/
fq6.go
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/
fq6.go
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package bls
import (
"fmt"
"io"
)
// FQ6 is an element of FQ6 represented by c0 + c1*v + v2*v**2
type FQ6 struct {
c0 FQ2
c1 FQ2
c2 FQ2
}
// NewFQ6 creates a new FQ6 element.
func NewFQ6(c0 FQ2, c1 FQ2, c2 FQ2) *FQ6 {
return &FQ6{
c0: c0,
c1: c1,
c2: c2,
}
}
func (f FQ6) String() string {
return fmt.Sprintf("Fq6(%s + %s*v + %s*v^2)", f.c0, f.c1, f.c2)
}
// Copy creates a copy of the field element.
func (f FQ6) Copy() *FQ6 {
return NewFQ6(f.c0, f.c1, f.c2)
}
// MulByNonresidueAssign multiplies by quadratic nonresidue v.
func (f *FQ6) MulByNonresidueAssign() {
f.c0, f.c1, f.c2 = f.c2, f.c0, f.c1
f.c0.MultiplyByNonresidueAssign()
}
// MulBy1Assign multiplies the FQ6 by an FQ2.
func (f *FQ6) MulBy1Assign(c1 FQ2) {
b := f.c1.Copy()
b.MulAssign(c1)
tmp := f.c1.Copy()
tmp.AddAssign(f.c2)
t1 := c1.Copy()
t1.MulAssign(tmp)
t1.SubAssign(b)
t1.MultiplyByNonresidueAssign()
tmp = f.c0.Copy()
tmp.AddAssign(f.c1)
t2 := c1.Copy()
t2.MulAssign(tmp)
t2.SubAssign(b)
f.c0 = t1
f.c1 = t2
f.c2 = b
}
// MulBy01Assign multiplies by c0 and c1.
func (f *FQ6) MulBy01Assign(c0 FQ2, c1 FQ2) {
a := f.c0.Copy()
a.MulAssign(c0)
b := f.c1.Copy()
b.MulAssign(c1)
tmp := f.c1.Copy()
tmp.AddAssign(f.c2)
t1 := c1.Copy()
t1.MulAssign(tmp)
t1.SubAssign(b)
t1.MultiplyByNonresidueAssign()
t1.AddAssign(a)
tmp = f.c0.Copy()
tmp.AddAssign(f.c2)
t3 := c0.Copy()
t3.MulAssign(tmp)
t3.SubAssign(a)
t3.AddAssign(b)
tmp = f.c0.Copy()
tmp.AddAssign(f.c1)
t2 := c0.Copy()
t2.AddAssign(c1)
t2.MulAssign(tmp)
t2.SubAssign(a)
t2.SubAssign(b)
f.c0 = t1
f.c1 = t2
f.c2 = t3
}
// FQ6Zero represents the zero value of FQ6.
var FQ6Zero = NewFQ6(FQ2Zero, FQ2Zero, FQ2Zero)
// FQ6One represents the one value of FQ6.
var FQ6One = NewFQ6(FQ2One, FQ2Zero, FQ2Zero)
// Equals checks if two FQ6 elements are equal.
func (f FQ6) Equals(other *FQ6) bool {
return f.c0.Equals(other.c0) && f.c1.Equals(other.c1) && f.c2.Equals(other.c2)
}
// IsZero checks if the FQ6 element is zero.
func (f FQ6) IsZero() bool {
return f.Equals(FQ6Zero)
}
// DoubleAssign doubles the coefficients of the FQ6 element.
func (f *FQ6) DoubleAssign() {
f.c0.DoubleAssign()
f.c1.DoubleAssign()
f.c2.DoubleAssign()
}
// NegAssign negates the coefficients of the FQ6 element.
func (f *FQ6) NegAssign() {
f.c0.NegAssign()
f.c1.NegAssign()
f.c2.NegAssign()
}
// AddAssign the coefficients of the FQ6 element to another.
func (f *FQ6) AddAssign(other *FQ6) {
f.c0.AddAssign(other.c0)
f.c1.AddAssign(other.c1)
f.c2.AddAssign(other.c2)
}
// SubAssign subtracts the coefficients of the FQ6 element from another.
func (f *FQ6) SubAssign(other *FQ6) {
f.c0.SubAssign(other.c0)
f.c1.SubAssign(other.c1)
f.c2.SubAssign(other.c2)
}
var bigThree = NewFQRepr(3)
var bigThreeFQ = FQReprToFQ(bigThree)
var fq2nqr = NewFQ2(
FQOne,
FQOne,
)
var frobeniusCoeffFQ6c1 = [6]FQ2{
// Fq2(u + 1)**(((q^0) - 1) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493}),
FQReprToFQRaw(FQRepr{0, 0, 0, 0, 0, 0}),
),
// Fq2(u + 1)**(((q^1) - 1) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
FQReprToFQRaw(FQRepr{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x3f97d6e83d050d2, 0x18f0206554638741}),
),
// Fq2(u + 1)**(((q^2) - 1) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x51ba4ab241b6160}),
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
),
// Fq2(u + 1)**(((q^3) - 1) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
FQReprToFQRaw(FQRepr{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493}),
),
// Fq2(u + 1)**(((q^4) - 1) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x3f97d6e83d050d2, 0x18f0206554638741}),
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
),
// Fq2(u + 1)**(((q^5) - 1) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
FQReprToFQRaw(FQRepr{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x51ba4ab241b6160}),
),
}
var frobeniusCoeffFQ6c2 = [6]FQ2{
// Fq2(u + 1)**(((2q^0) - 2) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493}),
FQReprToFQRaw(FQRepr{0, 0, 0, 0, 0, 0}),
),
// Fq2(u + 1)**(((2q^1) - 2) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0x890dc9e4867545c3, 0x2af322533285a5d5, 0x50880866309b7e2c, 0xa20d1b8c7e881024, 0x14e4f04fe2db9068, 0x14e56d3f1564853a}),
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
),
// Fq2(u + 1)**(((2q^2) - 2) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x3f97d6e83d050d2, 0x18f0206554638741}),
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
),
// Fq2(u + 1)**(((2q^3) - 2) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x7e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x40ab3263eff0206}),
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
),
// Fq2(u + 1)**(((2q^4) - 2) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x51ba4ab241b6160}),
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
),
// Fq2(u + 1)**(((2q^5) - 2) / 3)
NewFQ2(
FQReprToFQRaw(FQRepr{0xecfb361b798dba3a, 0xc100ddb891865a2c, 0xec08ff1232bda8e, 0xd5c13cc6f1ca4721, 0x47222a47bf7b5c04, 0x110f184e51c5f59}),
FQReprToFQRaw(FQRepr{0x0, 0x0, 0x0, 0x0, 0x0, 0x0}),
),
}
// FrobeniusMapAssign runs the frobenius map algorithm with a certain power.
func (f *FQ6) FrobeniusMapAssign(power uint8) {
f.c0.FrobeniusMapAssign(power)
f.c1.FrobeniusMapAssign(power)
f.c2.FrobeniusMapAssign(power)
f.c1.MulAssign(frobeniusCoeffFQ6c1[power%6])
f.c2.MulAssign(frobeniusCoeffFQ6c2[power%6])
}
// SquareAssign squares the FQ6 element.
func (f *FQ6) SquareAssign() {
s0 := f.c0.Copy()
s0.SquareAssign()
ab := f.c0.Copy()
ab.MulAssign(f.c1)
s1 := ab.Copy()
s1.DoubleAssign()
s2 := f.c0.Copy()
s2.SubAssign(f.c1)
s2.AddAssign(f.c2)
s2.SquareAssign()
bc := f.c1.Copy()
bc.MulAssign(f.c2)
s3 := bc.Copy()
s3.DoubleAssign()
s4 := f.c2.Copy()
s4.SquareAssign()
f.c0 = s3.Copy()
f.c0.MultiplyByNonresidueAssign()
f.c0.AddAssign(s0)
f.c1 = s4.Copy()
f.c1.MultiplyByNonresidueAssign()
f.c1.AddAssign(s1)
f.c2 = s1.Copy()
f.c2.AddAssign(s2)
f.c2.AddAssign(s3)
f.c2.SubAssign(s0)
f.c2.SubAssign(s4)
}
// MulAssign multiplies two FQ6 elements together.
func (f *FQ6) MulAssign(other *FQ6) {
aa := f.c0.Copy()
aa.MulAssign(other.c0)
bb := f.c1.Copy()
bb.MulAssign(other.c1)
cc := f.c2.Copy()
cc.MulAssign(other.c2)
tmp := f.c1.Copy()
tmp.AddAssign(f.c2)
t1 := other.c1.Copy()
t1.AddAssign(other.c2)
t1.MulAssign(tmp)
t1.SubAssign(bb)
t1.SubAssign(cc)
t1.MultiplyByNonresidueAssign()
t1.AddAssign(aa)
tmp = f.c0.Copy()
tmp.AddAssign(f.c2)
f.c2 = other.c0.Copy()
f.c2.AddAssign(other.c2)
f.c2.MulAssign(tmp)
f.c2.SubAssign(aa)
f.c2.AddAssign(bb)
f.c2.SubAssign(cc)
tmp = f.c0.Copy()
tmp.AddAssign(f.c1)
f.c1 = other.c0.Copy()
f.c1.AddAssign(other.c1)
f.c1.MulAssign(tmp)
f.c1.SubAssign(aa)
f.c1.SubAssign(bb)
cc.MultiplyByNonresidueAssign()
f.c1.AddAssign(cc)
f.c0 = t1
}
// InverseAssign finds the inverse of the FQ6 element.
func (f *FQ6) InverseAssign() bool {
c0 := f.c2.Copy()
c0.MultiplyByNonresidueAssign()
c0.MulAssign(f.c1)
c0.NegAssign()
c0s := f.c0.Copy()
c0s.SquareAssign()
c0.AddAssign(c0s)
c1 := f.c2.Copy()
c1.SquareAssign()
c1.MultiplyByNonresidueAssign()
c0c1 := f.c0.Copy()
c0c1.MulAssign(f.c1)
c0c2 := f.c0.Copy()
c0c2.MulAssign(f.c2)
c1c2 := f.c1.Copy()
c1c2.MulAssign(f.c2)
c1.SubAssign(c0c1)
c2 := f.c1.Copy()
c2.SquareAssign()
c2.SubAssign(c0c2)
tmp1 := f.c2.Copy()
tmp1.MulAssign(c1)
tmp2 := f.c1.Copy()
tmp2.MulAssign(c2)
tmp1.AddAssign(tmp2)
tmp1.MultiplyByNonresidueAssign()
tmp2 = f.c0.Copy()
tmp2.MulAssign(c0)
tmp1.AddAssign(tmp2)
if !tmp1.InverseAssign() {
return false
}
f.c0 = tmp1.Copy()
f.c0.MulAssign(c0)
f.c1 = tmp1.Copy()
f.c1.MulAssign(c1)
f.c2 = tmp1.Copy()
f.c2.MulAssign(c2)
return true
}
// Exp raises the element ot a specific power.
func (f FQ6) Exp(n *FQRepr) *FQ6 {
nCopy := n.Copy()
res := FQ6One.Copy()
fi := f.Copy()
for nCopy.Cmp(bigZero) != 0 {
if !isEven(nCopy) {
res.MulAssign(fi)
}
fi.MulAssign(fi)
nCopy.Rsh(1)
}
return res
}
// RandFQ6 generates a random FQ6 element.
func RandFQ6(reader io.Reader) (*FQ6, error) {
c0, err := RandFQ2(reader)
if err != nil {
return nil, err
}
c1, err := RandFQ2(reader)
if err != nil {
return nil, err
}
c2, err := RandFQ2(reader)
if err != nil {
return nil, err
}
return NewFQ6(c0, c1, c2), nil
}