edwards25519

package module
Version: v1.0.0-rc.1 Latest Latest
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Published: Jun 4, 2021 License: BSD-3-Clause Imports: 5 Imported by: 50

README

filippo.io/edwards25519

import "filippo.io/edwards25519"

This library implements the edwards25519 elliptic curve, exposing the necessary APIs to build a wide array of higher-level primitives. Read the docs at pkg.go.dev/filippo.io/edwards25519.

The code is originally derived from Adam Langley's internal implementation in the Go standard library, and includes George Tankersley's performance improvements. It was then further developed by Henry de Valence for use in ristretto255.

Most users don't need this package, and should instead use crypto/ed25519 for signatures, golang.org/x/crypto/curve25519 for Diffie-Hellman, or github.com/gtank/ristretto255 for prime order group logic. However, for anyone currently using a fork of crypto/ed25519/internal/edwards25519 or github.com/agl/edwards25519, this package should be a safer, faster, and more powerful alternative.

Since this package is meant to curb proliferation of edwards25519 implementations in the Go ecosystem, it welcomes requests for new APIs or reviewable performance improvements.

Documentation

Overview

Package edwards25519 implements group logic for the twisted Edwards curve

-x^2 + y^2 = 1 + -(121665/121666)*x^2*y^2

This is better known as the Edwards curve equivalent to Curve25519, and is the curve used by the Ed25519 signature scheme.

Most users don't need this package, and should instead use crypto/ed25519 for signatures, golang.org/x/crypto/curve25519 for Diffie-Hellman, or github.com/gtank/ristretto255 for prime order group logic.

However, developers who do need to interact with low-level edwards25519 operations can use this package, which is an extended version of crypto/ed25519/internal/edwards25519 from the standard library repackaged as an importable module.

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

This section is empty.

Types

type Point

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

Point represents a point on the edwards25519 curve.

This type works similarly to math/big.Int, and all arguments and receivers are allowed to alias.

The zero value is NOT valid, and it may be used only as a receiver.

func NewGeneratorPoint

func NewGeneratorPoint() *Point

NewGeneratorPoint returns a new Point set to the canonical generator.

func NewIdentityPoint

func NewIdentityPoint() *Point

NewIdentityPoint returns a new Point set to the identity.

func (*Point) Add

func (v *Point) Add(p, q *Point) *Point

Add sets v = p + q, and returns v.

func (*Point) Bytes

func (v *Point) Bytes() []byte

Bytes returns the canonical 32-byte encoding of v, according to RFC 8032, Section 5.1.2.

func (*Point) BytesMontgomery

func (v *Point) BytesMontgomery() []byte

BytesMontgomery converts v to a point on the birationally-equivalent Curve25519 Montgomery curve, and returns its canonical 32 bytes encoding according to RFC 7748.

Note that BytesMontgomery only encodes the u-coordinate, so v and -v encode to the same value. If v is the identity point, BytesMontgomery returns 32 zero bytes, analogously to the X25519 function.

func (*Point) Equal

func (v *Point) Equal(u *Point) int

Equal returns 1 if v is equivalent to u, and 0 otherwise.

func (*Point) ExtendedCoordinates

func (v *Point) ExtendedCoordinates() (X, Y, Z, T *field.Element)

ExtendedCoordinates returns v in extended coordinates (X:Y:Z:T) where x = X/Z, y = Y/Z, and xy = T/Z as in https://eprint.iacr.org/2008/522.

func (*Point) MultByCofactor

func (v *Point) MultByCofactor(p *Point) *Point

MultByCofactor sets v = 8 * p, and returns v.

func (*Point) MultiScalarMult

func (v *Point) MultiScalarMult(scalars []*Scalar, points []*Point) *Point

MultiScalarMult sets v = sum(scalars[i] * points[i]), and returns v.

Execution time depends only on the lengths of the two slices, which must match.

func (*Point) Negate

func (v *Point) Negate(p *Point) *Point

Negate sets v = -p, and returns v.

func (*Point) ScalarBaseMult

func (v *Point) ScalarBaseMult(x *Scalar) *Point

ScalarBaseMult sets v = x * B, where B is the canonical generator, and returns v.

The scalar multiplication is done in constant time.

func (*Point) ScalarMult

func (v *Point) ScalarMult(x *Scalar, q *Point) *Point

ScalarMult sets v = x * q, and returns v.

The scalar multiplication is done in constant time.

func (*Point) Set

func (v *Point) Set(u *Point) *Point

Set sets v = u, and returns v.

func (*Point) SetBytes

func (v *Point) SetBytes(x []byte) (*Point, error)

SetBytes sets v = x, where x is a 32-byte encoding of v. If x does not represent a valid point on the curve, SetBytes returns nil and an error and the receiver is unchanged. Otherwise, SetBytes returns v.

Note that SetBytes accepts all non-canonical encodings of valid points. That is, it follows decoding rules that match most implementations in the ecosystem rather than RFC 8032.

func (*Point) SetExtendedCoordinates

func (v *Point) SetExtendedCoordinates(X, Y, Z, T *field.Element) (*Point, error)

SetExtendedCoordinates sets v = (X:Y:Z:T) in extended coordinates where x = X/Z, y = Y/Z, and xy = T/Z as in https://eprint.iacr.org/2008/522.

If the coordinates are invalid or don't represent a valid point on the curve, SetExtendedCoordinates returns nil and an error and the receiver is unchanged. Otherwise, SetExtendedCoordinates returns v.

func (*Point) Subtract

func (v *Point) Subtract(p, q *Point) *Point

Subtract sets v = p - q, and returns v.

func (*Point) VarTimeDoubleScalarBaseMult

func (v *Point) VarTimeDoubleScalarBaseMult(a *Scalar, A *Point, b *Scalar) *Point

VarTimeDoubleScalarBaseMult sets v = a * A + b * B, where B is the canonical generator, and returns v.

Execution time depends on the inputs.

func (*Point) VarTimeMultiScalarMult

func (v *Point) VarTimeMultiScalarMult(scalars []*Scalar, points []*Point) *Point

VarTimeMultiScalarMult sets v = sum(scalars[i] * points[i]), and returns v.

Execution time depends on the inputs.

type Scalar

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

A Scalar is an integer modulo

l = 2^252 + 27742317777372353535851937790883648493

which is the prime order of the edwards25519 group.

This type works similarly to math/big.Int, and all arguments and receivers are allowed to alias.

The zero value is a valid zero element.

func NewScalar

func NewScalar() *Scalar

NewScalar returns a new zero Scalar.

func (*Scalar) Add

func (s *Scalar) Add(x, y *Scalar) *Scalar

Add sets s = x + y mod l, and returns s.

func (*Scalar) Bytes

func (s *Scalar) Bytes() []byte

Bytes returns the canonical 32-byte little-endian encoding of s.

func (*Scalar) Equal

func (s *Scalar) Equal(t *Scalar) int

Equal returns 1 if s and t are equal, and 0 otherwise.

func (*Scalar) Invert

func (s *Scalar) Invert(t *Scalar) *Scalar

Invert sets s to the inverse of a nonzero scalar v, and returns s.

If t is zero, Invert returns zero.

func (*Scalar) Multiply

func (s *Scalar) Multiply(x, y *Scalar) *Scalar

Multiply sets s = x * y mod l, and returns s.

func (*Scalar) MultiplyAdd

func (s *Scalar) MultiplyAdd(x, y, z *Scalar) *Scalar

MultiplyAdd sets s = x * y + z mod l, and returns s.

func (*Scalar) Negate

func (s *Scalar) Negate(x *Scalar) *Scalar

Negate sets s = -x mod l, and returns s.

func (*Scalar) Set

func (s *Scalar) Set(x *Scalar) *Scalar

Set sets s = x, and returns s.

func (*Scalar) SetBytesWithClamping

func (s *Scalar) SetBytesWithClamping(x []byte) (*Scalar, error)

SetBytesWithClamping applies the buffer pruning described in RFC 8032, Section 5.1.5 (also known as clamping) and sets s to the result. The input must be 32 bytes, and it is not modified. If x is not of the right length, SetBytesWithClamping returns nil and an error, and the receiver is unchanged.

Note that since Scalar values are always reduced modulo the prime order of the curve, the resulting value will not preserve any of the cofactor-clearing properties that clamping is meant to provide. It will however work as expected as long as it is applied to points on the prime order subgroup, like in Ed25519. In fact, it is lost to history why RFC 8032 adopted the irrelevant RFC 7748 clamping, but it is now required for compatibility.

func (*Scalar) SetCanonicalBytes

func (s *Scalar) SetCanonicalBytes(x []byte) (*Scalar, error)

SetCanonicalBytes sets s = x, where x is a 32-byte little-endian encoding of s, and returns s. If x is not a canonical encoding of s, SetCanonicalBytes returns nil and an error, and the receiver is unchanged.

func (*Scalar) SetUniformBytes

func (s *Scalar) SetUniformBytes(x []byte) (*Scalar, error)

SetUniformBytes sets s to an uniformly distributed value given 64 uniformly distributed random bytes. If x is not of the right length, SetUniformBytes returns nil and an error, and the receiver is unchanged.

func (*Scalar) Subtract

func (s *Scalar) Subtract(x, y *Scalar) *Scalar

Subtract sets s = x - y mod l, and returns s.

Directories

Path Synopsis
asm module
Package field implements fast arithmetic modulo 2^255-19.
Package field implements fast arithmetic modulo 2^255-19.

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