fields_bls12381

package
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 Go to latest Published: Feb 8, 2024 License: Apache-2.0 Imports: 5 Imported by: 0

Documentation

Overview

Package fields_bls12381 implements the fields arithmetic of the Fp12 tower used to compute the pairing over the BLS12-381 curve. 

𝔽p²[u] = 𝔽p/u²+1
𝔽p⁶[v] = 𝔽p²/v³-1-u
𝔽p¹²[w] = 𝔽p⁶/w²-v

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func GetHints 

func GetHints() []solver.Hint

GetHints returns all hint functions used in the package.

Types

type E12 

type E12 struct {
	C0, C1 E6
}

func FromE12 

func FromE12(y *bls12381.E12) E12

type E2 

type E2 struct {
	A0, A1 baseEl
}

func FromE2 

func FromE2(y *bls12381.E2) E2

type E6 

type E6 struct {
	B0, B1, B2 E2
}

func FromE6 

func FromE6(y *bls12381.E6) E6

type Ext12 

type Ext12 struct {
	*Ext6
}

func NewExt12 

func NewExt12(api frontend.API) *Ext12

func (Ext12) Add 

func (e Ext12) Add(x, y *E12) *E12

func (Ext12) AssertIsEqual 

func (e Ext12) AssertIsEqual(x, y *E12)

func (Ext12) CompressTorus 

func (e Ext12) CompressTorus(x *E12) *E6

CompressTorus compresses x ∈ E12 to (x.C0 + 1)/x.C1 ∈ E6

func (Ext12) Conjugate 

func (e Ext12) Conjugate(x *E12) *E12

func (Ext12) DecompressTorus 

func (e Ext12) DecompressTorus(y *E6) *E12

DecompressTorus decompresses y ∈ E6 to (y+w)/(y-w) ∈ E12

func (Ext12) DivUnchecked 

func (e Ext12) DivUnchecked(x, y *E12) *E12

func (Ext12) ExptHalfTorus 

func (e Ext12) ExptHalfTorus(x *E6) *E6

ExptHalfTorus set z to x^(t/2) in E6 and return z const t/2 uint64 = 7566188111470821376 // negative

func (Ext12) ExptTorus 

func (e Ext12) ExptTorus(x *E6) *E6

ExptTorus set z to xᵗ in E6 and return z const t uint64 = 15132376222941642752 // negative

func (Ext12) FrobeniusSquareTorus 

func (e Ext12) FrobeniusSquareTorus(y *E6) *E6

FrobeniusSquareTorus raises a compressed elements y ∈ E6 to the square modulus p^2 and returns y^(p^2) / v^((p^2-1)/2)

func (Ext12) FrobeniusTorus 

func (e Ext12) FrobeniusTorus(y *E6) *E6

FrobeniusTorus raises a compressed elements y ∈ E6 to the modulus p and returns y^p / v^((p-1)/2)

func (Ext12) Inverse 

func (e Ext12) Inverse(x *E12) *E12

func (Ext12) InverseTorus 

func (e Ext12) InverseTorus(y *E6) *E6

InverseTorus inverses a compressed elements y ∈ E6 and returns -y

func (Ext12) IsZero 

func (e Ext12) IsZero(z *E12) frontend.Variable

func (Ext12) Lookup2 

func (e Ext12) Lookup2(s1, s2 frontend.Variable, a, b, c, d *E12) *E12

func (Ext12) Mul 

func (e Ext12) Mul(x, y *E12) *E12

func (Ext12) Mul014By014 

func (e Ext12) Mul014By014(d0, d1, c0, c1 *E2) [5]*E2
multiplies two E12 sparse element of the form:

E12{
	C0: E6{B0: c0, B1: c1, B2: 0},
	C1: E6{B0: 0, B1: 1, B2: 0},
}

and 

E12{
	C0: E6{B0: d0, B1: d1, B2: 0},
	C1: E6{B0: 0, B1: 1, B2: 0},
}

func (*Ext12) MulBy01245 

func (e *Ext12) MulBy01245(z *E12, x [5]*E2) *E12

MulBy01245 multiplies z by an E12 sparse element of the form 

E12{
	C0: E6{B0: c0, B1: c1, B2: c2},
	C1: E6{B0: 0, B1: c4, B2: c5},
}

func (*Ext12) MulBy014 

func (e *Ext12) MulBy014(z *E12, c0, c1 *E2) *E12

MulBy014 multiplies z by an E12 sparse element of the form 

E12{
	C0: E6{B0: c0, B1: c1, B2: 0},
	C1: E6{B0: 0, B1: 1, B2: 0},
}

func (Ext12) MulTorus 

func (e Ext12) MulTorus(y1, y2 *E6) *E6

MulTorus multiplies two compressed elements y1, y2 ∈ E6 and returns (y1 * y2 + v)/(y1 + y2) N.B.: we use MulTorus in the final exponentiation throughout y1 ≠ -y2 always.

func (Ext12) One 

func (e Ext12) One() *E12

func (Ext12) Select 

func (e Ext12) Select(selector frontend.Variable, z1, z0 *E12) *E12

func (Ext12) Square 

func (e Ext12) Square(x *E12) *E12

func (Ext12) SquareTorus 

func (e Ext12) SquareTorus(y *E6) *E6

SquareTorus squares a compressed elements y ∈ E6 and returns (y + v/y)/2

It uses a hint to verify that (2x-y)y = v saving one E6 AssertIsEqual.

func (Ext12) Sub 

func (e Ext12) Sub(x, y *E12) *E12

func (Ext12) Zero 

func (e Ext12) Zero() *E12

type Ext2 

type Ext2 struct {
	// contains filtered or unexported fields
}

func NewExt2 

func NewExt2(api frontend.API) *Ext2

func (Ext2) Add 

func (e Ext2) Add(x, y *E2) *E2

func (Ext2) AssertIsEqual 

func (e Ext2) AssertIsEqual(x, y *E2)

func (Ext2) Conjugate 

func (e Ext2) Conjugate(x *E2) *E2

func (Ext2) DivUnchecked 

func (e Ext2) DivUnchecked(x, y *E2) *E2

func (Ext2) Double 

func (e Ext2) Double(x *E2) *E2

func (Ext2) Inverse 

func (e Ext2) Inverse(x *E2) *E2

func (Ext2) IsZero 

func (e Ext2) IsZero(z *E2) frontend.Variable

func (Ext2) Lookup2 

func (e Ext2) Lookup2(s1, s2 frontend.Variable, a, b, c, d *E2) *E2

func (Ext2) Mul 

func (e Ext2) Mul(x, y *E2) *E2

func (Ext2) MulByConstElement 

func (e Ext2) MulByConstElement(x *E2, y *big.Int) *E2

func (Ext2) MulByElement 

func (e Ext2) MulByElement(x *E2, y *baseEl) *E2

func (Ext2) MulByNonResidue 

func (e Ext2) MulByNonResidue(x *E2) *E2

MulByNonResidue returns x*(1+u)

func (Ext2) MulByNonResidue1Power1 

func (e Ext2) MulByNonResidue1Power1(x *E2) *E2

MulByNonResidue1Power1 returns x*(1+u)^(1*(p^1-1)/6)

func (Ext2) MulByNonResidue1Power2 

func (e Ext2) MulByNonResidue1Power2(x *E2) *E2

MulByNonResidue1Power2 returns x*(1+u)^(2*(p^1-1)/6)

func (Ext2) MulByNonResidue1Power3 

func (e Ext2) MulByNonResidue1Power3(x *E2) *E2

MulByNonResidue1Power3 returns x*(1+u)^(3*(p^1-1)/6)

func (Ext2) MulByNonResidue1Power4 

func (e Ext2) MulByNonResidue1Power4(x *E2) *E2

MulByNonResidue1Power4 returns x*(1+u)^(4*(p^1-1)/6)

func (Ext2) MulByNonResidue1Power5 

func (e Ext2) MulByNonResidue1Power5(x *E2) *E2

MulByNonResidue1Power5 returns x*(1+u)^(5*(p^1-1)/6)

func (Ext2) MulByNonResidue2Power1 

func (e Ext2) MulByNonResidue2Power1(x *E2) *E2

MulByNonResidue2Power1 returns x*(1+u)^(1*(p^2-1)/6)

func (Ext2) MulByNonResidue2Power2 

func (e Ext2) MulByNonResidue2Power2(x *E2) *E2

MulByNonResidue2Power2 returns x*(1+u)^(2*(p^2-1)/6)

func (Ext2) MulByNonResidue2Power3 

func (e Ext2) MulByNonResidue2Power3(x *E2) *E2

MulByNonResidue2Power3 returns x*(1+u)^(3*(p^2-1)/6)

func (Ext2) MulByNonResidue2Power4 

func (e Ext2) MulByNonResidue2Power4(x *E2) *E2

MulByNonResidue2Power4 returns x*(1+u)^(4*(p^2-1)/6)

func (Ext2) MulByNonResidue2Power5 

func (e Ext2) MulByNonResidue2Power5(x *E2) *E2

MulByNonResidue2Power5 returns x*(1+u)^(5*(p^2-1)/6)

func (Ext2) MulByNonResidueGeneric 

func (e Ext2) MulByNonResidueGeneric(x *E2, power, coef int) *E2

func (Ext2) Neg 

func (e Ext2) Neg(x *E2) *E2

func (Ext2) NonResidue 

func (e Ext2) NonResidue() *E2

returns 1+u

func (Ext2) One 

func (e Ext2) One() *E2

func (Ext2) Select 

func (e Ext2) Select(selector frontend.Variable, z1, z0 *E2) *E2

func (Ext2) Square 

func (e Ext2) Square(x *E2) *E2

func (Ext2) Sub 

func (e Ext2) Sub(x, y *E2) *E2

func (Ext2) Zero 

func (e Ext2) Zero() *E2

type Ext6 

type Ext6 struct {
	*Ext2
}

func NewExt6 

func NewExt6(api frontend.API) *Ext6

func (Ext6) Add 

func (e Ext6) Add(x, y *E6) *E6

func (Ext6) AssertIsEqual 

func (e Ext6) AssertIsEqual(x, y *E6)

func (Ext6) DivUnchecked 

func (e Ext6) DivUnchecked(x, y *E6) *E6

func (Ext6) Double 

func (e Ext6) Double(x *E6) *E6

func (Ext6) Inverse 

func (e Ext6) Inverse(x *E6) *E6

func (Ext6) IsZero 

func (e Ext6) IsZero(z *E6) frontend.Variable

func (Ext6) Lookup2 

func (e Ext6) Lookup2(s1, s2 frontend.Variable, a, b, c, d *E6) *E6

func (Ext6) Mul 

func (e Ext6) Mul(x, y *E6) *E6

func (Ext6) MulBy0 

func (e Ext6) MulBy0(z *E6, c0 *E2) *E6

MulBy0 multiplies z by an E6 sparse element of the form 

E6{
	B0: c0,
	B1: 0,
	B2: 0,
}

func (Ext6) MulBy01 

func (e Ext6) MulBy01(z *E6, c0, c1 *E2) *E6

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

func (Ext6) MulBy12 

func (e Ext6) MulBy12(x *E6, b1, b2 *E2) *E6

MulBy12 multiplication by sparse element (0,b1,b2)

func (Ext6) MulByE2 

func (e Ext6) MulByE2(x *E6, y *E2) *E6

func (Ext6) MulByNonResidue 

func (e Ext6) MulByNonResidue(x *E6) *E6

func (Ext6) Neg 

func (e Ext6) Neg(x *E6) *E6

func (Ext6) One 

func (e Ext6) One() *E6

func (Ext6) Select 

func (e Ext6) Select(selector frontend.Variable, z1, z0 *E6) *E6

func (Ext6) Square 

func (e Ext6) Square(x *E6) *E6

func (Ext6) Sub 

func (e Ext6) Sub(x, y *E6) *E6

func (Ext6) Zero 

func (e Ext6) Zero() *E6

Source Files

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