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e6_pairing.go
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e6_pairing.go
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package fptower
import "github.com/consensys/gnark-crypto/ecc/bw6-761/fp"
func (z *E6) nSquare(n int) {
for i := 0; i < n; i++ {
z.CyclotomicSquare(z)
}
}
func (z *E6) nSquareCompressed(n int) {
for i := 0; i < n; i++ {
z.CyclotomicSquareCompressed(z)
}
}
// Expt set z to x^t in E6 and return z
func (z *E6) Expt(x *E6) *E6 {
// const tAbsVal uint64 = 9586122913090633729
// tAbsVal in binary: 1000010100001000110000000000000000000000000000000000000000000001
// drop the low 46 bits (all 0 except the least significant bit): 100001010000100011 = 136227
// Shortest addition chains can be found at https://wwwhomes.uni-bielefeld.de/achim/addition_chain.html
var result, x33 E6
// a shortest addition chain for 136227
result.Set(x)
result.nSquare(5)
result.Mul(&result, x)
x33.Set(&result)
result.nSquare(7)
result.Mul(&result, &x33)
result.nSquare(4)
result.Mul(&result, x)
result.CyclotomicSquare(&result)
result.Mul(&result, x)
// the remaining 46 bits
result.nSquareCompressed(46)
result.DecompressKarabina(&result)
result.Mul(&result, x)
z.Set(&result)
return z
}
// Expc2 set z to x^c2 in E6 and return z
// ht, hy = 13, 9
// c1 = ht+hy = 22 (10110)
func (z *E6) Expc2(x *E6) *E6 {
var result E6
result.CyclotomicSquare(x)
result.CyclotomicSquare(&result)
result.Mul(&result, x)
result.CyclotomicSquare(&result)
result.Mul(&result, x)
result.CyclotomicSquare(&result)
z.Set(&result)
return z
}
// Expc1 set z to x^c1 in E6 and return z
// ht, hy = 13, 9
// c1 = ht**2+3*hy**2 = 412 (110011100)
func (z *E6) Expc1(x *E6) *E6 {
var result E6
result.CyclotomicSquare(x)
result.Mul(&result, x)
result.CyclotomicSquare(&result)
result.CyclotomicSquare(&result)
result.CyclotomicSquare(&result)
result.Mul(&result, x)
result.CyclotomicSquare(&result)
result.Mul(&result, x)
result.CyclotomicSquare(&result)
result.Mul(&result, x)
result.CyclotomicSquare(&result)
result.CyclotomicSquare(&result)
z.Set(&result)
return z
}
// MulBy034 multiplication by sparse element (c0,0,0,c3,c4,0)
func (z *E6) MulBy034(c0, c3, c4 *fp.Element) *E6 {
var a, b, d E3
a.MulByElement(&z.B0, c0)
b.Set(&z.B1)
b.MulBy01(c3, c4)
c0.Add(c0, c3)
d.Add(&z.B0, &z.B1)
d.MulBy01(c0, c4)
z.B1.Add(&a, &b).Neg(&z.B1).Add(&z.B1, &d)
z.B0.MulByNonResidue(&b).Add(&z.B0, &a)
return z
}
// Mul034By034 multiplication of sparse element (c0,0,0,c3,c4,0) by sparse element (d0,0,0,d3,d4,0)
func (z *E6) Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) *E6 {
var tmp, x0, x3, x4, x04, x03, x34 fp.Element
x0.Mul(c0, d0)
x3.Mul(c3, d3)
x4.Mul(c4, d4)
tmp.Add(c0, c4)
x04.Add(d0, d4).
Mul(&x04, &tmp).
Sub(&x04, &x0).
Sub(&x04, &x4)
tmp.Add(c0, c3)
x03.Add(d0, d3).
Mul(&x03, &tmp).
Sub(&x03, &x0).
Sub(&x03, &x3)
tmp.Add(c3, c4)
x34.Add(d3, d4).
Mul(&x34, &tmp).
Sub(&x34, &x3).
Sub(&x34, &x4)
z.B0.A0.MulByNonResidue(&x4).
Add(&z.B0.A0, &x0)
z.B0.A1.Set(&x3)
z.B0.A2.Set(&x34)
z.B1.A0.Set(&x03)
z.B1.A1.Set(&x04)
z.B1.A2.SetZero()
return z
}