From 9b11ae8280bdbec3d8a64eacd1085864a25b933a Mon Sep 17 00:00:00 2001 From: arnaucube Date: Sat, 24 Nov 2018 01:43:21 +0100 Subject: [PATCH] bn128 moved to it's own repository --- README.md | 174 +------------------ bn128/README.md | 174 +------------------ bn128/bn128.go | 407 -------------------------------------------- bn128/bn128_test.go | 65 ------- bn128/fq.go | 129 -------------- bn128/fq12.go | 161 ------------------ bn128/fq2.go | 154 ----------------- bn128/fq6.go | 192 --------------------- bn128/fqn_test.go | 160 ----------------- bn128/g1.go | 191 --------------------- bn128/g1_test.go | 31 ---- bn128/g2.go | 221 ------------------------ bn128/g2_test.go | 24 --- 13 files changed, 4 insertions(+), 2079 deletions(-) delete mode 100644 bn128/bn128.go delete mode 100644 bn128/bn128_test.go delete mode 100644 bn128/fq.go delete mode 100644 bn128/fq12.go delete mode 100644 bn128/fq2.go delete mode 100644 bn128/fq6.go delete mode 100644 bn128/fqn_test.go delete mode 100644 bn128/g1.go delete mode 100644 bn128/g1_test.go delete mode 100644 bn128/g2.go delete mode 100644 bn128/g2_test.go diff --git a/README.md b/README.md index bc021f7..f566e66 100644 --- a/README.md +++ b/README.md @@ -419,178 +419,8 @@ if verified { ## Bn128 - -This is implemented followng the info and the implementations from: -- `Multiplication and Squaring on Pairing-Friendly -Fields`, Augusto Jun Devegili, Colm Ó hÉigeartaigh, Michael Scott, and Ricardo Dahab https://pdfs.semanticscholar.org/3e01/de88d7428076b2547b60072088507d881bf1.pdf -- `Optimal Pairings`, Frederik Vercauteren https://www.cosic.esat.kuleuven.be/bcrypt/optimal.pdf , https://eprint.iacr.org/2008/096.pdf -- `Double-and-Add with Relative Jacobian -Coordinates`, Björn Fay https://eprint.iacr.org/2014/1014.pdf -- `Fast and Regular Algorithms for Scalar Multiplication -over Elliptic Curves`, Matthieu Rivain https://eprint.iacr.org/2011/338.pdf -- `High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves`, Jean-Luc Beuchat, Jorge E. González-Díaz, Shigeo Mitsunari, Eiji Okamoto, Francisco Rodríguez-Henríquez, and Tadanori Teruya https://eprint.iacr.org/2010/354.pdf -- `New software speed records for cryptographic pairings`, Michael Naehrig, Ruben Niederhagen, Peter Schwabe https://cryptojedi.org/papers/dclxvi-20100714.pdf -- https://github.com/zcash/zcash/tree/master/src/snark -- https://github.com/iden3/snarkjs -- https://github.com/ethereum/py_ecc/tree/master/py_ecc/bn128 - -- [x] Fq, Fq2, Fq6, Fq12 operations -- [x] G1, G2 operations -- [x] preparePairing -- [x] PreComupteG1, PreComupteG2 -- [x] DoubleStep, AddStep -- [x] MillerLoop -- [x] Pairing - - -#### Usage -First let's assume that we have these three basic functions to convert integer compositions to big integer compositions: -```go -func iToBig(a int) *big.Int { - return big.NewInt(int64(a)) -} - -func iiToBig(a, b int) [2]*big.Int { - return [2]*big.Int{iToBig(a), iToBig(b)} -} - -func iiiToBig(a, b int) [2]*big.Int { - return [2]*big.Int{iToBig(a), iToBig(b)} -} -``` - - -- Pairing -```go -bn128, err := NewBn128() -assert.Nil(t, err) - -big25 := big.NewInt(int64(25)) -big30 := big.NewInt(int64(30)) - -g1a := bn128.G1.MulScalar(bn128.G1.G, big25) -g2a := bn128.G2.MulScalar(bn128.G2.G, big30) - -g1b := bn128.G1.MulScalar(bn128.G1.G, big30) -g2b := bn128.G2.MulScalar(bn128.G2.G, big25) - -pA, err := bn128.Pairing(g1a, g2a) -assert.Nil(t, err) -pB, err := bn128.Pairing(g1b, g2b) -assert.Nil(t, err) -assert.True(t, bn128.Fq12.Equal(pA, pB)) -``` - -- Finite Fields (1, 2, 6, 12) operations -```go -// new finite field of order 1 -fq1 := NewFq(iToBig(7)) - -// basic operations of finite field 1 -res := fq1.Add(iToBig(4), iToBig(4)) -res = fq1.Double(iToBig(5)) -res = fq1.Sub(iToBig(5), iToBig(7)) -res = fq1.Neg(iToBig(5)) -res = fq1.Mul(iToBig(5), iToBig(11)) -res = fq1.Inverse(iToBig(4)) -res = fq1.Square(iToBig(5)) - -// new finite field of order 2 -nonResidueFq2str := "-1" // i/j -nonResidueFq2, ok := new(big.Int).SetString(nonResidueFq2str, 10) -fq2 := Fq2{fq1, nonResidueFq2} -nonResidueFq6 := iiToBig(9, 1) - -// basic operations of finite field of order 2 -res := fq2.Add(iiToBig(4, 4), iiToBig(3, 4)) -res = fq2.Double(iiToBig(5, 3)) -res = fq2.Sub(iiToBig(5, 3), iiToBig(7, 2)) -res = fq2.Neg(iiToBig(4, 4)) -res = fq2.Mul(iiToBig(4, 4), iiToBig(3, 4)) -res = fq2.Inverse(iiToBig(4, 4)) -res = fq2.Div(iiToBig(4, 4), iiToBig(3, 4)) -res = fq2.Square(iiToBig(4, 4)) - - -// new finite field of order 6 -nonResidueFq6 := iiToBig(9, 1) // TODO -fq6 := Fq6{fq2, nonResidueFq6} - -// define two new values of Finite Field 6, in order to be able to perform the operations -a := [3][2]*big.Int{ - iiToBig(1, 2), - iiToBig(3, 4), - iiToBig(5, 6)} -b := [3][2]*big.Int{ - iiToBig(12, 11), - iiToBig(10, 9), - iiToBig(8, 7)} - -// basic operations of finite field order 6 -res := fq6.Add(a, b) -res = fq6.Sub(a, b) -res = fq6.Mul(a, b) -divRes := fq6.Div(mulRes, b) - - -// new finite field of order 12 -q, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10) // i -if !ok { - fmt.Println("error parsing string to big integer") -} - -fq1 := NewFq(q) -nonResidueFq2, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208582", 10) // i -assert.True(t, ok) -nonResidueFq6 := iiToBig(9, 1) - -fq2 := Fq2{fq1, nonResidueFq2} -fq6 := Fq6{fq2, nonResidueFq6} -fq12 := Fq12{fq6, fq2, nonResidueFq6} - -``` - -- G1 operations -```go -bn128, err := NewBn128() -assert.Nil(t, err) - -r1 := big.NewInt(int64(33)) -r2 := big.NewInt(int64(44)) - -gr1 := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(r1)) -gr2 := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(r2)) - -grsum1 := bn128.G1.Add(gr1, gr2) -r1r2 := bn128.Fq1.Add(r1, r2) -grsum2 := bn128.G1.MulScalar(bn128.G1.G, r1r2) - -a := bn128.G1.Affine(grsum1) -b := bn128.G1.Affine(grsum2) -assert.Equal(t, a, b) -assert.Equal(t, "0x2f978c0ab89ebaa576866706b14787f360c4d6c3869efe5a72f7c3651a72ff00", utils.BytesToHex(a[0].Bytes())) -assert.Equal(t, "0x12e4ba7f0edca8b4fa668fe153aebd908d322dc26ad964d4cd314795844b62b2", utils.BytesToHex(a[1].Bytes())) -``` - -- G2 operations -```go -bn128, err := NewBn128() -assert.Nil(t, err) - -r1 := big.NewInt(int64(33)) -r2 := big.NewInt(int64(44)) - -gr1 := bn128.G2.MulScalar(bn128.G2.G, bn128.Fq1.Copy(r1)) -gr2 := bn128.G2.MulScalar(bn128.G2.G, bn128.Fq1.Copy(r2)) - -grsum1 := bn128.G2.Add(gr1, gr2) -r1r2 := bn128.Fq1.Add(r1, r2) -grsum2 := bn128.G2.MulScalar(bn128.G2.G, r1r2) - -a := bn128.G2.Affine(grsum1) -b := bn128.G2.Affine(grsum2) -assert.Equal(t, a, b) -``` +Implementation of the bn128 pairing. +Code moved to https://github.com/arnaucube/bn128 --- diff --git a/bn128/README.md b/bn128/README.md index 73bcf97..582e102 100644 --- a/bn128/README.md +++ b/bn128/README.md @@ -1,173 +1,3 @@ ## Bn128 - -This is implemented followng the info and the implementations from: -- `Multiplication and Squaring on Pairing-Friendly -Fields`, Augusto Jun Devegili, Colm Ó hÉigeartaigh, Michael Scott, and Ricardo Dahab https://pdfs.semanticscholar.org/3e01/de88d7428076b2547b60072088507d881bf1.pdf -- `Optimal Pairings`, Frederik Vercauteren https://www.cosic.esat.kuleuven.be/bcrypt/optimal.pdf , https://eprint.iacr.org/2008/096.pdf -- `Double-and-Add with Relative Jacobian -Coordinates`, Björn Fay https://eprint.iacr.org/2014/1014.pdf -- `Fast and Regular Algorithms for Scalar Multiplication -over Elliptic Curves`, Matthieu Rivain https://eprint.iacr.org/2011/338.pdf -- `High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves`, Jean-Luc Beuchat, Jorge E. González-Díaz, Shigeo Mitsunari, Eiji Okamoto, Francisco Rodríguez-Henríquez, and Tadanori Teruya https://eprint.iacr.org/2010/354.pdf -- `New software speed records for cryptographic pairings`, Michael Naehrig, Ruben Niederhagen, Peter Schwabe https://cryptojedi.org/papers/dclxvi-20100714.pdf -- https://github.com/zcash/zcash/tree/master/src/snark -- https://github.com/iden3/snarkjs -- https://github.com/ethereum/py_ecc/tree/master/py_ecc/bn128 - -- [x] Fq, Fq2, Fq6, Fq12 operations -- [x] G1, G2 operations -- [x] preparePairing -- [x] PreComupteG1, PreComupteG2 -- [x] DoubleStep, AddStep -- [x] MillerLoop -- [x] Pairing - - -#### Usage -First let's assume that we have these three basic functions to convert integer compositions to big integer compositions: -```go -func iToBig(a int) *big.Int { - return big.NewInt(int64(a)) -} - -func iiToBig(a, b int) [2]*big.Int { - return [2]*big.Int{iToBig(a), iToBig(b)} -} - -func iiiToBig(a, b int) [2]*big.Int { - return [2]*big.Int{iToBig(a), iToBig(b)} -} -``` - - -- Pairing -```go -bn128, err := NewBn128() -assert.Nil(t, err) - -big25 := big.NewInt(int64(25)) -big30 := big.NewInt(int64(30)) - -g1a := bn128.G1.MulScalar(bn128.G1.G, big25) -g2a := bn128.G2.MulScalar(bn128.G2.G, big30) - -g1b := bn128.G1.MulScalar(bn128.G1.G, big30) -g2b := bn128.G2.MulScalar(bn128.G2.G, big25) - -pA, err := bn128.Pairing(g1a, g2a) -assert.Nil(t, err) -pB, err := bn128.Pairing(g1b, g2b) -assert.Nil(t, err) -assert.True(t, bn128.Fq12.Equal(pA, pB)) -``` - -- Finite Fields (1, 2, 6, 12) operations -```go -// new finite field of order 1 -fq1 := NewFq(iToBig(7)) - -// basic operations of finite field 1 -res := fq1.Add(iToBig(4), iToBig(4)) -res = fq1.Double(iToBig(5)) -res = fq1.Sub(iToBig(5), iToBig(7)) -res = fq1.Neg(iToBig(5)) -res = fq1.Mul(iToBig(5), iToBig(11)) -res = fq1.Inverse(iToBig(4)) -res = fq1.Square(iToBig(5)) - -// new finite field of order 2 -nonResidueFq2str := "-1" // i/j -nonResidueFq2, ok := new(big.Int).SetString(nonResidueFq2str, 10) -fq2 := Fq2{fq1, nonResidueFq2} -nonResidueFq6 := iiToBig(9, 1) - -// basic operations of finite field of order 2 -res := fq2.Add(iiToBig(4, 4), iiToBig(3, 4)) -res = fq2.Double(iiToBig(5, 3)) -res = fq2.Sub(iiToBig(5, 3), iiToBig(7, 2)) -res = fq2.Neg(iiToBig(4, 4)) -res = fq2.Mul(iiToBig(4, 4), iiToBig(3, 4)) -res = fq2.Inverse(iiToBig(4, 4)) -res = fq2.Div(iiToBig(4, 4), iiToBig(3, 4)) -res = fq2.Square(iiToBig(4, 4)) - - -// new finite field of order 6 -nonResidueFq6 := iiToBig(9, 1) // TODO -fq6 := Fq6{fq2, nonResidueFq6} - -// define two new values of Finite Field 6, in order to be able to perform the operations -a := [3][2]*big.Int{ - iiToBig(1, 2), - iiToBig(3, 4), - iiToBig(5, 6)} -b := [3][2]*big.Int{ - iiToBig(12, 11), - iiToBig(10, 9), - iiToBig(8, 7)} - -// basic operations of finite field order 6 -res := fq6.Add(a, b) -res = fq6.Sub(a, b) -res = fq6.Mul(a, b) -divRes := fq6.Div(mulRes, b) - - -// new finite field of order 12 -q, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10) // i -if !ok { - fmt.Println("error parsing string to big integer") -} - -fq1 := NewFq(q) -nonResidueFq2, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208582", 10) // i -assert.True(t, ok) -nonResidueFq6 := iiToBig(9, 1) - -fq2 := Fq2{fq1, nonResidueFq2} -fq6 := Fq6{fq2, nonResidueFq6} -fq12 := Fq12{fq6, fq2, nonResidueFq6} - -``` - -- G1 operations -```go -bn128, err := NewBn128() -assert.Nil(t, err) - -r1 := big.NewInt(int64(33)) -r2 := big.NewInt(int64(44)) - -gr1 := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(r1)) -gr2 := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(r2)) - -grsum1 := bn128.G1.Add(gr1, gr2) -r1r2 := bn128.Fq1.Add(r1, r2) -grsum2 := bn128.G1.MulScalar(bn128.G1.G, r1r2) - -a := bn128.G1.Affine(grsum1) -b := bn128.G1.Affine(grsum2) -assert.Equal(t, a, b) -assert.Equal(t, "0x2f978c0ab89ebaa576866706b14787f360c4d6c3869efe5a72f7c3651a72ff00", utils.BytesToHex(a[0].Bytes())) -assert.Equal(t, "0x12e4ba7f0edca8b4fa668fe153aebd908d322dc26ad964d4cd314795844b62b2", utils.BytesToHex(a[1].Bytes())) -``` - -- G2 operations -```go -bn128, err := NewBn128() -assert.Nil(t, err) - -r1 := big.NewInt(int64(33)) -r2 := big.NewInt(int64(44)) - -gr1 := bn128.G2.MulScalar(bn128.G2.G, bn128.Fq1.Copy(r1)) -gr2 := bn128.G2.MulScalar(bn128.G2.G, bn128.Fq1.Copy(r2)) - -grsum1 := bn128.G2.Add(gr1, gr2) -r1r2 := bn128.Fq1.Add(r1, r2) -grsum2 := bn128.G2.MulScalar(bn128.G2.G, r1r2) - -a := bn128.G2.Affine(grsum1) -b := bn128.G2.Affine(grsum2) -assert.Equal(t, a, b) -``` +Implementation of the bn128 pairing. +Code moved to https://github.com/arnaucube/bn128 diff --git a/bn128/bn128.go b/bn128/bn128.go deleted file mode 100644 index 95a4ac8..0000000 --- a/bn128/bn128.go +++ /dev/null @@ -1,407 +0,0 @@ -package bn128 - -import ( - "bytes" - "errors" - "math/big" -) - -type Bn128 struct { - Q *big.Int - Gg1 [2]*big.Int - Gg2 [2][2]*big.Int - NonResidueFq2 *big.Int - NonResidueFq6 [2]*big.Int - Fq1 Fq - Fq2 Fq2 - Fq6 Fq6 - Fq12 Fq12 - G1 G1 - G2 G2 - LoopCount *big.Int - LoopCountNeg bool - - TwoInv *big.Int - CoefB *big.Int - TwistCoefB [2]*big.Int - Twist [2]*big.Int - FrobeniusCoeffsC11 *big.Int - TwistMulByQX [2]*big.Int - TwistMulByQY [2]*big.Int - FinalExp *big.Int -} - -func NewBn128() (Bn128, error) { - var b Bn128 - q, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10) // i - if !ok { - return b, errors.New("err with q") - } - b.Q = q - - b.Gg1 = [2]*big.Int{ - big.NewInt(int64(1)), - big.NewInt(int64(2)), - } - - g2_00, ok := new(big.Int).SetString("10857046999023057135944570762232829481370756359578518086990519993285655852781", 10) - if !ok { - return b, errors.New("err with g2_00") - } - g2_01, ok := new(big.Int).SetString("11559732032986387107991004021392285783925812861821192530917403151452391805634", 10) - if !ok { - return b, errors.New("err with g2_00") - } - g2_10, ok := new(big.Int).SetString("8495653923123431417604973247489272438418190587263600148770280649306958101930", 10) - if !ok { - return b, errors.New("err with g2_00") - } - g2_11, ok := new(big.Int).SetString("4082367875863433681332203403145435568316851327593401208105741076214120093531", 10) - if !ok { - return b, errors.New("err with g2_00") - } - - b.Gg2 = [2][2]*big.Int{ - [2]*big.Int{ - g2_00, - g2_01, - }, - [2]*big.Int{ - g2_10, - g2_11, - }, - } - - b.Fq1 = NewFq(q) - b.NonResidueFq2, ok = new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208582", 10) // i - if !ok { - return b, errors.New("err with nonResidueFq2") - } - b.NonResidueFq6 = [2]*big.Int{ - big.NewInt(int64(9)), - big.NewInt(int64(1)), - } - - b.Fq2 = NewFq2(b.Fq1, b.NonResidueFq2) - b.Fq6 = NewFq6(b.Fq2, b.NonResidueFq6) - b.Fq12 = NewFq12(b.Fq6, b.Fq2, b.NonResidueFq6) - - b.G1 = NewG1(b.Fq1, b.Gg1) - b.G2 = NewG2(b.Fq2, b.Gg2) - - err := b.preparePairing() - if err != nil { - return b, err - } - - return b, nil -} - -func BigIsOdd(n *big.Int) bool { - one := big.NewInt(int64(1)) - and := new(big.Int).And(n, one) - return bytes.Equal(and.Bytes(), big.NewInt(int64(1)).Bytes()) -} - -func (bn128 *Bn128) preparePairing() error { - var ok bool - bn128.LoopCount, ok = new(big.Int).SetString("29793968203157093288", 10) - if !ok { - return errors.New("err with LoopCount from string") - } - - bn128.LoopCountNeg = false - - bn128.TwoInv = bn128.Fq1.Inverse(big.NewInt(int64(2))) - - bn128.CoefB = big.NewInt(int64(3)) - bn128.Twist = [2]*big.Int{ - big.NewInt(int64(9)), - big.NewInt(int64(1)), - } - bn128.TwistCoefB = bn128.Fq2.MulScalar(bn128.Fq2.Inverse(bn128.Twist), bn128.CoefB) - - bn128.FrobeniusCoeffsC11, ok = new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208582", 10) - if !ok { - return errors.New("error parsing frobeniusCoeffsC11") - } - - a, ok := new(big.Int).SetString("21575463638280843010398324269430826099269044274347216827212613867836435027261", 10) - if !ok { - return errors.New("error parsing a") - } - b, ok := new(big.Int).SetString("10307601595873709700152284273816112264069230130616436755625194854815875713954", 10) - if !ok { - return errors.New("error parsing b") - } - bn128.TwistMulByQX = [2]*big.Int{ - a, - b, - } - - a, ok = new(big.Int).SetString("2821565182194536844548159561693502659359617185244120367078079554186484126554", 10) - if !ok { - return errors.New("error parsing a") - } - b, ok = new(big.Int).SetString("3505843767911556378687030309984248845540243509899259641013678093033130930403", 10) - if !ok { - return errors.New("error parsing b") - } - bn128.TwistMulByQY = [2]*big.Int{ - a, - b, - } - - bn128.FinalExp, ok = new(big.Int).SetString("552484233613224096312617126783173147097382103762957654188882734314196910839907541213974502761540629817009608548654680343627701153829446747810907373256841551006201639677726139946029199968412598804882391702273019083653272047566316584365559776493027495458238373902875937659943504873220554161550525926302303331747463515644711876653177129578303191095900909191624817826566688241804408081892785725967931714097716709526092261278071952560171111444072049229123565057483750161460024353346284167282452756217662335528813519139808291170539072125381230815729071544861602750936964829313608137325426383735122175229541155376346436093930287402089517426973178917569713384748081827255472576937471496195752727188261435633271238710131736096299798168852925540549342330775279877006784354801422249722573783561685179618816480037695005515426162362431072245638324744480", 10) - if !ok { - return errors.New("error parsing finalExp") - } - - return nil - -} - -func (bn128 Bn128) Pairing(p1 [3]*big.Int, p2 [3][2]*big.Int) ([2][3][2]*big.Int, error) { - pre1 := bn128.PreComputeG1(p1) - pre2, err := bn128.PreComputeG2(p2) - if err != nil { - return [2][3][2]*big.Int{}, err - } - - r1 := bn128.MillerLoop(pre1, pre2) - res := bn128.FinalExponentiation(r1) - return res, nil -} - -type AteG1Precomp struct { - Px *big.Int - Py *big.Int -} - -func (bn128 Bn128) PreComputeG1(p [3]*big.Int) AteG1Precomp { - pCopy := bn128.G1.Affine(p) - res := AteG1Precomp{ - Px: pCopy[0], - Py: pCopy[1], - } - return res -} - -type EllCoeffs struct { - Ell0 [2]*big.Int - EllVW [2]*big.Int - EllVV [2]*big.Int -} -type AteG2Precomp struct { - Qx [2]*big.Int - Qy [2]*big.Int - Coeffs []EllCoeffs -} - -func (bn128 Bn128) PreComputeG2(p [3][2]*big.Int) (AteG2Precomp, error) { - qCopy := bn128.G2.Affine(p) - res := AteG2Precomp{ - qCopy[0], - qCopy[1], - []EllCoeffs{}, - } - r := [3][2]*big.Int{ - bn128.Fq2.Copy(qCopy[0]), - bn128.Fq2.Copy(qCopy[1]), - bn128.Fq2.One(), - } - var c EllCoeffs - for i := bn128.LoopCount.BitLen() - 2; i >= 0; i-- { - bit := bn128.LoopCount.Bit(i) - - c, r = bn128.DoublingStep(r) - res.Coeffs = append(res.Coeffs, c) - if bit == 1 { - c, r = bn128.MixedAdditionStep(qCopy, r) - res.Coeffs = append(res.Coeffs, c) - } - } - - q1 := bn128.G2.Affine(bn128.G2MulByQ(qCopy)) - if !bn128.Fq2.Equal(q1[2], bn128.Fq2.One()) { - return res, errors.New("q1[2] != Fq2.One") - } - q2 := bn128.G2.Affine(bn128.G2MulByQ(q1)) - if !bn128.Fq2.Equal(q2[2], bn128.Fq2.One()) { - return res, errors.New("q2[2] != Fq2.One") - } - - if bn128.LoopCountNeg { - r[1] = bn128.Fq2.Neg(r[1]) - } - q2[1] = bn128.Fq2.Neg(q2[1]) - - c, r = bn128.MixedAdditionStep(q1, r) - res.Coeffs = append(res.Coeffs, c) - - c, r = bn128.MixedAdditionStep(q2, r) - res.Coeffs = append(res.Coeffs, c) - - return res, nil -} - -func (bn128 Bn128) DoublingStep(current [3][2]*big.Int) (EllCoeffs, [3][2]*big.Int) { - x := current[0] - y := current[1] - z := current[2] - - a := bn128.Fq2.MulScalar(bn128.Fq2.Mul(x, y), bn128.TwoInv) - b := bn128.Fq2.Square(y) - c := bn128.Fq2.Square(z) - d := bn128.Fq2.Add(c, bn128.Fq2.Add(c, c)) - e := bn128.Fq2.Mul(bn128.TwistCoefB, d) - f := bn128.Fq2.Add(e, bn128.Fq2.Add(e, e)) - g := bn128.Fq2.MulScalar(bn128.Fq2.Add(b, f), bn128.TwoInv) - h := bn128.Fq2.Sub( - bn128.Fq2.Square(bn128.Fq2.Add(y, z)), - bn128.Fq2.Add(b, c)) - i := bn128.Fq2.Sub(e, b) - j := bn128.Fq2.Square(x) - eSqr := bn128.Fq2.Square(e) - current[0] = bn128.Fq2.Mul(a, bn128.Fq2.Sub(b, f)) - current[1] = bn128.Fq2.Sub(bn128.Fq2.Sub(bn128.Fq2.Square(g), eSqr), - bn128.Fq2.Add(eSqr, eSqr)) - current[2] = bn128.Fq2.Mul(b, h) - res := EllCoeffs{ - Ell0: bn128.Fq2.Mul(i, bn128.Twist), - EllVW: bn128.Fq2.Neg(h), - EllVV: bn128.Fq2.Add(j, bn128.Fq2.Add(j, j)), - } - - return res, current -} - -func (bn128 Bn128) MixedAdditionStep(base, current [3][2]*big.Int) (EllCoeffs, [3][2]*big.Int) { - x1 := current[0] - y1 := current[1] - z1 := current[2] - x2 := base[0] - y2 := base[1] - - d := bn128.Fq2.Sub(x1, bn128.Fq2.Mul(x2, z1)) - e := bn128.Fq2.Sub(y1, bn128.Fq2.Mul(y2, z1)) - f := bn128.Fq2.Square(d) - g := bn128.Fq2.Square(e) - h := bn128.Fq2.Mul(d, f) - i := bn128.Fq2.Mul(x1, f) - j := bn128.Fq2.Sub( - bn128.Fq2.Add(h, bn128.Fq2.Mul(z1, g)), - bn128.Fq2.Add(i, i)) - - current[0] = bn128.Fq2.Mul(d, j) - current[1] = bn128.Fq2.Sub( - bn128.Fq2.Mul(e, bn128.Fq2.Sub(i, j)), - bn128.Fq2.Mul(h, y1)) - current[2] = bn128.Fq2.Mul(z1, h) - - coef := EllCoeffs{ - Ell0: bn128.Fq2.Mul( - bn128.Twist, - bn128.Fq2.Sub( - bn128.Fq2.Mul(e, x2), - bn128.Fq2.Mul(d, y2))), - EllVW: d, - EllVV: bn128.Fq2.Neg(e), - } - return coef, current -} -func (bn128 Bn128) G2MulByQ(p [3][2]*big.Int) [3][2]*big.Int { - fmx := [2]*big.Int{ - p[0][0], - bn128.Fq1.Mul(p[0][1], bn128.Fq1.Copy(bn128.FrobeniusCoeffsC11)), - } - fmy := [2]*big.Int{ - p[1][0], - bn128.Fq1.Mul(p[1][1], bn128.Fq1.Copy(bn128.FrobeniusCoeffsC11)), - } - fmz := [2]*big.Int{ - p[2][0], - bn128.Fq1.Mul(p[2][1], bn128.Fq1.Copy(bn128.FrobeniusCoeffsC11)), - } - - return [3][2]*big.Int{ - bn128.Fq2.Mul(bn128.TwistMulByQX, fmx), - bn128.Fq2.Mul(bn128.TwistMulByQY, fmy), - fmz, - } -} - -func (bn128 Bn128) MillerLoop(pre1 AteG1Precomp, pre2 AteG2Precomp) [2][3][2]*big.Int { - // https://cryptojedi.org/papers/dclxvi-20100714.pdf - // https://eprint.iacr.org/2008/096.pdf - - idx := 0 - var c EllCoeffs - f := bn128.Fq12.One() - - for i := bn128.LoopCount.BitLen() - 2; i >= 0; i-- { - bit := bn128.LoopCount.Bit(i) - - c = pre2.Coeffs[idx] - idx++ - f = bn128.Fq12.Square(f) - - f = bn128.MulBy024(f, - c.Ell0, - bn128.Fq2.MulScalar(c.EllVW, pre1.Py), - bn128.Fq2.MulScalar(c.EllVV, pre1.Px)) - - if bit == 1 { - c = pre2.Coeffs[idx] - idx++ - f = bn128.MulBy024( - f, - c.Ell0, - bn128.Fq2.MulScalar(c.EllVW, pre1.Py), - bn128.Fq2.MulScalar(c.EllVV, pre1.Px)) - } - } - if bn128.LoopCountNeg { - f = bn128.Fq12.Inverse(f) - } - - c = pre2.Coeffs[idx] - idx++ - f = bn128.MulBy024( - f, - c.Ell0, - bn128.Fq2.MulScalar(c.EllVW, pre1.Py), - bn128.Fq2.MulScalar(c.EllVV, pre1.Px)) - - c = pre2.Coeffs[idx] - idx++ - - f = bn128.MulBy024( - f, - c.Ell0, - bn128.Fq2.MulScalar(c.EllVW, pre1.Py), - bn128.Fq2.MulScalar(c.EllVV, pre1.Px)) - - return f -} - -func (bn128 Bn128) MulBy024(a [2][3][2]*big.Int, ell0, ellVW, ellVV [2]*big.Int) [2][3][2]*big.Int { - b := [2][3][2]*big.Int{ - [3][2]*big.Int{ - ell0, - bn128.Fq2.Zero(), - ellVV, - }, - [3][2]*big.Int{ - bn128.Fq2.Zero(), - ellVW, - bn128.Fq2.Zero(), - }, - } - return bn128.Fq12.Mul(a, b) -} - -func (bn128 Bn128) FinalExponentiation(r [2][3][2]*big.Int) [2][3][2]*big.Int { - res := bn128.Fq12.Exp(r, bn128.FinalExp) - return res -} diff --git a/bn128/bn128_test.go b/bn128/bn128_test.go deleted file mode 100644 index aaecf19..0000000 --- a/bn128/bn128_test.go +++ /dev/null @@ -1,65 +0,0 @@ -package bn128 - -import ( - "math/big" - "testing" - - "github.com/stretchr/testify/assert" -) - -func TestBN128(t *testing.T) { - bn128, err := NewBn128() - assert.Nil(t, err) - - big40 := big.NewInt(int64(40)) - big75 := big.NewInt(int64(75)) - - g1a := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(big40)) - g2a := bn128.G2.MulScalar(bn128.G2.G, bn128.Fq1.Copy(big75)) - - g1b := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(big75)) - g2b := bn128.G2.MulScalar(bn128.G2.G, bn128.Fq1.Copy(big40)) - - pre1a := bn128.PreComputeG1(g1a) - pre2a, err := bn128.PreComputeG2(g2a) - assert.Nil(t, err) - pre1b := bn128.PreComputeG1(g1b) - pre2b, err := bn128.PreComputeG2(g2b) - - r1 := bn128.MillerLoop(pre1a, pre2a) - r2 := bn128.MillerLoop(pre1b, pre2b) - - rbe := bn128.Fq12.Mul(r1, bn128.Fq12.Inverse(r2)) - - res := bn128.FinalExponentiation(rbe) - - a := bn128.Fq12.Affine(res) - b := bn128.Fq12.Affine(bn128.Fq12.One()) - - assert.True(t, bn128.Fq12.Equal(a, b)) - assert.True(t, bn128.Fq12.Equal(res, bn128.Fq12.One())) -} - -func TestBN128_PairingFunction(t *testing.T) { - bn128, err := NewBn128() - assert.Nil(t, err) - - big25 := big.NewInt(int64(25)) - big30 := big.NewInt(int64(30)) - - g1a := bn128.G1.MulScalar(bn128.G1.G, big25) - g2a := bn128.G2.MulScalar(bn128.G2.G, big30) - - g1b := bn128.G1.MulScalar(bn128.G1.G, big30) - g2b := bn128.G2.MulScalar(bn128.G2.G, big25) - - pA, err := bn128.Pairing(g1a, g2a) - assert.Nil(t, err) - pB, err := bn128.Pairing(g1b, g2b) - assert.Nil(t, err) - - assert.True(t, bn128.Fq12.Equal(pA, pB)) - - assert.Equal(t, pA[0][0][0].String(), "73680848340331011700282047627232219336104151861349893575958589557226556635706") - assert.Equal(t, bn128.Fq12.Affine(pA)[0][0][0].String(), "8016119724813186033542830391460394070015218389456422587891475873290878009957") -} diff --git a/bn128/fq.go b/bn128/fq.go deleted file mode 100644 index d3a89d5..0000000 --- a/bn128/fq.go +++ /dev/null @@ -1,129 +0,0 @@ -package bn128 - -import ( - "bytes" - "math/big" -) - -// Fq is the Z field over modulus Q -type Fq struct { - Q *big.Int // Q -} - -// NewFq generates a new Fq -func NewFq(q *big.Int) Fq { - return Fq{ - q, - } -} - -// Zero returns a Zero value on the Fq -func (fq Fq) Zero() *big.Int { - return big.NewInt(int64(0)) -} - -// One returns a One value on the Fq -func (fq Fq) One() *big.Int { - return big.NewInt(int64(1)) -} - -// Add performs an addition on the Fq -func (fq Fq) Add(a, b *big.Int) *big.Int { - r := new(big.Int).Add(a, b) - // return new(big.Int).Mod(r, fq.Q) - return r -} - -// Double performs a doubling on the Fq -func (fq Fq) Double(a *big.Int) *big.Int { - r := new(big.Int).Add(a, a) - // return new(big.Int).Mod(r, fq.Q) - return r -} - -// Sub performs a substraction on the Fq -func (fq Fq) Sub(a, b *big.Int) *big.Int { - r := new(big.Int).Sub(a, b) - // return new(big.Int).Mod(r, fq.Q) - return r -} - -// Neg performs a negation on the Fq -func (fq Fq) Neg(a *big.Int) *big.Int { - m := new(big.Int).Neg(a) - // return new(big.Int).Mod(m, fq.Q) - return m -} - -// Mul performs a multiplication on the Fq -func (fq Fq) Mul(a, b *big.Int) *big.Int { - m := new(big.Int).Mul(a, b) - return new(big.Int).Mod(m, fq.Q) - // return m -} - -func (fq Fq) MulScalar(base, e *big.Int) *big.Int { - return fq.Mul(base, e) -} - -// Inverse returns the inverse on the Fq -func (fq Fq) Inverse(a *big.Int) *big.Int { - return new(big.Int).ModInverse(a, fq.Q) - // q := bigCopy(fq.Q) - // t := big.NewInt(int64(0)) - // r := fq.Q - // newt := big.NewInt(int64(0)) - // newr := fq.Affine(a) - // for !bytes.Equal(newr.Bytes(), big.NewInt(int64(0)).Bytes()) { - // q := new(big.Int).Div(bigCopy(r), bigCopy(newr)) - // - // t = bigCopy(newt) - // newt = fq.Sub(t, fq.Mul(q, newt)) - // - // r = bigCopy(newr) - // newr = fq.Sub(r, fq.Mul(q, newr)) - // } - // if t.Cmp(big.NewInt(0)) == -1 { // t< 0 - // t = fq.Add(t, q) - // } - // return t -} - -// Square performs a square operation on the Fq -func (fq Fq) Square(a *big.Int) *big.Int { - m := new(big.Int).Mul(a, a) - return new(big.Int).Mod(m, fq.Q) -} - -func (fq Fq) IsZero(a *big.Int) bool { - return bytes.Equal(a.Bytes(), fq.Zero().Bytes()) -} - -func (fq Fq) Copy(a *big.Int) *big.Int { - return new(big.Int).SetBytes(a.Bytes()) -} - -func (fq Fq) Affine(a *big.Int) *big.Int { - nq := fq.Neg(fq.Q) - - aux := a - if aux.Cmp(big.NewInt(int64(0))) == -1 { // negative value - if aux.Cmp(nq) != 1 { // aux less or equal nq - aux = new(big.Int).Mod(aux, fq.Q) - } - if aux.Cmp(big.NewInt(int64(0))) == -1 { // negative value - aux = new(big.Int).Add(aux, fq.Q) - } - } else { - if aux.Cmp(fq.Q) != -1 { // aux greater or equal nq - aux = new(big.Int).Mod(aux, fq.Q) - } - } - return aux -} - -func (fq Fq) Equal(a, b *big.Int) bool { - aAff := fq.Affine(a) - bAff := fq.Affine(b) - return bytes.Equal(aAff.Bytes(), bAff.Bytes()) -} diff --git a/bn128/fq12.go b/bn128/fq12.go deleted file mode 100644 index 4665865..0000000 --- a/bn128/fq12.go +++ /dev/null @@ -1,161 +0,0 @@ -package bn128 - -import ( - "bytes" - "math/big" -) - -// Fq12 uses the same algorithms than Fq2, but with [2][3][2]*big.Int data structure - -// Fq12 is Field 12 -type Fq12 struct { - F Fq6 - Fq2 Fq2 - NonResidue [2]*big.Int -} - -// NewFq12 generates a new Fq12 -func NewFq12(f Fq6, fq2 Fq2, nonResidue [2]*big.Int) Fq12 { - fq12 := Fq12{ - f, - fq2, - nonResidue, - } - return fq12 -} - -// Zero returns a Zero value on the Fq12 -func (fq12 Fq12) Zero() [2][3][2]*big.Int { - return [2][3][2]*big.Int{fq12.F.Zero(), fq12.F.Zero()} -} - -// One returns a One value on the Fq12 -func (fq12 Fq12) One() [2][3][2]*big.Int { - return [2][3][2]*big.Int{fq12.F.One(), fq12.F.Zero()} -} - -func (fq12 Fq12) mulByNonResidue(a [3][2]*big.Int) [3][2]*big.Int { - return [3][2]*big.Int{ - fq12.Fq2.Mul(fq12.NonResidue, a[2]), - a[0], - a[1], - } -} - -// Add performs an addition on the Fq12 -func (fq12 Fq12) Add(a, b [2][3][2]*big.Int) [2][3][2]*big.Int { - return [2][3][2]*big.Int{ - fq12.F.Add(a[0], b[0]), - fq12.F.Add(a[1], b[1]), - } -} - -// Double performs a doubling on the Fq12 -func (fq12 Fq12) Double(a [2][3][2]*big.Int) [2][3][2]*big.Int { - return fq12.Add(a, a) -} - -// Sub performs a substraction on the Fq12 -func (fq12 Fq12) Sub(a, b [2][3][2]*big.Int) [2][3][2]*big.Int { - return [2][3][2]*big.Int{ - fq12.F.Sub(a[0], b[0]), - fq12.F.Sub(a[1], b[1]), - } -} - -// Neg performs a negation on the Fq12 -func (fq12 Fq12) Neg(a [2][3][2]*big.Int) [2][3][2]*big.Int { - return fq12.Sub(fq12.Zero(), a) -} - -// Mul performs a multiplication on the Fq12 -func (fq12 Fq12) Mul(a, b [2][3][2]*big.Int) [2][3][2]*big.Int { - // Multiplication and Squaring on Pairing-Friendly .pdf; Section 3 (Karatsuba) - v0 := fq12.F.Mul(a[0], b[0]) - v1 := fq12.F.Mul(a[1], b[1]) - return [2][3][2]*big.Int{ - fq12.F.Add(v0, fq12.mulByNonResidue(v1)), - fq12.F.Sub( - fq12.F.Mul( - fq12.F.Add(a[0], a[1]), - fq12.F.Add(b[0], b[1])), - fq12.F.Add(v0, v1)), - } -} - -func (fq12 Fq12) MulScalar(base [2][3][2]*big.Int, e *big.Int) [2][3][2]*big.Int { - // for more possible implementations see g2.go file, at the function g2.MulScalar() - - res := fq12.Zero() - rem := e - exp := base - - for !bytes.Equal(rem.Bytes(), big.NewInt(int64(0)).Bytes()) { - // if rem % 2 == 1 - if bytes.Equal(new(big.Int).Rem(rem, big.NewInt(int64(2))).Bytes(), big.NewInt(int64(1)).Bytes()) { - res = fq12.Add(res, exp) - } - exp = fq12.Double(exp) - rem = rem.Rsh(rem, 1) // rem = rem >> 1 - } - return res -} - -// Inverse returns the inverse on the Fq12 -func (fq12 Fq12) Inverse(a [2][3][2]*big.Int) [2][3][2]*big.Int { - t0 := fq12.F.Square(a[0]) - t1 := fq12.F.Square(a[1]) - t2 := fq12.F.Sub(t0, fq12.mulByNonResidue(t1)) - t3 := fq12.F.Inverse(t2) - return [2][3][2]*big.Int{ - fq12.F.Mul(a[0], t3), - fq12.F.Neg(fq12.F.Mul(a[1], t3)), - } -} - -// Div performs a division on the Fq12 -func (fq12 Fq12) Div(a, b [2][3][2]*big.Int) [2][3][2]*big.Int { - return fq12.Mul(a, fq12.Inverse(b)) -} - -// Square performs a square operation on the Fq12 -func (fq12 Fq12) Square(a [2][3][2]*big.Int) [2][3][2]*big.Int { - ab := fq12.F.Mul(a[0], a[1]) - - return [2][3][2]*big.Int{ - fq12.F.Sub( - fq12.F.Mul( - fq12.F.Add(a[0], a[1]), - fq12.F.Add( - a[0], - fq12.mulByNonResidue(a[1]))), - fq12.F.Add( - ab, - fq12.mulByNonResidue(ab))), - fq12.F.Add(ab, ab), - } -} - -func (fq12 Fq12) Exp(base [2][3][2]*big.Int, e *big.Int) [2][3][2]*big.Int { - res := fq12.One() - rem := fq12.Fq2.F.Copy(e) - exp := base - - for !bytes.Equal(rem.Bytes(), big.NewInt(int64(0)).Bytes()) { - if BigIsOdd(rem) { - res = fq12.Mul(res, exp) - } - exp = fq12.Square(exp) - rem = new(big.Int).Rsh(rem, 1) - } - return res -} -func (fq12 Fq12) Affine(a [2][3][2]*big.Int) [2][3][2]*big.Int { - return [2][3][2]*big.Int{ - fq12.F.Affine(a[0]), - fq12.F.Affine(a[1]), - } -} -func (fq12 Fq12) Equal(a, b [2][3][2]*big.Int) bool { - return fq12.F.Equal(a[0], b[0]) && fq12.F.Equal(a[1], b[1]) -} diff --git a/bn128/fq2.go b/bn128/fq2.go deleted file mode 100644 index fe27431..0000000 --- a/bn128/fq2.go +++ /dev/null @@ -1,154 +0,0 @@ -package bn128 - -import ( - "math/big" -) - -// Fq2 is Field 2 -type Fq2 struct { - F Fq - NonResidue *big.Int -} - -// NewFq2 generates a new Fq2 -func NewFq2(f Fq, nonResidue *big.Int) Fq2 { - fq2 := Fq2{ - f, - nonResidue, - } - return fq2 -} - -// Zero returns a Zero value on the Fq2 -func (fq2 Fq2) Zero() [2]*big.Int { - return [2]*big.Int{fq2.F.Zero(), fq2.F.Zero()} -} - -// One returns a One value on the Fq2 -func (fq2 Fq2) One() [2]*big.Int { - return [2]*big.Int{fq2.F.One(), fq2.F.Zero()} -} - -func (fq2 Fq2) mulByNonResidue(a *big.Int) *big.Int { - return fq2.F.Mul(fq2.NonResidue, a) -} - -// Add performs an addition on the Fq2 -func (fq2 Fq2) Add(a, b [2]*big.Int) [2]*big.Int { - return [2]*big.Int{ - fq2.F.Add(a[0], b[0]), - fq2.F.Add(a[1], b[1]), - } -} - -// Double performs a doubling on the Fq2 -func (fq2 Fq2) Double(a [2]*big.Int) [2]*big.Int { - return fq2.Add(a, a) -} - -// Sub performs a substraction on the Fq2 -func (fq2 Fq2) Sub(a, b [2]*big.Int) [2]*big.Int { - return [2]*big.Int{ - fq2.F.Sub(a[0], b[0]), - fq2.F.Sub(a[1], b[1]), - } -} - -// Neg performs a negation on the Fq2 -func (fq2 Fq2) Neg(a [2]*big.Int) [2]*big.Int { - return fq2.Sub(fq2.Zero(), a) -} - -// Mul performs a multiplication on the Fq2 -func (fq2 Fq2) Mul(a, b [2]*big.Int) [2]*big.Int { - // Multiplication and Squaring on Pairing-Friendly.pdf; Section 3 (Karatsuba) - // https://pdfs.semanticscholar.org/3e01/de88d7428076b2547b60072088507d881bf1.pdf - v0 := fq2.F.Mul(a[0], b[0]) - v1 := fq2.F.Mul(a[1], b[1]) - return [2]*big.Int{ - fq2.F.Add(v0, fq2.mulByNonResidue(v1)), - fq2.F.Sub( - fq2.F.Mul( - fq2.F.Add(a[0], a[1]), - fq2.F.Add(b[0], b[1])), - fq2.F.Add(v0, v1)), - } -} - -func (fq2 Fq2) MulScalar(p [2]*big.Int, e *big.Int) [2]*big.Int { - // for more possible implementations see g2.go file, at the function g2.MulScalar() - - q := fq2.Zero() - d := fq2.F.Copy(e) - r := p - - foundone := false - for i := d.BitLen(); i >= 0; i-- { - if foundone { - q = fq2.Double(q) - } - if d.Bit(i) == 1 { - foundone = true - q = fq2.Add(q, r) - } - } - return q -} - -// Inverse returns the inverse on the Fq2 -func (fq2 Fq2) Inverse(a [2]*big.Int) [2]*big.Int { - // High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves .pdf - // https://eprint.iacr.org/2010/354.pdf , algorithm 8 - t0 := fq2.F.Square(a[0]) - t1 := fq2.F.Square(a[1]) - t2 := fq2.F.Sub(t0, fq2.mulByNonResidue(t1)) - t3 := fq2.F.Inverse(t2) - return [2]*big.Int{ - fq2.F.Mul(a[0], t3), - fq2.F.Neg(fq2.F.Mul(a[1], t3)), - } -} - -// Div performs a division on the Fq2 -func (fq2 Fq2) Div(a, b [2]*big.Int) [2]*big.Int { - return fq2.Mul(a, fq2.Inverse(b)) -} - -// Square performs a square operation on the Fq2 -func (fq2 Fq2) Square(a [2]*big.Int) [2]*big.Int { - // https://pdfs.semanticscholar.org/3e01/de88d7428076b2547b60072088507d881bf1.pdf , complex squaring - ab := fq2.F.Mul(a[0], a[1]) - return [2]*big.Int{ - fq2.F.Sub( - fq2.F.Mul( - fq2.F.Add(a[0], a[1]), - fq2.F.Add( - a[0], - fq2.mulByNonResidue(a[1]))), - fq2.F.Add( - ab, - fq2.mulByNonResidue(ab))), - fq2.F.Add(ab, ab), - } -} - -func (fq2 Fq2) IsZero(a [2]*big.Int) bool { - return fq2.F.IsZero(a[0]) && fq2.F.IsZero(a[1]) -} - -func (fq2 Fq2) Affine(a [2]*big.Int) [2]*big.Int { - return [2]*big.Int{ - fq2.F.Affine(a[0]), - fq2.F.Affine(a[1]), - } -} -func (fq2 Fq2) Equal(a, b [2]*big.Int) bool { - return fq2.F.Equal(a[0], b[0]) && fq2.F.Equal(a[1], b[1]) -} - -func (fq2 Fq2) Copy(a [2]*big.Int) [2]*big.Int { - return [2]*big.Int{ - fq2.F.Copy(a[0]), - fq2.F.Copy(a[1]), - } -} diff --git a/bn128/fq6.go b/bn128/fq6.go deleted file mode 100644 index d0fc33f..0000000 --- a/bn128/fq6.go +++ /dev/null @@ -1,192 +0,0 @@ -package bn128 - -import ( - "bytes" - "math/big" -) - -// Fq6 is Field 6 -type Fq6 struct { - F Fq2 - NonResidue [2]*big.Int -} - -// NewFq6 generates a new Fq6 -func NewFq6(f Fq2, nonResidue [2]*big.Int) Fq6 { - fq6 := Fq6{ - f, - nonResidue, - } - return fq6 -} - -// Zero returns a Zero value on the Fq6 -func (fq6 Fq6) Zero() [3][2]*big.Int { - return [3][2]*big.Int{fq6.F.Zero(), fq6.F.Zero(), fq6.F.Zero()} -} - -// One returns a One value on the Fq6 -func (fq6 Fq6) One() [3][2]*big.Int { - return [3][2]*big.Int{fq6.F.One(), fq6.F.Zero(), fq6.F.Zero()} -} - -func (fq6 Fq6) mulByNonResidue(a [2]*big.Int) [2]*big.Int { - return fq6.F.Mul(fq6.NonResidue, a) -} - -// Add performs an addition on the Fq6 -func (fq6 Fq6) Add(a, b [3][2]*big.Int) [3][2]*big.Int { - return [3][2]*big.Int{ - fq6.F.Add(a[0], b[0]), - fq6.F.Add(a[1], b[1]), - fq6.F.Add(a[2], b[2]), - } -} - -func (fq6 Fq6) Double(a [3][2]*big.Int) [3][2]*big.Int { - return fq6.Add(a, a) -} - -// Sub performs a substraction on the Fq6 -func (fq6 Fq6) Sub(a, b [3][2]*big.Int) [3][2]*big.Int { - return [3][2]*big.Int{ - fq6.F.Sub(a[0], b[0]), - fq6.F.Sub(a[1], b[1]), - fq6.F.Sub(a[2], b[2]), - } -} - -// Neg performs a negation on the Fq6 -func (fq6 Fq6) Neg(a [3][2]*big.Int) [3][2]*big.Int { - return fq6.Sub(fq6.Zero(), a) -} - -// Mul performs a multiplication on the Fq6 -func (fq6 Fq6) Mul(a, b [3][2]*big.Int) [3][2]*big.Int { - v0 := fq6.F.Mul(a[0], b[0]) - v1 := fq6.F.Mul(a[1], b[1]) - v2 := fq6.F.Mul(a[2], b[2]) - return [3][2]*big.Int{ - fq6.F.Add( - v0, - fq6.mulByNonResidue( - fq6.F.Sub( - fq6.F.Mul( - fq6.F.Add(a[1], a[2]), - fq6.F.Add(b[1], b[2])), - fq6.F.Add(v1, v2)))), - - fq6.F.Add( - fq6.F.Sub( - fq6.F.Mul( - fq6.F.Add(a[0], a[1]), - fq6.F.Add(b[0], b[1])), - fq6.F.Add(v0, v1)), - fq6.mulByNonResidue(v2)), - - fq6.F.Add( - fq6.F.Sub( - fq6.F.Mul( - fq6.F.Add(a[0], a[2]), - fq6.F.Add(b[0], b[2])), - fq6.F.Add(v0, v2)), - v1), - } -} - -func (fq6 Fq6) MulScalar(base [3][2]*big.Int, e *big.Int) [3][2]*big.Int { - // for more possible implementations see g2.go file, at the function g2.MulScalar() - - res := fq6.Zero() - rem := e - exp := base - - for !bytes.Equal(rem.Bytes(), big.NewInt(int64(0)).Bytes()) { - // if rem % 2 == 1 - if bytes.Equal(new(big.Int).Rem(rem, big.NewInt(int64(2))).Bytes(), big.NewInt(int64(1)).Bytes()) { - res = fq6.Add(res, exp) - } - exp = fq6.Double(exp) - rem = rem.Rsh(rem, 1) // rem = rem >> 1 - } - return res -} - -// Inverse returns the inverse on the Fq6 -func (fq6 Fq6) Inverse(a [3][2]*big.Int) [3][2]*big.Int { - t0 := fq6.F.Square(a[0]) - t1 := fq6.F.Square(a[1]) - t2 := fq6.F.Square(a[2]) - t3 := fq6.F.Mul(a[0], a[1]) - t4 := fq6.F.Mul(a[0], a[2]) - t5 := fq6.F.Mul(a[1], a[2]) - - c0 := fq6.F.Sub(t0, fq6.mulByNonResidue(t5)) - c1 := fq6.F.Sub(fq6.mulByNonResidue(t2), t3) - c2 := fq6.F.Sub(t1, t4) - - t6 := fq6.F.Inverse( - fq6.F.Add( - fq6.F.Mul(a[0], c0), - fq6.mulByNonResidue( - fq6.F.Add( - fq6.F.Mul(a[2], c1), - fq6.F.Mul(a[1], c2))))) - return [3][2]*big.Int{ - fq6.F.Mul(t6, c0), - fq6.F.Mul(t6, c1), - fq6.F.Mul(t6, c2), - } -} - -// Div performs a division on the Fq6 -func (fq6 Fq6) Div(a, b [3][2]*big.Int) [3][2]*big.Int { - return fq6.Mul(a, fq6.Inverse(b)) -} - -// Square performs a square operation on the Fq6 -func (fq6 Fq6) Square(a [3][2]*big.Int) [3][2]*big.Int { - s0 := fq6.F.Square(a[0]) - ab := fq6.F.Mul(a[0], a[1]) - s1 := fq6.F.Add(ab, ab) - s2 := fq6.F.Square( - fq6.F.Add( - fq6.F.Sub(a[0], a[1]), - a[2])) - bc := fq6.F.Mul(a[1], a[2]) - s3 := fq6.F.Add(bc, bc) - s4 := fq6.F.Square(a[2]) - - return [3][2]*big.Int{ - fq6.F.Add( - s0, - fq6.mulByNonResidue(s3)), - fq6.F.Add( - s1, - fq6.mulByNonResidue(s4)), - fq6.F.Sub( - fq6.F.Add( - fq6.F.Add(s1, s2), - s3), - fq6.F.Add(s0, s4)), - } -} - -func (fq6 Fq6) Affine(a [3][2]*big.Int) [3][2]*big.Int { - return [3][2]*big.Int{ - fq6.F.Affine(a[0]), - fq6.F.Affine(a[1]), - fq6.F.Affine(a[2]), - } -} -func (fq6 Fq6) Equal(a, b [3][2]*big.Int) bool { - return fq6.F.Equal(a[0], b[0]) && fq6.F.Equal(a[1], b[1]) && fq6.F.Equal(a[2], b[2]) -} - -func (fq6 Fq6) Copy(a [3][2]*big.Int) [3][2]*big.Int { - return [3][2]*big.Int{ - fq6.F.Copy(a[0]), - fq6.F.Copy(a[1]), - fq6.F.Copy(a[2]), - } -} diff --git a/bn128/fqn_test.go b/bn128/fqn_test.go deleted file mode 100644 index a22e5eb..0000000 --- a/bn128/fqn_test.go +++ /dev/null @@ -1,160 +0,0 @@ -package bn128 - -import ( - "math/big" - "testing" - - "github.com/stretchr/testify/assert" -) - -func iToBig(a int) *big.Int { - return big.NewInt(int64(a)) -} - -func iiToBig(a, b int) [2]*big.Int { - return [2]*big.Int{iToBig(a), iToBig(b)} -} - -func iiiToBig(a, b int) [2]*big.Int { - return [2]*big.Int{iToBig(a), iToBig(b)} -} - -func TestFq1(t *testing.T) { - fq1 := NewFq(iToBig(7)) - - res := fq1.Add(iToBig(4), iToBig(4)) - assert.Equal(t, iToBig(1), fq1.Affine(res)) - - res = fq1.Double(iToBig(5)) - assert.Equal(t, iToBig(3), fq1.Affine(res)) - - res = fq1.Sub(iToBig(5), iToBig(7)) - assert.Equal(t, iToBig(5), fq1.Affine(res)) - - res = fq1.Neg(iToBig(5)) - assert.Equal(t, iToBig(2), fq1.Affine(res)) - - res = fq1.Mul(iToBig(5), iToBig(11)) - assert.Equal(t, iToBig(6), fq1.Affine(res)) - - res = fq1.Inverse(iToBig(4)) - assert.Equal(t, iToBig(2), res) - - res = fq1.Square(iToBig(5)) - assert.Equal(t, iToBig(4), res) -} - -func TestFq2(t *testing.T) { - fq1 := NewFq(iToBig(7)) - nonResidueFq2str := "-1" // i/j - nonResidueFq2, ok := new(big.Int).SetString(nonResidueFq2str, 10) - assert.True(t, ok) - assert.Equal(t, nonResidueFq2.String(), nonResidueFq2str) - - fq2 := Fq2{fq1, nonResidueFq2} - - res := fq2.Add(iiToBig(4, 4), iiToBig(3, 4)) - assert.Equal(t, iiToBig(0, 1), fq2.Affine(res)) - - res = fq2.Double(iiToBig(5, 3)) - assert.Equal(t, iiToBig(3, 6), fq2.Affine(res)) - - res = fq2.Sub(iiToBig(5, 3), iiToBig(7, 2)) - assert.Equal(t, iiToBig(5, 1), fq2.Affine(res)) - - res = fq2.Neg(iiToBig(4, 4)) - assert.Equal(t, iiToBig(3, 3), fq2.Affine(res)) - - res = fq2.Mul(iiToBig(4, 4), iiToBig(3, 4)) - assert.Equal(t, iiToBig(3, 0), fq2.Affine(res)) - - res = fq2.Inverse(iiToBig(4, 4)) - assert.Equal(t, iiToBig(1, 6), fq2.Affine(res)) - - res = fq2.Square(iiToBig(4, 4)) - assert.Equal(t, iiToBig(0, 4), fq2.Affine(res)) - res2 := fq2.Mul(iiToBig(4, 4), iiToBig(4, 4)) - assert.Equal(t, fq2.Affine(res), fq2.Affine(res2)) - assert.True(t, fq2.Equal(res, res2)) - - res = fq2.Square(iiToBig(3, 5)) - assert.Equal(t, iiToBig(5, 2), fq2.Affine(res)) - res2 = fq2.Mul(iiToBig(3, 5), iiToBig(3, 5)) - assert.Equal(t, fq2.Affine(res), fq2.Affine(res2)) -} - -func TestFq6(t *testing.T) { - bn128, err := NewBn128() - assert.Nil(t, err) - - a := [3][2]*big.Int{ - iiToBig(1, 2), - iiToBig(3, 4), - iiToBig(5, 6)} - b := [3][2]*big.Int{ - iiToBig(12, 11), - iiToBig(10, 9), - iiToBig(8, 7)} - - mulRes := bn128.Fq6.Mul(a, b) - divRes := bn128.Fq6.Div(mulRes, b) - assert.Equal(t, bn128.Fq6.Affine(a), bn128.Fq6.Affine(divRes)) -} - -func TestFq12(t *testing.T) { - q, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10) // i - assert.True(t, ok) - fq1 := NewFq(q) - nonResidueFq2, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208582", 10) // i - assert.True(t, ok) - nonResidueFq6 := iiToBig(9, 1) - - fq2 := Fq2{fq1, nonResidueFq2} - fq6 := Fq6{fq2, nonResidueFq6} - fq12 := Fq12{fq6, fq2, nonResidueFq6} - - a := [2][3][2]*big.Int{ - { - iiToBig(1, 2), - iiToBig(3, 4), - iiToBig(5, 6), - }, - { - iiToBig(7, 8), - iiToBig(9, 10), - iiToBig(11, 12), - }, - } - b := [2][3][2]*big.Int{ - { - iiToBig(12, 11), - iiToBig(10, 9), - iiToBig(8, 7), - }, - { - iiToBig(6, 5), - iiToBig(4, 3), - iiToBig(2, 1), - }, - } - - res := fq12.Add(a, b) - assert.Equal(t, - [2][3][2]*big.Int{ - { - iiToBig(13, 13), - iiToBig(13, 13), - iiToBig(13, 13), - }, - { - iiToBig(13, 13), - iiToBig(13, 13), - iiToBig(13, 13), - }, - }, - res) - - mulRes := fq12.Mul(a, b) - divRes := fq12.Div(mulRes, b) - assert.Equal(t, fq12.Affine(a), fq12.Affine(divRes)) -} diff --git a/bn128/g1.go b/bn128/g1.go deleted file mode 100644 index 4edd043..0000000 --- a/bn128/g1.go +++ /dev/null @@ -1,191 +0,0 @@ -package bn128 - -import ( - "math/big" -) - -type G1 struct { - F Fq - G [3]*big.Int -} - -func NewG1(f Fq, g [2]*big.Int) G1 { - var g1 G1 - g1.F = f - g1.G = [3]*big.Int{ - g[0], - g[1], - g1.F.One(), - } - return g1 -} - -func (g1 G1) Zero() [2]*big.Int { - return [2]*big.Int{g1.F.Zero(), g1.F.Zero()} -} -func (g1 G1) IsZero(p [3]*big.Int) bool { - return g1.F.IsZero(p[2]) -} - -func (g1 G1) Add(p1, p2 [3]*big.Int) [3]*big.Int { - - // https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates - // https://github.com/zcash/zcash/blob/master/src/snark/libsnark/algebra/curves/alt_bn128/alt_bn128_g1.cpp#L208 - // http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/addition/add-2007-bl.op3 - - if g1.IsZero(p1) { - return p2 - } - if g1.IsZero(p2) { - return p1 - } - - x1 := p1[0] - y1 := p1[1] - z1 := p1[2] - x2 := p2[0] - y2 := p2[1] - z2 := p2[2] - - z1z1 := g1.F.Square(z1) - z2z2 := g1.F.Square(z2) - - u1 := g1.F.Mul(x1, z2z2) - u2 := g1.F.Mul(x2, z1z1) - - t0 := g1.F.Mul(z2, z2z2) - s1 := g1.F.Mul(y1, t0) - - t1 := g1.F.Mul(z1, z1z1) - s2 := g1.F.Mul(y2, t1) - - h := g1.F.Sub(u2, u1) - t2 := g1.F.Add(h, h) - i := g1.F.Square(t2) - j := g1.F.Mul(h, i) - t3 := g1.F.Sub(s2, s1) - r := g1.F.Add(t3, t3) - v := g1.F.Mul(u1, i) - t4 := g1.F.Square(r) - t5 := g1.F.Add(v, v) - t6 := g1.F.Sub(t4, j) - x3 := g1.F.Sub(t6, t5) - t7 := g1.F.Sub(v, x3) - t8 := g1.F.Mul(s1, j) - t9 := g1.F.Add(t8, t8) - t10 := g1.F.Mul(r, t7) - - y3 := g1.F.Sub(t10, t9) - - t11 := g1.F.Add(z1, z2) - t12 := g1.F.Square(t11) - t13 := g1.F.Sub(t12, z1z1) - t14 := g1.F.Sub(t13, z2z2) - z3 := g1.F.Mul(t14, h) - - return [3]*big.Int{x3, y3, z3} -} - -func (g1 G1) Neg(p [3]*big.Int) [3]*big.Int { - return [3]*big.Int{ - p[0], - g1.F.Neg(p[1]), - p[2], - } -} -func (g1 G1) Sub(a, b [3]*big.Int) [3]*big.Int { - return g1.Add(a, g1.Neg(b)) -} -func (g1 G1) Double(p [3]*big.Int) [3]*big.Int { - - // https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates - // http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3 - // https://github.com/zcash/zcash/blob/master/src/snark/libsnark/algebra/curves/alt_bn128/alt_bn128_g1.cpp#L325 - - if g1.IsZero(p) { - return p - } - - a := g1.F.Square(p[0]) - b := g1.F.Square(p[1]) - c := g1.F.Square(b) - - t0 := g1.F.Add(p[0], b) - t1 := g1.F.Square(t0) - t2 := g1.F.Sub(t1, a) - t3 := g1.F.Sub(t2, c) - - d := g1.F.Double(t3) - e := g1.F.Add(g1.F.Add(a, a), a) - f := g1.F.Square(e) - - t4 := g1.F.Double(d) - x3 := g1.F.Sub(f, t4) - - t5 := g1.F.Sub(d, x3) - twoC := g1.F.Add(c, c) - fourC := g1.F.Add(twoC, twoC) - t6 := g1.F.Add(fourC, fourC) - t7 := g1.F.Mul(e, t5) - y3 := g1.F.Sub(t7, t6) - - t8 := g1.F.Mul(p[1], p[2]) - z3 := g1.F.Double(t8) - - return [3]*big.Int{x3, y3, z3} -} - -func (g1 G1) MulScalar(p [3]*big.Int, e *big.Int) [3]*big.Int { - // https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Double-and-add - // for more possible implementations see g2.go file, at the function g2.MulScalar() - - q := [3]*big.Int{g1.F.Zero(), g1.F.Zero(), g1.F.Zero()} - d := g1.F.Copy(e) - r := p - for i := d.BitLen() - 1; i >= 0; i-- { - q = g1.Double(q) - if d.Bit(i) == 1 { - q = g1.Add(q, r) - } - } - - return q -} - -func (g1 G1) Affine(p [3]*big.Int) [2]*big.Int { - if g1.IsZero(p) { - return g1.Zero() - } - - zinv := g1.F.Inverse(p[2]) - zinv2 := g1.F.Square(zinv) - x := g1.F.Mul(p[0], zinv2) - - zinv3 := g1.F.Mul(zinv2, zinv) - y := g1.F.Mul(p[1], zinv3) - - return [2]*big.Int{x, y} -} - -func (g1 G1) Equal(p1, p2 [3]*big.Int) bool { - if g1.IsZero(p1) { - return g1.IsZero(p2) - } - if g1.IsZero(p2) { - return g1.IsZero(p1) - } - - z1z1 := g1.F.Square(p1[2]) - z2z2 := g1.F.Square(p2[2]) - - u1 := g1.F.Mul(p1[0], z2z2) - u2 := g1.F.Mul(p2[0], z1z1) - - z1cub := g1.F.Mul(p1[2], z1z1) - z2cub := g1.F.Mul(p2[2], z2z2) - - s1 := g1.F.Mul(p1[1], z2cub) - s2 := g1.F.Mul(p2[1], z1cub) - - return g1.F.Equal(u1, u2) && g1.F.Equal(s1, s2) -} diff --git a/bn128/g1_test.go b/bn128/g1_test.go deleted file mode 100644 index e2bf533..0000000 --- a/bn128/g1_test.go +++ /dev/null @@ -1,31 +0,0 @@ -package bn128 - -import ( - "math/big" - "testing" - - "github.com/arnaucube/cryptofun/utils" - "github.com/stretchr/testify/assert" -) - -func TestG1(t *testing.T) { - bn128, err := NewBn128() - assert.Nil(t, err) - - r1 := big.NewInt(int64(33)) - r2 := big.NewInt(int64(44)) - - gr1 := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(r1)) - gr2 := bn128.G1.MulScalar(bn128.G1.G, bn128.Fq1.Copy(r2)) - - grsum1 := bn128.G1.Add(gr1, gr2) // g*33 + g*44 - r1r2 := bn128.Fq1.Add(r1, r2) // 33 + 44 - grsum2 := bn128.G1.MulScalar(bn128.G1.G, r1r2) // g * (33+44) - - assert.True(t, bn128.G1.Equal(grsum1, grsum2)) - a := bn128.G1.Affine(grsum1) - b := bn128.G1.Affine(grsum2) - assert.Equal(t, a, b) - assert.Equal(t, "0x2f978c0ab89ebaa576866706b14787f360c4d6c3869efe5a72f7c3651a72ff00", utils.BytesToHex(a[0].Bytes())) - assert.Equal(t, "0x12e4ba7f0edca8b4fa668fe153aebd908d322dc26ad964d4cd314795844b62b2", utils.BytesToHex(a[1].Bytes())) -} diff --git a/bn128/g2.go b/bn128/g2.go deleted file mode 100644 index f6b7cad..0000000 --- a/bn128/g2.go +++ /dev/null @@ -1,221 +0,0 @@ -package bn128 - -import ( - "math/big" -) - -type G2 struct { - F Fq2 - G [3][2]*big.Int -} - -func NewG2(f Fq2, g [2][2]*big.Int) G2 { - var g2 G2 - g2.F = f - g2.G = [3][2]*big.Int{ - g[0], - g[1], - g2.F.One(), - } - return g2 -} - -func (g2 G2) Zero() [3][2]*big.Int { - return [3][2]*big.Int{g2.F.Zero(), g2.F.One(), g2.F.Zero()} -} -func (g2 G2) IsZero(p [3][2]*big.Int) bool { - return g2.F.IsZero(p[2]) -} - -func (g2 G2) Add(p1, p2 [3][2]*big.Int) [3][2]*big.Int { - - // https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates - // https://github.com/zcash/zcash/blob/master/src/snark/libsnark/algebra/curves/alt_bn128/alt_bn128_g2.cpp#L208 - // http://hyperelliptic.org/EFD/g2p/auto-code/shortw/jacobian-0/addition/add-2007-bl.op3 - - if g2.IsZero(p1) { - return p2 - } - if g2.IsZero(p2) { - return p1 - } - - x1 := p1[0] - y1 := p1[1] - z1 := p1[2] - x2 := p2[0] - y2 := p2[1] - z2 := p2[2] - - z1z1 := g2.F.Square(z1) - z2z2 := g2.F.Square(z2) - - u1 := g2.F.Mul(x1, z2z2) - u2 := g2.F.Mul(x2, z1z1) - - t0 := g2.F.Mul(z2, z2z2) - s1 := g2.F.Mul(y1, t0) - - t1 := g2.F.Mul(z1, z1z1) - s2 := g2.F.Mul(y2, t1) - - h := g2.F.Sub(u2, u1) - t2 := g2.F.Add(h, h) - i := g2.F.Square(t2) - j := g2.F.Mul(h, i) - t3 := g2.F.Sub(s2, s1) - r := g2.F.Add(t3, t3) - v := g2.F.Mul(u1, i) - t4 := g2.F.Square(r) - t5 := g2.F.Add(v, v) - t6 := g2.F.Sub(t4, j) - x3 := g2.F.Sub(t6, t5) - t7 := g2.F.Sub(v, x3) - t8 := g2.F.Mul(s1, j) - t9 := g2.F.Add(t8, t8) - t10 := g2.F.Mul(r, t7) - - y3 := g2.F.Sub(t10, t9) - - t11 := g2.F.Add(z1, z2) - t12 := g2.F.Square(t11) - t13 := g2.F.Sub(t12, z1z1) - t14 := g2.F.Sub(t13, z2z2) - z3 := g2.F.Mul(t14, h) - - return [3][2]*big.Int{x3, y3, z3} -} - -func (g2 G2) Neg(p [3][2]*big.Int) [3][2]*big.Int { - return [3][2]*big.Int{ - p[0], - g2.F.Neg(p[1]), - p[2], - } -} - -func (g2 G2) Sub(a, b [3][2]*big.Int) [3][2]*big.Int { - return g2.Add(a, g2.Neg(b)) -} - -func (g2 G2) Double(p [3][2]*big.Int) [3][2]*big.Int { - - // https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates - // http://hyperelliptic.org/EFD/g2p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3 - // https://github.com/zcash/zcash/blob/master/src/snark/libsnark/algebra/curves/alt_bn128/alt_bn128_g2.cpp#L325 - - if g2.IsZero(p) { - return p - } - - a := g2.F.Square(p[0]) - b := g2.F.Square(p[1]) - c := g2.F.Square(b) - - t0 := g2.F.Add(p[0], b) - t1 := g2.F.Square(t0) - t2 := g2.F.Sub(t1, a) - t3 := g2.F.Sub(t2, c) - - d := g2.F.Double(t3) - e := g2.F.Add(g2.F.Add(a, a), a) - f := g2.F.Square(e) - - t4 := g2.F.Double(d) - x3 := g2.F.Sub(f, t4) - - t5 := g2.F.Sub(d, x3) - twoC := g2.F.Add(c, c) - fourC := g2.F.Add(twoC, twoC) - t6 := g2.F.Add(fourC, fourC) - t7 := g2.F.Mul(e, t5) - y3 := g2.F.Sub(t7, t6) - - t8 := g2.F.Mul(p[1], p[2]) - z3 := g2.F.Double(t8) - - return [3][2]*big.Int{x3, y3, z3} -} - -func (g2 G2) MulScalar(p [3][2]*big.Int, e *big.Int) [3][2]*big.Int { - // https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Double-and-add - - q := [3][2]*big.Int{g2.F.Zero(), g2.F.Zero(), g2.F.Zero()} - d := g2.F.F.Copy(e) // d := e - r := p - - /* - here are three possible implementations: - */ - - /* index decreasing: */ - for i := d.BitLen() - 1; i >= 0; i-- { - q = g2.Double(q) - if d.Bit(i) == 1 { - q = g2.Add(q, r) - } - } - - /* index increasing: */ - // for i := 0; i <= d.BitLen(); i++ { - // if d.Bit(i) == 1 { - // q = g2.Add(q, r) - // } - // r = g2.Double(r) - // } - - // foundone := false - // for i := d.BitLen(); i >= 0; i-- { - // if foundone { - // q = g2.Double(q) - // } - // if d.Bit(i) == 1 { - // foundone = true - // q = g2.Add(q, r) - // } - // } - - return q -} - -func (g2 G2) Affine(p [3][2]*big.Int) [3][2]*big.Int { - if g2.IsZero(p) { - return g2.Zero() - } - - zinv := g2.F.Inverse(p[2]) - zinv2 := g2.F.Square(zinv) - x := g2.F.Mul(p[0], zinv2) - - zinv3 := g2.F.Mul(zinv2, zinv) - y := g2.F.Mul(p[1], zinv3) - - return [3][2]*big.Int{ - g2.F.Affine(x), - g2.F.Affine(y), - g2.F.One(), - } -} - -func (g2 G2) Equal(p1, p2 [3][2]*big.Int) bool { - if g2.IsZero(p1) { - return g2.IsZero(p2) - } - if g2.IsZero(p2) { - return g2.IsZero(p1) - } - - z1z1 := g2.F.Square(p1[2]) - z2z2 := g2.F.Square(p2[2]) - - u1 := g2.F.Mul(p1[0], z2z2) - u2 := g2.F.Mul(p2[0], z1z1) - - z1cub := g2.F.Mul(p1[2], z1z1) - z2cub := g2.F.Mul(p2[2], z2z2) - - s1 := g2.F.Mul(p1[1], z2cub) - s2 := g2.F.Mul(p2[1], z1cub) - - return g2.F.Equal(u1, u2) && g2.F.Equal(s1, s2) -} diff --git a/bn128/g2_test.go b/bn128/g2_test.go deleted file mode 100644 index 0782ae0..0000000 --- a/bn128/g2_test.go +++ /dev/null @@ -1,24 +0,0 @@ -package bn128 - -import ( - "math/big" - "testing" - - "github.com/stretchr/testify/assert" -) - -func TestG2(t *testing.T) { - bn128, err := NewBn128() - assert.Nil(t, err) - - r1 := big.NewInt(int64(33)) - r2 := big.NewInt(int64(44)) - - gr1 := bn128.G2.Affine(bn128.G2.MulScalar(bn128.G2.G, r1)) - gr2 := bn128.G2.Affine(bn128.G2.MulScalar(bn128.G2.G, r2)) - - grsum1 := bn128.G2.Affine(bn128.G2.Add(gr1, gr2)) - r1r2 := bn128.Fq1.Affine(bn128.Fq1.Add(r1, r2)) - grsum2 := bn128.G2.Affine(bn128.G2.MulScalar(bn128.G2.G, r1r2)) - assert.True(t, bn128.G2.Equal(grsum1, grsum2)) -}