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Diffstat (limited to 'crypto/bn256/cloudflare/bn256.go')
| -rw-r--r-- | crypto/bn256/cloudflare/bn256.go | 481 |
1 files changed, 481 insertions, 0 deletions
diff --git a/crypto/bn256/cloudflare/bn256.go b/crypto/bn256/cloudflare/bn256.go new file mode 100644 index 000000000..c6ea2d07e --- /dev/null +++ b/crypto/bn256/cloudflare/bn256.go @@ -0,0 +1,481 @@ +// Package bn256 implements a particular bilinear group at the 128-bit security +// level. +// +// Bilinear groups are the basis of many of the new cryptographic protocols that +// have been proposed over the past decade. They consist of a triplet of groups +// (G₁, G₂ and GT) such that there exists a function e(g₁ˣ,g₂ʸ)=gTˣʸ (where gₓ +// is a generator of the respective group). That function is called a pairing +// function. +// +// This package specifically implements the Optimal Ate pairing over a 256-bit +// Barreto-Naehrig curve as described in +// http://cryptojedi.org/papers/dclxvi-20100714.pdf. Its output is compatible +// with the implementation described in that paper. +package bn256 + +import ( + "crypto/rand" + "errors" + "io" + "math/big" +) + +func randomK(r io.Reader) (k *big.Int, err error) { + for { + k, err = rand.Int(r, Order) + if k.Sign() > 0 || err != nil { + return + } + } +} + +// G1 is an abstract cyclic group. The zero value is suitable for use as the +// output of an operation, but cannot be used as an input. +type G1 struct { + p *curvePoint +} + +// RandomG1 returns x and g₁ˣ where x is a random, non-zero number read from r. +func RandomG1(r io.Reader) (*big.Int, *G1, error) { + k, err := randomK(r) + if err != nil { + return nil, nil, err + } + + return k, new(G1).ScalarBaseMult(k), nil +} + +func (g *G1) String() string { + return "bn256.G1" + g.p.String() +} + +// ScalarBaseMult sets e to g*k where g is the generator of the group and then +// returns e. +func (e *G1) ScalarBaseMult(k *big.Int) *G1 { + if e.p == nil { + e.p = &curvePoint{} + } + e.p.Mul(curveGen, k) + return e +} + +// ScalarMult sets e to a*k and then returns e. +func (e *G1) ScalarMult(a *G1, k *big.Int) *G1 { + if e.p == nil { + e.p = &curvePoint{} + } + e.p.Mul(a.p, k) + return e +} + +// Add sets e to a+b and then returns e. +func (e *G1) Add(a, b *G1) *G1 { + if e.p == nil { + e.p = &curvePoint{} + } + e.p.Add(a.p, b.p) + return e +} + +// Neg sets e to -a and then returns e. +func (e *G1) Neg(a *G1) *G1 { + if e.p == nil { + e.p = &curvePoint{} + } + e.p.Neg(a.p) + return e +} + +// Set sets e to a and then returns e. +func (e *G1) Set(a *G1) *G1 { + if e.p == nil { + e.p = &curvePoint{} + } + e.p.Set(a.p) + return e +} + +// Marshal converts e to a byte slice. +func (e *G1) Marshal() []byte { + // Each value is a 256-bit number. + const numBytes = 256 / 8 + + e.p.MakeAffine() + ret := make([]byte, numBytes*2) + if e.p.IsInfinity() { + return ret + } + temp := &gfP{} + + montDecode(temp, &e.p.x) + temp.Marshal(ret) + montDecode(temp, &e.p.y) + temp.Marshal(ret[numBytes:]) + + return ret +} + +// Unmarshal sets e to the result of converting the output of Marshal back into +// a group element and then returns e. +func (e *G1) Unmarshal(m []byte) ([]byte, error) { + // Each value is a 256-bit number. + const numBytes = 256 / 8 + if len(m) < 2*numBytes { + return nil, errors.New("bn256: not enough data") + } + // Unmarshal the points and check their caps + if e.p == nil { + e.p = &curvePoint{} + } else { + e.p.x, e.p.y = gfP{0}, gfP{0} + } + var err error + if err = e.p.x.Unmarshal(m); err != nil { + return nil, err + } + if err = e.p.y.Unmarshal(m[numBytes:]); err != nil { + return nil, err + } + // Encode into Montgomery form and ensure it's on the curve + montEncode(&e.p.x, &e.p.x) + montEncode(&e.p.y, &e.p.y) + + zero := gfP{0} + if e.p.x == zero && e.p.y == zero { + // This is the point at infinity. + e.p.y = *newGFp(1) + e.p.z = gfP{0} + e.p.t = gfP{0} + } else { + e.p.z = *newGFp(1) + e.p.t = *newGFp(1) + + if !e.p.IsOnCurve() { + return nil, errors.New("bn256: malformed point") + } + } + return m[2*numBytes:], nil +} + +// G2 is an abstract cyclic group. The zero value is suitable for use as the +// output of an operation, but cannot be used as an input. +type G2 struct { + p *twistPoint +} + +// RandomG2 returns x and g₂ˣ where x is a random, non-zero number read from r. +func RandomG2(r io.Reader) (*big.Int, *G2, error) { + k, err := randomK(r) + if err != nil { + return nil, nil, err + } + + return k, new(G2).ScalarBaseMult(k), nil +} + +func (e *G2) String() string { + return "bn256.G2" + e.p.String() +} + +// ScalarBaseMult sets e to g*k where g is the generator of the group and then +// returns out. +func (e *G2) ScalarBaseMult(k *big.Int) *G2 { + if e.p == nil { + e.p = &twistPoint{} + } + e.p.Mul(twistGen, k) + return e +} + +// ScalarMult sets e to a*k and then returns e. +func (e *G2) ScalarMult(a *G2, k *big.Int) *G2 { + if e.p == nil { + e.p = &twistPoint{} + } + e.p.Mul(a.p, k) + return e +} + +// Add sets e to a+b and then returns e. +func (e *G2) Add(a, b *G2) *G2 { + if e.p == nil { + e.p = &twistPoint{} + } + e.p.Add(a.p, b.p) + return e +} + +// Neg sets e to -a and then returns e. +func (e *G2) Neg(a *G2) *G2 { + if e.p == nil { + e.p = &twistPoint{} + } + e.p.Neg(a.p) + return e +} + +// Set sets e to a and then returns e. +func (e *G2) Set(a *G2) *G2 { + if e.p == nil { + e.p = &twistPoint{} + } + e.p.Set(a.p) + return e +} + +// Marshal converts e into a byte slice. +func (e *G2) Marshal() []byte { + // Each value is a 256-bit number. + const numBytes = 256 / 8 + + if e.p == nil { + e.p = &twistPoint{} + } + + e.p.MakeAffine() + ret := make([]byte, numBytes*4) + if e.p.IsInfinity() { + return ret + } + temp := &gfP{} + + montDecode(temp, &e.p.x.x) + temp.Marshal(ret) + montDecode(temp, &e.p.x.y) + temp.Marshal(ret[numBytes:]) + montDecode(temp, &e.p.y.x) + temp.Marshal(ret[2*numBytes:]) + montDecode(temp, &e.p.y.y) + temp.Marshal(ret[3*numBytes:]) + + return ret +} + +// Unmarshal sets e to the result of converting the output of Marshal back into +// a group element and then returns e. +func (e *G2) Unmarshal(m []byte) ([]byte, error) { + // Each value is a 256-bit number. + const numBytes = 256 / 8 + if len(m) < 4*numBytes { + return nil, errors.New("bn256: not enough data") + } + // Unmarshal the points and check their caps + if e.p == nil { + e.p = &twistPoint{} + } + var err error + if err = e.p.x.x.Unmarshal(m); err != nil { + return nil, err + } + if err = e.p.x.y.Unmarshal(m[numBytes:]); err != nil { + return nil, err + } + if err = e.p.y.x.Unmarshal(m[2*numBytes:]); err != nil { + return nil, err + } + if err = e.p.y.y.Unmarshal(m[3*numBytes:]); err != nil { + return nil, err + } + // Encode into Montgomery form and ensure it's on the curve + montEncode(&e.p.x.x, &e.p.x.x) + montEncode(&e.p.x.y, &e.p.x.y) + montEncode(&e.p.y.x, &e.p.y.x) + montEncode(&e.p.y.y, &e.p.y.y) + + if e.p.x.IsZero() && e.p.y.IsZero() { + // This is the point at infinity. + e.p.y.SetOne() + e.p.z.SetZero() + e.p.t.SetZero() + } else { + e.p.z.SetOne() + e.p.t.SetOne() + + if !e.p.IsOnCurve() { + return nil, errors.New("bn256: malformed point") + } + } + return m[4*numBytes:], nil +} + +// GT is an abstract cyclic group. The zero value is suitable for use as the +// output of an operation, but cannot be used as an input. +type GT struct { + p *gfP12 +} + +// Pair calculates an Optimal Ate pairing. +func Pair(g1 *G1, g2 *G2) *GT { + return >{optimalAte(g2.p, g1.p)} +} + +// PairingCheck calculates the Optimal Ate pairing for a set of points. +func PairingCheck(a []*G1, b []*G2) bool { + acc := new(gfP12) + acc.SetOne() + + for i := 0; i < len(a); i++ { + if a[i].p.IsInfinity() || b[i].p.IsInfinity() { + continue + } + acc.Mul(acc, miller(b[i].p, a[i].p)) + } + return finalExponentiation(acc).IsOne() +} + +// Miller applies Miller's algorithm, which is a bilinear function from the +// source groups to F_p^12. Miller(g1, g2).Finalize() is equivalent to Pair(g1, +// g2). +func Miller(g1 *G1, g2 *G2) *GT { + return >{miller(g2.p, g1.p)} +} + +func (g *GT) String() string { + return "bn256.GT" + g.p.String() +} + +// ScalarMult sets e to a*k and then returns e. +func (e *GT) ScalarMult(a *GT, k *big.Int) *GT { + if e.p == nil { + e.p = &gfP12{} + } + e.p.Exp(a.p, k) + return e +} + +// Add sets e to a+b and then returns e. +func (e *GT) Add(a, b *GT) *GT { + if e.p == nil { + e.p = &gfP12{} + } + e.p.Mul(a.p, b.p) + return e +} + +// Neg sets e to -a and then returns e. +func (e *GT) Neg(a *GT) *GT { + if e.p == nil { + e.p = &gfP12{} + } + e.p.Conjugate(a.p) + return e +} + +// Set sets e to a and then returns e. +func (e *GT) Set(a *GT) *GT { + if e.p == nil { + e.p = &gfP12{} + } + e.p.Set(a.p) + return e +} + +// Finalize is a linear function from F_p^12 to GT. +func (e *GT) Finalize() *GT { + ret := finalExponentiation(e.p) + e.p.Set(ret) + return e +} + +// Marshal converts e into a byte slice. +func (e *GT) Marshal() []byte { + // Each value is a 256-bit number. + const numBytes = 256 / 8 + + ret := make([]byte, numBytes*12) + temp := &gfP{} + + montDecode(temp, &e.p.x.x.x) + temp.Marshal(ret) + montDecode(temp, &e.p.x.x.y) + temp.Marshal(ret[numBytes:]) + montDecode(temp, &e.p.x.y.x) + temp.Marshal(ret[2*numBytes:]) + montDecode(temp, &e.p.x.y.y) + temp.Marshal(ret[3*numBytes:]) + montDecode(temp, &e.p.x.z.x) + temp.Marshal(ret[4*numBytes:]) + montDecode(temp, &e.p.x.z.y) + temp.Marshal(ret[5*numBytes:]) + montDecode(temp, &e.p.y.x.x) + temp.Marshal(ret[6*numBytes:]) + montDecode(temp, &e.p.y.x.y) + temp.Marshal(ret[7*numBytes:]) + montDecode(temp, &e.p.y.y.x) + temp.Marshal(ret[8*numBytes:]) + montDecode(temp, &e.p.y.y.y) + temp.Marshal(ret[9*numBytes:]) + montDecode(temp, &e.p.y.z.x) + temp.Marshal(ret[10*numBytes:]) + montDecode(temp, &e.p.y.z.y) + temp.Marshal(ret[11*numBytes:]) + + return ret +} + +// Unmarshal sets e to the result of converting the output of Marshal back into +// a group element and then returns e. +func (e *GT) Unmarshal(m []byte) ([]byte, error) { + // Each value is a 256-bit number. + const numBytes = 256 / 8 + + if len(m) < 12*numBytes { + return nil, errors.New("bn256: not enough data") + } + + if e.p == nil { + e.p = &gfP12{} + } + + var err error + if err = e.p.x.x.x.Unmarshal(m); err != nil { + return nil, err + } + if err = e.p.x.x.y.Unmarshal(m[numBytes:]); err != nil { + return nil, err + } + if err = e.p.x.y.x.Unmarshal(m[2*numBytes:]); err != nil { + return nil, err + } + if err = e.p.x.y.y.Unmarshal(m[3*numBytes:]); err != nil { + return nil, err + } + if err = e.p.x.z.x.Unmarshal(m[4*numBytes:]); err != nil { + return nil, err + } + if err = e.p.x.z.y.Unmarshal(m[5*numBytes:]); err != nil { + return nil, err + } + if err = e.p.y.x.x.Unmarshal(m[6*numBytes:]); err != nil { + return nil, err + } + if err = e.p.y.x.y.Unmarshal(m[7*numBytes:]); err != nil { + return nil, err + } + if err = e.p.y.y.x.Unmarshal(m[8*numBytes:]); err != nil { + return nil, err + } + if err = e.p.y.y.y.Unmarshal(m[9*numBytes:]); err != nil { + return nil, err + } + if err = e.p.y.z.x.Unmarshal(m[10*numBytes:]); err != nil { + return nil, err + } + if err = e.p.y.z.y.Unmarshal(m[11*numBytes:]); err != nil { + return nil, err + } + montEncode(&e.p.x.x.x, &e.p.x.x.x) + montEncode(&e.p.x.x.y, &e.p.x.x.y) + montEncode(&e.p.x.y.x, &e.p.x.y.x) + montEncode(&e.p.x.y.y, &e.p.x.y.y) + montEncode(&e.p.x.z.x, &e.p.x.z.x) + montEncode(&e.p.x.z.y, &e.p.x.z.y) + montEncode(&e.p.y.x.x, &e.p.y.x.x) + montEncode(&e.p.y.x.y, &e.p.y.x.y) + montEncode(&e.p.y.y.x, &e.p.y.y.x) + montEncode(&e.p.y.y.y, &e.p.y.y.y) + montEncode(&e.p.y.z.x, &e.p.y.z.x) + montEncode(&e.p.y.z.y, &e.p.y.z.y) + + return m[12*numBytes:], nil +} |