edwards25519

Documentation

Index

• Variables
• func FeAdd(out, a, b *FieldElement)
• func FeCMove(f, g *FieldElement, b int32)
• func FeCopy(dst, src *FieldElement)
• func FeFromBytes(v *FieldElement, x *[32]byte)
• func FeInvert(out, z *FieldElement)
• func FeIsNegative(f *FieldElement) byte
• func FeIsNonZero(f *FieldElement) int32
• func FeMul(out, a, b *FieldElement)
• func FeNeg(out, a *FieldElement)
• func FeOne(fe *FieldElement)
• func FeSquare(out, a *FieldElement)
• func FeSquare2(out, a *FieldElement)
• func FeSub(out, a, b *FieldElement)
• func FeToBytes(r *[32]byte, v *FieldElement)
• func FeZero(fe *FieldElement)
• func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte)
• func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte)
• func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32)
• func ScMulAdd(s, a, b, c *[32]byte)
• func ScReduce(out *[32]byte, s *[64]byte)
• type CachedGroupElement
• type CompletedGroupElement
  • func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement)
  • func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement)
• type ExtendedGroupElement
  • func (p *ExtendedGroupElement) Double(r *CompletedGroupElement)
  • func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool
  • func (p *ExtendedGroupElement) ToBytes(s *[32]byte)
  • func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement)
  • func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement)
  • func (p *ExtendedGroupElement) Zero()
• type FieldElement
• type PreComputedGroupElement
  • func (p *PreComputedGroupElement) Zero()
• type ProjectiveGroupElement
  • func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement)
  • func (p *ProjectiveGroupElement) ToBytes(s *[32]byte)
  • func (p *ProjectiveGroupElement) Zero()

Variables

var A = FieldElement{
	486662, 0, 0, 0, 0,
}

var SqrtM1 = FieldElement{
	1718705420411056, 234908883556509, 2233514472574048, 2117202627021982, 765476049583133,
}

Functions

func FeAdd

func FeAdd(out, a, b *FieldElement)

FeAdd sets out = a + b. Long sequences of additions without reduction that let coefficients grow larger than 54 bits would be a problem. Paper cautions: "do not have such sequences of additions".

func FeCMove

func FeCMove(f, g *FieldElement, b int32)

Replace (f,g) with (g,g) if b == 1; replace (f,g) with (f,g) if b == 0.

Preconditions: b in {0,1}.

func FeCopy

func FeCopy(dst, src *FieldElement)

func FeFromBytes

func FeFromBytes(v *FieldElement, x *[32]byte)

func FeInvert

func FeInvert(out, z *FieldElement)

func FeIsNegative

func FeIsNegative(f *FieldElement) byte

func FeIsNonZero

func FeIsNonZero(f *FieldElement) int32

func FeMul

func FeMul(out, a, b *FieldElement)

FeMul calculates out = a * b.

func FeNeg

func FeNeg(out, a *FieldElement)

FeNeg sets out = -a

func FeOne

func FeOne(fe *FieldElement)

func FeSquare

func FeSquare(out, a *FieldElement)

FeSquare calculates out = a * a.

func FeSquare2

func FeSquare2(out, a *FieldElement)

FeSquare2 calculates out = 2 * a * a.

func FeSub

func FeSub(out, a, b *FieldElement)

FeSub sets out = a - b

func FeToBytes

func FeToBytes(r *[32]byte, v *FieldElement)

func FeZero

func FeZero(fe *FieldElement)

func GeDoubleScalarMultVartime

func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte)

GeDoubleScalarMultVartime sets r = a*A + b*B where a = a[0]+256*a[1]+...+256^31 a[31]. and b = b[0]+256*b[1]+...+256^31 b[31]. B is the Ed25519 base point (x,4/5) with x positive.

func GeScalarMultBase

func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte)

GeScalarMultBase computes h = a*B, where

a = a[0]+256*a[1]+...+256^31 a[31]
B is the Ed25519 base point (x,4/5) with x positive.

Preconditions:

a[31] <= 127

func PreComputedGroupElementCMove

func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32)

func ScMulAdd

func ScMulAdd(s, a, b, c *[32]byte)

Input:

a[0]+256*a[1]+...+256^31*a[31] = a
b[0]+256*b[1]+...+256^31*b[31] = b
c[0]+256*c[1]+...+256^31*c[31] = c

Output:

s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
where l = 2^252 + 27742317777372353535851937790883648493.

func ScReduce

func ScReduce(out *[32]byte, s *[64]byte)

Input:

s[0]+256*s[1]+...+256^63*s[63] = s

Output:

s[0]+256*s[1]+...+256^31*s[31] = s mod l
where l = 2^252 + 27742317777372353535851937790883648493.

Types

type CachedGroupElement

type CachedGroupElement struct {
	Z, T2d FieldElement
	// contains filtered or unexported fields
}

type CompletedGroupElement

type CompletedGroupElement struct {
	X, Y, Z, T FieldElement
}

func (*CompletedGroupElement) ToExtended

func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement)

func (*CompletedGroupElement) ToProjective

func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement)

type ExtendedGroupElement

type ExtendedGroupElement struct {
	X, Y, Z, T FieldElement
}

func (*ExtendedGroupElement) Double

func (p *ExtendedGroupElement) Double(r *CompletedGroupElement)

func (*ExtendedGroupElement) FromBytes

func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool

func (*ExtendedGroupElement) ToBytes

func (p *ExtendedGroupElement) ToBytes(s *[32]byte)

func (*ExtendedGroupElement) ToCached

func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement)

func (*ExtendedGroupElement) ToProjective

func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement)

func (*ExtendedGroupElement) Zero

func (p *ExtendedGroupElement) Zero()

type FieldElement

type FieldElement [5]uint64

FieldElement represents an element of the field GF(2^255-19). An element t represents the integer t[0] + t[1]*2^51 + t[2]*2^102 + t[3]*2^153 + t[4]*2^204.

type PreComputedGroupElement

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

func (*PreComputedGroupElement) Zero

func (p *PreComputedGroupElement) Zero()

type ProjectiveGroupElement

type ProjectiveGroupElement struct {
	X, Y, Z FieldElement
}

func (*ProjectiveGroupElement) Double

func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement)

func (*ProjectiveGroupElement) ToBytes

func (p *ProjectiveGroupElement) ToBytes(s *[32]byte)

func (*ProjectiveGroupElement) Zero

func (p *ProjectiveGroupElement) Zero()