# elliptic

package standard library
Version: go1.17.1 Latest Latest Go to latest
Published: Sep 9, 2021 License: BSD-3-Clause

## Documentation ¶

### Overview ¶

Package elliptic implements several standard elliptic curves over prime fields.

### Constants ¶

This section is empty.

### Variables ¶

This section is empty.

### Functions ¶

#### 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 section 4.3.6 of ANSI X9.62.

#### func MarshalCompressed ¶ added in go1.15

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

MarshalCompressed converts a point on the curve into the compressed form specified in section 4.3.6 of ANSI X9.62.

#### 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 or is not on the curve. On error, x = nil.

#### func UnmarshalCompressed ¶ added in go1.15

`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 or is not on the curve. 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=-3.

Note that the point at infinity (0, 0) is not considered on the curve, and although it can be returned by Add, Double, ScalarMult, or ScalarBaseMult, it can't be marshaled or unmarshaled, and IsOnCurve will return false for it.

#### func P224 ¶

`func P224() Curve`

P224 returns a Curve which implements P-224 (see FIPS 186-3, section D.2.2).

The cryptographic operations are implemented using constant-time algorithms.

#### func P256 ¶

`func P256() Curve`

P256 returns a Curve which implements NIST P-256 (FIPS 186-3, section D.2.3), also known as secp256r1 or prime256v1. The CurveParams.Name of this Curve is "P-256".

Multiple invocations of this function will return the same value, so it can be used for equality checks and switch statements.

ScalarMult and ScalarBaseMult are implemented using constant-time algorithms.

#### func P384 ¶

`func P384() Curve`

P384 returns a Curve which implements NIST P-384 (FIPS 186-3, section D.2.4), also known as secp384r1. The CurveParams.Name of this Curve is "P-384".

Multiple invocations of this function will return the same value, so it can be used for equality checks and switch statements.

The cryptographic operations do not use constant-time algorithms.

#### func P521 ¶

`func P521() Curve`

P521 returns a Curve which implements NIST P-521 (FIPS 186-3, section D.2.5), also known as secp521r1. The CurveParams.Name of this Curve is "P-521".

Multiple invocations of this function will return the same value, so it can be used for equality checks and switch statements.

The cryptographic operations are implemented using constant-time algorithms.

#### 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 (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)`

## Directories ¶

Path Synopsis
internal
Package fiat implements prime order fields using formally verified algorithms from the Fiat Cryptography project.
Package fiat implements prime order fields using formally verified algorithms from the Fiat Cryptography project.