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- package bn256
- import (
- "math/big"
- )
- type gfP6 struct {
- x, y, z *gfP2
- }
- func newGFp6(pool *bnPool) *gfP6 {
- return &gfP6{newGFp2(pool), newGFp2(pool), newGFp2(pool)}
- }
- func (e *gfP6) String() string {
- return "(" + e.x.String() + "," + e.y.String() + "," + e.z.String() + ")"
- }
- func (e *gfP6) Put(pool *bnPool) {
- e.x.Put(pool)
- e.y.Put(pool)
- e.z.Put(pool)
- }
- func (e *gfP6) Set(a *gfP6) *gfP6 {
- e.x.Set(a.x)
- e.y.Set(a.y)
- e.z.Set(a.z)
- return e
- }
- func (e *gfP6) SetZero() *gfP6 {
- e.x.SetZero()
- e.y.SetZero()
- e.z.SetZero()
- return e
- }
- func (e *gfP6) SetOne() *gfP6 {
- e.x.SetZero()
- e.y.SetZero()
- e.z.SetOne()
- return e
- }
- func (e *gfP6) Minimal() {
- e.x.Minimal()
- e.y.Minimal()
- e.z.Minimal()
- }
- func (e *gfP6) IsZero() bool {
- return e.x.IsZero() && e.y.IsZero() && e.z.IsZero()
- }
- func (e *gfP6) IsOne() bool {
- return e.x.IsZero() && e.y.IsZero() && e.z.IsOne()
- }
- func (e *gfP6) Negative(a *gfP6) *gfP6 {
- e.x.Negative(a.x)
- e.y.Negative(a.y)
- e.z.Negative(a.z)
- return e
- }
- func (e *gfP6) Frobenius(a *gfP6, pool *bnPool) *gfP6 {
- e.x.Conjugate(a.x)
- e.y.Conjugate(a.y)
- e.z.Conjugate(a.z)
- e.x.Mul(e.x, xiTo2PMinus2Over3, pool)
- e.y.Mul(e.y, xiToPMinus1Over3, pool)
- return e
- }
- func (e *gfP6) FrobeniusP2(a *gfP6) *gfP6 {
-
- e.x.MulScalar(a.x, xiTo2PSquaredMinus2Over3)
-
- e.y.MulScalar(a.y, xiToPSquaredMinus1Over3)
- e.z.Set(a.z)
- return e
- }
- func (e *gfP6) Add(a, b *gfP6) *gfP6 {
- e.x.Add(a.x, b.x)
- e.y.Add(a.y, b.y)
- e.z.Add(a.z, b.z)
- return e
- }
- func (e *gfP6) Sub(a, b *gfP6) *gfP6 {
- e.x.Sub(a.x, b.x)
- e.y.Sub(a.y, b.y)
- e.z.Sub(a.z, b.z)
- return e
- }
- func (e *gfP6) Double(a *gfP6) *gfP6 {
- e.x.Double(a.x)
- e.y.Double(a.y)
- e.z.Double(a.z)
- return e
- }
- func (e *gfP6) Mul(a, b *gfP6, pool *bnPool) *gfP6 {
-
-
-
- v0 := newGFp2(pool)
- v0.Mul(a.z, b.z, pool)
- v1 := newGFp2(pool)
- v1.Mul(a.y, b.y, pool)
- v2 := newGFp2(pool)
- v2.Mul(a.x, b.x, pool)
- t0 := newGFp2(pool)
- t0.Add(a.x, a.y)
- t1 := newGFp2(pool)
- t1.Add(b.x, b.y)
- tz := newGFp2(pool)
- tz.Mul(t0, t1, pool)
- tz.Sub(tz, v1)
- tz.Sub(tz, v2)
- tz.MulXi(tz, pool)
- tz.Add(tz, v0)
- t0.Add(a.y, a.z)
- t1.Add(b.y, b.z)
- ty := newGFp2(pool)
- ty.Mul(t0, t1, pool)
- ty.Sub(ty, v0)
- ty.Sub(ty, v1)
- t0.MulXi(v2, pool)
- ty.Add(ty, t0)
- t0.Add(a.x, a.z)
- t1.Add(b.x, b.z)
- tx := newGFp2(pool)
- tx.Mul(t0, t1, pool)
- tx.Sub(tx, v0)
- tx.Add(tx, v1)
- tx.Sub(tx, v2)
- e.x.Set(tx)
- e.y.Set(ty)
- e.z.Set(tz)
- t0.Put(pool)
- t1.Put(pool)
- tx.Put(pool)
- ty.Put(pool)
- tz.Put(pool)
- v0.Put(pool)
- v1.Put(pool)
- v2.Put(pool)
- return e
- }
- func (e *gfP6) MulScalar(a *gfP6, b *gfP2, pool *bnPool) *gfP6 {
- e.x.Mul(a.x, b, pool)
- e.y.Mul(a.y, b, pool)
- e.z.Mul(a.z, b, pool)
- return e
- }
- func (e *gfP6) MulGFP(a *gfP6, b *big.Int) *gfP6 {
- e.x.MulScalar(a.x, b)
- e.y.MulScalar(a.y, b)
- e.z.MulScalar(a.z, b)
- return e
- }
- func (e *gfP6) MulTau(a *gfP6, pool *bnPool) {
- tz := newGFp2(pool)
- tz.MulXi(a.x, pool)
- ty := newGFp2(pool)
- ty.Set(a.y)
- e.y.Set(a.z)
- e.x.Set(ty)
- e.z.Set(tz)
- tz.Put(pool)
- ty.Put(pool)
- }
- func (e *gfP6) Square(a *gfP6, pool *bnPool) *gfP6 {
- v0 := newGFp2(pool).Square(a.z, pool)
- v1 := newGFp2(pool).Square(a.y, pool)
- v2 := newGFp2(pool).Square(a.x, pool)
- c0 := newGFp2(pool).Add(a.x, a.y)
- c0.Square(c0, pool)
- c0.Sub(c0, v1)
- c0.Sub(c0, v2)
- c0.MulXi(c0, pool)
- c0.Add(c0, v0)
- c1 := newGFp2(pool).Add(a.y, a.z)
- c1.Square(c1, pool)
- c1.Sub(c1, v0)
- c1.Sub(c1, v1)
- xiV2 := newGFp2(pool).MulXi(v2, pool)
- c1.Add(c1, xiV2)
- c2 := newGFp2(pool).Add(a.x, a.z)
- c2.Square(c2, pool)
- c2.Sub(c2, v0)
- c2.Add(c2, v1)
- c2.Sub(c2, v2)
- e.x.Set(c2)
- e.y.Set(c1)
- e.z.Set(c0)
- v0.Put(pool)
- v1.Put(pool)
- v2.Put(pool)
- c0.Put(pool)
- c1.Put(pool)
- c2.Put(pool)
- xiV2.Put(pool)
- return e
- }
- func (e *gfP6) Invert(a *gfP6, pool *bnPool) *gfP6 {
-
-
-
-
-
-
-
-
-
-
-
-
- t1 := newGFp2(pool)
- A := newGFp2(pool)
- A.Square(a.z, pool)
- t1.Mul(a.x, a.y, pool)
- t1.MulXi(t1, pool)
- A.Sub(A, t1)
- B := newGFp2(pool)
- B.Square(a.x, pool)
- B.MulXi(B, pool)
- t1.Mul(a.y, a.z, pool)
- B.Sub(B, t1)
- C := newGFp2(pool)
- C.Square(a.y, pool)
- t1.Mul(a.x, a.z, pool)
- C.Sub(C, t1)
- F := newGFp2(pool)
- F.Mul(C, a.y, pool)
- F.MulXi(F, pool)
- t1.Mul(A, a.z, pool)
- F.Add(F, t1)
- t1.Mul(B, a.x, pool)
- t1.MulXi(t1, pool)
- F.Add(F, t1)
- F.Invert(F, pool)
- e.x.Mul(C, F, pool)
- e.y.Mul(B, F, pool)
- e.z.Mul(A, F, pool)
- t1.Put(pool)
- A.Put(pool)
- B.Put(pool)
- C.Put(pool)
- F.Put(pool)
- return e
- }
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