bls

package module
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 Go to latest Published: May 25, 2020 License: Apache-2.0 Imports: 9 Imported by: 0

README

BLS

Pure GO bls library.

Implements the BLS12-381 curve.

Documentation

Index

Constants

View Source 
const (
	// LegendreZero is the legendre symbol of zero.
	LegendreZero = LegendreSymbol(iota)

	// LegendreQuadraticResidue is the legendre symbol of quadratic residue.
	LegendreQuadraticResidue

	// LegendreQuadraticNonResidue is the legendre symbol of quadratic non-residue.
	LegendreQuadraticNonResidue
)

Variables

View Source 
var BCoeff = FQReprToFQRaw(FQRepr{0xaa270000000cfff3, 0x53cc0032fc34000a, 0x478fe97a6b0a807f, 0xb1d37ebee6ba24d7, 0x8ec9733bbf78ab2f, 0x9d645513d83de7e})

BCoeff of the G1 curve.

View Source 
var BCoeffFQ2 = NewFQ2(BCoeff, BCoeff)

BCoeffFQ2 of the G2 curve.

View Source 
var FQ12One = NewFQ12(FQ6One, FQ6Zero)

FQ12One is the one element of FQ12.

View Source 
var FQ12Zero = NewFQ12(FQ6Zero, FQ6Zero)

FQ12Zero is the zero element of FQ12.

View Source 
var FQ2One = FQ2{
	// contains filtered or unexported fields
}

FQ2One gets the one-element of the field.

View Source 
var FQ2Zero = FQ2{
	// contains filtered or unexported fields
}

FQ2Zero gets the zero element of the field.

View Source 
var FQ6One = NewFQ6(FQ2One, FQ2Zero, FQ2Zero)

FQ6One represents the one value of FQ6.

View Source 
var FQ6Zero = NewFQ6(FQ2Zero, FQ2Zero, FQ2Zero)

FQ6Zero represents the zero value of FQ6.

View Source 
var FQOne = FQReprToFQ(bigOne)

FQOne is the one FQ element

View Source 
var FQR2, _ = FQReprFromString("2708263910654730174793787626328176511836455197166317677006154293982164122222515399004018013397331347120527951271750", 10)

FQR2 is R^2 % Q.

View Source 
var FQZero = FQReprToFQRaw(bigZero)

FQZero is the zero FQ element

View Source 
var FRR, _ = FRReprFromString("10920338887063814464675503992315976177888879664585288394250266608035967270910", 10)

FRR is 2**256 % r used for moving numbers into Montgomery form.

View Source 
var FRR2, _ = FRReprFromString("3294906474794265442129797520630710739278575682199800681788903916070560242797", 10)

FRR2 is R^2 % r.

View Source 
var G1AffineOne = &G1Affine{FQReprToFQ(g1GeneratorX), FQReprToFQ(g1GeneratorY), false}

G1AffineOne represents the point at 1 on G1.

View Source 
var G1AffineZero = &G1Affine{FQZero.Copy(), FQOne.Copy(), true}

G1AffineZero represents the point at infinity on G1.

View Source 
var G1ProjectiveOne = G1AffineOne.ToProjective()

G1ProjectiveOne is the generator point on G1.

View Source 
var G1ProjectiveZero = &G1Projective{FQZero.Copy(), FQOne.Copy(), FQZero.Copy()}

G1ProjectiveZero is the point at infinity where Z = 0.

View Source 
var G2AffineOne = &G2Affine{
	x: NewFQ2(
		FQReprToFQ(g2GeneratorXC0),
		FQReprToFQ(g2GeneratorXC1),
	),
	y: NewFQ2(
		FQReprToFQ(g2GeneratorYC0),
		FQReprToFQ(g2GeneratorYC1),
	), infinity: false}

G2AffineOne represents the point at 1 on G2.

View Source 
var G2AffineZero = &G2Affine{FQ2Zero, FQ2One, true}

G2AffineZero represents the point at infinity on G2.

View Source 
var G2ProjectiveOne = G2AffineOne.ToProjective()

G2ProjectiveOne is the generator point on G2.

View Source 
var G2ProjectiveZero = &G2Projective{FQ2Zero.Copy(), FQ2One.Copy(), FQ2Zero.Copy()}

G2ProjectiveZero is the point at infinity where Z = 0.

View Source 
var QFieldModulus, _ = FQReprFromString("4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787", 10)

QFieldModulus is the modulus of the field.

View Source 
var RFieldModulus, _ = FRReprFromString("52435875175126190479447740508185965837690552500527637822603658699938581184513", 10)

RFieldModulus is the modulus of the R field.

Functions

func AddNoCarry 

func AddNoCarry(a, b [6]uint64) [6]uint64

AddNoCarry finds the value of 384-bit a + b and returns the resulting 384-bit value.

func AddWithCarry 

func AddWithCarry(a, b, carry uint64) (uint64, uint64)

AddWithCarry finds the value a + b + carry and returns the full 128-bit value in 2 64-bit integers.

func CompareTwoPairings 

func CompareTwoPairings(P1 *G1Projective, Q1 *G2Projective, P2 *G1Projective, Q2 *G2Projective) bool

CompareTwoPairings checks e(P1, Q1) == e(P2, Q2) <=> FE(ML(P1, Q1)ML(-P2, Q2)) == 1

func CompressG1 

func CompressG1(affine *G1Affine) [48]byte

CompressG1 compresses a G1 point into an int.

func CompressG2 

func CompressG2(affine *G2Affine) [96]byte

CompressG2 compresses a G2 point into an int.

func MACWithCarry 

func MACWithCarry(a, b, c, carry uint64) (uint64, uint64)

MACWithCarry finds the value a + b * c + carry and returns the full 128-bit value in 2 64-bit integers.

func MontReduce 

func MontReduce(hi, lo [6]uint64) (out [6]uint64)

MontReduce reduces the 768-bit value using montgomery reduction.

func MultiplyFQRepr 

func MultiplyFQRepr(a, b [6]uint64) (hi [6]uint64, lo [6]uint64)

MultiplyFQRepr multiplies two FQRepr values together.

func SubNoBorrow 

func SubNoBorrow(a, b [6]uint64) [6]uint64

SubNoBorrow finds the value of 384-bit a - b and returns the resulting 384-bit value.

func SubWithBorrow 

func SubWithBorrow(a, b, borrow uint64) (uint64, uint64)

SubWithBorrow finds the value a - b - borrow and returns the result and the borrow.

Types

type BitIterator 

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

BitIterator is an iterator through bits.

func NewBitIterator 

func NewBitIterator(arr []uint64) BitIterator

NewBitIterator creates a new bit iterator given an array of ints.

func (*BitIterator) Next 

func (bi *BitIterator) Next() (bool, bool)

Next returns the next bit in the bit iterator with the second return value as true when finished.

type FQ 

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

FQ is an element in a field.

func FQReprToFQ 

func FQReprToFQ(o FQRepr) FQ

FQReprToFQ gets a pointer to a FQ given a pointer to an FQRepr

func FQReprToFQRaw 

func FQReprToFQRaw(o FQRepr) FQ

FQReprToFQRaw gets a pointer to a FQ without converting to montgomery form.

func HashFQ 

func HashFQ(hasher hash.Hash) FQ

HashFQ calculates a new FQ2 value based on a hash.

func RandFQ 

func RandFQ(reader io.Reader) (FQ, error)

RandFQ generates a random FQ element.

func (*FQ) AddAssign 

func (f *FQ) AddAssign(other FQ)

AddAssign multiplies a field element by this one.

func (FQ) Cmp 

func (f FQ) Cmp(other FQ) int

Cmp compares this field element to another.

func (FQ) Copy 

func (f FQ) Copy() FQ

Copy creates a copy of the field element.

func (*FQ) DivAssign 

func (f *FQ) DivAssign(other FQ)

DivAssign divides the field element by another

func (*FQ) DoubleAssign 

func (f *FQ) DoubleAssign()

DoubleAssign doubles the element

func (FQ) Equals 

func (f FQ) Equals(other FQ) bool

Equals checks equality of two field elements.

func (FQ) Exp 

func (f FQ) Exp(n FQRepr) FQ

Exp raises the element to a specific power.

func (FQ) Inverse 

func (f FQ) Inverse() (FQ, bool)

Inverse finds the inverse of the field element.

func (*FQ) IsValid 

func (f *FQ) IsValid() bool

IsValid checks if the element is valid.

func (FQ) IsZero 

func (f FQ) IsZero() bool

IsZero checks if the field element is zero.

func (*FQ) Legendre 

func (f *FQ) Legendre() LegendreSymbol

Legendre gets the legendre symbol of the element.

func (*FQ) MulAssign 

func (f *FQ) MulAssign(other FQ)

MulAssign multiplies a field element by this one.

func (FQ) MulBits 

func (f FQ) MulBits(b *FQRepr) FQ

MulBits multiplies the number by a big number.

func (FQ) MulBytes 

func (f FQ) MulBytes(b []byte) FQ

MulBytes multiplies the number by some bytes.

func (*FQ) NegAssign 

func (f *FQ) NegAssign()

NegAssign gets the negative value of the field element mod QFieldModulus.

func (FQ) Parity 

func (f FQ) Parity() bool

Parity checks if the point is greater than the point negated.

func (FQ) Sqrt 

func (f FQ) Sqrt() (FQ, bool)

Sqrt calculates the square root of the field element.

func (*FQ) SquareAssign 

func (f *FQ) SquareAssign()

SquareAssign squares a field element.

func (FQ) String 

func (f FQ) String() string

func (*FQ) SubAssign 

func (f *FQ) SubAssign(other FQ)

SubAssign subtracts a field element from this one.

func (*FQ) ToRepr 

func (f *FQ) ToRepr() FQRepr

ToRepr gets the 256-bit representation of the field element.

type FQ12 

type FQ12 struct {
	// contains filtered or unexported fields
}

FQ12 is an element of Fq12, represented by c0 + c1 * w.

func FinalExponentiation 

func FinalExponentiation(r *FQ12) *FQ12

FinalExponentiation performs the final exponentiation on the FQ12 element.

func MillerLoop 

func MillerLoop(items []MillerLoopItem) *FQ12

MillerLoop runs the miller loop algorithm.

func NewFQ12 

func NewFQ12(c0 *FQ6, c1 *FQ6) *FQ12

NewFQ12 creates a new FQ12 element from two FQ6 elements.

func Pairing 

func Pairing(p *G1Projective, q *G2Projective) *FQ12

Pairing performs a pairing given the G1 and G2 elements.

func RandFQ12 

func RandFQ12(reader io.Reader) (*FQ12, error)

RandFQ12 generates a random FQ12 element.

func (*FQ12) AddAssign 

func (f *FQ12) AddAssign(other *FQ12)

AddAssign adds two FQ12 elements together.

func (*FQ12) ConjugateAssign 

func (f *FQ12) ConjugateAssign()

ConjugateAssign returns the conjugate of the FQ12 element.

func (FQ12) Copy 

func (f FQ12) Copy() *FQ12

Copy returns a copy of the FQ12 element.

func (*FQ12) DoubleAssign 

func (f *FQ12) DoubleAssign()

DoubleAssign doubles each coefficient in an FQ12 element.

func (FQ12) Equals 

func (f FQ12) Equals(other *FQ12) bool

Equals checks if two FQ12 elements are equal.

func (FQ12) Exp 

func (f FQ12) Exp(n FQRepr) *FQ12

Exp raises the element ot a specific power.

func (*FQ12) FrobeniusMapAssign 

func (f *FQ12) FrobeniusMapAssign(power uint8)

FrobeniusMapAssign calculates the frobenius map of an FQ12 element.

func (*FQ12) InverseAssign 

func (f *FQ12) InverseAssign() bool

InverseAssign finds the inverse of an FQ12

func (*FQ12) IsZero 

func (f *FQ12) IsZero() bool

IsZero returns if the FQ12 element is zero.

func (*FQ12) MulAssign 

func (f *FQ12) MulAssign(other *FQ12)

MulAssign multiplies two FQ12 elements together.

func (*FQ12) MulBy014Assign 

func (f *FQ12) MulBy014Assign(c0 FQ2, c1 FQ2, c4 FQ2)

MulBy014Assign multiplies FQ12 element by 3 FQ2 elements.

func (*FQ12) NegAssign 

func (f *FQ12) NegAssign()

NegAssign negates each coefficient in an FQ12 element.

func (*FQ12) SquareAssign 

func (f *FQ12) SquareAssign()

SquareAssign squares the FQ2 element.

func (*FQ12) String 

func (f *FQ12) String() string

func (*FQ12) SubAssign 

func (f *FQ12) SubAssign(other *FQ12)

SubAssign subtracts one FQ12 element from another.

type FQ2 

type FQ2 struct {
	// contains filtered or unexported fields
}

FQ2 represents an element of Fq2, represented by c0 + c1 * u.

func HashFQ2 

func HashFQ2(hasher hash.Hash) FQ2

HashFQ2 calculates a new FQ2 value based on a hash.

func NewFQ2 

func NewFQ2(c0 FQ, c1 FQ) FQ2

NewFQ2 constructs a new FQ2 element given two FQ elements.

func RandFQ2 

func RandFQ2(reader io.Reader) (FQ2, error)

RandFQ2 generates a random FQ2 element.

func (*FQ2) AddAssign 

func (f *FQ2) AddAssign(other FQ2)

AddAssign adds two FQ2 elements together.

func (FQ2) Cmp 

func (f FQ2) Cmp(other FQ2) int

Cmp compares two FQ2 elements.

func (*FQ2) Copy 

func (f *FQ2) Copy() FQ2

Copy returns a copy of the field element.

func (*FQ2) DivAssign 

func (f *FQ2) DivAssign(other FQ2)

DivAssign divides the FQ2 element by another FQ2 element.

func (*FQ2) DoubleAssign 

func (f *FQ2) DoubleAssign()

DoubleAssign doubles an FQ2 element.

func (FQ2) Equals 

func (f FQ2) Equals(other FQ2) bool

Equals checks if this FQ2 equals another one.

func (FQ2) Exp 

func (f FQ2) Exp(n FQRepr) FQ2

Exp raises the element ot a specific power.

func (*FQ2) FrobeniusMapAssign 

func (f *FQ2) FrobeniusMapAssign(power uint8)

FrobeniusMapAssign multiplies the element by the Frobenius automorphism coefficient.

func (*FQ2) InverseAssign 

func (f *FQ2) InverseAssign() bool

InverseAssign finds the inverse of the field element.

func (FQ2) IsZero 

func (f FQ2) IsZero() bool

IsZero checks if the field element is zero.

func (FQ2) Legendre 

func (f FQ2) Legendre() LegendreSymbol

Legendre gets the legendre symbol of the FQ2 element.

func (*FQ2) MulAssign 

func (f *FQ2) MulAssign(other FQ2)

MulAssign multiplies two FQ2 elements together.

func (FQ2) MulBits 

func (f FQ2) MulBits(b *big.Int) FQ2

MulBits multiplies the number by a big number.

func (*FQ2) MultiplyByNonresidueAssign 

func (f *FQ2) MultiplyByNonresidueAssign()

MultiplyByNonresidueAssign multiplies this element by the cubic and quadratic nonresidue 1 + u.

func (*FQ2) NegAssign 

func (f *FQ2) NegAssign()

NegAssign negates a FQ2 element.

func (*FQ2) Norm 

func (f *FQ2) Norm() FQ

Norm gets the norm of Fq2 as extension field in i over Fq.

func (FQ2) Parity 

func (f FQ2) Parity() bool

Parity checks if the point is greater than the point negated.

func (FQ2) Sqrt 

func (f FQ2) Sqrt() (FQ2, bool)

Sqrt finds the sqrt of a field element.

func (*FQ2) SquareAssign 

func (f *FQ2) SquareAssign()

SquareAssign squares the FQ2 element.

func (FQ2) String 

func (f FQ2) String() string

func (*FQ2) SubAssign 

func (f *FQ2) SubAssign(other FQ2)

SubAssign subtracts one field element from another.

type FQ6 

type FQ6 struct {
	// contains filtered or unexported fields
}

FQ6 is an element of FQ6 represented by c0 + c1*v + v2*v**2

func NewFQ6 

func NewFQ6(c0 FQ2, c1 FQ2, c2 FQ2) *FQ6

NewFQ6 creates a new FQ6 element.

func RandFQ6 

func RandFQ6(reader io.Reader) (*FQ6, error)

RandFQ6 generates a random FQ6 element.

func (*FQ6) AddAssign 

func (f *FQ6) AddAssign(other *FQ6)

AddAssign the coefficients of the FQ6 element to another.

func (FQ6) Copy 

func (f FQ6) Copy() *FQ6

Copy creates a copy of the field element.

func (*FQ6) DoubleAssign 

func (f *FQ6) DoubleAssign()

DoubleAssign doubles the coefficients of the FQ6 element.

func (FQ6) Equals 

func (f FQ6) Equals(other *FQ6) bool

Equals checks if two FQ6 elements are equal.

func (FQ6) Exp 

func (f FQ6) Exp(n *FQRepr) *FQ6

Exp raises the element ot a specific power.

func (*FQ6) FrobeniusMapAssign 

func (f *FQ6) FrobeniusMapAssign(power uint8)

FrobeniusMapAssign runs the frobenius map algorithm with a certain power.

func (*FQ6) InverseAssign 

func (f *FQ6) InverseAssign() bool

InverseAssign finds the inverse of the FQ6 element.

func (FQ6) IsZero 

func (f FQ6) IsZero() bool

IsZero checks if the FQ6 element is zero.

func (*FQ6) MulAssign 

func (f *FQ6) MulAssign(other *FQ6)

MulAssign multiplies two FQ6 elements together.

func (*FQ6) MulBy01Assign 

func (f *FQ6) MulBy01Assign(c0 FQ2, c1 FQ2)

MulBy01Assign multiplies by c0 and c1.

func (*FQ6) MulBy1Assign 

func (f *FQ6) MulBy1Assign(c1 FQ2)

MulBy1Assign multiplies the FQ6 by an FQ2.

func (*FQ6) MulByNonresidueAssign 

func (f *FQ6) MulByNonresidueAssign()

MulByNonresidueAssign multiplies by quadratic nonresidue v.

func (*FQ6) NegAssign 

func (f *FQ6) NegAssign()

NegAssign negates the coefficients of the FQ6 element.

func (*FQ6) SquareAssign 

func (f *FQ6) SquareAssign()

SquareAssign squares the FQ6 element.

func (FQ6) String 

func (f FQ6) String() string

func (*FQ6) SubAssign 

func (f *FQ6) SubAssign(other *FQ6)

SubAssign subtracts the coefficients of the FQ6 element from another.

type FQRepr 

type FQRepr [6]uint64

FQRepr represents a uint384. The least significant bits are first.

func FQReprFromBigInt 

func FQReprFromBigInt(n *big.Int) (FQRepr, error)

FQReprFromBigInt create a FQRepr from a big.Int.

func FQReprFromBytes 

func FQReprFromBytes(b [48]byte) FQRepr

FQReprFromBytes gets a new FQRepr from big-endian bytes.

func FQReprFromString 

func FQReprFromString(s string, b uint) (FQRepr, error)

FQReprFromString creates a FQRepr from a string.

func NewFQRepr 

func NewFQRepr(n uint64) FQRepr

NewFQRepr creates a new number given a uint64.

func (*FQRepr) AddNoCarry 

func (f *FQRepr) AddNoCarry(g FQRepr)

AddNoCarry adds two FQReprs to another and does not handle carry.

func (FQRepr) Bit 

func (f FQRepr) Bit(n uint) bool

Bit checks if a bit is set (little-endian)

func (FQRepr) BitLen 

func (f FQRepr) BitLen() uint

BitLen counts the number of bits the number is.

func (FQRepr) Bytes 

func (f FQRepr) Bytes() [48]byte

Bytes gets the bytes used for an FQRepr.

func (*FQRepr) Cmp 

func (f *FQRepr) Cmp(g FQRepr) int

Cmp compares two FQRepr's

func (*FQRepr) Copy 

func (f *FQRepr) Copy() FQRepr

Copy copies a FQRepr to a new instance and returns it.

func (*FQRepr) Div2 

func (f *FQRepr) Div2()

Div2 divides the FQRepr by 2.

func (*FQRepr) Equals 

func (f *FQRepr) Equals(g FQRepr) bool

Equals checks if two FQRepr's are equal.

func (FQRepr) IsEven 

func (f FQRepr) IsEven() bool

IsEven checks if the FQRepr is even.

func (FQRepr) IsOdd 

func (f FQRepr) IsOdd() bool

IsOdd checks if the FQRepr is odd.

func (FQRepr) IsZero 

func (f FQRepr) IsZero() bool

IsZero checks if the FQRepr is zero.

func (*FQRepr) Lsh 

func (f *FQRepr) Lsh(n uint)

Lsh shifts the FQRepr left by a certain number of bits.

func (*FQRepr) Mul2 

func (f *FQRepr) Mul2()

Mul2 multiplies the FQRepr by 2.

func (*FQRepr) Rsh 

func (f *FQRepr) Rsh(n uint)

Rsh shifts the FQRepr right by a certain number of bits.

func (FQRepr) String 

func (f FQRepr) String() string

ToString converts the FQRepr to a string.

func (*FQRepr) SubNoBorrow 

func (f *FQRepr) SubNoBorrow(g FQRepr)

SubNoBorrow subtracts two FQReprs from another and does not handle borrow.

func (FQRepr) ToBig 

func (f FQRepr) ToBig() *big.Int

ToBig gets the big.Int representation of the FQRepr.

type FR 

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

FR is an element in a field.

func FRReprToFR 

func FRReprToFR(o *FRRepr) *FR

FRReprToFR gets a pointer to a FR given a pointer to an FRRepr

func HashFR 

func HashFR(hasher hash.Hash) *FR

HashFR calculates a new FR2 value based on a hash.

func HashSecretKey 

func HashSecretKey(b [32]byte) *FR

func RandFR 

func RandFR(reader io.Reader) (*FR, error)

RandFR generates a random FR element.

func (*FR) AddAssign 

func (f *FR) AddAssign(other *FR)

AddAssign multiplies a field element by this one.

func (*FR) Bytes 

func (f *FR) Bytes() [32]byte

Bytes gets the representation of the FR in bytes.

func (FR) Cmp 

func (f FR) Cmp(other *FR) int

Cmp compares this field element to another.

func (*FR) Copy 

func (f *FR) Copy() *FR

Copy copies an FR element.

func (*FR) DoubleAssign 

func (f *FR) DoubleAssign()

DoubleAssign doubles the element

func (FR) Equals 

func (f FR) Equals(other *FR) bool

Equals checks equality of two field elements.

func (*FR) Exp 

func (f *FR) Exp(n *FRRepr) *FR

Exp raises the element to a specific power.

func (FR) Inverse 

func (f FR) Inverse() *FR

Inverse finds the inverse of the field element.

func (*FR) IsValid 

func (f *FR) IsValid() bool

IsValid checks if the element is valid.

func (FR) IsZero 

func (f FR) IsZero() bool

IsZero checks if the field element is zero.

func (*FR) Legendre 

func (f *FR) Legendre() LegendreSymbol

Legendre gets the legendre symbol of the element.

func (FR) MulAssign 

func (f FR) MulAssign(other *FR)

MulAssign multiplies a field element by this one.

func (FR) MulBits 

func (f FR) MulBits(b *FRRepr) *FR

MulBits multiplies the number by a big number.

func (FR) MulBytes 

func (f FR) MulBytes(b []byte) *FR

MulBytes multiplies the number by some bytes.

func (*FR) NegAssign 

func (f *FR) NegAssign()

NegAssign gets the negative value of the field element mod RFieldModulus.

func (FR) Parity 

func (f FR) Parity() bool

Parity checks if the point is greater than the point negated.

func (FR) Sqrt 

func (f FR) Sqrt() *FR

Sqrt calculates the square root of the field element.

func (*FR) SquareAssign 

func (f *FR) SquareAssign()

SquareAssign squares a field element.

func (FR) String 

func (f FR) String() string

func (*FR) SubAssign 

func (f *FR) SubAssign(other *FR)

SubAssign subtracts a field element from this one.

func (*FR) ToRepr 

func (f *FR) ToRepr() *FRRepr

ToRepr gets the 256-bit representation of the field element.

type FRRepr 

type FRRepr [4]uint64

FRRepr represents a uint256.

func FRReprFromBigInt 

func FRReprFromBigInt(n *big.Int) (*FRRepr, error)

FRReprFromBigInt create a FRRepr from a big.Int.

func FRReprFromBytes 

func FRReprFromBytes(b [32]byte) *FRRepr

FRReprFromBytes gets a new FRRepr from big-endian bytes.

func FRReprFromString 

func FRReprFromString(s string, b uint) (*FRRepr, error)

FRReprFromString creates a FRRepr from a string.

func NewFRRepr 

func NewFRRepr(n uint64) *FRRepr

NewFRRepr creates a new number given a uint64.

func (*FRRepr) AddNoCarry 

func (f *FRRepr) AddNoCarry(g *FRRepr)

AddNoCarry adds two FRReprs to another and does not handle carry.

func (FRRepr) Bit 

func (f FRRepr) Bit(n uint) bool

Bit checks if a bit is set (little-endian)

func (FRRepr) BitLen 

func (f FRRepr) BitLen() uint

BitLen counts the number of bits the number is.

func (FRRepr) Bytes 

func (f FRRepr) Bytes() [32]byte

Bytes gets the bytes used for an FRRepr.

func (*FRRepr) Cmp 

func (f *FRRepr) Cmp(g *FRRepr) int

Cmp compares two FRRepr's

func (*FRRepr) Copy 

func (f *FRRepr) Copy() *FRRepr

Copy copies a FRRepr to a new instance and returns it.

func (*FRRepr) Div2 

func (f *FRRepr) Div2()

Div2 divides the FRRepr by 2.

func (*FRRepr) Equals 

func (f *FRRepr) Equals(g *FRRepr) bool

Equals checks if two FRRepr's are equal.

func (FRRepr) IsEven 

func (f FRRepr) IsEven() bool

IsEven checks if the FRRepr is even.

func (FRRepr) IsOdd 

func (f FRRepr) IsOdd() bool

IsOdd checks if the FRRepr is odd.

func (FRRepr) IsZero 

func (f FRRepr) IsZero() bool

IsZero checks if the FRRepr is zero.

func (*FRRepr) Lsh 

func (f *FRRepr) Lsh(n uint)

Lsh shifts the FRRepr left by a certain number of bits.

func (*FRRepr) Mul2 

func (f *FRRepr) Mul2()

Mul2 multiplies the FRRepr by 2.

func (*FRRepr) Rsh 

func (f *FRRepr) Rsh(n uint)

Rsh shifts the FRRepr right by a certain number of bits.

func (FRRepr) String 

func (f FRRepr) String() string

ToString converts the FRRepr to a string.

func (*FRRepr) SubNoBorrow 

func (f *FRRepr) SubNoBorrow(g *FRRepr)

SubNoBorrow subtracts two FRReprs from another and does not handle borrow.

func (FRRepr) ToBig 

func (f FRRepr) ToBig() *big.Int

ToBig gets the big.Int representation of the FRRepr.

func (*FRRepr) ToFQ 

func (f *FRRepr) ToFQ() FQRepr

ToFQ converts an FRRepr to an FQ.

type G1Affine 

type G1Affine struct {
	// contains filtered or unexported fields
}

G1Affine is an affine point on the G1 curve.

func ClearH 

func ClearH(p *G1Affine) *G1Affine

ClearH clears the cofactor for Ell1.

func DecompressG1 

func DecompressG1(b [48]byte) (*G1Affine, error)

DecompressG1 decompresses the big int into an affine point and checks if it is in the correct prime group.

func DecompressG1Unchecked 

func DecompressG1Unchecked(b [48]byte) (*G1Affine, error)

DecompressG1Unchecked decompresses the big int into an affine point without checking if it's in the correct prime group.

func GetG1PointFromX 

func GetG1PointFromX(x FQ, greatest bool) (*G1Affine, error)

GetG1PointFromX attempts to reconstruct an affine point given an x-coordinate. The point is not guaranteed to be in the subgroup. If and only if `greatest` is set will the lexicographically largest y-coordinate be selected.

func HashG1 

func HashG1(msg []byte) *G1Affine

HashG1 converts a message to a point on the G2 curve.

func NewG1Affine 

func NewG1Affine(x FQ, y FQ) *G1Affine

NewG1Affine constructs a new G1Affine point.

func (G1Affine) Copy 

func (g G1Affine) Copy() *G1Affine

Copy returns a copy of the G1Affine point.

func (G1Affine) Equals 

func (g G1Affine) Equals(other *G1Affine) bool

Equals checks if two affine points are equal.

func (G1Affine) IsInCorrectSubgroupAssumingOnCurve 

func (g G1Affine) IsInCorrectSubgroupAssumingOnCurve() bool

IsInCorrectSubgroupAssumingOnCurve checks if the point multiplied by the field characteristic equals zero.

func (G1Affine) IsOnCurve 

func (g G1Affine) IsOnCurve() bool

IsOnCurve checks if a point is on the G1 curve.

func (G1Affine) IsZero 

func (g G1Affine) IsZero() bool

IsZero checks if the point is infinity.

func (G1Affine) Mul 

func (g G1Affine) Mul(b FQRepr) *G1Projective

Mul performs a EC multiply operation on the point.

func (G1Affine) MulFR 

func (g G1Affine) MulFR(b *FRRepr) *G1Projective

MulFR performs a EC multiply operation on the point.

func (*G1Affine) NegAssign 

func (g *G1Affine) NegAssign()

NegAssign negates the point.

func (G1Affine) ScaleByCofactor 

func (g G1Affine) ScaleByCofactor() *G1Projective

ScaleByCofactor scales the G1Affine point by the cofactor.

func (*G1Affine) SerializeBytes 

func (g *G1Affine) SerializeBytes() [96]byte

SerializeBytes returns the serialized bytes for the point represented.

func (*G1Affine) SetRawBytes 

func (g *G1Affine) SetRawBytes(uncompressed [96]byte)

SetRawBytes sets the coords given the serialized bytes.

func (G1Affine) String 

func (g G1Affine) String() string

func (G1Affine) ToProjective 

func (g G1Affine) ToProjective() *G1Projective

ToProjective converts an affine point to a projective one.

type G1Projective 

type G1Projective struct {
	// contains filtered or unexported fields
}

G1Projective is a projective point on the G1 curve.

func NewG1Projective 

func NewG1Projective(x FQ, y FQ, z FQ) *G1Projective

NewG1Projective creates a new G1Projective point.

func RandG1 

func RandG1(r io.Reader) (*G1Projective, error)

RandG1 generates a random G1 element.

func (G1Projective) Add 

func (g G1Projective) Add(other *G1Projective) *G1Projective

Add performs an EC Add operation with another point.

func (G1Projective) AddAffine 

func (g G1Projective) AddAffine(other *G1Affine) *G1Projective

AddAffine performs an EC Add operation with an affine point.

func (G1Projective) Copy 

func (g G1Projective) Copy() *G1Projective

Copy returns a copy of the G1Projective point.

func (G1Projective) Double 

func (g G1Projective) Double() *G1Projective

Double performs EC doubling on the point.

func (G1Projective) Equal 

func (g G1Projective) Equal(other *G1Projective) bool

Equal checks if two projective points are equal.

func (G1Projective) IsZero 

func (g G1Projective) IsZero() bool

IsZero checks if the G1Projective point is zero.

func (G1Projective) Mul 

func (g G1Projective) Mul(b FQRepr) *G1Projective

Mul performs a EC multiply operation on the point.

func (G1Projective) MulFR 

func (g G1Projective) MulFR(b *FRRepr) *G1Projective

MulFR performs a EC multiply operation on the point.

func (*G1Projective) NegAssign 

func (g *G1Projective) NegAssign()

NegAssign negates the point.

func (G1Projective) String 

func (g G1Projective) String() string

func (G1Projective) ToAffine 

func (g G1Projective) ToAffine() *G1Affine

ToAffine converts a G1Projective point to affine form.

type G2Affine 

type G2Affine struct {
	// contains filtered or unexported fields
}

G2Affine is an affine point on the G2 curve.

func DecompressG2 

func DecompressG2(c [96]byte) (*G2Affine, error)

DecompressG2 decompresses a G2 point from a big int and checks if it is in the correct subgroup.

func DecompressG2Unchecked 

func DecompressG2Unchecked(c [96]byte) (*G2Affine, error)

DecompressG2Unchecked decompresses a G2 point from a big int.

func GetG2PointFromX 

func GetG2PointFromX(x FQ2, greatest bool) (*G2Affine, error)

GetG2PointFromX attempts to reconstruct an affine point given an x-coordinate. The point is not guaranteed to be in the subgroup. If and only if `greatest` is set will the lexicographically largest y-coordinate be selected.

func HashG2 

func HashG2(msg []byte) *G2Affine

HashG2 converts a message to a point on the G2 curve.

func NewG2Affine 

func NewG2Affine(x FQ2, y FQ2) *G2Affine

NewG2Affine constructs a new G2Affine point.

func OptimizedSWU2MapHelper 

func OptimizedSWU2MapHelper(t FQ2) *G2Affine

func SWEncodeG2 

func SWEncodeG2(t FQ2) *G2Affine

SWEncodeG2 implements the Shallue-van de Woestijne encoding.

func (G2Affine) Copy 

func (g G2Affine) Copy() *G2Affine

Copy returns a copy of the G2Affine point.

func (G2Affine) Equals 

func (g G2Affine) Equals(other *G2Affine) bool

Equals checks if two affine points are equal.

func (G2Affine) IsInCorrectSubgroupAssumingOnCurve 

func (g G2Affine) IsInCorrectSubgroupAssumingOnCurve() bool

IsInCorrectSubgroupAssumingOnCurve checks if the point multiplied by the field characteristic equals zero.

func (G2Affine) IsOnCurve 

func (g G2Affine) IsOnCurve() bool

IsOnCurve checks if a point is on the G2 curve.

func (G2Affine) IsZero 

func (g G2Affine) IsZero() bool

IsZero checks if the point is infinity.

func (G2Affine) Mul 

func (g G2Affine) Mul(b FQRepr) *G2Projective

Mul performs a EC multiply operation on the point.

func (G2Affine) MulBig 

func (g G2Affine) MulBig(b big.Int) *G2Projective

MulBig performs a EC multiply operation on the point.

func (G2Affine) MulFR 

func (g G2Affine) MulFR(b *FRRepr) *G2Projective

MulFR performs a EC multiply operation on the point.

func (*G2Affine) NegAssign 

func (g *G2Affine) NegAssign()

NegAssign negates the point.

func (G2Affine) ScaleByCofactor 

func (g G2Affine) ScaleByCofactor() *G2Projective

ScaleByCofactor scales the G2Affine point by the cofactor.

func (*G2Affine) SerializeBytes 

func (g *G2Affine) SerializeBytes() [192]byte

SerializeBytes returns the serialized bytes for the points represented.

func (*G2Affine) SetRawBytes 

func (g *G2Affine) SetRawBytes(uncompressed [192]byte) error

SetRawBytes sets the coords given the serialized bytes.

func (G2Affine) String 

func (g G2Affine) String() string

func (G2Affine) ToProjective 

func (g G2Affine) ToProjective() *G2Projective

ToProjective converts an affine point to a projective one.

type G2Prepared 

type G2Prepared struct {
	// contains filtered or unexported fields
}

G2Prepared is a prepared G2 point multiplication by blsX.

func G2AffineToPrepared 

func G2AffineToPrepared(q *G2Affine) *G2Prepared

G2AffineToPrepared performs multiplication of the affine point by blsX.

func (G2Prepared) IsZero 

func (g G2Prepared) IsZero() bool

IsZero checks if the point is at infinity.

type G2Projective 

type G2Projective struct {
	// contains filtered or unexported fields
}

G2Projective is a projective point on the G2 curve.

func HashG2WithDomain 

func HashG2WithDomain(messageHash [32]byte, domain [8]byte) *G2Projective

Warning: See BLS standardisation process. This implementation is known to be unsecure.

func NewG2Projective 

func NewG2Projective(x FQ2, y FQ2, z FQ2) *G2Projective

NewG2Projective creates a new G2Projective point.

func RandG2 

func RandG2(r io.Reader) (*G2Projective, error)

RandG2 generates a random G2 element.

func (G2Projective) Add 

func (g G2Projective) Add(other *G2Projective) *G2Projective

Add performs an EC Add operation with another point.

func (G2Projective) AddAffine 

func (g G2Projective) AddAffine(other *G2Affine) *G2Projective

AddAffine performs an EC Add operation with an affine point.

func (G2Projective) Copy 

func (g G2Projective) Copy() *G2Projective

Copy returns a copy of the G2Projective point.

func (G2Projective) Double 

func (g G2Projective) Double() *G2Projective

Double performs EC doubling on the point.

func (G2Projective) Equals 

func (g G2Projective) Equals(other *G2Projective) bool

Equal checks if two projective points are equal.

func (G2Projective) IsZero 

func (g G2Projective) IsZero() bool

IsZero checks if the G2Projective point is zero.

func (G2Projective) Mul 

func (g G2Projective) Mul(b FQRepr) *G2Projective

Mul performs a EC multiply operation on the point.

func (G2Projective) MulFR 

func (g G2Projective) MulFR(b *FRRepr) *G2Projective

MulFR performs a EC multiply operation on the point.

func (G2Projective) String 

func (g G2Projective) String() string

func (G2Projective) ToAffine 

func (g G2Projective) ToAffine() *G2Affine

ToAffine converts a G2Projective point to affine form.

type LegendreSymbol 

type LegendreSymbol uint8

LegendreSymbol is the legendre symbol of an element.

type MillerLoopItem 

type MillerLoopItem struct {
	P *G1Affine
	Q *G2Prepared
}

MillerLoopItem are the inputs to the miller loop.

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