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package edwards25519
type NielsPoint struct {
YPlusX, YMinusX, XY2D FieldElement
}
// Precomputed scalar multiplication table
type ScalarMultTable [32][8]NielsPoint
// Set p to zero, the neutral element. Return p.
func (p *NielsPoint) SetZero() *NielsPoint {
p.YMinusX.SetOne()
p.YPlusX.SetOne()
p.XY2D.SetZero()
return p
}
// Set p to q. Returns p.
func (p *NielsPoint) Set(q *NielsPoint) *NielsPoint {
p.YPlusX.Set(&q.YPlusX)
p.YMinusX.Set(&q.YMinusX)
p.XY2D.Set(&q.XY2D)
return p
}
// Set p to q if b == 1. Assumes b is 0 or 1. Returns p.
func (p *NielsPoint) ConditionalSet(q *NielsPoint, b int32) *NielsPoint {
p.YPlusX.ConditionalSet(&q.YPlusX, b)
p.YMinusX.ConditionalSet(&q.YMinusX, b)
p.XY2D.ConditionalSet(&q.XY2D, b)
return p
}
// Set p to -q. Returns p.
func (p *NielsPoint) Neg(q *NielsPoint) *NielsPoint {
p.YMinusX.Set(&q.YPlusX)
p.YPlusX.Set(&q.YMinusX)
p.XY2D.Neg(&q.XY2D)
return p
}
// Sets p to q+r. Returns p.
func (p *CompletedPoint) AddExtendedNiels(q *ExtendedPoint, r *NielsPoint) *CompletedPoint {
var t0 FieldElement
p.X.add(&q.Y, &q.X)
p.Y.sub(&q.Y, &q.X)
p.Z.Mul(&p.X, &r.YPlusX)
p.Y.Mul(&p.Y, &r.YMinusX)
p.T.Mul(&r.XY2D, &q.T)
t0.add(&q.Z, &q.Z)
p.X.sub(&p.Z, &p.Y)
p.Y.add(&p.Z, &p.Y)
p.Z.add(&t0, &p.T)
p.T.sub(&t0, &p.T)
return p
}
// Set p to q-r. Returns p.
func (p *CompletedPoint) SubExtendedNiels(q *ExtendedPoint, r *NielsPoint) *CompletedPoint {
var t0 FieldElement
p.X.add(&q.Y, &q.X)
p.Y.sub(&q.Y, &q.X)
p.Z.Mul(&p.X, &r.YMinusX)
p.Y.Mul(&p.Y, &r.YPlusX)
p.T.Mul(&r.XY2D, &q.T)
t0.add(&q.Z, &q.Z)
p.X.sub(&p.Z, &p.Y)
p.Y.add(&p.Z, &p.Y)
p.Z.sub(&t0, &p.T)
p.T.add(&t0, &p.T)
return p
}
// Sets p to q. Returns p.
func (p *NielsPoint) SetExtended(q *ExtendedPoint) *NielsPoint {
var x, y, zInv FieldElement
zInv.Inverse(&q.Z)
x.Mul(&q.X, &zInv)
y.Mul(&q.Y, &zInv)
p.YPlusX.Add(&y, &x)
p.YMinusX.Sub(&y, &x)
p.XY2D.Mul(&x, &y)
p.XY2D.Add(&p.XY2D, &p.XY2D)
p.XY2D.Mul(&p.XY2D, &feD)
return p
}
// Fill the table t with data for the point p.
func (t *ScalarMultTable) Compute(p *ExtendedPoint) {
var c, cp ExtendedPoint
var c_pp ProjectivePoint
var c_cp CompletedPoint
cp.Set(p)
for i := 0; i < 32; i++ {
c.SetZero()
for v := 0; v < 8; v++ {
c.Add(&c, &cp)
t[i][v].SetExtended(&c)
}
c_cp.DoubleExtended(&c)
c_pp.SetCompleted(&c_cp)
c_cp.DoubleProjective(&c_pp)
c_pp.SetCompleted(&c_cp)
c_cp.DoubleProjective(&c_pp)
c_pp.SetCompleted(&c_cp)
c_cp.DoubleProjective(&c_pp)
c_pp.SetCompleted(&c_cp)
c_cp.DoubleProjective(&c_pp)
cp.SetCompleted(&c_cp)
}
}
// Compute 4-bit signed window for the scalar s
func computeScalarWindow4(s *[32]byte, w *[64]int8) {
for i := 0; i < 32; i++ {
w[2*i] = int8(s[i] & 15)
w[2*i+1] = int8((s[i] >> 4) & 15)
}
carry := int8(0)
for i := 0; i < 63; i++ {
w[i] += carry
carry = (w[i] + 8) >> 4
w[i] -= carry << 4
}
w[63] += carry
}
// Set p to s * q, where t was computed for q using t.Compute(q).
func (t *ScalarMultTable) ScalarMult(p *ExtendedPoint, s *[32]byte) {
var w [64]int8
computeScalarWindow4(s, &w)
p.SetZero()
var np NielsPoint
var cp CompletedPoint
var pp ProjectivePoint
for i := int32(0); i < 32; i++ {
t.selectPoint(&np, i, int32(w[2*i+1]))
cp.AddExtendedNiels(p, &np)
p.SetCompleted(&cp)
}
cp.DoubleExtended(p)
pp.SetCompleted(&cp)
cp.DoubleProjective(&pp)
pp.SetCompleted(&cp)
cp.DoubleProjective(&pp)
pp.SetCompleted(&cp)
cp.DoubleProjective(&pp)
p.SetCompleted(&cp)
for i := int32(0); i < 32; i++ {
t.selectPoint(&np, i, int32(w[2*i]))
cp.AddExtendedNiels(p, &np)
p.SetCompleted(&cp)
}
}
func (t *ScalarMultTable) VarTimeScalarMult(p *ExtendedPoint, s *[32]byte) {
var w [64]int8
computeScalarWindow4(s, &w)
p.SetZero()
var np NielsPoint
var cp CompletedPoint
var pp ProjectivePoint
for i := int32(0); i < 32; i++ {
if t.varTimeSelectPoint(&np, i, int32(w[2*i+1])) {
cp.AddExtendedNiels(p, &np)
p.SetCompleted(&cp)
}
}
cp.DoubleExtended(p)
pp.SetCompleted(&cp)
cp.DoubleProjective(&pp)
pp.SetCompleted(&cp)
cp.DoubleProjective(&pp)
pp.SetCompleted(&cp)
cp.DoubleProjective(&pp)
p.SetCompleted(&cp)
for i := int32(0); i < 32; i++ {
if t.varTimeSelectPoint(&np, i, int32(w[2*i])) {
cp.AddExtendedNiels(p, &np)
p.SetCompleted(&cp)
}
}
}
func (t *ScalarMultTable) selectPoint(p *NielsPoint, pos int32, b int32) {
bNegative := negative(b)
bAbs := b - (((-bNegative) & b) << 1)
p.SetZero()
for i := int32(0); i < 8; i++ {
p.ConditionalSet(&t[pos][i], equal30(bAbs, i+1))
}
var negP NielsPoint
negP.Neg(p)
p.ConditionalSet(&negP, bNegative)
}
func (t *ScalarMultTable) varTimeSelectPoint(p *NielsPoint, pos int32, b int32) bool {
if b == 0 {
return false
}
if b < 0 {
p.Neg(&t[pos][-b-1])
} else {
p.Set(&t[pos][b-1])
}
return true
}
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