bn256

package
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 Go to latest Published: Aug 13, 2022 License: MIT Imports: 10 Imported by: 0

README

This part codes mainly refer two projects:

  1. bn256, 主要是基域运算。这个项目的主要问题在于测试太少。
  2. gmssl sm9，主要是2-4-12塔式扩域，以及r-ate等。这个项目的主要问题在于性能没有怎么优化。基于性能考虑，后续r-rate还是参考了bn256的op-ate，并结合sm9的特殊性做了适应性改造。
  3. SM9 precompute pairing per master public key level。
  4. G1, G2曲线倍点运算预计算。

Documentation

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 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(k *big.Int) *G1

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

func (*G1) ScalarMult 

func (e *G1) ScalarMult(a *G1, k *big.Int) *G1

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(k []byte) (*big.Int, *big.Int)

func (*G1Curve) ScalarMult 

func (g1 *G1Curve) ScalarMult(Bx, By *big.Int, k []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(k *big.Int) *G2

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, k *big.Int) *G2

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, r *big.Int) *GT

ScalarBaseMultGT compute basepoint^r with precomputed table

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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