fields_bls24315

package
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 Go to latest Published: Oct 7, 2024 License: Apache-2.0 Imports: 6 Imported by: 0

Documentation

Overview

Package fields_bls24315 implements the fields arithmetic of the Fp24 tower used to compute the pairing over the BLS24-315 curve. 

𝔽p²[u] = 𝔽p/u²-13
𝔽p⁴[v] = 𝔽p²/v²-u
𝔽p¹²[w] = 𝔽p⁴/w³-v
𝔽p²⁴[i] = 𝔽p¹²/i²-w

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

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func GetHints 

func GetHints() []solver.Hint

func Mul034By034 

func Mul034By034(api frontend.API, d3, d4, c3, c4 E4) *[5]E4

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, C2 E4
}

E12 element in a quadratic extension

func NewFp12Zero 

func NewFp12Zero(api frontend.API) *E12

NewFp12Zero creates a new

func (*E12) Add 

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

Add creates a fp12elmt from fp elmts

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 *bls24315.E12)

Assign a value to self (witness assignment)

func (*E12) DivUnchecked 

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

DivUnchecked e12 elmts

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 creates a fp12elmt from fp elmts icube is the imaginary elmt to the cube

func (*E12) Mul0By01 

func (e *E12) Mul0By01(api frontend.API, a0, b0, b1 E4) *E12

func (*E12) MulBy01 

func (e *E12) MulBy01(api frontend.API, c0, c1 E4) *E12

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

func (*E12) MulByE4 

func (e *E12) MulByE4(api frontend.API, e1 E12, e2 E4) *E12

MulByE4 multiplies an element in E12 by an element in E4

func (*E12) MulByFp2 

func (e *E12) MulByFp2(api frontend.API, e1 E12, e2 E4) *E12

MulByFp2 creates a fp12elmt from fp elmts icube is the imaginary elmt to the cube

func (*E12) MulByNonResidue 

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

MulByNonResidue multiplies e by the imaginary elmt of Fp12 (noted a+bV+cV where V**3 in F²)

func (*E12) Neg 

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

Neg negates an Fp12 elmt

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 sets z to the E12 product of x,x, returns e

func (*E12) Sub 

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

Sub creates a fp12elmt from fp elmts

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 *bls24315.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: 5C

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 E24 

type E24 struct {
	D0, D1 E12
}

E24 element in a quadratic extension

func (*E24) Add 

func (e *E24) Add(api frontend.API, e1, e2 E24) *E24

Add adds 2 elmts in Fp24

func (*E24) AssertIsEqual 

func (e *E24) AssertIsEqual(api frontend.API, other E24)

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

func (*E24) Assign 

func (e *E24) Assign(a *bls24315.E24)

Assign a value to self (witness assignment)

func (*E24) Conjugate 

func (e *E24) Conjugate(api frontend.API, e1 E24) *E24

Conjugate applies Frob**6 (conjugation over Fp6)

func (*E24) CyclotomicSquare 

func (e *E24) CyclotomicSquare(api frontend.API, x E24) *E24

Granger-Scott's cyclotomic square squares a Fp24 elt in the cyclotomic group https://eprint.iacr.org/2009/565.pdf, 3.2

func (*E24) CyclotomicSquareKarabina2345 

func (e *E24) CyclotomicSquareKarabina2345(api frontend.API, x E24) *E24

Karabina's compressed cyclotomic square https://eprint.iacr.org/2010/542.pdf

func (*E24) DecompressKarabina2345 

func (e *E24) DecompressKarabina2345(api frontend.API, x E24) *E24

DecompressKarabina2345 Karabina's cyclotomic square result

func (*E24) DivUnchecked 

func (e *E24) DivUnchecked(api frontend.API, e1, e2 E24) *E24

DivUnchecked e24 elmts

func (*E24) Expt 

func (e *E24) Expt(api frontend.API, x E24) *E24

Expt compute e1**exponent, where the exponent is hardcoded This function is only used for the final expo of the pairing for bls24315, so the exponent is supposed to be hardcoded and on 32 bits.

func (*E24) Frobenius 

func (e *E24) Frobenius(api frontend.API, x E24) *E24

Frobenius applies frob to an fp24 elmt

func (*E24) FrobeniusQuad 

func (e *E24) FrobeniusQuad(api frontend.API, x E24) *E24

FrobeniusQuad applies frob**4 to an fp24 elmt

func (*E24) FrobeniusSquare 

func (e *E24) FrobeniusSquare(api frontend.API, x E24) *E24

FrobeniusSquare applies frob**2 to an fp24 elmt

func (*E24) Inverse 

func (e *E24) Inverse(api frontend.API, e1 E24) *E24

Inverse e24 elmts

func (*E24) Mul 

func (e *E24) Mul(api frontend.API, e1, e2 E24) *E24

Mul multiplies 2 elmts in Fp24

func (*E24) MulBy034 

func (e *E24) MulBy034(api frontend.API, c3, c4 E4) *E24

MulBy034 multiplication by sparse element

func (*E24) Neg 

func (e *E24) Neg(api frontend.API, e1 E24) *E24

Neg negates an Fp6elmt

func (*E24) SetOne 

func (e *E24) SetOne() *E24

SetOne returns a newly allocated element equal to 1

func (*E24) SetZero 

func (e *E24) SetZero() *E24

SetZero returns a newly allocated element equal to 0

func (*E24) Square 

func (e *E24) Square(api frontend.API, x E24) *E24

Square squares an element in Fp24

func (*E24) Square034 

func (e *E24) Square034(api frontend.API, x E24) *E24

Square034 squares a sparse element in Fp24

func (*E24) Sub 

func (e *E24) Sub(api frontend.API, e1, e2 E24) *E24

Sub subtracts 2 elmts in Fp24

type E4 

type E4 struct {
	B0, B1 E2
}

E4 element in a quadratic extension

func NewFp4Zero 

func NewFp4Zero(api frontend.API) *E4

NewFp4Zero creates a new

func (*E4) Add 

func (e *E4) Add(api frontend.API, e1, e2 E4) *E4

Add e4 elmts

func (*E4) AssertIsEqual 

func (e *E4) AssertIsEqual(api frontend.API, other E4)

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

func (*E4) Assign 

func (e *E4) Assign(a *bls24315.E4)

Assign a value to self (witness assignment)

func (*E4) Conjugate 

func (e *E4) Conjugate(api frontend.API, e1 E4) *E4

Conjugate conjugation of an e4 elmt

func (*E4) DivUnchecked 

func (e *E4) DivUnchecked(api frontend.API, e1, e2 E4) *E4

DivUnchecked e4 elmts

func (*E4) Double 

func (e *E4) Double(api frontend.API, e1 E4) *E4

Double e4 elmt

func (*E4) Inverse 

func (e *E4) Inverse(api frontend.API, e1 E4) *E4

Inverse e4 elmts

func (*E4) IsZero 

func (e *E4) IsZero(api frontend.API) frontend.Variable

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

func (*E4) Lookup2 

func (e *E4) Lookup2(api frontend.API, b1, b2 frontend.Variable, r1, r2, r3, r4 E4) *E4

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 (*E4) Mul 

func (e *E4) Mul(api frontend.API, e1, e2 E4) *E4

Mul e4 elmts: 5C

func (*E4) MulByFp 

func (e *E4) MulByFp(api frontend.API, e1 E4, c interface{}) *E4

MulByFp multiplies an e4 elmt by an fp elmt

func (*E4) MulByNonResidue 

func (e *E4) MulByNonResidue(api frontend.API, e1 E4) *E4

MulByNonResidue multiplies an e4 elmt by the imaginary elmt ext.uSquare is the square of the imaginary root

func (*E4) Neg 

func (e *E4) Neg(api frontend.API, e1 E4) *E4

Neg negates a e4 elmt

func (*E4) Select 

func (e *E4) Select(api frontend.API, b frontend.Variable, r1, r2 E4) *E4

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

func (*E4) SetOne 

func (e *E4) SetOne() *E4

SetOne returns a newly allocated element equal to 1

func (*E4) SetZero 

func (e *E4) SetZero() *E4

SetZero returns a newly allocated element equal to 0

func (*E4) Square 

func (e *E4) Square(api frontend.API, x E4) *E4

Square e4 elt

func (*E4) Sub 

func (e *E4) Sub(api frontend.API, e1, e2 E4) *E4

Sub e4 elmts

type Extension 

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

Extension stores the non residue elmt for an extension of type Fp->Fp2->Fp4->Fp12->Fp24 (Fp2 = Fp(u), Fp4 = Fp2(v), Fp12 = Fp4(w), Fp24 = Fp6(i))

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