fields_bls12377

package
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 Go to latest Published: Feb 5, 2024 License: Apache-2.0 Imports: 5 Imported by: 0

Documentation

Overview

Package fields_bls12377 implements the fields arithmetic of the Fp12 tower used to compute the pairing over the BLS12-377 curve. 

𝔽p²[u] = 𝔽p/u²+5
𝔽p⁶[v] = 𝔽p²/v³-u
𝔽p¹²[w] = 𝔽p⁶/w²-v

Reference: https://eprint.iacr.org/2022/1162

Index

Constants

This section is empty.

Variables

View Source 
var DivE12Hint = func(_ *big.Int, inputs []*big.Int, res []*big.Int) error {
	var a, b, c bls12377.E12

	a.C0.B0.A0.SetBigInt(inputs[0])
	a.C0.B0.A1.SetBigInt(inputs[1])
	a.C0.B1.A0.SetBigInt(inputs[2])
	a.C0.B1.A1.SetBigInt(inputs[3])
	a.C0.B2.A0.SetBigInt(inputs[4])
	a.C0.B2.A1.SetBigInt(inputs[5])
	a.C1.B0.A0.SetBigInt(inputs[6])
	a.C1.B0.A1.SetBigInt(inputs[7])
	a.C1.B1.A0.SetBigInt(inputs[8])
	a.C1.B1.A1.SetBigInt(inputs[9])
	a.C1.B2.A0.SetBigInt(inputs[10])
	a.C1.B2.A1.SetBigInt(inputs[11])

	b.C0.B0.A0.SetBigInt(inputs[12])
	b.C0.B0.A1.SetBigInt(inputs[13])
	b.C0.B1.A0.SetBigInt(inputs[14])
	b.C0.B1.A1.SetBigInt(inputs[15])
	b.C0.B2.A0.SetBigInt(inputs[16])
	b.C0.B2.A1.SetBigInt(inputs[17])
	b.C1.B0.A0.SetBigInt(inputs[18])
	b.C1.B0.A1.SetBigInt(inputs[19])
	b.C1.B1.A0.SetBigInt(inputs[20])
	b.C1.B1.A1.SetBigInt(inputs[21])
	b.C1.B2.A0.SetBigInt(inputs[22])
	b.C1.B2.A1.SetBigInt(inputs[23])

	c.Inverse(&b).Mul(&c, &a)

	c.C0.B0.A0.BigInt(res[0])
	c.C0.B0.A1.BigInt(res[1])
	c.C0.B1.A0.BigInt(res[2])
	c.C0.B1.A1.BigInt(res[3])
	c.C0.B2.A0.BigInt(res[4])
	c.C0.B2.A1.BigInt(res[5])
	c.C1.B0.A0.BigInt(res[6])
	c.C1.B0.A1.BigInt(res[7])
	c.C1.B1.A0.BigInt(res[8])
	c.C1.B1.A1.BigInt(res[9])
	c.C1.B2.A0.BigInt(res[10])
	c.C1.B2.A1.BigInt(res[11])

	return nil
}
View Source 
var DivE2Hint = func(_ *big.Int, inputs []*big.Int, res []*big.Int) error {
	var a, b, c bls12377.E2

	a.A0.SetBigInt(inputs[0])
	a.A1.SetBigInt(inputs[1])
	b.A0.SetBigInt(inputs[2])
	b.A1.SetBigInt(inputs[3])

	c.Inverse(&b).Mul(&c, &a)

	c.A0.BigInt(res[0])
	c.A1.BigInt(res[1])

	return nil
}
View Source 
var DivE6Hint = func(_ *big.Int, inputs []*big.Int, res []*big.Int) error {
	var a, b, c bls12377.E6

	a.B0.A0.SetBigInt(inputs[0])
	a.B0.A1.SetBigInt(inputs[1])
	a.B1.A0.SetBigInt(inputs[2])
	a.B1.A1.SetBigInt(inputs[3])
	a.B2.A0.SetBigInt(inputs[4])
	a.B2.A1.SetBigInt(inputs[5])

	b.B0.A0.SetBigInt(inputs[6])
	b.B0.A1.SetBigInt(inputs[7])
	b.B1.A0.SetBigInt(inputs[8])
	b.B1.A1.SetBigInt(inputs[9])
	b.B2.A0.SetBigInt(inputs[10])
	b.B2.A1.SetBigInt(inputs[11])

	c.Inverse(&b).Mul(&c, &a)

	c.B0.A0.BigInt(res[0])
	c.B0.A1.BigInt(res[1])
	c.B1.A0.BigInt(res[2])
	c.B1.A1.BigInt(res[3])
	c.B2.A0.BigInt(res[4])
	c.B2.A1.BigInt(res[5])

	return nil
}
View Source 
var InverseE12Hint = func(_ *big.Int, inputs []*big.Int, res []*big.Int) error {
	var a, c bls12377.E12

	a.C0.B0.A0.SetBigInt(inputs[0])
	a.C0.B0.A1.SetBigInt(inputs[1])
	a.C0.B1.A0.SetBigInt(inputs[2])
	a.C0.B1.A1.SetBigInt(inputs[3])
	a.C0.B2.A0.SetBigInt(inputs[4])
	a.C0.B2.A1.SetBigInt(inputs[5])
	a.C1.B0.A0.SetBigInt(inputs[6])
	a.C1.B0.A1.SetBigInt(inputs[7])
	a.C1.B1.A0.SetBigInt(inputs[8])
	a.C1.B1.A1.SetBigInt(inputs[9])
	a.C1.B2.A0.SetBigInt(inputs[10])
	a.C1.B2.A1.SetBigInt(inputs[11])

	c.Inverse(&a)

	c.C0.B0.A0.BigInt(res[0])
	c.C0.B0.A1.BigInt(res[1])
	c.C0.B1.A0.BigInt(res[2])
	c.C0.B1.A1.BigInt(res[3])
	c.C0.B2.A0.BigInt(res[4])
	c.C0.B2.A1.BigInt(res[5])
	c.C1.B0.A0.BigInt(res[6])
	c.C1.B0.A1.BigInt(res[7])
	c.C1.B1.A0.BigInt(res[8])
	c.C1.B1.A1.BigInt(res[9])
	c.C1.B2.A0.BigInt(res[10])
	c.C1.B2.A1.BigInt(res[11])

	return nil
}
View Source 
var InverseE2Hint = func(_ *big.Int, inputs []*big.Int, res []*big.Int) error {
	var a, c bls12377.E2

	a.A0.SetBigInt(inputs[0])
	a.A1.SetBigInt(inputs[1])

	c.Inverse(&a)

	c.A0.BigInt(res[0])
	c.A1.BigInt(res[1])

	return nil
}
View Source 
var InverseE6Hint = func(_ *big.Int, inputs []*big.Int, res []*big.Int) error {
	var a, c bls12377.E6

	a.B0.A0.SetBigInt(inputs[0])
	a.B0.A1.SetBigInt(inputs[1])
	a.B1.A0.SetBigInt(inputs[2])
	a.B1.A1.SetBigInt(inputs[3])
	a.B2.A0.SetBigInt(inputs[4])
	a.B2.A1.SetBigInt(inputs[5])

	c.Inverse(&a)

	c.B0.A0.BigInt(res[0])
	c.B0.A1.BigInt(res[1])
	c.B1.A0.BigInt(res[2])
	c.B1.A1.BigInt(res[3])
	c.B2.A0.BigInt(res[4])
	c.B2.A1.BigInt(res[5])

	return nil
}

Functions

func Mul034By034 

func Mul034By034(api frontend.API, d3, d4, c3, c4 E2) *[5]E2

Mul034By034 multiplication of sparse element (1,0,0,c3,c4,0) by sparse element (1,0,0,d3,d4,0)

Types

type E12 

type E12 struct {
	C0, C1 E6
}

E12 element in a quadratic extension

func Mul01234By034 

func Mul01234By034(api frontend.API, x [5]E2, z3, z4 E2) *E12

func (*E12) Add 

func (e *E12) Add(api frontend.API, e1, e2 E12) *E12

Add adds 2 elmts in Fp12

func (*E12) AssertIsEqual 

func (e *E12) AssertIsEqual(api frontend.API, other E12)

AssertIsEqual constraint self to be equal to other into the given constraint system

func (*E12) Assign 

func (e *E12) Assign(a *bls12377.E12)

Assign a value to self (witness assignment)

func (*E12) Conjugate 

func (e *E12) Conjugate(api frontend.API, e1 E12) *E12

Conjugate applies Frob**6 (conjugation over Fp6)

func (*E12) CyclotomicSquare 

func (e *E12) CyclotomicSquare(api frontend.API, x E12) *E12

Granger-Scott's cyclotomic square squares a Fp12 elt in the cyclotomic group https://eprint.iacr.org/2009/565.pdf, 3.2

func (*E12) CyclotomicSquareKarabina12345 

func (e *E12) CyclotomicSquareKarabina12345(api frontend.API, x E12) *E12

func (*E12) CyclotomicSquareKarabina2345 

func (e *E12) CyclotomicSquareKarabina2345(api frontend.API, x E12) *E12

Karabina's compressed cyclotomic square https://eprint.iacr.org/2010/542.pdf Th. 3.2 with minor modifications to fit our tower

func (*E12) DecompressKarabina12345 

func (e *E12) DecompressKarabina12345(api frontend.API, x E12) *E12

DecompressKarabina12345 Karabina's cyclotomic square result SQR12345

func (*E12) DecompressKarabina2345 

func (e *E12) DecompressKarabina2345(api frontend.API, x E12) *E12

DecompressKarabina2345 Karabina's cyclotomic square result SQR2345

func (*E12) DivUnchecked 

func (e *E12) DivUnchecked(api frontend.API, e1, e2 E12) *E12

DivUnchecked e12 elmts

func (*E12) ExpX0 

func (e *E12) ExpX0(api frontend.API, e1 E12) *E12

ExpX0 compute e1^X0, where X0=9586122913090633729

func (*E12) ExpX0Minus1Square 

func (e *E12) ExpX0Minus1Square(api frontend.API, e1 E12) *E12

ExpX0Minus1Square computes e1^((X0-1)^2), where X0=9586122913090633729

func (*E12) Frobenius 

func (e *E12) Frobenius(api frontend.API, e1 E12) *E12

Frobenius applies frob to an fp12 elmt

func (*E12) FrobeniusSquare 

func (e *E12) FrobeniusSquare(api frontend.API, e1 E12) *E12

FrobeniusSquare applies frob**2 to an fp12 elmt

func (*E12) Inverse 

func (e *E12) Inverse(api frontend.API, e1 E12) *E12

Inverse e12 elmts

func (*E12) Mul 

func (e *E12) Mul(api frontend.API, e1, e2 E12) *E12

Mul multiplies 2 elmts in Fp12

func (*E12) MulBy01234 

func (e *E12) MulBy01234(api frontend.API, x [5]E2) *E12

func (*E12) MulBy034 

func (e *E12) MulBy034(api frontend.API, c3, c4 E2) *E12

MulBy034 multiplication by sparse element

func (*E12) Neg 

func (e *E12) Neg(api frontend.API, e1 E12) *E12

Neg negates an Fp6elmt

func (*E12) Select 

func (e *E12) Select(api frontend.API, b frontend.Variable, r1, r2 E12) *E12

Select sets e to r1 if b=1, r2 otherwise

func (*E12) SetOne 

func (e *E12) SetOne() *E12

SetOne returns a newly allocated element equal to 1

func (*E12) SetZero 

func (e *E12) SetZero() *E12

SetZero returns a newly allocated element equal to 0

func (*E12) Square 

func (e *E12) Square(api frontend.API, x E12) *E12

Square squares an element in Fp12

func (*E12) Square034 

func (e *E12) Square034(api frontend.API, x E12) *E12

Square034 squares a sparse element in Fp12

func (*E12) Sub 

func (e *E12) Sub(api frontend.API, e1, e2 E12) *E12

Sub substracts 2 elmts in Fp12

type E2 

type E2 struct {
	A0, A1 frontend.Variable
}

E2 element in a quadratic extension

func (*E2) Add 

func (e *E2) Add(api frontend.API, e1, e2 E2) *E2

Add e2 elmts

func (*E2) AssertIsEqual 

func (e *E2) AssertIsEqual(api frontend.API, other E2)

AssertIsEqual constraint self to be equal to other into the given constraint system

func (*E2) Assign 

func (e *E2) Assign(a *bls12377.E2)

Assign a value to self (witness assignment)

func (*E2) Conjugate 

func (e *E2) Conjugate(api frontend.API, e1 E2) *E2

Conjugate conjugation of an e2 elmt

func (*E2) DivUnchecked 

func (e *E2) DivUnchecked(api frontend.API, e1, e2 E2) *E2

DivUnchecked e2 elmts

func (*E2) Double 

func (e *E2) Double(api frontend.API, e1 E2) *E2

Double e2 elmt

func (*E2) Inverse 

func (e *E2) Inverse(api frontend.API, e1 E2) *E2

Inverse e2 elmts

func (*E2) IsZero 

func (e *E2) IsZero(api frontend.API) frontend.Variable

IsZero returns 1 if the element is equal to 0 and 0 otherwise

func (*E2) Lookup2 

func (e *E2) Lookup2(api frontend.API, b1, b2 frontend.Variable, r1, r2, r3, r4 E2) *E2

Lookup2 implements two-bit lookup. It returns:

  • r1 if b1=0 and b2=0,
  • r2 if b1=0 and b2=1,
  • r3 if b1=1 and b2=0,
  • r3 if b1=1 and b2=1.

func (*E2) Mul 

func (e *E2) Mul(api frontend.API, e1, e2 E2) *E2

Mul e2 elmts

func (*E2) MulByFp 

func (e *E2) MulByFp(api frontend.API, e1 E2, c interface{}) *E2

MulByFp multiplies an fp2 elmt by an fp elmt

func (*E2) MulByNonResidue 

func (e *E2) MulByNonResidue(api frontend.API, e1 E2) *E2

MulByNonResidue multiplies an fp2 elmt by the imaginary elmt ext.uSquare is the square of the imaginary root

func (*E2) Neg 

func (e *E2) Neg(api frontend.API, e1 E2) *E2

Neg negates a e2 elmt

func (*E2) Select 

func (e *E2) Select(api frontend.API, b frontend.Variable, r1, r2 E2) *E2

Select sets e to r1 if b=1, r2 otherwise

func (*E2) SetOne 

func (e *E2) SetOne() *E2

SetOne returns a newly allocated element equal to 1

func (*E2) SetZero 

func (e *E2) SetZero() *E2

SetZero returns a newly allocated element equal to 0

func (*E2) Square 

func (e *E2) Square(api frontend.API, x E2) *E2

Square e2 elt

func (*E2) Sub 

func (e *E2) Sub(api frontend.API, e1, e2 E2) *E2

Sub e2 elmts

type E6 

type E6 struct {
	B0, B1, B2 E2
}

E6 element in a quadratic extension

func Mul01By01 

func Mul01By01(api frontend.API, c0, c1, d0, d1 E2) *E6

func NewFp6Zero 

func NewFp6Zero(api frontend.API) *E6

NewFp6Zero creates a new

func (*E6) Add 

func (e *E6) Add(api frontend.API, e1, e2 E6) *E6

Add creates a fp6elmt from fp elmts

func (*E6) AssertIsEqual 

func (e *E6) AssertIsEqual(api frontend.API, other E6)

AssertIsEqual constraint self to be equal to other into the given constraint system

func (*E6) Assign 

func (e *E6) Assign(a *bls12377.E6)

Assign a value to self (witness assignment)

func (*E6) DivUnchecked 

func (e *E6) DivUnchecked(api frontend.API, e1, e2 E6) *E6

DivUnchecked e6 elmts

func (*E6) Inverse 

func (e *E6) Inverse(api frontend.API, e1 E6) *E6

Inverse e6 elmts

func (*E6) Mul 

func (e *E6) Mul(api frontend.API, e1, e2 E6) *E6

Mul creates a fp6elmt from fp elmts icube is the imaginary elmt to the cube

func (*E6) Mul0By01 

func (e *E6) Mul0By01(api frontend.API, a0, b0, b1 E2) *E6

func (*E6) MulBy01 

func (e *E6) MulBy01(api frontend.API, c0, c1 E2) *E6

MulBy01 multiplication by sparse element (c0,c1,0)

func (*E6) MulByE2 

func (e *E6) MulByE2(api frontend.API, e1 E6, e2 E2) *E6

MulByE2 multiplies an element in E6 by an element in E2

func (*E6) MulByFp2 

func (e *E6) MulByFp2(api frontend.API, e1 E6, e2 E2) *E6

MulByFp2 creates a fp6elmt from fp elmts icube is the imaginary elmt to the cube

func (*E6) MulByNonResidue 

func (e *E6) MulByNonResidue(api frontend.API, e1 E6) *E6

MulByNonResidue multiplies e by the imaginary elmt of Fp6 (noted a+bV+cV where V**3 in F²)

func (*E6) Neg 

func (e *E6) Neg(api frontend.API, e1 E6) *E6

Neg negates an Fp6 elmt

func (*E6) Select 

func (e *E6) Select(api frontend.API, b frontend.Variable, r1, r2 E6) *E6

Select sets e to r1 if b=1, r2 otherwise

func (*E6) SetOne 

func (e *E6) SetOne() *E6

SetOne returns a newly allocated element equal to 1

func (*E6) SetZero 

func (e *E6) SetZero() *E6

SetZero returns a newly allocated element equal to 0

func (*E6) Square 

func (e *E6) Square(api frontend.API, x E6) *E6

Square sets z to the E6 product of x,x, returns e

func (*E6) Sub 

func (e *E6) Sub(api frontend.API, e1, e2 E6) *E6

Sub creates a fp6elmt from fp elmts

type Extension 

type Extension struct {
	// contains filtered or unexported fields
}

Extension stores the non residue elmt for an extension of type Fp->Fp2->Fp6->Fp12 (Fp2 = Fp(u), Fp6 = Fp2(v), Fp12 = Fp6(w))

Source Files

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