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(curve Curve, x, y *big.Int) []byte
Marshal converts a point into the uncompressed form specified in section 4.3.6 of ANSI X9.62.
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.
A Curve represents a short-form Weierstrass curve with a=-3. See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
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)
}
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() Curve
P256 returns a Curve which implements P-256 (see FIPS 186-3, section D.2.3)
The cryptographic operations are implemented using constant-time algorithms.
func P384() Curve
P384 returns a Curve which implements P-384 (see FIPS 186-3, section D.2.4)
The cryptographic operations do not use constant-time algorithms.
func P521() Curve
P521 returns a Curve which implements P-521 (see FIPS 186-3, section D.2.5)
The cryptographic operations do not use constant-time algorithms.
CurveParams contains the parameters of an elliptic curve and also provides a generic, non-constant time implementation of Curve.
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
}
func (curve *CurveParams) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)
func (curve *CurveParams) Double(x1, y1 *big.Int) (*big.Int, *big.Int)
func (curve *CurveParams) IsOnCurve(x, y *big.Int) bool
func (curve *CurveParams) Params() *CurveParams
func (curve *CurveParams) ScalarBaseMult(k []byte) (*big.Int, *big.Int)
func (curve *CurveParams) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)