1package bn128
  2
  3import (
  4	"math/big"
  5)
  6
  7// Fq2 is Field 2
  8type Fq2 struct {
  9	F          Fq
 10	NonResidue *big.Int
 11}
 12
 13// NewFq2 generates a new Fq2
 14func NewFq2(f Fq, nonResidue *big.Int) Fq2 {
 15	fq2 := Fq2{
 16		f,
 17		nonResidue,
 18	}
 19	return fq2
 20}
 21
 22// Zero returns a Zero value on the Fq2
 23func (fq2 Fq2) Zero() [2]*big.Int {
 24	return [2]*big.Int{fq2.F.Zero(), fq2.F.Zero()}
 25}
 26
 27// One returns a One value on the Fq2
 28func (fq2 Fq2) One() [2]*big.Int {
 29	return [2]*big.Int{fq2.F.One(), fq2.F.One()}
 30}
 31
 32func (fq2 Fq2) mulByNonResidue(a *big.Int) *big.Int {
 33	return fq2.F.Mul(fq2.NonResidue, a)
 34}
 35
 36// Add performs an addition on the Fq2
 37func (fq2 Fq2) Add(a, b [2]*big.Int) [2]*big.Int {
 38	return [2]*big.Int{
 39		fq2.F.Add(a[0], b[0]),
 40		fq2.F.Add(a[1], b[1]),
 41	}
 42}
 43
 44// Double performs a doubling on the Fq2
 45func (fq2 Fq2) Double(a [2]*big.Int) [2]*big.Int {
 46	return fq2.Add(a, a)
 47}
 48
 49// Sub performs a substraction on the Fq2
 50func (fq2 Fq2) Sub(a, b [2]*big.Int) [2]*big.Int {
 51	return [2]*big.Int{
 52		fq2.F.Sub(a[0], b[0]),
 53		fq2.F.Sub(a[1], b[1]),
 54	}
 55}
 56
 57// Neg performs a negation on the Fq2
 58func (fq2 Fq2) Neg(a [2]*big.Int) [2]*big.Int {
 59	return fq2.Sub(fq2.Zero(), a)
 60}
 61
 62// Mul performs a multiplication on the Fq2
 63func (fq2 Fq2) Mul(a, b [2]*big.Int) [2]*big.Int {
 64	// Multiplication and Squaring on Pairing-Friendly.pdf; Section 3 (Karatsuba)
 65	v0 := fq2.F.Mul(a[0], b[0])
 66	v1 := fq2.F.Mul(a[1], b[1])
 67	return [2]*big.Int{
 68		fq2.F.Add(v0, fq2.mulByNonResidue(v1)),
 69		fq2.F.Sub(
 70			fq2.F.Mul(
 71				fq2.F.Add(a[0], a[1]),
 72				fq2.F.Add(b[0], b[1])),
 73			fq2.F.Add(v0, v1)),
 74	}
 75}
 76
 77// Inverse returns the inverse on the Fq2
 78func (fq2 Fq2) Inverse(a [2]*big.Int) [2]*big.Int {
 79	t0 := fq2.F.Square(a[0])
 80	t1 := fq2.F.Square(a[1])
 81	t2 := fq2.F.Sub(t0, fq2.mulByNonResidue(t1))
 82	t3 := fq2.F.Inverse(t2)
 83	return [2]*big.Int{
 84		fq2.F.Mul(a[0], t3),
 85		fq2.F.Neg(fq2.F.Mul(a[1], t3)),
 86	}
 87}
 88
 89// Div performs a division on the Fq2
 90func (fq2 Fq2) Div(a, b [2]*big.Int) [2]*big.Int {
 91	return fq2.Mul(a, fq2.Inverse(b))
 92}
 93
 94// Square performs a square operation on the Fq2
 95func (fq2 Fq2) Square(a [2]*big.Int) [2]*big.Int {
 96	ab := fq2.F.Mul(a[0], a[1])
 97
 98	return [2]*big.Int{
 99		fq2.F.Sub(
100			fq2.F.Mul(
101				fq2.F.Add(a[0], a[1]),
102				fq2.F.Add(
103					a[0],
104					fq2.mulByNonResidue(a[1]))),
105			fq2.F.Add(
106				ab,
107				fq2.mulByNonResidue(ab))),
108		fq2.F.Add(ab, ab),
109	}
110}