bn256

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Published: Dec 19, 2023 License: Apache-2.0 Imports: 10 Imported by: 0

Documentation

Overview

Package bn256 defines/implements ShangMi(SM) sm9's curves and pairing.

Code generated by addchain. DO NOT EDIT.

Code generated by addchain. DO NOT EDIT.

Index

Constants

This section is empty.

Variables

View Source
var Gen1 = &G1{curveGen}

Gen1 is the generator of G1.

View Source
var Gen2 = &G2{twistGen}

Gen2 is the generator of G2.

View Source
var Order = bigFromHex("b640000002a3a6f1d603ab4ff58ec74449f2934b18ea8beee56ee19cd69ecf25")

Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u²+6u+1.

Functions

func GenerateGTFieldTable

func GenerateGTFieldTable(basePoint *GT) *[32 * 2]GTFieldTable

func GenerateKey

func GenerateKey(curve Curve, rand io.Reader) (priv []byte, x, y *big.Int, err error)

GenerateKey returns a public/private key pair. The private key is generated using the given reader, which must return random data.

func Marshal

func Marshal(curve Curve, x, y *big.Int) []byte

Marshal converts a point on the curve into the uncompressed form specified in SEC 1, Version 2.0, Section 2.3.3. If the point is not on the curve (or is the conventional point at infinity), the behavior is undefined.

func MarshalCompressed

func MarshalCompressed(curve Curve, x, y *big.Int) []byte

MarshalCompressed converts a point on the curve into the compressed form specified in SEC 1, Version 2.0, Section 2.3.3. If the point is not on the curve (or is the conventional point at infinity), the behavior is undefined.

func NewCurveGenerator

func NewCurveGenerator() *curvePoint

func NewCurvePoint

func NewCurvePoint() *curvePoint

func NewTwistGenerator

func NewTwistGenerator() *twistPoint

func NewTwistPoint

func NewTwistPoint() *twistPoint

func NormalizeScalar

func NormalizeScalar(scalar []byte) []byte

func Sqrt

func Sqrt(e, x *gfP) (isSquare bool)

Sqrt sets e to a square root of x. If x is not a square, Sqrt returns false and e is unchanged. e and x can overlap.

func Unmarshal

func Unmarshal(curve Curve, data []byte) (x, y *big.Int)

Unmarshal converts a point, serialized by Marshal, into an x, y pair. It is an error if the point is not in uncompressed form, is not on the curve, or is the point at infinity. On error, x = nil.

func UnmarshalCompressed

func UnmarshalCompressed(curve Curve, data []byte) (x, y *big.Int)

UnmarshalCompressed converts a point, serialized by MarshalCompressed, into an x, y pair. It is an error if the point is not in compressed form, is not on the curve, or is the point at infinity. On error, x = nil.

Types

type Curve

type Curve interface {
	// Params returns the parameters for the curve.
	Params() *CurveParams
	// IsOnCurve reports whether the given (x,y) lies on the curve.
	IsOnCurve(x, y *big.Int) bool
	// Add returns the sum of (x1,y1) and (x2,y2)
	Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int)
	// Double returns 2*(x,y)
	Double(x1, y1 *big.Int) (x, y *big.Int)
	// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
	ScalarMult(x1, y1 *big.Int, k []byte) (x, y *big.Int)
	// ScalarBaseMult returns k*G, where G is the base point of the group
	// and k is an integer in big-endian form.
	ScalarBaseMult(k []byte) (x, y *big.Int)
}

A Curve represents a short-form Weierstrass curve with a=0.

The behavior of Add, Double, and ScalarMult when the input is not a point on the curve is undefined.

Note that the conventional point at infinity (0, 0) is not considered on the curve, although it can be returned by Add, Double, ScalarMult, or ScalarBaseMult (but not the Unmarshal or UnmarshalCompressed functions).

type CurveParams

type CurveParams struct {
	P       *big.Int // the order of the underlying field
	N       *big.Int // the order of the base point
	B       *big.Int // the constant of the curve equation
	Gx, Gy  *big.Int // (x,y) of the base point
	BitSize int      // the size of the underlying field
	Name    string   // the canonical name of the curve
}

CurveParams contains the parameters of an elliptic curve and also provides a generic, non-constant time implementation of Curve.

func (*CurveParams) Add

func (curve *CurveParams) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)

func (*CurveParams) Double

func (curve *CurveParams) Double(x1, y1 *big.Int) (*big.Int, *big.Int)

func (*CurveParams) IsOnCurve

func (curve *CurveParams) IsOnCurve(x, y *big.Int) bool

func (*CurveParams) Params

func (curve *CurveParams) Params() *CurveParams

func (*CurveParams) ScalarBaseMult

func (curve *CurveParams) ScalarBaseMult(k []byte) (*big.Int, *big.Int)

func (*CurveParams) ScalarMult

func (curve *CurveParams) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)

type G1

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

G1 is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.

func RandomG1

func RandomG1(r io.Reader) (*big.Int, *G1, error)

RandomG1 returns x and g₁ˣ where x is a random, non-zero number read from r.

func (*G1) Add

func (e *G1) Add(a, b *G1) *G1

Add sets e to a+b and then returns e.

func (*G1) Double

func (e *G1) Double(a *G1) *G1

Double sets e to [2]a and then returns e.

func (*G1) Equal

func (e *G1) Equal(other *G1) bool

Equal compare e and other

func (*G1) IsOnCurve

func (e *G1) IsOnCurve() bool

IsOnCurve returns true if e is on the curve.

func (*G1) Marshal

func (e *G1) Marshal() []byte

Marshal converts e to a byte slice.

func (*G1) MarshalCompressed

func (e *G1) MarshalCompressed() []byte

MarshalCompressed converts e to a byte slice with compress prefix. If the point is not on the curve (or is the conventional point at infinity), the behavior is undefined.

func (*G1) MarshalUncompressed

func (e *G1) MarshalUncompressed() []byte

MarshalUncompressed converts e to a byte slice with prefix

func (*G1) Neg

func (e *G1) Neg(a *G1) *G1

Neg sets e to -a and then returns e.

func (*G1) ScalarBaseMult

func (e *G1) ScalarBaseMult(scalar []byte) (*G1, error)

ScalarBaseMult sets e to scaler*g where g is the generator of the group and then returns e.

func (*G1) ScalarMult

func (e *G1) ScalarMult(a *G1, scalar []byte) (*G1, error)

ScalarMult sets e to a*k and then returns e.

func (*G1) Set

func (e *G1) Set(a *G1) *G1

Set sets e to a and then returns e.

func (*G1) String

func (g *G1) String() string

func (*G1) Unmarshal

func (e *G1) Unmarshal(m []byte) ([]byte, error)

Unmarshal sets e to the result of converting the output of Marshal back into a group element and then returns e.

func (*G1) UnmarshalCompressed

func (e *G1) UnmarshalCompressed(data []byte) ([]byte, error)

UnmarshalCompressed sets e to the result of converting the output of Marshal back into a group element and then returns e.

type G1Curve

type G1Curve struct {
	// contains filtered or unexported fields
}

func (*G1Curve) Add

func (g1 *G1Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)

func (*G1Curve) Double

func (g1 *G1Curve) Double(x, y *big.Int) (*big.Int, *big.Int)

func (*G1Curve) IsOnCurve

func (g1 *G1Curve) IsOnCurve(x, y *big.Int) bool

func (*G1Curve) Params

func (g1 *G1Curve) Params() *CurveParams

func (*G1Curve) ScalarBaseMult

func (g1 *G1Curve) ScalarBaseMult(scalar []byte) (*big.Int, *big.Int)

func (*G1Curve) ScalarMult

func (g1 *G1Curve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int)

func (*G1Curve) Unmarshal

func (curve *G1Curve) Unmarshal(data []byte) (x, y *big.Int)

func (*G1Curve) UnmarshalCompressed

func (curve *G1Curve) UnmarshalCompressed(data []byte) (x, y *big.Int)

type G2

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

G2 is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.

func RandomG2

func RandomG2(r io.Reader) (*big.Int, *G2, error)

RandomG2 returns x and g₂ˣ where x is a random, non-zero number read from r.

func (*G2) Add

func (e *G2) Add(a, b *G2) *G2

Add sets e to a+b and then returns e.

func (*G2) Equal

func (e *G2) Equal(other *G2) bool

Equal compare e and other

func (*G2) IsOnCurve

func (e *G2) IsOnCurve() bool

IsOnCurve returns true if e is on the twist curve.

func (*G2) Marshal

func (e *G2) Marshal() []byte

Marshal converts e into a byte slice.

func (*G2) MarshalCompressed

func (e *G2) MarshalCompressed() []byte

MarshalCompressed converts e into a byte slice with uncompressed point prefix

func (*G2) MarshalUncompressed

func (e *G2) MarshalUncompressed() []byte

MarshalUncompressed converts e into a byte slice with uncompressed point prefix

func (*G2) Neg

func (e *G2) Neg(a *G2) *G2

Neg sets e to -a and then returns e.

func (*G2) ScalarBaseMult

func (e *G2) ScalarBaseMult(scalar []byte) (*G2, error)

ScalarBaseMult sets e to g*k where g is the generator of the group and then returns out.

func (*G2) ScalarMult

func (e *G2) ScalarMult(a *G2, scalar []byte) (*G2, error)

ScalarMult sets e to a*k and then returns e.

func (*G2) Set

func (e *G2) Set(a *G2) *G2

Set sets e to a and then returns e.

func (*G2) String

func (e *G2) String() string

func (*G2) Unmarshal

func (e *G2) Unmarshal(m []byte) ([]byte, error)

Unmarshal sets e to the result of converting the output of Marshal back into a group element and then returns e.

func (*G2) UnmarshalCompressed

func (e *G2) UnmarshalCompressed(data []byte) ([]byte, error)

UnmarshalCompressed sets e to the result of converting the output of Marshal back into a group element and then returns e.

type GT

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

GT is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.

func Miller

func Miller(g1 *G1, g2 *G2) *GT

Miller applies Miller's algorithm, which is a bilinear function from the source groups to F_p^12. Miller(g1, g2).Finalize() is equivalent to Pair(g1, g2).

func Pair

func Pair(g1 *G1, g2 *G2) *GT

Pair calculates an R-Ate pairing.

func RandomGT

func RandomGT(r io.Reader) (*big.Int, *GT, error)

RandomGT returns x and e(g₁, g₂)ˣ where x is a random, non-zero number read from r.

func ScalarBaseMultGT

func ScalarBaseMultGT(tables *[32 * 2]GTFieldTable, scalar []byte) (*GT, error)

ScalarBaseMultGT compute basepoint^r with precomputed table

func ScalarMultGT

func ScalarMultGT(a *GT, scalar []byte) (*GT, error)

ScalarMultGT compute a^scalar

func (*GT) Add

func (e *GT) Add(a, b *GT) *GT

Add sets e to a+b and then returns e.

func (*GT) Finalize

func (e *GT) Finalize() *GT

Finalize is a linear function from F_p^12 to GT.

func (*GT) Marshal

func (e *GT) Marshal() []byte

Marshal converts e into a byte slice.

func (*GT) ScalarBaseMult

func (e *GT) ScalarBaseMult(k *big.Int) *GT

ScalarBaseMult sets e to g*k where g is the generator of the group and then returns out.

func (*GT) ScalarMult

func (e *GT) ScalarMult(a *GT, k *big.Int) *GT

ScalarMult sets e to a*k and then returns e.

func (*GT) Set

func (e *GT) Set(a *GT) *GT

Set sets e to a and then returns e.

func (*GT) SetOne

func (e *GT) SetOne() *GT

Set sets e to one and then returns e.

func (*GT) String

func (g *GT) String() string

func (*GT) Unmarshal

func (e *GT) Unmarshal(m []byte) ([]byte, error)

Unmarshal sets e to the result of converting the output of Marshal back into a group element and then returns e.

type GTFieldTable

type GTFieldTable [15]*GT

A GTFieldTable holds the first 15 Exp of a value at offset -1, so P is at table[0], P^15 is at table[14], and P^0 is implicitly the identity point.

func (*GTFieldTable) Select

func (table *GTFieldTable) Select(p *GT, n uint8)

Select selects the n-th multiple of the table base point into p. It works in constant time by iterating over every entry of the table. n must be in [0, 15].

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