bls12381

package
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 Go to latest Published: Jan 31, 2022 License: Apache-2.0, Apache-2.0 Imports: 10 Imported by: 0

README

bls12381

import "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"

Index

Variables

var G1One = g1One

var G2One = g2One

Inp = -p^(-1) mod 2^64

var Inp uint64 = 0x89f3fffcfffcfffd

type E

E is type for target group element

type E = fe12
func (*E) Equal
func (g *E) Equal(g2 *E) bool

Equal returns true if given two element is equal, otherwise returns false

func (*E) IsOne
func (e *E) IsOne() bool

IsOne returns true if given element equals to one

func (*E) One
func (e *E) One() *E

One sets a new target group element to one

func (*E) Set
func (e *E) Set(e2 *E) *E

Set copies given value into the destination

type Engine

Engine is BLS12-381 elliptic curve pairing engine

type Engine struct {
    G1  *G1
    G2  *G2
    // contains filtered or unexported fields
}
func NewEngine
func NewEngine() *Engine

NewEngine creates new pairing engine insteace.

func (*Engine) AddPair
func (e *Engine) AddPair(g1 *PointG1, g2 *PointG2) *Engine

AddPair adds a g1, g2 point pair to pairing engine returns nil if no more pairs can be added

func (*Engine) AddPairInv
func (e *Engine) AddPairInv(g1 *PointG1, g2 *PointG2) *Engine

AddPairInv adds a G1, G2 point pair to pairing engine. G1 point is negated. returns nil if no more pairs can be added

func (*Engine) Check
func (e *Engine) Check() (bool, error)

Check computes pairing and checks if result is equal to one

func (*Engine) GT
func (e *Engine) GT() *GT

GT returns target group instance.

func (*Engine) Reset
func (e *Engine) Reset() *Engine

Reset deletes added pairs.

func (*Engine) Result
func (e *Engine) Result() (*E, error)

Result computes pairing and returns target group element as result.

type G1

G1 is struct for G1 group.

type G1 struct {
    // contains filtered or unexported fields
}
func NewG1
func NewG1() *G1

NewG1 constructs a new G1 instance.

func (*G1) Add
func (g *G1) Add(r, p1, p2 *PointG1) *PointG1

Add adds two G1 points p1, p2 and assigns the result to point at first argument.

func (*G1) Affine
func (g *G1) Affine(p *PointG1) *PointG1

Add adds two G1 points p1, p2 and assigns the result to point at first argument.

func (*G1) ClearCofactor
func (g *G1) ClearCofactor(p *PointG1)

ClearCofactor maps given a G1 point to correct subgroup

func (*G1) Double
func (g *G1) Double(r, p *PointG1) *PointG1

Double doubles a G1 point p and assigns the result to the point at first argument.

func (*G1) EncodeToCurve
func (g *G1) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error)

EncodeToCurve given a message and domain seperator tag returns the hash result which is a valid curve point. Implementation follows BLS12381G1_XMD:SHA-256_SSWU_NU_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08

func (*G1) Equal
func (g *G1) Equal(p1, p2 *PointG1) bool

Equal checks if given two G1 point is equal in their affine form.

func (*G1) FromBytes
func (g *G1) FromBytes(in []byte) (*PointG1, error)

FromBytes constructs a new point given uncompressed byte input. FromBytes does not take zcash flags into account. Byte input expected to be larger than 96 bytes. First 96 bytes should be concatenation of x and y values. Point (0, 0) is considered as infinity.

func (*G1) FromCompressed
func (g *G1) FromCompressed(compressed []byte) (*PointG1, error)

FromCompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G1. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G1) FromUncompressed
func (g *G1) FromUncompressed(uncompressed []byte) (*PointG1, error)

FromUncompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G1. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G1) HashToCurve
func (g *G1) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error)

HashToCurve given a message and domain seperator tag returns the hash result which is a valid curve point. Implementation follows BLS12381G1_XMD:SHA-256_SSWU_RO_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08

func (*G1) InCorrectSubgroup
func (g *G1) InCorrectSubgroup(p *PointG1) bool

InCorrectSubgroup checks whether given point is in correct subgroup.

func (*G1) IsAffine
func (g *G1) IsAffine(p *PointG1) bool

IsAffine checks a G1 point whether it is in affine form.

func (*G1) IsOnCurve
func (g *G1) IsOnCurve(p *PointG1) bool

IsOnCurve checks a G1 point is on curve.

func (*G1) IsZero
func (g *G1) IsZero(p *PointG1) bool

IsZero returns true if given point is equal to zero.

func (*G1) MapToCurve
func (g *G1) MapToCurve(in []byte) (*PointG1, error)

MapToCurve given a byte slice returns a valid G1 point. This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method. https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08 Input byte slice should be a valid field element, otherwise an error is returned.

func (*G1) MulScalar
func (g *G1) MulScalar(c, p *PointG1, e *big.Int) *PointG1

MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.

func (*G1) MultiExp
func (g *G1) MultiExp(r *PointG1, points []*PointG1, powers []*big.Int) (*PointG1, error)

MultiExp calculates multi exponentiation. Given pairs of G1 point and scalar values (P_0, e_0), (P_1, e_1), ... (P_n, e_n) calculates r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n Length of points and scalars are expected to be equal, otherwise an error is returned. Result is assigned to point at first argument.

func (*G1) Neg
func (g *G1) Neg(r, p *PointG1) *PointG1

Neg negates a G1 point p and assigns the result to the point at first argument.

func (*G1) New
func (g *G1) New() *PointG1

New creates a new G1 Point which is equal to zero in other words point at infinity.

func (*G1) One
func (g *G1) One() *PointG1

One returns a new G1 Point which is equal to generator point.

func (*G1) Q
func (g *G1) Q() *big.Int

Q returns group order in big.Int.

func (*G1) Sub
func (g *G1) Sub(c, a, b *PointG1) *PointG1

Sub subtracts two G1 points p1, p2 and assigns the result to point at first argument.

func (*G1) ToBytes
func (g *G1) ToBytes(p *PointG1) []byte

ToBytes serializes a point into bytes in uncompressed form. ToBytes does not take zcash flags into account. ToBytes returns (0, 0) if point is infinity.

func (*G1) ToCompressed
func (g *G1) ToCompressed(p *PointG1) []byte

ToCompressed given a G1 point returns bytes in compressed form of the point. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G1) ToUncompressed
func (g *G1) ToUncompressed(p *PointG1) ([]byte, error)

ToUncompressed given a G1 point returns bytes in uncompressed (x, y) form of the point. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G1) Zero
func (g *G1) Zero() *PointG1

Zero returns a new G1 Point which is equal to point at infinity.

type G2

G2 is struct for G2 group.

type G2 struct {
    // contains filtered or unexported fields
}
func NewG2
func NewG2() *G2

NewG2 constructs a new G2 instance.

func (*G2) Add
func (g *G2) Add(r, p1, p2 *PointG2) *PointG2

Add adds two G2 points p1, p2 and assigns the result to point at first argument.

func (*G2) Affine
func (g *G2) Affine(p *PointG2) *PointG2

Affine calculates affine form of given G2 point.

func (*G2) ClearCofactor
func (g *G2) ClearCofactor(p *PointG2) *PointG2

ClearCofactor maps given a G2 point to correct subgroup

func (*G2) Double
func (g *G2) Double(r, p *PointG2) *PointG2

Double doubles a G2 point p and assigns the result to the point at first argument.

func (*G2) EncodeToCurve
func (g *G2) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error)

EncodeToCurve given a message and domain seperator tag returns the hash result which is a valid curve point. Implementation follows BLS12381G1_XMD:SHA-256_SSWU_NU_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08

func (*G2) Equal
func (g *G2) Equal(p1, p2 *PointG2) bool

Equal checks if given two G2 point is equal in their affine form.

func (*G2) FromBytes
func (g *G2) FromBytes(in []byte) (*PointG2, error)

FromBytes constructs a new point given uncompressed byte input. FromBytes does not take zcash flags into account. Byte input expected to be larger than 96 bytes. First 192 bytes should be concatenation of x and y values Point (0, 0) is considered as infinity.

func (*G2) FromCompressed
func (g *G2) FromCompressed(compressed []byte) (*PointG2, error)

FromCompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G2. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G2) FromUncompressed
func (g *G2) FromUncompressed(uncompressed []byte) (*PointG2, error)

FromUncompressed expects byte slice larger than 192 bytes and given bytes returns a new point in G2. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G2) HashToCurve
func (g *G2) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error)

HashToCurve given a message and domain seperator tag returns the hash result which is a valid curve point. Implementation follows BLS12381G1_XMD:SHA-256_SSWU_RO_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08

func (*G2) InCorrectSubgroup
func (g *G2) InCorrectSubgroup(p *PointG2) bool

InCorrectSubgroup checks whether given point is in correct subgroup.

func (*G2) IsAffine
func (g *G2) IsAffine(p *PointG2) bool

IsAffine checks a G2 point whether it is in affine form.

func (*G2) IsOnCurve
func (g *G2) IsOnCurve(p *PointG2) bool

IsOnCurve checks a G2 point is on curve.

func (*G2) IsZero
func (g *G2) IsZero(p *PointG2) bool

IsZero returns true if given point is equal to zero.

func (*G2) MapToCurve
func (g *G2) MapToCurve(in []byte) (*PointG2, error)

MapToCurve given a byte slice returns a valid G2 point. This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method. https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-05#section-6.6.2 Input byte slice should be a valid field element, otherwise an error is returned.

func (*G2) MulScalar
func (g *G2) MulScalar(c, p *PointG2, e *big.Int) *PointG2

MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.

func (*G2) MultiExp
func (g *G2) MultiExp(r *PointG2, points []*PointG2, powers []*big.Int) (*PointG2, error)

MultiExp calculates multi exponentiation. Given pairs of G2 point and scalar values (P_0, e_0), (P_1, e_1), ... (P_n, e_n) calculates r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n Length of points and scalars are expected to be equal, otherwise an error is returned. Result is assigned to point at first argument.

func (*G2) Neg
func (g *G2) Neg(r, p *PointG2) *PointG2

Neg negates a G2 point p and assigns the result to the point at first argument.

func (*G2) New
func (g *G2) New() *PointG2

New creates a new G2 Point which is equal to zero in other words point at infinity.

func (*G2) One
func (g *G2) One() *PointG2

One returns a new G2 Point which is equal to generator point.

func (*G2) Q
func (g *G2) Q() *big.Int

Q returns group order in big.Int.

func (*G2) Sub
func (g *G2) Sub(c, a, b *PointG2) *PointG2

Sub subtracts two G2 points p1, p2 and assigns the result to point at first argument.

func (*G2) ToBytes
func (g *G2) ToBytes(p *PointG2) []byte

ToBytes serializes a point into bytes in uncompressed form, does not take zcash flags into account, returns (0, 0) if point is infinity.

func (*G2) ToCompressed
func (g *G2) ToCompressed(p *PointG2) []byte

ToCompressed given a G2 point returns bytes in compressed form of the point. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G2) ToUncompressed
func (g *G2) ToUncompressed(p *PointG2) ([]byte, error)

ToUncompressed given a G2 point returns bytes in uncompressed (x, y) form of the point. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G2) Zero
func (g *G2) Zero() *PointG2

Zero returns a new G2 Point which is equal to point at infinity.

type GT

GT is type for target multiplicative group GT.

type GT struct {
    // contains filtered or unexported fields
}
func NewGT
func NewGT() *GT

NewGT constructs new target group instance.

func (*GT) Add
func (g *GT) Add(c, a, b *E)

Add adds two field element `a` and `b` and assigns the result to the element in first argument.

func (*GT) Exp
func (g *GT) Exp(c, a *E, s *big.Int)

Exp exponents an element `a` by a scalar `s` and assigns the result to the element in first argument.

func (*GT) FromBytes
func (g *GT) FromBytes(in []byte) (*E, error)

FromBytes expects 576 byte input and returns target group element FromBytes returns error if given element is not on correct subgroup.

func (*GT) Inverse
func (g *GT) Inverse(c, a *E)

Inverse inverses an element `a` and assigns the result to the element in first argument.

func (*GT) IsValid
func (g *GT) IsValid(e *E) bool

IsValid checks whether given target group element is in correct subgroup.

func (*GT) Mul
func (g *GT) Mul(c, a, b *E)

Mul multiplies two field element `a` and `b` and assigns the result to the element in first argument.

func (*GT) New
func (g *GT) New() *E

New initializes a new target group element which is equal to one

func (*GT) Q
func (g *GT) Q() *big.Int

Q returns group order in big.Int.

func (*GT) Square
func (g *GT) Square(c, a *E)

Square squares an element `a` and assigns the result to the element in first argument.

func (*GT) Sub
func (g *GT) Sub(c, a, b *E)

Sub subtracts two field element `a` and `b`, and assigns the result to the element in first argument.

func (*GT) ToBytes
func (g *GT) ToBytes(e *E) []byte

ToBytes serializes target group element.

type PointG1

PointG1 is type for point in G1. PointG1 is both used for Affine and Jacobian point representation. If z is equal to one the point is accounted as in affine form.

type PointG1 [3]fe
func (*PointG1) Set
func (p *PointG1) Set(p2 *PointG1) *PointG1
func (*PointG1) Zero
func (p *PointG1) Zero() *PointG1

type PointG2

PointG2 is type for point in G2. PointG2 is both used for Affine and Jacobian point representation. If z is equal to one the point is accounted as in affine form.

type PointG2 [3]fe2
func (*PointG2) Set
func (p *PointG2) Set(p2 *PointG2) *PointG2

Set copies valeus of one point to another.

func (*PointG2) Zero
func (p *PointG2) Zero() *PointG2

Generated by gomarkdoc

Documentation

Index

Constants

This section is empty.

Variables

View Source 
var G1One = g1One
View Source 
var G2One = g2One
View Source 
var Inp uint64 = 0x89f3fffcfffcfffd

Inp = -p^(-1) mod 2^64

Functions

This section is empty.

Types

type E 

type E = fe12

E is type for target group element

func (*E) Equal 

func (g *E) Equal(g2 *E) bool

Equal returns true if given two element is equal, otherwise returns false

func (*E) IsOne 

func (e *E) IsOne() bool

IsOne returns true if given element equals to one

func (*E) One 

func (e *E) One() *E

One sets a new target group element to one

func (*E) Set 

func (e *E) Set(e2 *E) *E

Set copies given value into the destination

type Engine 

type Engine struct {
	G1 *G1
	G2 *G2
	// contains filtered or unexported fields
}

Engine is BLS12-381 elliptic curve pairing engine

func NewEngine 

func NewEngine() *Engine

NewEngine creates new pairing engine insteace.

func (*Engine) AddPair 

func (e *Engine) AddPair(g1 *PointG1, g2 *PointG2) *Engine

AddPair adds a g1, g2 point pair to pairing engine returns nil if no more pairs can be added

func (*Engine) AddPairInv 

func (e *Engine) AddPairInv(g1 *PointG1, g2 *PointG2) *Engine

AddPairInv adds a G1, G2 point pair to pairing engine. G1 point is negated. returns nil if no more pairs can be added

func (*Engine) Check 

func (e *Engine) Check() (bool, error)

Check computes pairing and checks if result is equal to one

func (*Engine) GT 

func (e *Engine) GT() *GT

GT returns target group instance.

func (*Engine) Reset 

func (e *Engine) Reset() *Engine

Reset deletes added pairs.

func (*Engine) Result 

func (e *Engine) Result() (*E, error)

Result computes pairing and returns target group element as result.

type G1 

type G1 struct {
	// contains filtered or unexported fields
}

G1 is struct for G1 group.

func NewG1 

func NewG1() *G1

NewG1 constructs a new G1 instance.

func (*G1) Add 

func (g *G1) Add(r, p1, p2 *PointG1) *PointG1

Add adds two G1 points p1, p2 and assigns the result to point at first argument.

func (*G1) Affine 

func (g *G1) Affine(p *PointG1) *PointG1

Add adds two G1 points p1, p2 and assigns the result to point at first argument.

func (*G1) ClearCofactor 

func (g *G1) ClearCofactor(p *PointG1)

ClearCofactor maps given a G1 point to correct subgroup

func (*G1) Double 

func (g *G1) Double(r, p *PointG1) *PointG1

Double doubles a G1 point p and assigns the result to the point at first argument.

func (*G1) EncodeToCurve 

func (g *G1) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error)

EncodeToCurve given a message and domain seperator tag returns the hash result which is a valid curve point. Implementation follows BLS12381G1_XMD:SHA-256_SSWU_NU_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08

func (*G1) Equal 

func (g *G1) Equal(p1, p2 *PointG1) bool

Equal checks if given two G1 point is equal in their affine form.

func (*G1) FromBytes 

func (g *G1) FromBytes(in []byte) (*PointG1, error)

FromBytes constructs a new point given uncompressed byte input. FromBytes does not take zcash flags into account. Byte input expected to be larger than 96 bytes. First 96 bytes should be concatenation of x and y values. Point (0, 0) is considered as infinity.

func (*G1) FromCompressed 

func (g *G1) FromCompressed(compressed []byte) (*PointG1, error)

FromCompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G1. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G1) FromUncompressed 

func (g *G1) FromUncompressed(uncompressed []byte) (*PointG1, error)

FromUncompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G1. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G1) HashToCurve 

func (g *G1) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error)

HashToCurve given a message and domain seperator tag returns the hash result which is a valid curve point. Implementation follows BLS12381G1_XMD:SHA-256_SSWU_RO_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08

func (*G1) InCorrectSubgroup 

func (g *G1) InCorrectSubgroup(p *PointG1) bool

InCorrectSubgroup checks whether given point is in correct subgroup.

func (*G1) IsAffine 

func (g *G1) IsAffine(p *PointG1) bool

IsAffine checks a G1 point whether it is in affine form.

func (*G1) IsOnCurve 

func (g *G1) IsOnCurve(p *PointG1) bool

IsOnCurve checks a G1 point is on curve.

func (*G1) IsZero 

func (g *G1) IsZero(p *PointG1) bool

IsZero returns true if given point is equal to zero.

func (*G1) MapToCurve 

func (g *G1) MapToCurve(in []byte) (*PointG1, error)

MapToCurve given a byte slice returns a valid G1 point. This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method. https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08 Input byte slice should be a valid field element, otherwise an error is returned.

func (*G1) MulScalar 

func (g *G1) MulScalar(c, p *PointG1, e *big.Int) *PointG1

MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.

func (*G1) MultiExp 

func (g *G1) MultiExp(r *PointG1, points []*PointG1, powers []*big.Int) (*PointG1, error)

MultiExp calculates multi exponentiation. Given pairs of G1 point and scalar values (P_0, e_0), (P_1, e_1), ... (P_n, e_n) calculates r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n Length of points and scalars are expected to be equal, otherwise an error is returned. Result is assigned to point at first argument.

func (*G1) Neg 

func (g *G1) Neg(r, p *PointG1) *PointG1

Neg negates a G1 point p and assigns the result to the point at first argument.

func (*G1) New 

func (g *G1) New() *PointG1

New creates a new G1 Point which is equal to zero in other words point at infinity.

func (*G1) One 

func (g *G1) One() *PointG1

One returns a new G1 Point which is equal to generator point.

func (*G1) Q 

func (g *G1) Q() *big.Int

Q returns group order in big.Int.

func (*G1) Sub 

func (g *G1) Sub(c, a, b *PointG1) *PointG1

Sub subtracts two G1 points p1, p2 and assigns the result to point at first argument.

func (*G1) ToBytes 

func (g *G1) ToBytes(p *PointG1) []byte

ToBytes serializes a point into bytes in uncompressed form. ToBytes does not take zcash flags into account. ToBytes returns (0, 0) if point is infinity.

func (*G1) ToCompressed 

func (g *G1) ToCompressed(p *PointG1) []byte

ToCompressed given a G1 point returns bytes in compressed form of the point. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G1) ToUncompressed 

func (g *G1) ToUncompressed(p *PointG1) ([]byte, error)

ToUncompressed given a G1 point returns bytes in uncompressed (x, y) form of the point. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G1) Zero 

func (g *G1) Zero() *PointG1

Zero returns a new G1 Point which is equal to point at infinity.

type G2 

type G2 struct {
	// contains filtered or unexported fields
}

G2 is struct for G2 group.

func NewG2 

func NewG2() *G2

NewG2 constructs a new G2 instance.

func (*G2) Add 

func (g *G2) Add(r, p1, p2 *PointG2) *PointG2

Add adds two G2 points p1, p2 and assigns the result to point at first argument.

func (*G2) Affine 

func (g *G2) Affine(p *PointG2) *PointG2

Affine calculates affine form of given G2 point.

func (*G2) ClearCofactor 

func (g *G2) ClearCofactor(p *PointG2) *PointG2

ClearCofactor maps given a G2 point to correct subgroup

func (*G2) Double 

func (g *G2) Double(r, p *PointG2) *PointG2

Double doubles a G2 point p and assigns the result to the point at first argument.

func (*G2) EncodeToCurve 

func (g *G2) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error)

EncodeToCurve given a message and domain seperator tag returns the hash result which is a valid curve point. Implementation follows BLS12381G1_XMD:SHA-256_SSWU_NU_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08

func (*G2) Equal 

func (g *G2) Equal(p1, p2 *PointG2) bool

Equal checks if given two G2 point is equal in their affine form.

func (*G2) FromBytes 

func (g *G2) FromBytes(in []byte) (*PointG2, error)

FromBytes constructs a new point given uncompressed byte input. FromBytes does not take zcash flags into account. Byte input expected to be larger than 96 bytes. First 192 bytes should be concatenation of x and y values Point (0, 0) is considered as infinity.

func (*G2) FromCompressed 

func (g *G2) FromCompressed(compressed []byte) (*PointG2, error)

FromCompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G2. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G2) FromUncompressed 

func (g *G2) FromUncompressed(uncompressed []byte) (*PointG2, error)

FromUncompressed expects byte slice larger than 192 bytes and given bytes returns a new point in G2. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G2) HashToCurve 

func (g *G2) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error)

HashToCurve given a message and domain seperator tag returns the hash result which is a valid curve point. Implementation follows BLS12381G1_XMD:SHA-256_SSWU_RO_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08

func (*G2) InCorrectSubgroup 

func (g *G2) InCorrectSubgroup(p *PointG2) bool

InCorrectSubgroup checks whether given point is in correct subgroup.

func (*G2) IsAffine 

func (g *G2) IsAffine(p *PointG2) bool

IsAffine checks a G2 point whether it is in affine form.

func (*G2) IsOnCurve 

func (g *G2) IsOnCurve(p *PointG2) bool

IsOnCurve checks a G2 point is on curve.

func (*G2) IsZero 

func (g *G2) IsZero(p *PointG2) bool

IsZero returns true if given point is equal to zero.

func (*G2) MapToCurve 

func (g *G2) MapToCurve(in []byte) (*PointG2, error)

MapToCurve given a byte slice returns a valid G2 point. This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method. https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-05#section-6.6.2 Input byte slice should be a valid field element, otherwise an error is returned.

func (*G2) MulScalar 

func (g *G2) MulScalar(c, p *PointG2, e *big.Int) *PointG2

MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.

func (*G2) MultiExp 

func (g *G2) MultiExp(r *PointG2, points []*PointG2, powers []*big.Int) (*PointG2, error)

MultiExp calculates multi exponentiation. Given pairs of G2 point and scalar values (P_0, e_0), (P_1, e_1), ... (P_n, e_n) calculates r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n Length of points and scalars are expected to be equal, otherwise an error is returned. Result is assigned to point at first argument.

func (*G2) Neg 

func (g *G2) Neg(r, p *PointG2) *PointG2

Neg negates a G2 point p and assigns the result to the point at first argument.

func (*G2) New 

func (g *G2) New() *PointG2

New creates a new G2 Point which is equal to zero in other words point at infinity.

func (*G2) One 

func (g *G2) One() *PointG2

One returns a new G2 Point which is equal to generator point.

func (*G2) Q 

func (g *G2) Q() *big.Int

Q returns group order in big.Int.

func (*G2) Sub 

func (g *G2) Sub(c, a, b *PointG2) *PointG2

Sub subtracts two G2 points p1, p2 and assigns the result to point at first argument.

func (*G2) ToBytes 

func (g *G2) ToBytes(p *PointG2) []byte

ToBytes serializes a point into bytes in uncompressed form, does not take zcash flags into account, returns (0, 0) if point is infinity.

func (*G2) ToCompressed 

func (g *G2) ToCompressed(p *PointG2) []byte

ToCompressed given a G2 point returns bytes in compressed form of the point. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G2) ToUncompressed 

func (g *G2) ToUncompressed(p *PointG2) ([]byte, error)

ToUncompressed given a G2 point returns bytes in uncompressed (x, y) form of the point. Serialization rules are in line with zcash library. See below for details. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html

func (*G2) Zero 

func (g *G2) Zero() *PointG2

Zero returns a new G2 Point which is equal to point at infinity.

type GT 

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

GT is type for target multiplicative group GT.

func NewGT 

func NewGT() *GT

NewGT constructs new target group instance.

func (*GT) Add 

func (g *GT) Add(c, a, b *E)

Add adds two field element `a` and `b` and assigns the result to the element in first argument.

func (*GT) Exp 

func (g *GT) Exp(c, a *E, s *big.Int)

Exp exponents an element `a` by a scalar `s` and assigns the result to the element in first argument.

func (*GT) FromBytes 

func (g *GT) FromBytes(in []byte) (*E, error)

FromBytes expects 576 byte input and returns target group element FromBytes returns error if given element is not on correct subgroup.

func (*GT) Inverse 

func (g *GT) Inverse(c, a *E)

Inverse inverses an element `a` and assigns the result to the element in first argument.

func (*GT) IsValid 

func (g *GT) IsValid(e *E) bool

IsValid checks whether given target group element is in correct subgroup.

func (*GT) Mul 

func (g *GT) Mul(c, a, b *E)

Mul multiplies two field element `a` and `b` and assigns the result to the element in first argument.

func (*GT) New 

func (g *GT) New() *E

New initializes a new target group element which is equal to one

func (*GT) Q 

func (g *GT) Q() *big.Int

Q returns group order in big.Int.

func (*GT) Square 

func (g *GT) Square(c, a *E)

Square squares an element `a` and assigns the result to the element in first argument.

func (*GT) Sub 

func (g *GT) Sub(c, a, b *E)

Sub subtracts two field element `a` and `b`, and assigns the result to the element in first argument.

func (*GT) ToBytes 

func (g *GT) ToBytes(e *E) []byte

ToBytes serializes target group element.

type PointG1 

type PointG1 [3]fe

PointG1 is type for point in G1. PointG1 is both used for Affine and Jacobian point representation. If z is equal to one the point is accounted as in affine form.

func (*PointG1) Set 

func (p *PointG1) Set(p2 *PointG1) *PointG1

func (*PointG1) Zero 

func (p *PointG1) Zero() *PointG1

type PointG2 

type PointG2 [3]fe2

PointG2 is type for point in G2. PointG2 is both used for Affine and Jacobian point representation. If z is equal to one the point is accounted as in affine form.

func (*PointG2) Set 

func (p *PointG2) Set(p2 *PointG2) *PointG2

Set copies valeus of one point to another.

func (*PointG2) Zero 

func (p *PointG2) Zero() *PointG2

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