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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.One(), fq6.F.One()}
}
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 {
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)),
}
}