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// Copyright (c) 2019 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package edwards25519
import (
"crypto/subtle"
)
// A dynamic lookup table for variable-base, constant-time scalar muls.
type projLookupTable struct {
points [8]projCached
}
// A precomputed lookup table for fixed-base, constant-time scalar muls.
type affineLookupTable struct {
points [8]affineCached
}
// A dynamic lookup table for variable-base, variable-time scalar muls.
type nafLookupTable5 struct {
points [8]projCached
}
// A precomputed lookup table for fixed-base, variable-time scalar muls.
type nafLookupTable8 struct {
points [64]affineCached
}
// Constructors.
// Builds a lookup table at runtime. Fast.
func (v *projLookupTable) FromP3(q *Point) {
// Goal: v.points[i] = (i+1)*Q, i.e., Q, 2Q, ..., 8Q
// This allows lookup of -8Q, ..., -Q, 0, Q, ..., 8Q
v.points[0].FromP3(q)
tmpP3 := Point{}
tmpP1xP1 := projP1xP1{}
for i := 0; i < 7; i++ {
// Compute (i+1)*Q as Q + i*Q and convert to a projCached
// This is needlessly complicated because the API has explicit
// receivers instead of creating stack objects and relying on RVO
v.points[i+1].FromP3(tmpP3.fromP1xP1(tmpP1xP1.Add(q, &v.points[i])))
}
}
// This is not optimised for speed; fixed-base tables should be precomputed.
func (v *affineLookupTable) FromP3(q *Point) {
// Goal: v.points[i] = (i+1)*Q, i.e., Q, 2Q, ..., 8Q
// This allows lookup of -8Q, ..., -Q, 0, Q, ..., 8Q
v.points[0].FromP3(q)
tmpP3 := Point{}
tmpP1xP1 := projP1xP1{}
for i := 0; i < 7; i++ {
// Compute (i+1)*Q as Q + i*Q and convert to affineCached
v.points[i+1].FromP3(tmpP3.fromP1xP1(tmpP1xP1.AddAffine(q, &v.points[i])))
}
}
// Builds a lookup table at runtime. Fast.
func (v *nafLookupTable5) FromP3(q *Point) {
// Goal: v.points[i] = (2*i+1)*Q, i.e., Q, 3Q, 5Q, ..., 15Q
// This allows lookup of -15Q, ..., -3Q, -Q, 0, Q, 3Q, ..., 15Q
v.points[0].FromP3(q)
q2 := Point{}
q2.Add(q, q)
tmpP3 := Point{}
tmpP1xP1 := projP1xP1{}
for i := 0; i < 7; i++ {
v.points[i+1].FromP3(tmpP3.fromP1xP1(tmpP1xP1.Add(&q2, &v.points[i])))
}
}
// This is not optimised for speed; fixed-base tables should be precomputed.
func (v *nafLookupTable8) FromP3(q *Point) {
v.points[0].FromP3(q)
q2 := Point{}
q2.Add(q, q)
tmpP3 := Point{}
tmpP1xP1 := projP1xP1{}
for i := 0; i < 63; i++ {
v.points[i+1].FromP3(tmpP3.fromP1xP1(tmpP1xP1.AddAffine(&q2, &v.points[i])))
}
}
// Selectors.
// Set dest to x*Q, where -8 <= x <= 8, in constant time.
func (v *projLookupTable) SelectInto(dest *projCached, x int8) {
// Compute xabs = |x|
xmask := x >> 7
xabs := uint8((x + xmask) ^ xmask)
dest.Zero()
for j := 1; j <= 8; j++ {
// Set dest = j*Q if |x| = j
cond := subtle.ConstantTimeByteEq(xabs, uint8(j))
dest.Select(&v.points[j-1], dest, cond)
}
// Now dest = |x|*Q, conditionally negate to get x*Q
dest.CondNeg(int(xmask & 1))
}
// Set dest to x*Q, where -8 <= x <= 8, in constant time.
func (v *affineLookupTable) SelectInto(dest *affineCached, x int8) {
// Compute xabs = |x|
xmask := x >> 7
xabs := uint8((x + xmask) ^ xmask)
dest.Zero()
for j := 1; j <= 8; j++ {
// Set dest = j*Q if |x| = j
cond := subtle.ConstantTimeByteEq(xabs, uint8(j))
dest.Select(&v.points[j-1], dest, cond)
}
// Now dest = |x|*Q, conditionally negate to get x*Q
dest.CondNeg(int(xmask & 1))
}
// Given odd x with 0 < x < 2^4, return x*Q (in variable time).
func (v *nafLookupTable5) SelectInto(dest *projCached, x int8) {
*dest = v.points[x/2]
}
// Given odd x with 0 < x < 2^7, return x*Q (in variable time).
func (v *nafLookupTable8) SelectInto(dest *affineCached, x int8) {
*dest = v.points[x/2]
}
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