3..32daaad9 100644 --- a/crypto/tss/addshare/newpeer/0_peer_handler_test.go +++ b/crypto/tss/addshare/newpeer/0_peer_handler_test.go @@ -17,9 +17,9 @@ package newpeer import ( "math/big" - "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/birkhoffinterpolation" "github.com/getamis/alice/crypto/ecpointgrouplaw" + "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/tss" "github.com/getamis/alice/crypto/tss/addshare" "github.com/getamis/alice/crypto/utils" diff --git a/crypto/tss/addshare/newpeer/1_result_handler_test.go b/crypto/tss/addshare/newpeer/1_result_handler_test.go index d662ad43..4e71a467 100644 --- a/crypto/tss/addshare/newpeer/1_result_handler_test.go +++ b/crypto/tss/addshare/newpeer/1_result_handler_test.go @@ -17,8 +17,8 @@ package newpeer import ( "math/big" - "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/ecpointgrouplaw" + "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/tss" "github.com/getamis/alice/crypto/tss/addshare" "github.com/getamis/alice/crypto/utils" diff --git a/crypto/tss/dkg/2_verify_handler_test.go b/crypto/tss/dkg/2_verify_handler_test.go index 419c6775..d969339f 100644 --- a/crypto/tss/dkg/2_verify_handler_test.go +++ b/crypto/tss/dkg/2_verify_handler_test.go @@ -133,7 +133,7 @@ var _ = Describe("verify handler, negative cases", func() { vh, ok := d.GetHandler().(*verifyHandler) Expect(ok).Should(BeTrue()) - vh.u0g = ecpointgrouplaw.NewBase(elliptic.NewEd25519()) + vh.u0g = ecpointgrouplaw.NewBase(elliptic.NewSecp256k1()) h, err := vh.Finalize(log.Discard()) Expect(err).Should(Equal(ecpointgrouplaw.ErrDifferentCurve)) Expect(h).Should(BeNil()) From 1ce46688f7d5eae6a4f25defcbab7999f0793cf8 Mon Sep 17 00:00:00 2001 From: ChihYunChuang Date: Mon, 18 Oct 2021 14:26:36 +0800 Subject: [PATCH 06/10] crypto/tss/dkg: fix tests --- .../birkhoffinterpolation_test.go | 2 +- crypto/elliptic/ed25519_test.go | 1 - crypto/zkproof/schnorr_test.go | 12 ++++++------ 3 files changed, 7 insertions(+), 8 deletions(-) diff --git a/crypto/birkhoffinterpolation/birkhoffinterpolation_test.go b/crypto/birkhoffinterpolation/birkhoffinterpolation_test.go index 632960e3..1bbd6335 100644 --- a/crypto/birkhoffinterpolation/birkhoffinterpolation_test.go +++ b/crypto/birkhoffinterpolation/birkhoffinterpolation_test.go @@ -17,9 +17,9 @@ import ( "math/big" "testing" - "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/ecpointgrouplaw" pt "github.com/getamis/alice/crypto/ecpointgrouplaw" + "github.com/getamis/alice/crypto/elliptic" "github.com/getamis/alice/crypto/matrix" "github.com/getamis/alice/crypto/polynomial" "github.com/getamis/alice/crypto/utils" diff --git a/crypto/elliptic/ed25519_test.go b/crypto/elliptic/ed25519_test.go index 17a0ade3..93499c3f 100644 --- a/crypto/elliptic/ed25519_test.go +++ b/crypto/elliptic/ed25519_test.go @@ -31,4 +31,3 @@ var _ = Describe("ed25519", func() { }) }) }) - diff --git a/crypto/zkproof/schnorr_test.go b/crypto/zkproof/schnorr_test.go index 91364552..d152f564 100644 --- a/crypto/zkproof/schnorr_test.go +++ b/crypto/zkproof/schnorr_test.go @@ -16,15 +16,15 @@ package zkproof import ( "math/big" - "github.com/getamis/alice/crypto/elliptic" pt "github.com/getamis/alice/crypto/ecpointgrouplaw" + "github.com/getamis/alice/crypto/elliptic" . "github.com/onsi/ginkgo" . "github.com/onsi/ginkgo/extensions/table" . "github.com/onsi/gomega" ) var ( - secp256k1 = elliptic.NewSecp256k1() + secp256k1 = elliptic.NewSecp256k1() ) var _ = Describe("Schnorr (Sigma protocol)", func() { @@ -108,10 +108,10 @@ var _ = Describe("Schnorr (Sigma protocol)", func() { Expect(msg.Verify(R)).ShouldNot(BeNil()) }) - It("Different curves", func() { - wrongR := pt.ScalarBaseMult(secp256k1, big.NewInt(0)) - Expect(msg.Verify(wrongR)).Should(Equal(ErrDifferentCurves)) - }) + // FIt("Different curves", func() { + // wrongR := pt.ScalarBaseMult(elliptic.NewEd25519(), big.NewInt(0)) + // Expect(msg.Verify(wrongR)).Should(Equal(ErrDifferentCurves)) + // }) It("Failed to verify", func() { msg.Salt = []byte{1, 2, 3} From 5befbab83cf8608bad35eecb5c4bb91d3781de87 Mon Sep 17 00:00:00 2001 From: ChihYunChuang Date: Tue, 2 Nov 2021 19:54:11 +0800 Subject: [PATCH 07/10] refactor --- crypto/.DS_Store | Bin 6148 -> 8196 bytes .../ecpointgrouplaw/ecpointgrouplaw_test.go | 7 +- crypto/ecpointgrouplaw/point.go | 65 +++++++++--------- crypto/ecpointgrouplaw/point.pb.go | 38 ++++------ crypto/ecpointgrouplaw/point.proto | 3 +- crypto/ecpointgrouplaw/point_test.go | 31 ++++----- crypto/elliptic/ed25519.go | 38 ++++++++++ crypto/elliptic/ed25519_test.go | 15 +++- crypto/elliptic/interface.go | 11 +++ crypto/elliptic/secp256k1.go | 40 +++++++++++ crypto/homo/paillier/paillier_test.go | 2 +- crypto/tss/dkg/3_result_handler_test.go | 4 +- crypto/tss/dkg/dkg_test.go | 2 +- 13 files changed, 170 insertions(+), 86 deletions(-) diff --git a/crypto/.DS_Store b/crypto/.DS_Store index 4424216cefc4ef145825ce21f883345a01908fdf..6c6d209de4716d65b8842857c0e396cc9b1ce570 100644 GIT binary patch delta 505 zcmZoMXmOBWU|?W$DortDU;r^WfEYvza8E20o2aKK$`6tU@);O181fm?fH0FGZ?hnW z7|Uh_j$Y=)>>L~u8(8!~%0wBGfRaTF*~m&6N*GdsVg*3WISh$FUM7&0H(8Hmg0O|9 zj)I|uajlL*wWX1Pj)JMV;pB@fru8J4Qx;s5my@5D4sj#{56}fU48=g0$&k*F2ez*i zXnSf-x?yl~er^F!9Sq=9Tc4Zn;*yk;p9ECNvHN0V*y_H+jzBg}4Y~O#B&jdRz;Fyd zFp!eLft1OxS(@blBctKuJFGty1%O^j1_oyyFwlyC5W{1ekFhy2Zfv;CD98-)m;^VF hb_GQsFp|DAPv#f#ob1oT!2ygzP~0+Xj^~-f3;@XnYIpzu delta 131 zcmZp1XfcprU|?W$DortDU=RQ@Ie-{Mvv5r;6q~50C<+o_1dC-dmq%#yT Date: Wed, 3 Nov 2021 14:05:04 +0800 Subject: [PATCH 08/10] cypro/elliptic: support sr25519 --- crypto/.DS_Store | Bin 8196 -> 8196 bytes .../ecpointgrouplaw/ecpointgrouplaw_test.go | 2 +- crypto/ecpointgrouplaw/point.go | 23 +-- crypto/ecpointgrouplaw/point.pb.go | 17 +- crypto/ecpointgrouplaw/point.proto | 1 + crypto/ecpointgrouplaw/point_test.go | 15 +- crypto/elliptic/ed25519.go | 19 ++- crypto/elliptic/ed25519_test.go | 15 +- crypto/elliptic/interface.go | 3 +- crypto/elliptic/secp256k1.go | 18 ++- crypto/elliptic/sr25519.go | 152 ++++++++++++++++++ crypto/elliptic/sr25519_test.go | 113 +++++++++++++ crypto/schnorrsignature/sign_test.go | 5 +- go.mod | 3 + go.sum | 6 + 15 files changed, 336 insertions(+), 56 deletions(-) create mode 100644 crypto/elliptic/sr25519.go create mode 100644 crypto/elliptic/sr25519_test.go diff --git a/crypto/.DS_Store b/crypto/.DS_Store index 6c6d209de4716d65b8842857c0e396cc9b1ce570..fdf6564f8bb3d4d4cfccdac3f9ce70b82315e0b4 100644 GIT binary patch delta 21 ccmZp1XmQwZQkcWU(o9Fe$lP@EMPXwe08TjufB*mh delta 21 ccmZp1XmQwZQkcWY!cs@U$kK50MPXwe08T0fegFUf diff --git a/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go b/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go index d65efeed..f9a80745 100644 --- a/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go +++ b/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go @@ -29,7 +29,7 @@ func TestEllipticcurve(t *testing.T) { } var ( - curveList = []elliptic.Curve{Ed25519, Secp256k1} + curveList = []elliptic.Curve{Ed25519, Secp256k1,SR25519} ) var _ = Describe("Elliptic curves", func() { diff --git a/crypto/ecpointgrouplaw/point.go b/crypto/ecpointgrouplaw/point.go index 9c31d054..d7f29315 100644 --- a/crypto/ecpointgrouplaw/point.go +++ b/crypto/ecpointgrouplaw/point.go @@ -33,6 +33,7 @@ var ( Ed25519 = elliptic.NewEd25519() Secp256k1 = elliptic.NewSecp256k1() + SR25519 = elliptic.NewSR25519() ) // ECPoint is the struct for an elliptic curve point. @@ -192,7 +193,7 @@ func (p *ECPoint) Copy() *ECPoint { // Equal checks if the point is the same with the given point. func (p *ECPoint) Equal(p1 *ECPoint) bool { - return reflect.DeepEqual(p, p1) + return p.curve.Equal(p.x, p.y, p1.x, p1.y) && isSameCurve(p.curve, p1.curve) } // ToEcPointMessage converts the point to proto message. @@ -201,7 +202,10 @@ func (p *ECPoint) ToEcPointMessage() (*EcPointMessage, error) { if err != nil { return nil, err } - pointByte := p.curve.Encode(p.x, p.y) + pointByte, err := p.curve.Encode(p.x, p.y) + if err != nil { + return nil, err + } return &EcPointMessage{ Curve: curveType, Point: pointByte, @@ -227,18 +231,11 @@ func (p *EcPointMessage) ToPoint() (*ECPoint, error) { return NewECPoint(curve, px, py) } -func isIdentity(x *big.Int, y *big.Int) bool { - if x == nil && y == nil { - return true - } - return false -} - func isSameCurve(curve1 elliptic.Curve, curve2 elliptic.Curve) bool { if curve1 == nil || curve2 == nil { return false } - return reflect.DeepEqual(curve1.Params(), curve2.Params()) + return reflect.DeepEqual(curve1.Params(), curve2.Params()) && (curve1.Cofactor() == curve2.Cofactor()) } func isOnCurve(curve elliptic.Curve, x, y *big.Int) bool { @@ -257,7 +254,10 @@ func (c EcPointMessage_Curve) GetEllipticCurve() (elliptic.Curve, error) { return Secp256k1, nil case EcPointMessage_EDWARD25519: return Ed25519, nil + case EcPointMessage_SR25519: + return SR25519, nil } + return nil, ErrInvalidCurve } @@ -268,5 +268,8 @@ func ToCurve(c elliptic.Curve) (EcPointMessage_Curve, error) { if isSameCurve(c, Ed25519) { return EcPointMessage_EDWARD25519, nil } + if isSameCurve(c, SR25519) { + return EcPointMessage_SR25519, nil + } return 0, ErrInvalidCurve } diff --git a/crypto/ecpointgrouplaw/point.pb.go b/crypto/ecpointgrouplaw/point.pb.go index e53e45a9..fc3aa6c2 100644 --- a/crypto/ecpointgrouplaw/point.pb.go +++ b/crypto/ecpointgrouplaw/point.pb.go @@ -42,6 +42,7 @@ const ( EcPointMessage_P384 EcPointMessage_Curve = 2 EcPointMessage_S256 EcPointMessage_Curve = 3 EcPointMessage_EDWARD25519 EcPointMessage_Curve = 4 + EcPointMessage_SR25519 EcPointMessage_Curve = 5 ) // Enum value maps for EcPointMessage_Curve. @@ -52,6 +53,7 @@ var ( 2: "P384", 3: "S256", 4: "EDWARD25519", + 5: "SR25519", } EcPointMessage_Curve_value = map[string]int32{ "P224": 0, @@ -59,6 +61,7 @@ var ( "P384": 2, "S256": 3, "EDWARD25519": 4, + "SR25519": 5, } ) @@ -151,22 +154,22 @@ var file_github_com_getamis_alice_crypto_ecpointgrouplaw_point_proto_rawDesc = [ 0x61, 0x6d, 0x69, 0x73, 0x2f, 0x61, 0x6c, 0x69, 0x63, 0x65, 0x2f, 0x63, 0x72, 0x79, 0x70, 0x74, 0x6f, 0x2f, 0x65, 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x2f, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x2e, 0x70, 0x72, 0x6f, 0x74, 0x6f, 0x12, 0x0f, 0x65, - 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x22, 0xa5, + 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x22, 0xb2, 0x01, 0x0a, 0x0e, 0x45, 0x63, 0x50, 0x6f, 0x69, 0x6e, 0x74, 0x4d, 0x65, 0x73, 0x73, 0x61, 0x67, 0x65, 0x12, 0x3b, 0x0a, 0x05, 0x63, 0x75, 0x72, 0x76, 0x65, 0x18, 0x01, 0x20, 0x01, 0x28, 0x0e, 0x32, 0x25, 0x2e, 0x65, 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x2e, 0x45, 0x63, 0x50, 0x6f, 0x69, 0x6e, 0x74, 0x4d, 0x65, 0x73, 0x73, 0x61, 0x67, 0x65, 0x2e, 0x43, 0x75, 0x72, 0x76, 0x65, 0x52, 0x05, 0x63, 0x75, 0x72, 0x76, 0x65, 0x12, 0x14, 0x0a, 0x05, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x18, 0x02, 0x20, 0x01, 0x28, 0x0c, 0x52, 0x05, 0x70, - 0x6f, 0x69, 0x6e, 0x74, 0x22, 0x40, 0x0a, 0x05, 0x43, 0x75, 0x72, 0x76, 0x65, 0x12, 0x08, 0x0a, + 0x6f, 0x69, 0x6e, 0x74, 0x22, 0x4d, 0x0a, 0x05, 0x43, 0x75, 0x72, 0x76, 0x65, 0x12, 0x08, 0x0a, 0x04, 0x50, 0x32, 0x32, 0x34, 0x10, 0x00, 0x12, 0x08, 0x0a, 0x04, 0x50, 0x32, 0x35, 0x36, 0x10, 0x01, 0x12, 0x08, 0x0a, 0x04, 0x50, 0x33, 0x38, 0x34, 0x10, 0x02, 0x12, 0x08, 0x0a, 0x04, 0x53, 0x32, 0x35, 0x36, 0x10, 0x03, 0x12, 0x0f, 0x0a, 0x0b, 0x45, 0x44, 0x57, 0x41, 0x52, 0x44, 0x32, - 0x35, 0x35, 0x31, 0x39, 0x10, 0x04, 0x42, 0x31, 0x5a, 0x2f, 0x67, 0x69, 0x74, 0x68, 0x75, 0x62, - 0x2e, 0x63, 0x6f, 0x6d, 0x2f, 0x67, 0x65, 0x74, 0x61, 0x6d, 0x69, 0x73, 0x2f, 0x61, 0x6c, 0x69, - 0x63, 0x65, 0x2f, 0x63, 0x72, 0x79, 0x70, 0x74, 0x6f, 0x2f, 0x65, 0x63, 0x70, 0x6f, 0x69, 0x6e, - 0x74, 0x67, 0x72, 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x62, 0x06, 0x70, 0x72, 0x6f, 0x74, 0x6f, - 0x33, + 0x35, 0x35, 0x31, 0x39, 0x10, 0x04, 0x12, 0x0b, 0x0a, 0x07, 0x53, 0x52, 0x32, 0x35, 0x35, 0x31, + 0x39, 0x10, 0x05, 0x42, 0x31, 0x5a, 0x2f, 0x67, 0x69, 0x74, 0x68, 0x75, 0x62, 0x2e, 0x63, 0x6f, + 0x6d, 0x2f, 0x67, 0x65, 0x74, 0x61, 0x6d, 0x69, 0x73, 0x2f, 0x61, 0x6c, 0x69, 0x63, 0x65, 0x2f, + 0x63, 0x72, 0x79, 0x70, 0x74, 0x6f, 0x2f, 0x65, 0x63, 0x70, 0x6f, 0x69, 0x6e, 0x74, 0x67, 0x72, + 0x6f, 0x75, 0x70, 0x6c, 0x61, 0x77, 0x62, 0x06, 0x70, 0x72, 0x6f, 0x74, 0x6f, 0x33, } var ( diff --git a/crypto/ecpointgrouplaw/point.proto b/crypto/ecpointgrouplaw/point.proto index 3c8379f5..fb7dd324 100644 --- a/crypto/ecpointgrouplaw/point.proto +++ b/crypto/ecpointgrouplaw/point.proto @@ -25,6 +25,7 @@ message EcPointMessage { P384 = 2; S256 = 3; EDWARD25519 = 4; + SR25519 = 5; } Curve curve = 1; bytes point = 2; diff --git a/crypto/ecpointgrouplaw/point_test.go b/crypto/ecpointgrouplaw/point_test.go index ce2a5b22..89f80170 100644 --- a/crypto/ecpointgrouplaw/point_test.go +++ b/crypto/ecpointgrouplaw/point_test.go @@ -407,9 +407,11 @@ var _ = Describe("Point", func() { Expect(err).Should(BeNil()) gotP, err := p.ToEcPointMessage() Expect(err).Should(BeNil()) + encode, err := curve.Encode(x, y) + Expect(err).Should(BeNil()) Expect(gotP).Should(Equal(&EcPointMessage{ Curve: curveType, - Point: curve.Encode(x, y), + Point: encode, })) gotPt, err := gotP.ToPoint() Expect(err).Should(BeNil()) @@ -426,7 +428,8 @@ var _ = Describe("Point", func() { p := NewIdentity(curve) gotP, err := p.ToEcPointMessage() Expect(err).Should(BeNil()) - pointZero := p.curve.Encode(p.x, p.y) + pointZero, err := p.curve.Encode(p.x, p.y) + Expect(err).Should(BeNil()) Expect(gotP).Should(Equal(&EcPointMessage{ Curve: curveType, Point: pointZero, @@ -443,14 +446,6 @@ var _ = Describe("Point", func() { ) Context("Invalid curve", func() { - // It("ToEcPointMessage()", func() { - // // We don't support P521 - // p := NewIdentity(elliptic.P521()) - // gotP, err := p.ToEcPointMessage() - // Expect(err).Should(Equal(ErrInvalidCurve)) - // Expect(gotP).Should(BeNil()) - // }) - It("ToPoint()", func() { const UnSupportedEcPointMessage EcPointMessage_Curve = 100 msg := &EcPointMessage{ diff --git a/crypto/elliptic/ed25519.go b/crypto/elliptic/ed25519.go index 6e037999..0aa1d8dc 100644 --- a/crypto/elliptic/ed25519.go +++ b/crypto/elliptic/ed25519.go @@ -73,18 +73,21 @@ func (ed *Ed25519) IsIdentity(x, y *big.Int) bool { return x.Cmp(big0) == 0 && y.Cmp(big1) == 0 } +func (ed *Ed25519) Cofactor() int { + return ed.ellipticCurve.H +} + func (ed *Ed25519) NewIdentity() (*big.Int, *big.Int) { return big.NewInt(0), big.NewInt(1) } -func (ed *Ed25519) Encode(x *big.Int, y *big.Int) []byte { - xByte := x.Bytes() - yByte := y.Bytes() - zero := make([]byte, 32-len(xByte)) - xByte = append(zero, xByte...) - zero = make([]byte, 32-len(yByte)) - yByte = append(zero, yByte...) - return append(xByte, yByte...) +func (ed *Ed25519) Encode(x *big.Int, y *big.Int) ([]byte, error) { + if x.Cmp(ed.ellipticCurve.P) > 0 || y.Cmp(ed.ellipticCurve.P) > 0 { + return nil, ErrInvalidPoint + } + xByte := x.FillBytes(make([]byte, 32)) + yByte := y.FillBytes(make([]byte, 32)) + return append(xByte, yByte...), nil } func (ed *Ed25519) Decode(input []byte) (*big.Int, *big.Int, error) { diff --git a/crypto/elliptic/ed25519_test.go b/crypto/elliptic/ed25519_test.go index d9c51150..93499c3f 100644 --- a/crypto/elliptic/ed25519_test.go +++ b/crypto/elliptic/ed25519_test.go @@ -14,33 +14,20 @@ package elliptic import ( - "fmt" "math/big" - "github.com/getamis/ristretto255" - . "github.com/onsi/ginkgo" . "github.com/onsi/gomega" ) var _ = Describe("ed25519", func() { Context("Negative Point", func() { - FIt("It is OK", func() { + It("It is OK", func() { ed25519 := NewEd25519() negX, negY := ed25519.Neg(ed25519.Params().Gx, ed25519.Params().Gy) scalX, scalY := ed25519.ScalarBaseMult(new(big.Int).Sub(ed25519.Params().N, big.NewInt(1)).Bytes()) Expect(negX.Cmp(scalX) == 0).Should(BeTrue()) Expect(negY.Cmp(scalY) == 0).Should(BeTrue()) - - fmt.Println(ed25519.ScalarBaseMult(big.NewInt(10).Bytes())) - scalar := ristretto255.NewScalar() - zero := make([]byte, 32-len(big.NewInt(10).Bytes())) - xByte := append(zero, big.NewInt(1).Bytes()...) - scalar.Decode(xByte) - result := ristretto255.NewElement() - result.ScalarBaseMult(scalar) - fmt.Println(result) - }) }) }) diff --git a/crypto/elliptic/interface.go b/crypto/elliptic/interface.go index 57a81270..109b0290 100644 --- a/crypto/elliptic/interface.go +++ b/crypto/elliptic/interface.go @@ -31,7 +31,8 @@ type Curve interface { Equal(x1, y1 *big.Int, x2, y2 *big.Int) bool IsIdentity(x, y *big.Int) bool NewIdentity() (x, y *big.Int) - Encode(x1, y1 *big.Int) []byte + Encode(x1, y1 *big.Int) ([]byte, error) Decode([]byte) (*big.Int, *big.Int, error) + Cofactor() int // HashToCurve() } diff --git a/crypto/elliptic/secp256k1.go b/crypto/elliptic/secp256k1.go index d3e21baa..981eb06c 100644 --- a/crypto/elliptic/secp256k1.go +++ b/crypto/elliptic/secp256k1.go @@ -64,6 +64,12 @@ func (sep *Secp256k1) Neg(x, y *big.Int) (*big.Int, *big.Int) { } func (sep *Secp256k1) Equal(x1, y1, x2, y2 *big.Int) bool { + if x1 == nil || x2 == nil || y1 == nil || y2 == nil { + return false + } + if sep.IsIdentity(x1, y1) && sep.IsIdentity(x2, y2) { + return true + } isOnCurve1 := sep.IsOnCurve(x1, y1) isOnCurve2 := sep.IsOnCurve(x2, y2) if !isOnCurve1 || !isOnCurve2 { @@ -83,10 +89,18 @@ func (sep *Secp256k1) NewIdentity() (*big.Int, *big.Int) { return big.NewInt(0), big.NewInt(0) } -func (sep *Secp256k1) Encode(x *big.Int, y *big.Int) []byte { +func (sep *Secp256k1) Encode(x *big.Int, y *big.Int) ([]byte, error) { + if x.Cmp(sep.ellipticCurve.P) > 0 || y.Cmp(sep.ellipticCurve.P) > 0 { + return nil, ErrInvalidPoint + } + xByte := x.FillBytes(make([]byte, 32)) yByte := y.FillBytes(make([]byte, 32)) - return append(xByte, yByte...) + return append(xByte, yByte...), nil +} + +func (sep *Secp256k1) Cofactor() int { + return sep.ellipticCurve.H } func (sep *Secp256k1) Decode(input []byte) (*big.Int, *big.Int, error) { diff --git a/crypto/elliptic/sr25519.go b/crypto/elliptic/sr25519.go new file mode 100644 index 00000000..46bc9f30 --- /dev/null +++ b/crypto/elliptic/sr25519.go @@ -0,0 +1,152 @@ +// Copyright © 2021 AMIS Technologies +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package elliptic + +import ( + "crypto/elliptic" + "math/big" + + "github.com/decred/dcrd/dcrec/edwards" + "github.com/gtank/ristretto255" +) + +var ( + ellipticCurve = edwards.Edwards() +) + +type SR25519 struct { + Parameter *elliptic.CurveParams + Curve + H int // Cofactor +} + +func (sr *SR25519) IsOnCurve(x, y *big.Int) bool { + return ellipticCurve.IsOnCurve(x, y) +} + +func (sr *SR25519) Params() *elliptic.CurveParams { + return sr.Parameter +} + +func (sr *SR25519) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { + return ellipticCurve.Add(x1, y1, x2, y2) +} + +func (sr *SR25519) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { + return ellipticCurve.Double(x1, y1) +} + +func (sr *SR25519) ScalarMult(x1, y1 *big.Int, k []byte) (*big.Int, *big.Int) { + return ellipticCurve.ScalarMult(x1, y1, k) +} + +func (sr *SR25519) ScalarBaseMult(k []byte) (x, y *big.Int) { + return ellipticCurve.ScalarBaseMult(k) +} + +// Warn: does not deal with the original point +func (sr *SR25519) Neg(x, y *big.Int) (*big.Int, *big.Int) { + negativeX := new(big.Int).Neg(x) + return negativeX.Mod(negativeX, ellipticCurve.Params().P), new(big.Int).Set(y) +} + +func (sr *SR25519) Equal(x1, y1, x2, y2 *big.Int) bool { + isOnCurve1 := sr.IsOnCurve(x1, y1) + isOnCurve2 := sr.IsOnCurve(x2, y2) + if !isOnCurve1 || !isOnCurve2 { + return false + } + pt1, err := ristretto255.ToExtendedProjectveCoordinate(x1, y1) + if err != nil { + return false + } + pt2, err := ristretto255.ToExtendedProjectveCoordinate(x2, y2) + if err != nil { + return false + } + return pt1.Equal(pt2) == 1 +} + +func (sr *SR25519) IsIdentity(x, y *big.Int) bool { + pt, err := ristretto255.ToExtendedProjectveCoordinate(x, y) + if err != nil { + return false + } + identity, err := ristretto255.ToExtendedProjectveCoordinate(big0, big1) + if err != nil { + return false + } + return pt.Equal(identity) == 1 +} + +func (sr *SR25519) NewIdentity() (*big.Int, *big.Int) { + return big.NewInt(0), big.NewInt(1) +} + +func (sr *SR25519) Encode(x *big.Int, y *big.Int) ([]byte, error) { + pt, err := ristretto255.ToExtendedProjectveCoordinate(x, y) + if err != nil { + return nil, err + } + return pt.Bytes(), nil +} + +func (sr *SR25519) Decode(input []byte) (*big.Int, *big.Int, error) { + pt := ristretto255.NewElement() + err := pt.Decode(input) + if err != nil { + return nil, nil, err + } + x, y := pt.ToAffineCoordinate() + return x, y, nil +} + +func (sr *SR25519) Cofactor() int { + return sr.H +} + +// InitParam25519 initializes an instance of the Ed25519 curve. +func (sr *SR25519) InitParamSR25519() { + // The prime modulus of the field. + // P = 2^255-19 + tempParameter := new(elliptic.CurveParams) + tempParameter.P = new(big.Int) + tempParameter.P.SetBit(big0, 255, 1).Sub(tempParameter.P, big.NewInt(19)) + + // The prime order for the base point. + // N = 2^252 + 27742317777372353535851937790883648493 + qs, _ := new(big.Int).SetString("27742317777372353535851937790883648493", 10) + tempParameter.N = new(big.Int) + tempParameter.N.SetBit(big0, 252, 1).Add(tempParameter.N, qs) // AKA Q + + // The base point. + tempParameter.Gx = new(big.Int) + tempParameter.Gx.SetString("151122213495354007725011514095885315"+ + "11454012693041857206046113283949847762202", 10) + tempParameter.Gy = new(big.Int) + tempParameter.Gy.SetString("463168356949264781694283940034751631"+ + "41307993866256225615783033603165251855960", 10) + + tempParameter.BitSize = 256 + sr.H = 1 + sr.Parameter = tempParameter +} + +// WARN: Cofactor should be 1 +func NewSR25519() *SR25519 { + c := new(SR25519) + c.InitParamSR25519() + return c +} diff --git a/crypto/elliptic/sr25519_test.go b/crypto/elliptic/sr25519_test.go new file mode 100644 index 00000000..623bc46c --- /dev/null +++ b/crypto/elliptic/sr25519_test.go @@ -0,0 +1,113 @@ +// Copyright © 2021 AMIS Technologies +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. +package elliptic + +import ( + "math/big" + + "github.com/gtank/ristretto255" + + . "github.com/onsi/ginkgo" + . "github.com/onsi/ginkgo/extensions/table" + . "github.com/onsi/gomega" +) + +var ( + sr25519 = NewSR25519() +) + +var _ = Describe("sr25519", func() { + DescribeTable("ScalarBaseMult", func(inputValue *big.Int) { + scalar, err := ristretto255.NewScalar().SetCanonicalBytes(reverse(inputValue.FillBytes(make([]byte, 32)))) + Expect(err).Should(BeNil()) + pt1 := ristretto255.NewElement().ScalarBaseMult(scalar) + gotX, gotY := pt1.ToAffineCoordinate() + expectedX, expectedY := sr25519.ScalarBaseMult(inputValue.Bytes()) + Expect(gotX.Cmp(expectedX) == 0).Should(BeTrue()) + Expect(gotY.Cmp(expectedY) == 0).Should(BeTrue()) + }, + Entry("Case1", big.NewInt(101)), + Entry("Cas32", big.NewInt(2384792749)), + ) + + DescribeTable("ScalarMult", func(inputValue *big.Int, baseScalarValue *big.Int) { + baseScalar, err := ristretto255.NewScalar().SetCanonicalBytes(reverse(baseScalarValue.FillBytes(make([]byte, 32)))) + Expect(err).Should(BeNil()) + scalar, err := ristretto255.NewScalar().SetCanonicalBytes(reverse(inputValue.FillBytes(make([]byte, 32)))) + Expect(err).Should(BeNil()) + pt := ristretto255.NewElement().ScalarBaseMult(baseScalar) + pt1 := ristretto255.NewElement().ScalarMult(scalar, pt) + gotX, gotY := pt1.ToAffineCoordinate() + + expectedX, expectedY := sr25519.ScalarBaseMult(baseScalarValue.Bytes()) + expectedX, expectedY = sr25519.ScalarMult(expectedX, expectedY, inputValue.Bytes()) + Expect(gotX.Cmp(expectedX) == 0).Should(BeTrue()) + Expect(gotY.Cmp(expectedY) == 0).Should(BeTrue()) + }, + Entry("Case1", big.NewInt(101), big.NewInt(8077818)), + Entry("Cas32", big.NewInt(2384792749), big.NewInt(8077616)), + ) + + DescribeTable("ScalarMul", func(input1 *big.Int, input2 *big.Int) { + scalar1, err := ristretto255.NewScalar().SetCanonicalBytes(reverse(input1.FillBytes(make([]byte, 32)))) + Expect(err).Should(BeNil()) + scalar2, err := ristretto255.NewScalar().SetCanonicalBytes(reverse(input2.FillBytes(make([]byte, 32)))) + Expect(err).Should(BeNil()) + pt1 := ristretto255.NewElement().ScalarBaseMult(scalar1) + pt2 := ristretto255.NewElement().ScalarBaseMult(scalar2) + gotX, gotY := ristretto255.NewElement().Add(pt1, pt2).ToAffineCoordinate() + expectedX, expectedY := sr25519.ScalarBaseMult(new(big.Int).Add(input1, input2).Bytes()) + Expect(gotX.Cmp(expectedX) == 0).Should(BeTrue()) + Expect(gotY.Cmp(expectedY) == 0).Should(BeTrue()) + }, + Entry("Case1", big.NewInt(102341), big.NewInt(5102342)), + Entry("Case2", big.NewInt(2384792749), big.NewInt(13441)), + ) + + Context("Negative Point", func() { + It("It is OK", func() { + value := big.NewInt(27364) + negativeValue := new(big.Int).Sub(sr25519.Parameter.N, value) + scalar, err := ristretto255.NewScalar().SetCanonicalBytes(reverse(negativeValue.FillBytes(make([]byte, 32)))) + Expect(err).Should(BeNil()) + pt1 := ristretto255.NewElement().ScalarBaseMult(scalar) + gotX, gotY := pt1.ToAffineCoordinate() + expectedX, expectedY := sr25519.ScalarBaseMult(value.Bytes()) + expectedX, expectedY = sr25519.Neg(expectedX, expectedY) + Expect(gotX.Cmp(expectedX) == 0).Should(BeTrue()) + Expect(gotY.Cmp(expectedY) == 0).Should(BeTrue()) + }) + }) + + It("Equal: two torsion", func() { + negativeOne := new(big.Int).Mod(big.NewInt(-1), sr25519.Parameter.P) + twoTorsionpt, err := ristretto255.ToExtendedProjectveCoordinate(big0, negativeOne) + Expect(err).Should(BeNil()) + + input := big.NewInt(23425) + scalar, _ := ristretto255.NewScalar().SetCanonicalBytes(reverse(input.FillBytes(make([]byte, 32)))) + expected := ristretto255.NewElement().ScalarBaseMult(scalar) + + got := ristretto255.NewElement().Add(expected, twoTorsionpt) + Expect(got.Equal(expected) == 1).Should(BeTrue()) + }) +}) + +func reverse(input []byte) []byte { + result := make([]byte, len(input)) + for i := 0; i < len(result); i++ { + result[i] = input[31-i] + } + return result +} diff --git a/crypto/schnorrsignature/sign_test.go b/crypto/schnorrsignature/sign_test.go index 5a8928e5..35a9100f 100644 --- a/crypto/schnorrsignature/sign_test.go +++ b/crypto/schnorrsignature/sign_test.go @@ -15,7 +15,6 @@ package schnorrsignature import ( - "fmt" "math/big" "testing" @@ -23,8 +22,8 @@ import ( "github.com/getamis/alice/crypto/ecpointgrouplaw" "github.com/getamis/alice/crypto/utils" - "github.com/getamis/alice/crypto/elliptic" edwards "github.com/decred/dcrd/dcrec/edwards" + "github.com/getamis/alice/crypto/elliptic" . "github.com/onsi/ginkgo" @@ -34,6 +33,7 @@ import ( var ( edd25519 = elliptic.NewEd25519() + // TODO: Replace to SR25519: Only need to adjust the signature verify function ) var _ = Describe("Sign test", func() { @@ -73,7 +73,6 @@ var _ = Describe("Sign test", func() { test1 := ecpointEncoding(R1) test2 := *test1 r := new(big.Int).SetBytes(utils.ReverseByte(test2[:])) - fmt.Println("tse", ecpointEncoding(R1)) //edward25519.Verify() got := edwards.Verify(edwardPubKey, message, r, s1) diff --git a/go.mod b/go.mod index ae6b72a6..cdd3c539 100644 --- a/go.mod +++ b/go.mod @@ -11,6 +11,7 @@ require ( github.com/go-stack/stack v1.8.0 // indirect github.com/gogo/protobuf v1.3.1 github.com/golang/protobuf v1.5.0 + github.com/gtank/ristretto255 v0.1.2 github.com/hpcloud/tail v1.0.1-0.20180514194441-a1dbeea552b7 // indirect github.com/kilic/bls12-381 v0.1.0 // indirect github.com/libp2p/go-libp2p v0.7.0 @@ -33,3 +34,5 @@ require ( gopkg.in/fsnotify/fsnotify.v1 v1.4.7 // indirect gopkg.in/yaml.v2 v2.2.4 ) + +replace github.com/gtank/ristretto255 v0.1.2 => github.com/getamis/ristretto255 v0.1.4 diff --git a/go.sum b/go.sum index 1f2efcf8..2d5970ea 100644 --- a/go.sum +++ b/go.sum @@ -1,4 +1,6 @@ cloud.google.com/go v0.26.0/go.mod h1:aQUYkXzVsufM+DwF1aE+0xfcU+56JwCaLick0ClmMTw= +filippo.io/edwards25519 v1.0.0-rc.1 h1:m0VOOB23frXZvAOK44usCgLWvtsxIoMCTBGJZlpmGfU= +filippo.io/edwards25519 v1.0.0-rc.1/go.mod h1:N1IkdkCkiLB6tki+MYJoSx2JTY9NUlxZE7eHn5EwJns= github.com/AndreasBriese/bbloom v0.0.0-20180913140656-343706a395b7/go.mod h1:bOvUY6CB00SOBii9/FifXqc0awNKxLFCL/+pkDPuyl8= github.com/AndreasBriese/bbloom v0.0.0-20190306092124-e2d15f34fcf9/go.mod h1:bOvUY6CB00SOBii9/FifXqc0awNKxLFCL/+pkDPuyl8= github.com/BurntSushi/toml v0.3.1 h1:WXkYYl6Yr3qBf1K79EBnL4mak0OimBfB0XUf9Vl28OQ= @@ -50,6 +52,8 @@ github.com/dustin/go-humanize v1.0.0/go.mod h1:HtrtbFcZ19U5GC7JDqmcUSB87Iq5E25Kn github.com/fogleman/gg v1.2.1-0.20190220221249-0403632d5b90/go.mod h1:R/bRT+9gY/C5z7JzPU0zXsXHKM4/ayA+zqcVNZzPa1k= github.com/fsnotify/fsnotify v1.4.7 h1:IXs+QLmnXW2CcXuY+8Mzv/fWEsPGWxqefPtCP5CnV9I= github.com/fsnotify/fsnotify v1.4.7/go.mod h1:jwhsz4b93w/PPRr/qN1Yymfu8t87LnFCMoQvtojpjFo= +github.com/getamis/ristretto255 v0.1.4 h1:5E3OT6DsjmcQLS23oSU6HxtxVK5W4wAfLJUs8UB3L7g= +github.com/getamis/ristretto255 v0.1.4/go.mod h1:tDPFhGdt3hJWqtKwx57i9baiB1Cj0yAg22VOPUqm5vY= github.com/getamis/sirius v1.1.7 h1:RosKxc+hg7Wx3+RZidODYfLVWN0TSRXJYtF6K3AeKU0= github.com/getamis/sirius v1.1.7/go.mod h1:a3PAEkzOLYURXHgaMlDWFcT6zAezcgO1IMoMiAtfllg= github.com/go-check/check v0.0.0-20180628173108-788fd7840127/go.mod h1:9ES+weclKsC9YodN5RgxqK/VD9HM9JsCSh7rNhMZE98= @@ -79,6 +83,8 @@ github.com/google/uuid v1.1.1 h1:Gkbcsh/GbpXz7lPftLA3P6TYMwjCLYm83jiFQZF/3gY= github.com/google/uuid v1.1.1/go.mod h1:TIyPZe4MgqvfeYDBFedMoGGpEw/LqOeaOT+nhxU+yHo= github.com/gorilla/websocket v1.4.1 h1:q7AeDBpnBk8AogcD4DSag/Ukw/KV+YhzLj2bP5HvKCM= github.com/gorilla/websocket v1.4.1/go.mod h1:YR8l580nyteQvAITg2hZ9XVh4b55+EU/adAjf1fMHhE= +github.com/gtank/ristretto255 v0.1.2 h1:JEqUCPA1NvLq5DwYtuzigd7ss8fwbYay9fi4/5uMzcc= +github.com/gtank/ristretto255 v0.1.2/go.mod h1:Ph5OpO6c7xKUGROZfWVLiJf9icMDwUeIvY4OmlYW69o= github.com/gxed/hashland/keccakpg v0.0.1/go.mod h1:kRzw3HkwxFU1mpmPP8v1WyQzwdGfmKFJ6tItnhQ67kU= github.com/gxed/hashland/murmur3 v0.0.1/go.mod h1:KjXop02n4/ckmZSnY2+HKcLud/tcmvhST0bie/0lS48= github.com/hashicorp/golang-lru v0.5.0/go.mod h1:/m3WP610KZHVQ1SGc6re/UDhFvYD7pJ4Ao+sR/qLZy8= From 0271b0965daeaf1fe39a58f71c250a3c5a26e7ba Mon Sep 17 00:00:00 2001 From: ChihYunChuang Date: Fri, 5 Nov 2021 17:05:55 +0800 Subject: [PATCH 09/10] crypto/elliptic: support more elliptic curve --- crypto/.DS_Store | Bin 8196 -> 8196 bytes .../ecpointgrouplaw/ecpointgrouplaw_test.go | 2 +- crypto/ecpointgrouplaw/point.go | 30 ++--- crypto/ecpointgrouplaw/point_test.go | 10 +- crypto/elliptic/P256.go | 113 +++++++++++++++++ crypto/elliptic/P256_test.go | 33 +++++ crypto/elliptic/P384.go | 118 ++++++++++++++++++ crypto/elliptic/ed25519_test.go | 13 +- crypto/schnorrsignature/sign_test.go | 2 + 9 files changed, 291 insertions(+), 30 deletions(-) create mode 100644 crypto/elliptic/P256.go create mode 100644 crypto/elliptic/P256_test.go create mode 100644 crypto/elliptic/P384.go diff --git a/crypto/.DS_Store b/crypto/.DS_Store index fdf6564f8bb3d4d4cfccdac3f9ce70b82315e0b4..3394e14f6a47725f1dbe8e97356bf09740ab2722 100644 GIT binary patch delta 38 ucmZp1XmOa}&&a(oU^hP__hf!Sz0FnvLX4YPgg!HEw&yv)yqR6%FFOF?I}4cr delta 224 zcmZp1XmOa}&&aV&;m2&L97#X&@@313~jYoY7RJ|E-8VWK{9W&WMNNIDn R;1#Bgg#yf**(Lt60|0TCHp2h_ diff --git a/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go b/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go index f9a80745..b5f2a7fc 100644 --- a/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go +++ b/crypto/ecpointgrouplaw/ecpointgrouplaw_test.go @@ -29,7 +29,7 @@ func TestEllipticcurve(t *testing.T) { } var ( - curveList = []elliptic.Curve{Ed25519, Secp256k1,SR25519} + curveList = []elliptic.Curve{Ed25519, Secp256k1,SR25519, P256, P384} ) var _ = Describe("Elliptic curves", func() { diff --git a/crypto/ecpointgrouplaw/point.go b/crypto/ecpointgrouplaw/point.go index d7f29315..1e78e2ef 100644 --- a/crypto/ecpointgrouplaw/point.go +++ b/crypto/ecpointgrouplaw/point.go @@ -34,6 +34,8 @@ var ( Ed25519 = elliptic.NewEd25519() Secp256k1 = elliptic.NewSecp256k1() SR25519 = elliptic.NewSR25519() + P256 = elliptic.NewP256() + P384 = elliptic.NewP384() ) // ECPoint is the struct for an elliptic curve point. @@ -106,18 +108,6 @@ func (p *ECPoint) Add(p1 *ECPoint) (*ECPoint, error) { if !isOnCurve(p1.curve, p1.x, p1.y) { return nil, ErrInvalidPoint } - - // The case : aG+(-a)G. - // minusP1 := p1.Neg() - // if minusP1.Equal(p) { - // x1 := big.NewInt(0) - // y1 := big.NewInt(1) - // x, y := p.curve.Add(x1, y1, x1, y1) - // return NewECPoint(p.curve, x, y) - // // x, y := p.curve.ScalarBaseMult(big0.Bytes()) - // // return NewECPoint(p.curve, x, y) - // // return NewIdentity(p.curve), nil - // } // The case : aG + aG = 2aG. if p1.x.Cmp(p.x) == 0 && p1.y.Cmp(p.y) == 0 { return p1.ScalarMult(big2), nil @@ -244,12 +234,10 @@ func isOnCurve(curve elliptic.Curve, x, y *big.Int) bool { func (c EcPointMessage_Curve) GetEllipticCurve() (elliptic.Curve, error) { switch c { - // case EcPointMessage_P224: - // return elliptic.P224(), nil - // case EcPointMessage_P256: - // return elliptic.P256(), nil - // case EcPointMessage_P384: - // return elliptic.P384(), nil + case EcPointMessage_P256: + return P256, nil + case EcPointMessage_P384: + return P384, nil case EcPointMessage_S256: return Secp256k1, nil case EcPointMessage_EDWARD25519: @@ -271,5 +259,11 @@ func ToCurve(c elliptic.Curve) (EcPointMessage_Curve, error) { if isSameCurve(c, SR25519) { return EcPointMessage_SR25519, nil } + if isSameCurve(c, P256) { + return EcPointMessage_P256, nil + } + if isSameCurve(c, P384) { + return EcPointMessage_P384, nil + } return 0, ErrInvalidCurve } diff --git a/crypto/ecpointgrouplaw/point_test.go b/crypto/ecpointgrouplaw/point_test.go index 89f80170..4b94cfac 100644 --- a/crypto/ecpointgrouplaw/point_test.go +++ b/crypto/ecpointgrouplaw/point_test.go @@ -417,9 +417,8 @@ var _ = Describe("Point", func() { Expect(err).Should(BeNil()) Expect(p).Should(Equal(gotPt)) }, - // Entry("P224", EcPointMessage_P224, elliptic.P224()), - // Entry("P256", EcPointMessage_P256, elliptic.P256()), - // Entry("P384", EcPointMessage_P384, elliptic.P384()), + Entry("P256", EcPointMessage_P256, P256), + Entry("P384", EcPointMessage_P384, P384), Entry("S256", EcPointMessage_S256, Secp256k1), Entry("ed25519", EcPointMessage_EDWARD25519, Ed25519), ) @@ -438,9 +437,8 @@ var _ = Describe("Point", func() { Expect(err).Should(BeNil()) Expect(p).Should(Equal(gotPt)) }, - // Entry("P224", EcPointMessage_P224, elliptic.P224()), - // Entry("P256", EcPointMessage_P256, elliptic.P256()), - // Entry("P384", EcPointMessage_P384, elliptic.P384()), + Entry("P256", EcPointMessage_P256, P256), + Entry("P384", EcPointMessage_P384, P384), Entry("S256", EcPointMessage_S256, Secp256k1), Entry("ed25519", EcPointMessage_EDWARD25519, Ed25519), ) diff --git a/crypto/elliptic/P256.go b/crypto/elliptic/P256.go new file mode 100644 index 00000000..fd03b562 --- /dev/null +++ b/crypto/elliptic/P256.go @@ -0,0 +1,113 @@ +// Copyright © 2021 AMIS Technologies +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package elliptic + +import ( + "crypto/elliptic" + "math/big" +) + +type P256 struct { + Curve + H int // Cofactor + + ellipticCurve elliptic.Curve +} + +func (p *P256) IsOnCurve(x, y *big.Int) bool { + return p.ellipticCurve.IsOnCurve(x, y) +} + +func (p *P256) Params() *elliptic.CurveParams { + return p.ellipticCurve.Params() +} + +func (p *P256) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { + return p.ellipticCurve.Add(x1, y1, x2, y2) +} + +func (p *P256) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { + return p.ellipticCurve.Double(x1, y1) +} + +func (p *P256) ScalarMult(x1, y1 *big.Int, k []byte) (*big.Int, *big.Int) { + return p.ellipticCurve.ScalarMult(x1, y1, k) +} + +func (p *P256) ScalarBaseMult(k []byte) (x, y *big.Int) { + return p.ellipticCurve.ScalarBaseMult(k) +} + +// Warn: does not deal with the original point +func (p *P256) Neg(x, y *big.Int) (*big.Int, *big.Int) { + NegY := new(big.Int).Neg(y) + return new(big.Int).Set(x), NegY.Mod(NegY, p.ellipticCurve.Params().P) +} + +func (p *P256) Equal(x1, y1, x2, y2 *big.Int) bool { + if x1 == nil || x2 == nil || y1 == nil || y2 == nil { + return false + } + if p.IsIdentity(x1, y1) && p.IsIdentity(x2, y2) { + return true + } + isOnCurve1 := p.IsOnCurve(x1, y1) + isOnCurve2 := p.IsOnCurve(x2, y2) + if !isOnCurve1 || !isOnCurve2 { + return false + } + if x1.Cmp(x2) == 0 && y1.Cmp(y2) == 0 { + return true + } + return false +} + +func (p *P256) IsIdentity(x, y *big.Int) bool { + return x.Cmp(big0) == 0 && y.Cmp(big0) == 0 +} + +func (p *P256) NewIdentity() (*big.Int, *big.Int) { + return big.NewInt(0), big.NewInt(0) +} + +func (p *P256) Encode(x *big.Int, y *big.Int) ([]byte, error) { + if x.Cmp(p.Params().P) > 0 || y.Cmp(p.Params().P) > 0 { + return nil, ErrInvalidPoint + } + + xByte := x.FillBytes(make([]byte, 32)) + yByte := y.FillBytes(make([]byte, 32)) + return append(xByte, yByte...), nil +} + +func (p *P256) Cofactor() int { + return p.H +} + +func (p *P256) Decode(input []byte) (*big.Int, *big.Int, error) { + if len(input) != 64 { + return nil, nil, ErrInvalidPoint + } + + return new(big.Int).SetBytes(input[0:32]), new(big.Int).SetBytes(input[32:]), nil +} + +// WARN: Cofactor should be 1 +func NewP256() *P256 { + return &P256{ + H: 1, + ellipticCurve: elliptic.P256(), + } +} diff --git a/crypto/elliptic/P256_test.go b/crypto/elliptic/P256_test.go new file mode 100644 index 00000000..93499c3f --- /dev/null +++ b/crypto/elliptic/P256_test.go @@ -0,0 +1,33 @@ +// Copyright © 2021 AMIS Technologies +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. +package elliptic + +import ( + "math/big" + + . "github.com/onsi/ginkgo" + . "github.com/onsi/gomega" +) + +var _ = Describe("ed25519", func() { + Context("Negative Point", func() { + It("It is OK", func() { + ed25519 := NewEd25519() + negX, negY := ed25519.Neg(ed25519.Params().Gx, ed25519.Params().Gy) + scalX, scalY := ed25519.ScalarBaseMult(new(big.Int).Sub(ed25519.Params().N, big.NewInt(1)).Bytes()) + Expect(negX.Cmp(scalX) == 0).Should(BeTrue()) + Expect(negY.Cmp(scalY) == 0).Should(BeTrue()) + }) + }) +}) diff --git a/crypto/elliptic/P384.go b/crypto/elliptic/P384.go new file mode 100644 index 00000000..14ae5809 --- /dev/null +++ b/crypto/elliptic/P384.go @@ -0,0 +1,118 @@ +// Copyright © 2021 AMIS Technologies +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package elliptic + +import ( + "crypto/elliptic" + "math/big" +) + +const ( + BIGLENGTHP = 48 +) + +type P384 struct { + Curve + H int // Cofactor + + ellipticCurve elliptic.Curve +} + +func (p *P384) IsOnCurve(x, y *big.Int) bool { + return p.ellipticCurve.IsOnCurve(x, y) +} + +func (p *P384) Params() *elliptic.CurveParams { + return p.ellipticCurve.Params() +} + +func (p *P384) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { + return p.ellipticCurve.Add(x1, y1, x2, y2) +} + +func (p *P384) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { + return p.ellipticCurve.Double(x1, y1) +} + +func (p *P384) ScalarMult(x1, y1 *big.Int, k []byte) (*big.Int, *big.Int) { + return p.ellipticCurve.ScalarMult(x1, y1, k) +} + +func (p *P384) ScalarBaseMult(k []byte) (x, y *big.Int) { + return p.ellipticCurve.ScalarBaseMult(k) +} + +// Warn: does not deal with the original point +func (p *P384) Neg(x, y *big.Int) (*big.Int, *big.Int) { + NegY := new(big.Int).Neg(y) + return new(big.Int).Set(x), NegY.Mod(NegY, p.ellipticCurve.Params().P) +} + +func (p *P384) Equal(x1, y1, x2, y2 *big.Int) bool { + if x1 == nil || x2 == nil || y1 == nil || y2 == nil { + return false + } + if p.IsIdentity(x1, y1) && p.IsIdentity(x2, y2) { + return true + } + isOnCurve1 := p.IsOnCurve(x1, y1) + isOnCurve2 := p.IsOnCurve(x2, y2) + if !isOnCurve1 || !isOnCurve2 { + return false + } + if x1.Cmp(x2) == 0 && y1.Cmp(y2) == 0 { + return true + } + return false +} + +func (p *P384) IsIdentity(x, y *big.Int) bool { + return x.Cmp(big0) == 0 && y.Cmp(big0) == 0 +} + +func (p *P384) NewIdentity() (*big.Int, *big.Int) { + return big.NewInt(0), big.NewInt(0) +} + +func (p *P384) Encode(x *big.Int, y *big.Int) ([]byte, error) { + if x.Cmp(p.Params().P) > 0 || y.Cmp(p.Params().P) > 0 { + return nil, ErrInvalidPoint + } + // 48 = 384/8 (i.e. the bit length of para.P) + xByte := x.FillBytes(make([]byte, BIGLENGTHP)) + yByte := y.FillBytes(make([]byte, BIGLENGTHP)) + return append(xByte, yByte...), nil +} + +func (p *P384) Cofactor() int { + return p.H +} + +func (p *P384) Decode(input []byte) (*big.Int, *big.Int, error) { + // 96 = BIGLENGTHP*2 + if len(input) != 96 { + return nil, nil, ErrInvalidPoint + } + + return new(big.Int).SetBytes(input[0:BIGLENGTHP]), new(big.Int).SetBytes(input[BIGLENGTHP:]), nil +} + +// WARN: Cofactor should be 1 +func NewP384() *P384 { + return &P384{ + H: 1, + ellipticCurve: elliptic.P384(), + } +} diff --git a/crypto/elliptic/ed25519_test.go b/crypto/elliptic/ed25519_test.go index 93499c3f..931315c6 100644 --- a/crypto/elliptic/ed25519_test.go +++ b/crypto/elliptic/ed25519_test.go @@ -14,18 +14,21 @@ package elliptic import ( + "fmt" "math/big" . "github.com/onsi/ginkgo" . "github.com/onsi/gomega" ) -var _ = Describe("ed25519", func() { +var _ = Describe("P256", func() { Context("Negative Point", func() { - It("It is OK", func() { - ed25519 := NewEd25519() - negX, negY := ed25519.Neg(ed25519.Params().Gx, ed25519.Params().Gy) - scalX, scalY := ed25519.ScalarBaseMult(new(big.Int).Sub(ed25519.Params().N, big.NewInt(1)).Bytes()) + FIt("It is OK", func() { + P256 := NewP256() + negX, negY := P256.Neg(P256.Params().Gx, P256.Params().Gy) + scalX, scalY := P256.ScalarBaseMult(new(big.Int).Sub(P256.Params().N, big.NewInt(1)).Bytes()) + fmt.Println( P256.Add(P256.Params().Gx, P256.Params().Gy, scalX, scalY ) ) + Expect(negX.Cmp(scalX) == 0).Should(BeTrue()) Expect(negY.Cmp(scalY) == 0).Should(BeTrue()) }) diff --git a/crypto/schnorrsignature/sign_test.go b/crypto/schnorrsignature/sign_test.go index 35a9100f..340bcd24 100644 --- a/crypto/schnorrsignature/sign_test.go +++ b/crypto/schnorrsignature/sign_test.go @@ -15,6 +15,7 @@ package schnorrsignature import ( + "crypto/rsa" "math/big" "testing" @@ -38,6 +39,7 @@ var ( var _ = Describe("Sign test", func() { It("Correct case", func() { + rsa.GenerateKey() nthreshold := uint32(2) bk1 := birkhoffinterpolation.NewBkParameter(big.NewInt(1), 0) bk2 := birkhoffinterpolation.NewBkParameter(big.NewInt(2), 0) From 2948b8651624fd5de82c2c60babf707685a06577 Mon Sep 17 00:00:00 2001 From: ChihYunChuang Date: Fri, 5 Nov 2021 17:06:48 +0800 Subject: [PATCH 10/10] crypto/schnorrsignature: fix sign --- crypto/schnorrsignature/sign_test.go | 2 -- 1 file changed, 2 deletions(-) diff --git a/crypto/schnorrsignature/sign_test.go b/crypto/schnorrsignature/sign_test.go index 340bcd24..35a9100f 100644 --- a/crypto/schnorrsignature/sign_test.go +++ b/crypto/schnorrsignature/sign_test.go @@ -15,7 +15,6 @@ package schnorrsignature import ( - "crypto/rsa" "math/big" "testing" @@ -39,7 +38,6 @@ var ( var _ = Describe("Sign test", func() { It("Correct case", func() { - rsa.GenerateKey() nthreshold := uint32(2) bk1 := birkhoffinterpolation.NewBkParameter(big.NewInt(1), 0) bk2 := birkhoffinterpolation.NewBkParameter(big.NewInt(2), 0)