field

package
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Published: Dec 10, 2023 License: BSD-3-Clause

Documentation ¶

Overview ¶

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

Constants ¶

This section is empty.

Variables ¶

This section is empty.

Functions ¶

This section is empty.

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 (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.