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