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Published: May 6, 2024 License: BSD-3-Clause Imports: 3 Imported by: 0


This package is kept in sync with crypto/ed25519/internal/edwards25519/field in
the standard library.

If there are any changes in the standard library that need to be synced to this
package, run It will not overwrite any local changes made since the
previous sync, so it's ok to land changes in this package first, and then sync
to the standard library later.



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



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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

SetBytes sets v to x, which must be a 32-byte little-endian encoding.

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.

func (*Element) SqrtRatio

func (r *Element) SqrtRatio(u, v *Element) (rr *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.

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