package bn128
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import (
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"bytes"
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"math/big"
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)
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// Fq2 is Field 2
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type Fq2 struct {
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F Fq
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NonResidue *big.Int
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}
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// NewFq2 generates a new Fq2
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func NewFq2(f Fq, nonResidue *big.Int) Fq2 {
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fq2 := Fq2{
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f,
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nonResidue,
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}
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return fq2
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}
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// Zero returns a Zero value on the Fq2
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func (fq2 Fq2) Zero() [2]*big.Int {
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return [2]*big.Int{fq2.F.Zero(), fq2.F.Zero()}
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}
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// One returns a One value on the Fq2
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func (fq2 Fq2) One() [2]*big.Int {
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return [2]*big.Int{fq2.F.One(), fq2.F.One()}
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}
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func (fq2 Fq2) mulByNonResidue(a *big.Int) *big.Int {
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return fq2.F.Mul(fq2.NonResidue, a)
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}
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// Add performs an addition on the Fq2
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func (fq2 Fq2) Add(a, b [2]*big.Int) [2]*big.Int {
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return [2]*big.Int{
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fq2.F.Add(a[0], b[0]),
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fq2.F.Add(a[1], b[1]),
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}
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}
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// Double performs a doubling on the Fq2
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func (fq2 Fq2) Double(a [2]*big.Int) [2]*big.Int {
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return fq2.Add(a, a)
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}
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// Sub performs a substraction on the Fq2
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func (fq2 Fq2) Sub(a, b [2]*big.Int) [2]*big.Int {
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return [2]*big.Int{
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fq2.F.Sub(a[0], b[0]),
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fq2.F.Sub(a[1], b[1]),
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}
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}
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// Neg performs a negation on the Fq2
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func (fq2 Fq2) Neg(a [2]*big.Int) [2]*big.Int {
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return fq2.Sub(fq2.Zero(), a)
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}
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// Mul performs a multiplication on the Fq2
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func (fq2 Fq2) Mul(a, b [2]*big.Int) [2]*big.Int {
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// Multiplication and Squaring on Pairing-Friendly.pdf; Section 3 (Karatsuba)
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v0 := fq2.F.Mul(a[0], b[0])
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v1 := fq2.F.Mul(a[1], b[1])
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return [2]*big.Int{
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fq2.F.Add(v0, fq2.mulByNonResidue(v1)),
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fq2.F.Sub(
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fq2.F.Mul(
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fq2.F.Add(a[0], a[1]),
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fq2.F.Add(b[0], b[1])),
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fq2.F.Add(v0, v1)),
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}
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}
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func (fq2 Fq2) MulScalar(base [2]*big.Int, e *big.Int) [2]*big.Int {
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res := fq2.Zero()
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rem := e
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exp := base
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for !bytes.Equal(rem.Bytes(), big.NewInt(int64(0)).Bytes()) {
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// if rem % 2 == 1
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if bytes.Equal(new(big.Int).Rem(rem, big.NewInt(int64(2))).Bytes(), big.NewInt(int64(1)).Bytes()) {
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res = fq2.Add(res, exp)
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}
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exp = fq2.Double(exp)
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rem = rem.Rsh(rem, 1) // rem = rem >> 1
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}
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return res
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}
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// Inverse returns the inverse on the Fq2
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func (fq2 Fq2) Inverse(a [2]*big.Int) [2]*big.Int {
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t0 := fq2.F.Square(a[0])
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t1 := fq2.F.Square(a[1])
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t2 := fq2.F.Sub(t0, fq2.mulByNonResidue(t1))
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t3 := fq2.F.Inverse(t2)
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return [2]*big.Int{
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fq2.F.Mul(a[0], t3),
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fq2.F.Neg(fq2.F.Mul(a[1], t3)),
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}
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}
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// Div performs a division on the Fq2
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func (fq2 Fq2) Div(a, b [2]*big.Int) [2]*big.Int {
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return fq2.Mul(a, fq2.Inverse(b))
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}
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// Square performs a square operation on the Fq2
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func (fq2 Fq2) Square(a [2]*big.Int) [2]*big.Int {
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ab := fq2.F.Mul(a[0], a[1])
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return [2]*big.Int{
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fq2.F.Sub(
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fq2.F.Mul(
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fq2.F.Add(a[0], a[1]),
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fq2.F.Add(
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a[0],
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fq2.mulByNonResidue(a[1]))),
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fq2.F.Add(
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ab,
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fq2.mulByNonResidue(ab))),
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fq2.F.Add(ab, ab),
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}
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}
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func (fq2 Fq2) IsZero(a [2]*big.Int) bool {
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return fq2.F.IsZero(a[0]) && fq2.F.IsZero(a[1])
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}
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func (fq2 Fq2) Affine(a [2]*big.Int) [2]*big.Int {
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return [2]*big.Int{
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fq2.F.Affine(a[0]),
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fq2.F.Affine(a[1]),
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}
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}
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func (fq2 Fq2) Equal(a, b [2]*big.Int) bool {
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return fq2.F.Equal(a[0], b[0]) && fq2.F.Equal(a[1], b[1])
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}
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