field

Documentation

Overview

Package field implements fast arithmetic modulo 2^255-19.

Index

• type Element
  • func (v *Element) Absolute(u *Element) *Element
  • func (v *Element) Add(a, b *Element) *Element
  • func (v *Element) Bytes() []byte
  • func (v *Element) Equal(u *Element) int
  • func (v *Element) Invert(z *Element) *Element
  • func (v *Element) IsNegative() int
  • func (v *Element) Mult32(x *Element, y uint32) *Element
  • func (v *Element) Multiply(x, y *Element) *Element
  • func (v *Element) Negate(a *Element) *Element
  • func (v *Element) One() *Element
  • func (v *Element) Pow22523(x *Element) *Element
  • func (v *Element) Select(a, b *Element, cond int) *Element
  • func (v *Element) Set(a *Element) *Element
  • func (v *Element) SetBytes(x []byte) (*Element, error)
  • func (v *Element) SetWideBytes(x []byte) (*Element, error)
  • func (r *Element) SqrtRatio(u, v *Element) (R *Element, wasSquare int)
  • func (v *Element) Square(x *Element) *Element
  • func (v *Element) Subtract(a, b *Element) *Element
  • func (v *Element) Swap(u *Element, cond int)
  • func (v *Element) Zero() *Element

Types

type Element

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

Element represents an element of the field GF(2^255-19). Note that this is not a cryptographically secure group, and should only be used to interact with edwards25519.Point coordinates.

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 (*Element) Absolute

func (v *Element) Absolute(u *Element) *Element

Absolute sets v to |u|, and returns v.

func (*Element) Add

func (v *Element) Add(a, b *Element) *Element

Add sets v = a + b, and returns v.

func (*Element) Bytes

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

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

func (*Element) Equal

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

Equal returns 1 if v and u are equal, and 0 otherwise.

func (*Element) Invert

func (v *Element) Invert(z *Element) *Element

Invert sets v = 1/z mod p, and returns v.

If z == 0, Invert returns v = 0.

func (*Element) IsNegative

func (v *Element) IsNegative() int

IsNegative returns 1 if v is negative, and 0 otherwise.

func (*Element) Mult32

func (v *Element) Mult32(x *Element, y uint32) *Element

Mult32 sets v = x * y, and returns v.

func (*Element) Multiply

func (v *Element) Multiply(x, y *Element) *Element

Multiply sets v = x * y, and returns v.

func (*Element) Negate

func (v *Element) Negate(a *Element) *Element

Negate sets v = -a, and returns v.

func (*Element) One

func (v *Element) One() *Element

One sets v = 1, and returns v.

func (*Element) Pow22523

func (v *Element) Pow22523(x *Element) *Element

Pow22523 set v = x^((p-5)/8), and returns v. (p-5)/8 is 2^252-3.

func (*Element) Select

func (v *Element) Select(a, b *Element, cond int) *Element

Select sets v to a if cond == 1, and to b if cond == 0.

func (*Element) Set

func (v *Element) Set(a *Element) *Element

Set sets v = a, and returns v.

func (*Element) SetBytes

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

SetBytes sets v to x, where x is a 32-byte little-endian encoding. If x is not of the right length, SetBytes returns nil and an error, and the receiver is unchanged.

Consistent with RFC 7748, the most significant bit (the high bit of the last byte) is ignored, and non-canonical values (2^255-19 through 2^255-1) are accepted. Note that this is laxer than specified by RFC 8032, but consistent with most Ed25519 implementations.

func (*Element) SetWideBytes

func (v *Element) SetWideBytes(x []byte) (*Element, error)

SetWideBytes sets v to x, where x is a 64-byte little-endian encoding, which is reduced modulo the field order. If x is not of the right length, SetWideBytes returns nil and an error, and the receiver is unchanged.

SetWideBytes is not necessary to select a uniformly distributed value, and is only provided for compatibility: SetBytes can be used instead as the chance of bias is less than 2⁻²⁵⁰.

func (*Element) SqrtRatio

func (r *Element) SqrtRatio(u, v *Element) (R *Element, wasSquare int)

SqrtRatio sets r to the non-negative square root of the ratio of u and v.

If u/v is square, SqrtRatio returns r and 1. If u/v is not square, SqrtRatio sets r according to Section 4.3 of draft-irtf-cfrg-ristretto255-decaf448-00, and returns r and 0.

func (*Element) Square

func (v *Element) Square(x *Element) *Element

Square sets v = x * x, and returns v.

func (*Element) Subtract

func (v *Element) Subtract(a, b *Element) *Element

Subtract sets v = a - b, and returns v.

func (*Element) Swap

func (v *Element) Swap(u *Element, cond int)

Swap swaps v and u if cond == 1 or leaves them unchanged if cond == 0, and returns v.

func (*Element) Zero

func (v *Element) Zero() *Element

Zero sets v = 0, and returns v.