// Copyright 2016 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.
// +build s390x
package elliptic
import (
"crypto/subtle"
"math/big"
)
type p256CurveFast struct {
*CurveParams
}
type p256Point struct {
x [32]byte
y [32]byte
z [32]byte
}
var (
p256 Curve
p256PreFast *[37][64]p256Point
)
// hasVectorFacility reports whether the machine has the z/Architecture
// vector facility installed and enabled.
func hasVectorFacility() bool
var hasVX = hasVectorFacility()
func initP256Arch() {
if hasVX {
p256 = p256CurveFast{p256Params}
initTable()
return
}
// No vector support, use pure Go implementation.
p256 = p256Curve{p256Params}
return
}
func (curve p256CurveFast) Params() *CurveParams {
return curve.CurveParams
}
// Functions implemented in p256_asm_s390x.s
// Montgomery multiplication modulo P256
//
//go:noescape
func p256MulAsm(res, in1, in2 []byte)
// Montgomery square modulo P256
func p256Sqr(res, in []byte) {
p256MulAsm(res, in, in)
}
// Montgomery multiplication by 1
//
//go:noescape
func p256FromMont(res, in []byte)
// iff cond == 1 val <- -val
//
//go:noescape
func p256NegCond(val *p256Point, cond int)
// if cond == 0 res <- b; else res <- a
//
//go:noescape
func p256MovCond(res, a, b *p256Point, cond int)
// Constant time table access
//
//go:noescape
func p256Select(point *p256Point, table []p256Point, idx int)
//go:noescape
func p256SelectBase(point *p256Point, table []p256Point, idx int)
// Montgomery multiplication modulo Ord(G)
//
//go:noescape
func p256OrdMul(res, in1, in2 []byte)
// Montgomery square modulo Ord(G), repeated n times
func p256OrdSqr(res, in []byte, n int) {
copy(res, in)
for i := 0; i < n; i += 1 {
p256OrdMul(res, res, res)
}
}
// Point add with P2 being affine point
// If sign == 1 -> P2 = -P2
// If sel == 0 -> P3 = P1
// if zero == 0 -> P3 = P2
//
//go:noescape
func p256PointAddAffineAsm(P3, P1, P2 *p256Point, sign, sel, zero int)
// Point add
//
//go:noescape
func p256PointAddAsm(P3, P1, P2 *p256Point) int
//go:noescape
func p256PointDoubleAsm(P3, P1 *p256Point)
func (curve p256CurveFast) Inverse(k *big.Int) *big.Int {
if k.Cmp(p256Params.N) >= 0 {
// This should never happen.
reducedK := new(big.Int).Mod(k, p256Params.N)
k = reducedK
}
// table will store precomputed powers of x. The 32 bytes at index
// i store x^(i+1).
var table [15][32]byte
x := fromBig(k)
// This code operates in the Montgomery domain where R = 2^256 mod n
// and n is the order of the scalar field. (See initP256 for the
// value.) Elements in the Montgomery domain take the form a×R and
// multiplication of x and y in the calculates (x × y × R^-1) mod n. RR
// is R×R mod n thus the Montgomery multiplication x and RR gives x×R,
// i.e. converts x into the Montgomery domain. Stored in BigEndian form
RR := []byte{0x66, 0xe1, 0x2d, 0x94, 0xf3, 0xd9, 0x56, 0x20, 0x28, 0x45, 0xb2, 0x39, 0x2b, 0x6b, 0xec, 0x59,
0x46, 0x99, 0x79, 0x9c, 0x49, 0xbd, 0x6f, 0xa6, 0x83, 0x24, 0x4c, 0x95, 0xbe, 0x79, 0xee, 0xa2}
p256OrdMul(table[0][:], x, RR)
// Prepare the table, no need in constant time access, because the
// power is not a secret. (Entry 0 is never used.)
for i := 2; i < 16; i += 2 {
p256OrdSqr(table[i-1][:], table[(i/2)-1][:], 1)
p256OrdMul(table[i][:], table[i-1][:], table[0][:])
}
copy(x, table[14][:]) // f
p256OrdSqr(x[0:32], x[0:32], 4)
p256OrdMul(x[0:32], x[0:32], table[14][:]) // ff
t := make([]byte, 32)
copy(t, x)
p256OrdSqr(x, x, 8)
p256OrdMul(x, x, t) // ffff
copy(t, x)
p256OrdSqr(x, x, 16)
p256OrdMul(x, x, t) // ffffffff
copy(t, x)
p256OrdSqr(x, x, 64) // ffffffff0000000000000000
p256OrdMul(x, x, t) // ffffffff00000000ffffffff
p256OrdSqr(x, x, 32) // ffffffff00000000ffffffff00000000
p256OrdMul(x, x, t) // ffffffff00000000ffffffffffffffff
// Remaining 32 windows
expLo := [32]byte{0xb, 0xc, 0xe, 0x6, 0xf, 0xa, 0xa, 0xd, 0xa, 0x7, 0x1, 0x7, 0x9, 0xe, 0x8, 0x4,
0xf, 0x3, 0xb, 0x9, 0xc, 0xa, 0xc, 0x2, 0xf, 0xc, 0x6, 0x3, 0x2, 0x5, 0x4, 0xf}
for i := 0; i < 32; i++ {
p256OrdSqr(x, x, 4)
p256OrdMul(x, x, table[expLo[i]-1][:])
}
// Multiplying by one in the Montgomery domain converts a Montgomery
// value out of the domain.
one := []byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}
p256OrdMul(x, x, one)
return new(big.Int).SetBytes(x)
}
// fromBig converts a *big.Int into a format used by this code.
func fromBig(big *big.Int) []byte {
// This could be done a lot more efficiently...
res := big.Bytes()
if 32 == len(res) {
return res
}
t := make([]byte, 32)
offset := 32 - len(res)
for i := len(res) - 1; i >= 0; i-- {
t[i+offset] = res[i]
}
return t
}
// p256GetMultiplier makes sure byte array will have 32 byte elements, If the scalar
// is equal or greater than the order of the group, it's reduced modulo that order.
func p256GetMultiplier(in []byte) []byte {
n := new(big.Int).SetBytes(in)
if n.Cmp(p256Params.N) >= 0 {
n.Mod(n, p256Params.N)
}
return fromBig(n)
}
// p256MulAsm operates in a Montgomery domain with R = 2^256 mod p, where p is the
// underlying field of the curve. (See initP256 for the value.) Thus rr here is
// R×R mod p. See comment in Inverse about how this is used.
var rr = []byte{0x00, 0x00, 0x00, 0x04, 0xff, 0xff, 0xff, 0xfd, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xff, 0xff, 0xff, 0xfb, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03}
// (This is one, in the Montgomery domain.)
var one = []byte{0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}
func maybeReduceModP(in *big.Int) *big.Int {
if in.Cmp(p256Params.P) < 0 {
return in
}
return new(big.Int).Mod(in, p256Params.P)
}
func (curve p256CurveFast) CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int) {
var r1, r2 p256Point
scalarReduced := p256GetMultiplier(baseScalar)
r1IsInfinity := scalarIsZero(scalarReduced)
r1.p256BaseMult(scalarReduced)
copy(r2.x[:], fromBig(maybeReduceModP(bigX)))
copy(r2.y[:], fromBig(maybeReduceModP(bigY)))
copy(r2.z[:], one)
p256MulAsm(r2.x[:], r2.x[:], rr[:])
p256MulAsm(r2.y[:], r2.y[:], rr[:])
scalarReduced = p256GetMultiplier(scalar)
r2IsInfinity := scalarIsZero(scalarReduced)
r2.p256ScalarMult(p256GetMultiplier(scalar))
var sum, double p256Point
pointsEqual := p256PointAddAsm(&sum, &r1, &r2)
p256PointDoubleAsm(&double, &r1)
p256MovCond(&sum, &double, &sum, pointsEqual)
p256MovCond(&sum, &r1, &sum, r2IsInfinity)
p256MovCond(&sum, &r2, &sum, r1IsInfinity)
return sum.p256PointToAffine()
}
func (curve p256CurveFast) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
var r p256Point
r.p256BaseMult(p256GetMultiplier(scalar))
return r.p256PointToAffine()
}
func (curve p256CurveFast) ScalarMult(bigX, bigY *big.Int, scalar []byte) (x, y *big.Int) {
var r p256Point
copy(r.x[:], fromBig(maybeReduceModP(bigX)))
copy(r.y[:], fromBig(maybeReduceModP(bigY)))
copy(r.z[:], one)
p256MulAsm(r.x[:], r.x[:], rr[:])
p256MulAsm(r.y[:], r.y[:], rr[:])
r.p256ScalarMult(p256GetMultiplier(scalar))
return r.p256PointToAffine()
}
// scalarIsZero returns 1 if scalar represents the zero value, and zero
// otherwise.
func scalarIsZero(scalar []byte) int {
b := byte(0)
for _, s := range scalar {
b |= s
}
return subtle.ConstantTimeByteEq(b, 0)
}
func (p *p256Point) p256PointToAffine() (x, y *big.Int) {
zInv := make([]byte, 32)
zInvSq := make([]byte, 32)
p256Inverse(zInv, p.z[:])
p256Sqr(zInvSq, zInv)
p256MulAsm(zInv, zInv, zInvSq)
p256MulAsm(zInvSq, p.x[:], zInvSq)
p256MulAsm(zInv, p.y[:], zInv)
p256FromMont(zInvSq, zInvSq)
p256FromMont(zInv, zInv)
return new(big.Int).SetBytes(zInvSq), new(big.Int).SetBytes(zInv)
}
// p256Inverse sets out to in^-1 mod p.
func p256Inverse(out, in []byte) {
var stack [6 * 32]byte
p2 := stack[32*0 : 32*0+32]
p4 := stack[32*1 : 32*1+32]
p8 := stack[32*2 : 32*2+32]
p16 := stack[32*3 : 32*3+32]
p32 := stack[32*4 : 32*4+32]
p256Sqr(out, in)
p256MulAsm(p2, out, in) // 3*p
p256Sqr(out, p2)
p256Sqr(out, out)
p256MulAsm(p4, out, p2) // f*p
p256Sqr(out, p4)
p256Sqr(out, out)
p256Sqr(out, out)
p256Sqr(out, out)
p256MulAsm(p8, out, p4) // ff*p
p256Sqr(out, p8)
for i := 0; i < 7; i++ {
p256Sqr(out, out)
}
p256MulAsm(p16, out, p8) // ffff*p
p256Sqr(out, p16)
for i := 0; i < 15; i++ {
p256Sqr(out, out)
}
p256MulAsm(p32, out, p16) // ffffffff*p
p256Sqr(out, p32)
for i := 0; i < 31; i++ {
p256Sqr(out, out)
}
p256MulAsm(out, out, in)
for i := 0; i < 32*4; i++ {
p256Sqr(out, out)
}
p256MulAsm(out, out, p32)
for i := 0; i < 32; i++ {
p256Sqr(out, out)
}
p256MulAsm(out, out, p32)
for i := 0; i < 16; i++ {
p256Sqr(out, out)
}
p256MulAsm(out, out, p16)
for i := 0; i < 8; i++ {
p256Sqr(out, out)
}
p256MulAsm(out, out, p8)
p256Sqr(out, out)
p256Sqr(out, out)
p256Sqr(out, out)
p256Sqr(out, out)
p256MulAsm(out, out, p4)
p256Sqr(out, out)
p256Sqr(out, out)
p256MulAsm(out, out, p2)
p256Sqr(out, out)
p256Sqr(out, out)
p256MulAsm(out, out, in)
}
func boothW5(in uint) (int, int) {
var s uint = ^((in >> 5) - 1)
var d uint = (1 << 6) - in - 1
d = (d & s) | (in & (^s))
d = (d >> 1) + (d & 1)
return int(d), int(s & 1)
}
func boothW7(in uint) (int, int) {
var s uint = ^((in >> 7) - 1)
var d uint = (1 << 8) - in - 1
d = (d & s) | (in & (^s))
d = (d >> 1) + (d & 1)
return int(d), int(s & 1)
}
func initTable() {
p256PreFast = new([37][64]p256Point) //z coordinate not used
basePoint := p256Point{
x: [32]byte{0x18, 0x90, 0x5f, 0x76, 0xa5, 0x37, 0x55, 0xc6, 0x79, 0xfb, 0x73, 0x2b, 0x77, 0x62, 0x25, 0x10,
0x75, 0xba, 0x95, 0xfc, 0x5f, 0xed, 0xb6, 0x01, 0x79, 0xe7, 0x30, 0xd4, 0x18, 0xa9, 0x14, 0x3c}, //(p256.x*2^256)%p
y: [32]byte{0x85, 0x71, 0xff, 0x18, 0x25, 0x88, 0x5d, 0x85, 0xd2, 0xe8, 0x86, 0x88, 0xdd, 0x21, 0xf3, 0x25,
0x8b, 0x4a, 0xb8, 0xe4, 0xba, 0x19, 0xe4, 0x5c, 0xdd, 0xf2, 0x53, 0x57, 0xce, 0x95, 0x56, 0x0a}, //(p256.y*2^256)%p
z: [32]byte{0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, //(p256.z*2^256)%p
}
t1 := new(p256Point)
t2 := new(p256Point)
*t2 = basePoint
zInv := make([]byte, 32)
zInvSq := make([]byte, 32)
for j := 0; j < 64; j++ {
*t1 = *t2
for i := 0; i < 37; i++ {
// The window size is 7 so we need to double 7 times.
if i != 0 {
for k := 0; k < 7; k++ {
p256PointDoubleAsm(t1, t1)
}
}
// Convert the point to affine form. (Its values are
// still in Montgomery form however.)
p256Inverse(zInv, t1.z[:])
p256Sqr(zInvSq, zInv)
p256MulAsm(zInv, zInv, zInvSq)
p256MulAsm(t1.x[:], t1.x[:], zInvSq)
p256MulAsm(t1.y[:], t1.y[:], zInv)
copy(t1.z[:], basePoint.z[:])
// Update the table entry
copy(p256PreFast[i][j].x[:], t1.x[:])
copy(p256PreFast[i][j].y[:], t1.y[:])
}
if j == 0 {
p256PointDoubleAsm(t2, &basePoint)
} else {
p256PointAddAsm(t2, t2, &basePoint)
}
}
}
func (p *p256Point) p256BaseMult(scalar []byte) {
wvalue := (uint(scalar[31]) << 1) & 0xff
sel, sign := boothW7(uint(wvalue))
p256SelectBase(p, p256PreFast[0][:], sel)
p256NegCond(p, sign)
copy(p.z[:], one[:])
var t0 p256Point
copy(t0.z[:], one[:])
index := uint(6)
zero := sel
for i := 1; i < 37; i++ {
if index < 247 {
wvalue = ((uint(scalar[31-index/8]) >> (index % 8)) + (uint(scalar[31-index/8-1]) << (8 - (index % 8)))) & 0xff
} else {
wvalue = (uint(scalar[31-index/8]) >> (index % 8)) & 0xff
}
index += 7
sel, sign = boothW7(uint(wvalue))
p256SelectBase(&t0, p256PreFast[i][:], sel)
p256PointAddAffineAsm(p, p, &t0, sign, sel, zero)
zero |= sel
}
}
func (p *p256Point) p256ScalarMult(scalar []byte) {
// precomp is a table of precomputed points that stores powers of p
// from p^1 to p^16.
var precomp [16]p256Point
var t0, t1, t2, t3 p256Point
// Prepare the table
*&precomp[0] = *p
p256PointDoubleAsm(&t0, p)
p256PointDoubleAsm(&t1, &t0)
p256PointDoubleAsm(&t2, &t1)
p256PointDoubleAsm(&t3, &t2)
*&precomp[1] = t0 // 2
*&precomp[3] = t1 // 4
*&precomp[7] = t2 // 8
*&precomp[15] = t3 // 16
p256PointAddAsm(&t0, &t0, p)
p256PointAddAsm(&t1, &t1, p)
p256PointAddAsm(&t2, &t2, p)
*&precomp[2] = t0 // 3
*&precomp[4] = t1 // 5
*&precomp[8] = t2 // 9
p256PointDoubleAsm(&t0, &t0)
p256PointDoubleAsm(&t1, &t1)
*&precomp[5] = t0 // 6
*&precomp[9] = t1 // 10
p256PointAddAsm(&t2, &t0, p)
p256PointAddAsm(&t1, &t1, p)
*&precomp[6] = t2 // 7
*&precomp[10] = t1 // 11
p256PointDoubleAsm(&t0, &t0)
p256PointDoubleAsm(&t2, &t2)
*&precomp[11] = t0 // 12
*&precomp[13] = t2 // 14
p256PointAddAsm(&t0, &t0, p)
p256PointAddAsm(&t2, &t2, p)
*&precomp[12] = t0 // 13
*&precomp[14] = t2 // 15
// Start scanning the window from top bit
index := uint(254)
var sel, sign int
wvalue := (uint(scalar[31-index/8]) >> (index % 8)) & 0x3f
sel, _ = boothW5(uint(wvalue))
p256Select(p, precomp[:], sel)
zero := sel
for index > 4 {
index -= 5
p256PointDoubleAsm(p, p)
p256PointDoubleAsm(p, p)
p256PointDoubleAsm(p, p)
p256PointDoubleAsm(p, p)
p256PointDoubleAsm(p, p)
if index < 247 {
wvalue = ((uint(scalar[31-index/8]) >> (index % 8)) + (uint(scalar[31-index/8-1]) << (8 - (index % 8)))) & 0x3f
} else {
wvalue = (uint(scalar[31-index/8]) >> (index % 8)) & 0x3f
}
sel, sign = boothW5(uint(wvalue))
p256Select(&t0, precomp[:], sel)
p256NegCond(&t0, sign)
p256PointAddAsm(&t1, p, &t0)
p256MovCond(&t1, &t1, p, sel)
p256MovCond(p, &t1, &t0, zero)
zero |= sel
}
p256PointDoubleAsm(p, p)
p256PointDoubleAsm(p, p)
p256PointDoubleAsm(p, p)
p256PointDoubleAsm(p, p)
p256PointDoubleAsm(p, p)
wvalue = (uint(scalar[31]) << 1) & 0x3f
sel, sign = boothW5(uint(wvalue))
p256Select(&t0, precomp[:], sel)
p256NegCond(&t0, sign)
p256PointAddAsm(&t1, p, &t0)
p256MovCond(&t1, &t1, p, sel)
p256MovCond(p, &t1, &t0, zero)
}