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// Copyright (c) 2018, Google Inc.
//
// Permission to use, copy, modify, and/or distribute this software for any
// purpose with or without fee is hereby granted, provided that the above
// copyright notice and this permission notice appear in all copies.
//
// THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
// SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
// WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
// OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
// CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
//go:build ignore
package main
import (
"crypto/aes"
"crypto/cipher"
"crypto/elliptic"
"crypto/rand"
"fmt"
"io"
"math/big"
)
var (
p256 elliptic.Curve
zero, one, p, R, Rinv *big.Int
deterministicRand io.Reader
)
type coordinates int
const (
affine coordinates = iota
jacobian
)
func init() {
p256 = elliptic.P256()
zero = new(big.Int)
one = new(big.Int).SetInt64(1)
p = p256.Params().P
R = new(big.Int)
R.SetBit(R, 256, 1)
R.Mod(R, p)
Rinv = new(big.Int).ModInverse(R, p)
deterministicRand = newDeterministicRand()
}
func modMul(z, x, y *big.Int) *big.Int {
z.Mul(x, y)
return z.Mod(z, p)
}
func toMontgomery(z, x *big.Int) *big.Int {
return modMul(z, x, R)
}
func fromMontgomery(z, x *big.Int) *big.Int {
return modMul(z, x, Rinv)
}
func isAffineInfinity(x, y *big.Int) bool {
// Infinity, in affine coordinates, is represented as (0, 0) by
// both Go, p256-x86_64-asm.pl and p256-armv8-asm.pl.
return x.Sign() == 0 && y.Sign() == 0
}
func randNonZeroInt(max *big.Int) *big.Int {
for {
r, err := rand.Int(deterministicRand, max)
if err != nil {
panic(err)
}
if r.Sign() != 0 {
return r
}
}
}
func randPoint() (x, y *big.Int) {
k := randNonZeroInt(p256.Params().N)
return p256.ScalarBaseMult(k.Bytes())
}
func toJacobian(xIn, yIn *big.Int) (x, y, z *big.Int) {
if isAffineInfinity(xIn, yIn) {
// The Jacobian representation of infinity has Z = 0. Depending
// on the implementation, X and Y may be further constrained.
// Generalizing the curve equation to Jacobian coordinates for
// non-zero Z gives:
//
// y² = x³ - 3x + b, where x = X/Z² and y = Y/Z³
// Y² = X³ + aXZ⁴ + bZ⁶
//
// Taking that formula at Z = 0 gives Y² = X³. This constraint
// allows removing a special case in the point-on-curve check.
//
// BoringSSL, however, historically generated infinities with
// arbitrary X and Y and include the special case. We also have
// not verified that add and double preserve this
// property. Thus, generate test vectors with unrelated X and Y,
// to test that p256-x86_64-asm.pl and p256-armv8-asm.pl correctly
// handle unconstrained representations of infinity.
x = randNonZeroInt(p)
y = randNonZeroInt(p)
z = zero
return
}
z = randNonZeroInt(p)
// X = xZ²
y = modMul(new(big.Int), z, z)
x = modMul(new(big.Int), xIn, y)
// Y = yZ³
modMul(y, y, z)
modMul(y, y, yIn)
return
}
func printMontgomery(name string, a *big.Int) {
a = toMontgomery(new(big.Int), a)
fmt.Printf("%s = %064x\n", name, a)
}
func printTestCase(ax, ay *big.Int, aCoord coordinates, bx, by *big.Int, bCoord coordinates) {
rx, ry := p256.Add(ax, ay, bx, by)
var az *big.Int
if aCoord == jacobian {
ax, ay, az = toJacobian(ax, ay)
} else if isAffineInfinity(ax, ay) {
az = zero
} else {
az = one
}
var bz *big.Int
if bCoord == jacobian {
bx, by, bz = toJacobian(bx, by)
} else if isAffineInfinity(bx, by) {
bz = zero
} else {
bz = one
}
fmt.Printf("Test = PointAdd\n")
printMontgomery("A.X", ax)
printMontgomery("A.Y", ay)
printMontgomery("A.Z", az)
printMontgomery("B.X", bx)
printMontgomery("B.Y", by)
printMontgomery("B.Z", bz)
printMontgomery("Result.X", rx)
printMontgomery("Result.Y", ry)
fmt.Printf("\n")
}
func main() {
fmt.Printf("# ∞ + ∞ = ∞.\n")
printTestCase(zero, zero, affine, zero, zero, affine)
fmt.Printf("# ∞ + ∞ = ∞, with an alternate representation of ∞.\n")
printTestCase(zero, zero, jacobian, zero, zero, jacobian)
gx, gy := p256.Params().Gx, p256.Params().Gy
fmt.Printf("# g + ∞ = g.\n")
printTestCase(gx, gy, affine, zero, zero, affine)
fmt.Printf("# g + ∞ = g, with an alternate representation of ∞.\n")
printTestCase(gx, gy, affine, zero, zero, jacobian)
fmt.Printf("# g + -g = ∞.\n")
minusGy := new(big.Int).Sub(p, gy)
printTestCase(gx, gy, affine, gx, minusGy, affine)
fmt.Printf("# Test some random Jacobian sums.\n")
for i := 0; i < 4; i++ {
ax, ay := randPoint()
bx, by := randPoint()
printTestCase(ax, ay, jacobian, bx, by, jacobian)
}
fmt.Printf("# Test some random Jacobian doublings.\n")
for i := 0; i < 4; i++ {
ax, ay := randPoint()
printTestCase(ax, ay, jacobian, ax, ay, jacobian)
}
fmt.Printf("# Test some random affine sums.\n")
for i := 0; i < 4; i++ {
ax, ay := randPoint()
bx, by := randPoint()
printTestCase(ax, ay, affine, bx, by, affine)
}
fmt.Printf("# Test some random affine doublings.\n")
for i := 0; i < 4; i++ {
ax, ay := randPoint()
printTestCase(ax, ay, affine, ax, ay, affine)
}
}
type deterministicRandom struct {
stream cipher.Stream
}
func newDeterministicRand() io.Reader {
block, err := aes.NewCipher(make([]byte, 128/8))
if err != nil {
panic(err)
}
stream := cipher.NewCTR(block, make([]byte, block.BlockSize()))
return &deterministicRandom{stream}
}
func (r *deterministicRandom) Read(b []byte) (n int, err error) {
for i := range b {
b[i] = 0
}
r.stream.XORKeyStream(b, b)
return len(b), nil
}
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