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e12_pairing.go
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e12_pairing.go
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package fields_bls12377
import "github.com/airchains-network/gnark/frontend"
// nSquareKarabina2345 repeated compressed cyclotmic square
func (e *E12) nSquareKarabina2345(api frontend.API, n int) {
for i := 0; i < n; i++ {
e.CyclotomicSquareKarabina2345(api, *e)
}
}
// nSquareKarabina12345 repeated compressed cyclotmic square
func (e *E12) nSquareKarabina12345(api frontend.API, n int) {
for i := 0; i < n; i++ {
e.CyclotomicSquareKarabina12345(api, *e)
}
}
// Square034 squares a sparse element in Fp12
func (e *E12) Square034(api frontend.API, x E12) *E12 {
var c0, c2, c3 E6
c0.B0.Sub(api, x.C0.B0, x.C1.B0)
c0.B1.Neg(api, x.C1.B1)
c0.B2 = E2{0, 0}
c3.B0 = x.C0.B0
c3.B1.Neg(api, x.C1.B0)
c3.B2.Neg(api, x.C1.B1)
c2.Mul0By01(api, x.C0.B0, x.C1.B0, x.C1.B1)
c3.MulBy01(api, c0.B0, c0.B1).Add(api, c3, c2)
e.C1.B0.Add(api, c2.B0, c2.B0)
e.C1.B1.Add(api, c2.B1, c2.B1)
e.C0.B0 = c3.B0
e.C0.B1.Add(api, c3.B1, c2.B0)
e.C0.B2.Add(api, c3.B2, c2.B1)
return e
}
// MulBy034 multiplication by sparse element
func (e *E12) MulBy034(api frontend.API, c3, c4 E2) *E12 {
var d E6
a := e.C0
b := e.C1
b.MulBy01(api, c3, c4)
c3.Add(api, E2{A0: 1, A1: 0}, c3)
d.Add(api, e.C0, e.C1)
d.MulBy01(api, c3, c4)
e.C1.Add(api, a, b).Neg(api, e.C1).Add(api, e.C1, d)
e.C0.MulByNonResidue(api, b).Add(api, e.C0, a)
return e
}
// Mul034By034 multiplication of sparse element (1,0,0,c3,c4,0) by sparse element (1,0,0,d3,d4,0)
func Mul034By034(api frontend.API, d3, d4, c3, c4 E2) *[5]E2 {
var one, tmp, x00, x3, x4, x04, x03, x34 E2
one.SetOne()
x3.Mul(api, c3, d3)
x4.Mul(api, c4, d4)
x04.Add(api, c4, d4)
x03.Add(api, c3, d3)
tmp.Add(api, c3, c4)
x34.Add(api, d3, d4).
Mul(api, x34, tmp).
Sub(api, x34, x3).
Sub(api, x34, x4)
x00.MulByNonResidue(api, x4)
x00.A0 = api.Add(x00.A0, 1)
return &[5]E2{x00, x3, x34, x03, x04}
}
func Mul01234By034(api frontend.API, x [5]E2, z3, z4 E2) *E12 {
var a, b, z1, z0, one E6
var zero E2
zero.SetZero()
one.SetOne()
c0 := &E6{B0: x[0], B1: x[1], B2: x[2]}
c1 := &E6{B0: x[3], B1: x[4], B2: zero}
a.Add(api, one, E6{B0: z3, B1: z4, B2: zero})
b.Add(api, *c0, *c1)
a.Mul(api, a, b)
c := *Mul01By01(api, z3, z4, x[3], x[4])
z1.Sub(api, a, *c0)
z1.Sub(api, z1, c)
z0.MulByNonResidue(api, c)
z0.Add(api, z0, *c0)
return &E12{
C0: z0,
C1: z1,
}
}
func (e *E12) MulBy01234(api frontend.API, x [5]E2) *E12 {
var a, b, c, z1, z0 E6
var zero E2
zero.SetZero()
c0 := &E6{B0: x[0], B1: x[1], B2: x[2]}
c1 := &E6{B0: x[3], B1: x[4], B2: zero}
a.Add(api, e.C0, e.C1)
b.Add(api, *c0, *c1)
a.Mul(api, a, b)
b.Mul(api, e.C0, *c0)
c = e.C1
c.MulBy01(api, x[3], x[4])
z1.Sub(api, a, b)
z1.Sub(api, z1, c)
z0.MulByNonResidue(api, c)
z0.Add(api, z0, b)
e.C0 = z0
e.C1 = z1
return e
}
// ExpX0 compute e1^X0, where X0=9586122913090633729
func (e *E12) ExpX0(api frontend.API, e1 E12) *E12 {
res := e1
res.nSquareKarabina2345(api, 5)
res.DecompressKarabina2345(api, res)
res.Mul(api, res, e1)
x33 := res
res.nSquareKarabina2345(api, 7)
res.DecompressKarabina2345(api, res)
res.Mul(api, res, x33)
res.nSquareKarabina2345(api, 4)
res.DecompressKarabina2345(api, res)
res.Mul(api, res, e1)
res.CyclotomicSquare(api, res)
res.Mul(api, res, e1)
res.nSquareKarabina2345(api, 46)
res.DecompressKarabina2345(api, res)
res.Mul(api, res, e1)
*e = res
return e
}
// ExpX0Minus1Square computes e1^((X0-1)^2), where X0=9586122913090633729
func (e *E12) ExpX0Minus1Square(api frontend.API, e1 E12) *E12 {
var t0, t1, t2, t3, res E12
res = e1
res.nSquareKarabina12345(api, 3)
res.DecompressKarabina12345(api, res)
t0.CyclotomicSquare(api, res)
t2.Mul(api, e1, t0)
res.Mul(api, res, t2)
t0.Mul(api, e1, res)
t1.CyclotomicSquare(api, t0)
t1.Mul(api, t2, t1)
t3 = t1
t3.nSquareKarabina2345(api, 7)
t3.DecompressKarabina2345(api, t3)
t2.Mul(api, t2, t3)
t2.nSquareKarabina2345(api, 11)
t2.DecompressKarabina2345(api, t2)
t1.Mul(api, t1, t2)
t0.Mul(api, t0, t1)
t0.nSquareKarabina2345(api, 7)
t0.DecompressKarabina2345(api, t0)
res.Mul(api, res, t0)
res.nSquareKarabina12345(api, 3)
res.DecompressKarabina12345(api, res)
res.Mul(api, e1, res)
res.nSquareKarabina2345(api, 92)
e.DecompressKarabina2345(api, res)
return e
}