bw761

package
v0.3.3 Latest Latest
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 Go to latest Published: Sep 23, 2020 License: Apache-2.0 Imports: 10 Imported by: 0

Documentation

Overview

Package bw761 provides efficient elliptic curve and pairing implementation for bw761

Index

Constants

This section is empty.

Variables

View Source 
var B fp.Element

B b coeff of the curve

View Source 
var Btwist fp.Element

Btwist b coeff of the twist (defined over Fp) curve

View Source 
var ID = gurvy.BW761

ID bls377 ID

Functions

func BatchJacobianToAffineG1 added in v0.3.0 

func BatchJacobianToAffineG1(points []G1Jac, result []G1Affine)

BatchJacobianToAffineG1 converts points in Jacobian coordinates to Affine coordinates performing a single field inversion (Montgomery batch inversion trick) result must be allocated with len(result) == len(points)

func Generators added in v0.3.0 

func Generators() (g1 G1Jac, g2 G2Jac, g1Aff G1Affine, g2Aff G2Affine)

Generators return the generators of the r-torsion group, resp. in ker(pi-id), ker(Tr)

Types

type G1Affine 

type G1Affine struct {
	X, Y fp.Element
}

G1Affine point in affine coordinates

func BatchScalarMultiplicationG1 added in v0.3.0 

func BatchScalarMultiplicationG1(base *G1Affine, scalars []fr.Element) []G1Affine

BatchScalarMultiplicationG1 multiplies the same base (generator) by all scalars and return resulting points in affine coordinates uses a simple windowed-NAF like exponentiation algorithm

func (*G1Affine) Equal 

func (p *G1Affine) Equal(a *G1Affine) bool

Equal tests if two points (in Affine coordinates) are equal

func (*G1Affine) FromJacobian 

func (p *G1Affine) FromJacobian(p1 *G1Jac) *G1Affine

FromJacobian rescale a point in Jacobian coord in z=1 plane

func (*G1Affine) IsInSubGroup added in v0.3.3 

func (p *G1Affine) IsInSubGroup() bool

IsInSubGroup returns true if p is in the correct subgroup, false otherwise

func (*G1Affine) IsInfinity 

func (p *G1Affine) IsInfinity() bool

IsInfinity checks if the point is infinity (in affine, it's encoded as (0,0))

func (*G1Affine) IsOnCurve added in v0.3.0 

func (p *G1Affine) IsOnCurve() bool

IsOnCurve returns true if p in on the curve

func (*G1Affine) Neg 

func (p *G1Affine) Neg(a *G1Affine) *G1Affine

Neg computes -G

func (*G1Affine) String 

func (p *G1Affine) String() string

type G1Jac 

type G1Jac struct {
	X, Y, Z fp.Element
}

G1Jac is a point with fp.Element coordinates

func (*G1Jac) AddAssign 

func (p *G1Jac) AddAssign(a *G1Jac) *G1Jac

AddAssign point addition in montgomery form https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl

func (*G1Jac) AddMixed 

func (p *G1Jac) AddMixed(a *G1Affine) *G1Jac

AddMixed point addition http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-madd-2007-bl

func (*G1Jac) ClearCofactor added in v0.3.0 

func (p *G1Jac) ClearCofactor(a *G1Jac) *G1Jac

ClearCofactor maps a point in E(Fp) to E(Fp2-)[r] https://eprint.iacr.org/2020/351.pdf

func (*G1Jac) Double 

func (p *G1Jac) Double(q *G1Jac) *G1Jac

Double doubles a point in Jacobian coordinates https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2007-bl

func (*G1Jac) DoubleAssign 

func (p *G1Jac) DoubleAssign() *G1Jac

DoubleAssign doubles a point in Jacobian coordinates https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2007-bl

func (*G1Jac) Equal 

func (p *G1Jac) Equal(a *G1Jac) bool

Equal tests if two points (in Jacobian coordinates) are equal

func (*G1Jac) FromAffine 

func (p *G1Jac) FromAffine(Q *G1Affine) *G1Jac

FromAffine sets p = Q, p in Jacboian, Q in affine

func (*G1Jac) IsInSubGroup added in v0.3.3 

func (p *G1Jac) IsInSubGroup() bool

IsInSubGroup returns true if p is on the r-torsion, false otherwise. Z[r,0]+Z[-lambdaG1, 1] is the kernel of (u,v)->u+lambdaG1v mod r. Expressing r, lambdaG1 as polynomials in x, a short vector of this Zmodule is (x+1), (x**3-x**2+1). So we check that (x+1)p+(x**3-x**2+1)*phi(p) is the infinity.

func (*G1Jac) IsOnCurve added in v0.3.0 

func (p *G1Jac) IsOnCurve() bool

IsOnCurve returns true if p in on the curve

func (*G1Jac) MultiExp 

func (p *G1Jac) MultiExp(points []G1Affine, scalars []fr.Element, opts ...*MultiExpOptions) *G1Jac

MultiExp implements section 4 of https://eprint.iacr.org/2012/549.pdf optionally, takes as parameter a MultiExpOptions struct enabling to set * max number of cpus to use

func (*G1Jac) Neg 

func (p *G1Jac) Neg(a *G1Jac) *G1Jac

Neg computes -G

func (*G1Jac) ScalarMultiplication 

func (p *G1Jac) ScalarMultiplication(a *G1Jac, s *big.Int) *G1Jac

ScalarMultiplication computes and returns p = a*s see https://www.iacr.org/archive/crypto2001/21390189.pdf

func (*G1Jac) Set 

func (p *G1Jac) Set(a *G1Jac) *G1Jac

Set set p to the provided point

func (*G1Jac) String 

func (p *G1Jac) String() string

func (*G1Jac) SubAssign 

func (p *G1Jac) SubAssign(a *G1Jac) *G1Jac

SubAssign substracts two points on the curve

type G1Proj 

type G1Proj struct {
	X, Y, Z fp.Element
}

G1Proj point in projective coordinates

func (*G1Proj) FromJacobian 

func (p *G1Proj) FromJacobian(Q *G1Jac) *G1Proj

FromJacobian converts a point from Jacobian to projective coordinates

func (*G1Proj) IsOnCurve added in v0.3.0 

func (p *G1Proj) IsOnCurve() bool

IsOnCurve returns true if p in on the curve

type G2Affine 

type G2Affine struct {
	X, Y fp.Element
}

G2Affine point in affine coordinates

func BatchScalarMultiplicationG2 added in v0.3.0 

func BatchScalarMultiplicationG2(base *G2Affine, scalars []fr.Element) []G2Affine

BatchScalarMultiplicationG2 multiplies the same base (generator) by all scalars and return resulting points in affine coordinates uses a simple windowed-NAF like exponentiation algorithm

func (*G2Affine) Equal added in v0.3.0 

func (p *G2Affine) Equal(a *G2Affine) bool

Equal tests if two points (in Affine coordinates) are equal

func (*G2Affine) FromJacobian added in v0.3.0 

func (p *G2Affine) FromJacobian(p1 *G2Jac) *G2Affine

FromJacobian rescale a point in Jacobian coord in z=1 plane

func (*G2Affine) IsInSubGroup added in v0.3.3 

func (p *G2Affine) IsInSubGroup() bool

IsInSubGroup returns true if p is in the correct subgroup, false otherwise

func (*G2Affine) IsInfinity added in v0.3.0 

func (p *G2Affine) IsInfinity() bool

IsInfinity checks if the point is infinity (in affine, it's encoded as (0,0))

func (*G2Affine) IsOnCurve added in v0.3.0 

func (p *G2Affine) IsOnCurve() bool

IsOnCurve returns true if p in on the curve

func (*G2Affine) Neg added in v0.3.0 

func (p *G2Affine) Neg(a *G2Affine) *G2Affine

Neg computes -G

func (*G2Affine) String added in v0.3.0 

func (p *G2Affine) String() string

type G2Jac 

type G2Jac struct {
	X, Y, Z fp.Element
}

G2Jac is a point with fp.Element coordinates

func (*G2Jac) AddAssign added in v0.3.0 

func (p *G2Jac) AddAssign(a *G2Jac) *G2Jac

AddAssign point addition in montgomery form https://hyperelliptic.org/EFD/g2p/auto-shortw-jacobian-3.html#addition-add-2007-bl

func (*G2Jac) AddMixed added in v0.3.0 

func (p *G2Jac) AddMixed(a *G2Affine) *G2Jac

AddMixed point addition http://www.hyperelliptic.org/EFD/g2p/auto-shortw-jacobian-0.html#addition-madd-2007-bl

func (*G2Jac) ClearCofactor added in v0.3.0 

func (p *G2Jac) ClearCofactor(a *G2Jac) *G2Jac

ClearCofactor maps a point in E(Fp) to E(Fp2-)[r] https://eprint.iacr.org/2020/351.pdf

func (*G2Jac) Double added in v0.3.0 

func (p *G2Jac) Double(q *G2Jac) *G2Jac

Double doubles a point in Jacobian coordinates https://hyperelliptic.org/EFD/g2p/auto-shortw-jacobian-3.html#doubling-dbl-2007-bl

func (*G2Jac) DoubleAssign added in v0.3.0 

func (p *G2Jac) DoubleAssign() *G2Jac

DoubleAssign doubles a point in Jacobian coordinates https://hyperelliptic.org/EFD/g2p/auto-shortw-jacobian-3.html#doubling-dbl-2007-bl

func (*G2Jac) Equal added in v0.3.0 

func (p *G2Jac) Equal(a *G2Jac) bool

Equal tests if two points (in Jacobian coordinates) are equal

func (*G2Jac) FromAffine added in v0.3.0 

func (p *G2Jac) FromAffine(Q *G2Affine) *G2Jac

FromAffine sets p = Q, p in Jacboian, Q in affine

func (*G2Jac) IsInSubGroup added in v0.3.3 

func (p *G2Jac) IsInSubGroup() bool

IsInSubGroup returns true if p is on the r-torsion, false otherwise. Z[r,0]+Z[-lambdaG2, 1] is the kernel of (u,v)->u+lambdaG2v mod r. Expressing r, lambdaG2 as polynomials in x, a short vector of this Zmodule is (x+1), (x**3-x**2+1). So we check that (x+1)p+(x**3-x**2+1)*phi(p) is the infinity.

func (*G2Jac) IsOnCurve added in v0.3.0 

func (p *G2Jac) IsOnCurve() bool

IsOnCurve returns true if p in on the curve

func (*G2Jac) MultiExp added in v0.3.0 

func (p *G2Jac) MultiExp(points []G2Affine, scalars []fr.Element, opts ...*MultiExpOptions) *G2Jac

MultiExp implements section 4 of https://eprint.iacr.org/2012/549.pdf optionally, takes as parameter a MultiExpOptions struct enabling to set * max number of cpus to use

func (*G2Jac) Neg added in v0.3.0 

func (p *G2Jac) Neg(a *G2Jac) *G2Jac

Neg computes -G

func (*G2Jac) ScalarMultiplication added in v0.3.0 

func (p *G2Jac) ScalarMultiplication(a *G2Jac, s *big.Int) *G2Jac

ScalarMultiplication computes and returns p = a*s see https://www.iacr.org/archive/crypto2001/21390189.pdf

func (*G2Jac) Set added in v0.3.0 

func (p *G2Jac) Set(a *G2Jac) *G2Jac

Set set p to the provided point

func (*G2Jac) String added in v0.3.0 

func (p *G2Jac) String() string

func (*G2Jac) SubAssign added in v0.3.0 

func (p *G2Jac) SubAssign(a *G2Jac) *G2Jac

SubAssign substracts two points on the curve

type G2Proj 

type G2Proj struct {
	X, Y, Z fp.Element
}

G2Proj point in projective coordinates

func (*G2Proj) FromJacobian added in v0.3.0 

func (p *G2Proj) FromJacobian(Q *G2Jac) *G2Proj

FromJacobian converts a point from Jacobian to projective coordinates

func (*G2Proj) IsOnCurve added in v0.3.0 

func (p *G2Proj) IsOnCurve() bool

IsOnCurve returns true if p in on the curve

type GT added in v0.3.3 

type GT = e6

GT target group of the pairing

func FinalExponentiation 

func FinalExponentiation(z *GT, _z ...*GT) GT

FinalExponentiation computes the final expo x**(p**6-1)(p**2+1)(p**4 - p**2 +1)/r

func MillerLoop 

func MillerLoop(P G1Affine, Q G2Affine) *GT

MillerLoop Miller loop

func (*GT) Expt added in v0.3.3 

func (z *GT) Expt(x *GT) *GT

Expt set z to x^t in GT and return z

func (*GT) FinalExponentiation added in v0.3.3 

func (z *GT) FinalExponentiation(x *GT) *GT

FinalExponentiation sets z to the final expo x**((p**6 - 1)/r), returns z

func (*GT) Frobenius added in v0.3.3 

func (z *GT) Frobenius(x *GT) *GT

Frobenius set z to Frobenius(x), return z

func (*GT) FrobeniusCube added in v0.3.3 

func (z *GT) FrobeniusCube(x *GT) *GT

FrobeniusCube set z to Frobenius^3(x), return z

func (*GT) FrobeniusSquare added in v0.3.3 

func (z *GT) FrobeniusSquare(x *GT) *GT

FrobeniusSquare set z to Frobenius^2(x), and return z

func (*GT) MulByVMinusThree added in v0.3.3 

func (z *GT) MulByVMinusThree(x *GT, y *fp.Element) *GT

MulByVMinusThree set z to x*(y*v**-3) and return z (Fp6(v) where v**3=u, v**6=-4, so v**-3 = u**-1 = (-4)**-1*u)

func (*GT) MulByVminusFive added in v0.3.3 

func (z *GT) MulByVminusFive(x *GT, y *fp.Element) *GT

MulByVminusFive set z to x*(y*v**-5) and return z (Fp6(v) where v**3=u, v**6=-4, so v**-5 = (-4)**-1*v)

func (*GT) MulByVminusTwo added in v0.3.3 

func (z *GT) MulByVminusTwo(x *GT, y *fp.Element) *GT

MulByVminusTwo set z to x*(y*v**-2) and return z (Fp6(v) where v**3=u, v**6=-4, so v**-2 = (-4)**-1*u*v)

type MultiExpOptions added in v0.3.0 

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

MultiExpOptions enables users to set optional parameters to the multiexp

func NewMultiExpOptions added in v0.3.0 

func NewMultiExpOptions(numCpus int) *MultiExpOptions

NewMultiExpOptions returns a new multiExp options to be used with MultiExp this option can be shared between different MultiExp calls and will ensure only numCpus are used through a semaphore

Source Files

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Directories

Path Synopsis
Package fp contains field arithmetic operations for modulus 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
 Package fp contains field arithmetic operations for modulus 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
Package fr contains field arithmetic operations for modulus 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
 Package fr contains field arithmetic operations for modulus 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177

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