Current File : //usr/local/go119/src/crypto/internal/nistec/p256_asm.go
// Copyright 2015 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.
// This file contains the Go wrapper for the constant-time, 64-bit assembly
// implementation of P256. The optimizations performed here are described in
// detail in:
// S.Gueron and V.Krasnov, "Fast prime field elliptic-curve cryptography with
// 256-bit primes"
// https://link.springer.com/article/10.1007%2Fs13389-014-0090-x
// https://eprint.iacr.org/2013/816.pdf
//go:build amd64 || arm64 || ppc64le || s390x
package nistec
import (
_ "embed"
"encoding/binary"
"errors"
"math/bits"
"runtime"
"unsafe"
)
// p256Element is a P-256 base field element in [0, P-1] in the Montgomery
// domain (with R 2²⁵⁶) as four limbs in little-endian order value.
type p256Element [4]uint64
// p256One is one in the Montgomery domain.
var p256One = p256Element{0x0000000000000001, 0xffffffff00000000,
0xffffffffffffffff, 0x00000000fffffffe}
var p256Zero = p256Element{}
// p256P is 2²⁵⁶ - 2²²⁴ + 2¹⁹² + 2⁹⁶ - 1 in the Montgomery domain.
var p256P = p256Element{0xffffffffffffffff, 0x00000000ffffffff,
0x0000000000000000, 0xffffffff00000001}
// P256Point is a P-256 point. The zero value should not be assumed to be valid
// (although it is in this implementation).
type P256Point struct {
// (X:Y:Z) are Jacobian coordinates where x = X/Z² and y = Y/Z³. The point
// at infinity can be represented by any set of coordinates with Z = 0.
x, y, z p256Element
}
// NewP256Point returns a new P256Point representing the point at infinity.
func NewP256Point() *P256Point {
return &P256Point{
x: p256One, y: p256One, z: p256Zero,
}
}
// NewP256Generator returns a new P256Point set to the canonical generator.
func NewP256Generator() *P256Point {
return &P256Point{
x: p256Element{0x79e730d418a9143c, 0x75ba95fc5fedb601,
0x79fb732b77622510, 0x18905f76a53755c6},
y: p256Element{0xddf25357ce95560a, 0x8b4ab8e4ba19e45c,
0xd2e88688dd21f325, 0x8571ff1825885d85},
z: p256One,
}
}
// Set sets p = q and returns p.
func (p *P256Point) Set(q *P256Point) *P256Point {
p.x, p.y, p.z = q.x, q.y, q.z
return p
}
const p256ElementLength = 32
const p256UncompressedLength = 1 + 2*p256ElementLength
const p256CompressedLength = 1 + p256ElementLength
// SetBytes sets p to the compressed, uncompressed, or infinity value encoded in
// b, as specified in SEC 1, Version 2.0, Section 2.3.4. If the point is not on
// the curve, it returns nil and an error, and the receiver is unchanged.
// Otherwise, it returns p.
func (p *P256Point) SetBytes(b []byte) (*P256Point, error) {
// p256Mul operates in the Montgomery domain with R = 2²⁵⁶ mod p. Thus rr
// here is R in the Montgomery domain, or R×R mod p. See comment in
// P256OrdInverse about how this is used.
rr := p256Element{0x0000000000000003, 0xfffffffbffffffff,
0xfffffffffffffffe, 0x00000004fffffffd}
switch {
// Point at infinity.
case len(b) == 1 && b[0] == 0:
return p.Set(NewP256Point()), nil
// Uncompressed form.
case len(b) == p256UncompressedLength && b[0] == 4:
var r P256Point
p256BigToLittle(&r.x, (*[32]byte)(b[1:33]))
p256BigToLittle(&r.y, (*[32]byte)(b[33:65]))
if p256LessThanP(&r.x) == 0 || p256LessThanP(&r.y) == 0 {
return nil, errors.New("invalid P256 element encoding")
}
p256Mul(&r.x, &r.x, &rr)
p256Mul(&r.y, &r.y, &rr)
if err := p256CheckOnCurve(&r.x, &r.y); err != nil {
return nil, err
}
r.z = p256One
return p.Set(&r), nil
// Compressed form.
case len(b) == p256CompressedLength && (b[0] == 2 || b[0] == 3):
var r P256Point
p256BigToLittle(&r.x, (*[32]byte)(b[1:33]))
if p256LessThanP(&r.x) == 0 {
return nil, errors.New("invalid P256 element encoding")
}
p256Mul(&r.x, &r.x, &rr)
// y² = x³ - 3x + b
p256Polynomial(&r.y, &r.x)
if !p256Sqrt(&r.y, &r.y) {
return nil, errors.New("invalid P256 compressed point encoding")
}
// Select the positive or negative root, as indicated by the least
// significant bit, based on the encoding type byte.
yy := new(p256Element)
p256FromMont(yy, &r.y)
cond := int(yy[0]&1) ^ int(b[0]&1)
p256NegCond(&r.y, cond)
r.z = p256One
return p.Set(&r), nil
default:
return nil, errors.New("invalid P256 point encoding")
}
}
// p256Polynomial sets y2 to x³ - 3x + b, and returns y2.
func p256Polynomial(y2, x *p256Element) *p256Element {
x3 := new(p256Element)
p256Sqr(x3, x, 1)
p256Mul(x3, x3, x)
threeX := new(p256Element)
p256Add(threeX, x, x)
p256Add(threeX, threeX, x)
p256NegCond(threeX, 1)
p256B := &p256Element{0xd89cdf6229c4bddf, 0xacf005cd78843090,
0xe5a220abf7212ed6, 0xdc30061d04874834}
p256Add(x3, x3, threeX)
p256Add(x3, x3, p256B)
*y2 = *x3
return y2
}
func p256CheckOnCurve(x, y *p256Element) error {
// y² = x³ - 3x + b
rhs := p256Polynomial(new(p256Element), x)
lhs := new(p256Element)
p256Sqr(lhs, y, 1)
if p256Equal(lhs, rhs) != 1 {
return errors.New("P256 point not on curve")
}
return nil
}
// p256LessThanP returns 1 if x < p, and 0 otherwise. Note that a p256Element is
// not allowed to be equal to or greater than p, so if this function returns 0
// then x is invalid.
func p256LessThanP(x *p256Element) int {
var b uint64
_, b = bits.Sub64(x[0], p256P[0], b)
_, b = bits.Sub64(x[1], p256P[1], b)
_, b = bits.Sub64(x[2], p256P[2], b)
_, b = bits.Sub64(x[3], p256P[3], b)
return int(b)
}
// p256Add sets res = x + y.
func p256Add(res, x, y *p256Element) {
var c, b uint64
t1 := make([]uint64, 4)
t1[0], c = bits.Add64(x[0], y[0], 0)
t1[1], c = bits.Add64(x[1], y[1], c)
t1[2], c = bits.Add64(x[2], y[2], c)
t1[3], c = bits.Add64(x[3], y[3], c)
t2 := make([]uint64, 4)
t2[0], b = bits.Sub64(t1[0], p256P[0], 0)
t2[1], b = bits.Sub64(t1[1], p256P[1], b)
t2[2], b = bits.Sub64(t1[2], p256P[2], b)
t2[3], b = bits.Sub64(t1[3], p256P[3], b)
// Three options:
// - a+b < p
// then c is 0, b is 1, and t1 is correct
// - p <= a+b < 2^256
// then c is 0, b is 0, and t2 is correct
// - 2^256 <= a+b
// then c is 1, b is 1, and t2 is correct
t2Mask := (c ^ b) - 1
res[0] = (t1[0] & ^t2Mask) | (t2[0] & t2Mask)
res[1] = (t1[1] & ^t2Mask) | (t2[1] & t2Mask)
res[2] = (t1[2] & ^t2Mask) | (t2[2] & t2Mask)
res[3] = (t1[3] & ^t2Mask) | (t2[3] & t2Mask)
}
// p256Sqrt sets e to a square root of x. If x is not a square, p256Sqrt returns
// false and e is unchanged. e and x can overlap.
func p256Sqrt(e, x *p256Element) (isSquare bool) {
t0, t1 := new(p256Element), new(p256Element)
// Since p = 3 mod 4, exponentiation by (p + 1) / 4 yields a square root candidate.
//
// The sequence of 7 multiplications and 253 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
//
// _10 = 2*1
// _11 = 1 + _10
// _1100 = _11 << 2
// _1111 = _11 + _1100
// _11110000 = _1111 << 4
// _11111111 = _1111 + _11110000
// x16 = _11111111 << 8 + _11111111
// x32 = x16 << 16 + x16
// return ((x32 << 32 + 1) << 96 + 1) << 94
//
p256Sqr(t0, x, 1)
p256Mul(t0, x, t0)
p256Sqr(t1, t0, 2)
p256Mul(t0, t0, t1)
p256Sqr(t1, t0, 4)
p256Mul(t0, t0, t1)
p256Sqr(t1, t0, 8)
p256Mul(t0, t0, t1)
p256Sqr(t1, t0, 16)
p256Mul(t0, t0, t1)
p256Sqr(t0, t0, 32)
p256Mul(t0, x, t0)
p256Sqr(t0, t0, 96)
p256Mul(t0, x, t0)
p256Sqr(t0, t0, 94)
p256Sqr(t1, t0, 1)
if p256Equal(t1, x) != 1 {
return false
}
*e = *t0
return true
}
// The following assembly functions are implemented in p256_asm_*.s
// Montgomery multiplication. Sets res = in1 * in2 * R⁻¹ mod p.
//
//go:noescape
func p256Mul(res, in1, in2 *p256Element)
// Montgomery square, repeated n times (n >= 1).
//
//go:noescape
func p256Sqr(res, in *p256Element, n int)
// Montgomery multiplication by R⁻¹, or 1 outside the domain.
// Sets res = in * R⁻¹, bringing res out of the Montgomery domain.
//
//go:noescape
func p256FromMont(res, in *p256Element)
// If cond is not 0, sets val = -val mod p.
//
//go:noescape
func p256NegCond(val *p256Element, cond int)
// If cond is 0, sets res = b, otherwise sets res = a.
//
//go:noescape
func p256MovCond(res, a, b *P256Point, cond int)
//go:noescape
func p256BigToLittle(res *p256Element, in *[32]byte)
//go:noescape
func p256LittleToBig(res *[32]byte, in *p256Element)
//go:noescape
func p256OrdBigToLittle(res *p256OrdElement, in *[32]byte)
//go:noescape
func p256OrdLittleToBig(res *[32]byte, in *p256OrdElement)
// p256Table is a table of the first 16 multiples of a point. Points are stored
// at an index offset of -1 so [8]P is at index 7, P is at 0, and [16]P is at 15.
// [0]P is the point at infinity and it's not stored.
type p256Table [16]P256Point
// p256Select sets res to the point at index idx in the table.
// idx must be in [0, 15]. It executes in constant time.
//
//go:noescape
func p256Select(res *P256Point, table *p256Table, idx int)
// p256AffinePoint is a point in affine coordinates (x, y). x and y are still
// Montgomery domain elements. The point can't be the point at infinity.
type p256AffinePoint struct {
x, y p256Element
}
// p256AffineTable is a table of the first 32 multiples of a point. Points are
// stored at an index offset of -1 like in p256Table, and [0]P is not stored.
type p256AffineTable [32]p256AffinePoint
// p256Precomputed is a series of precomputed multiples of G, the canonical
// generator. The first p256AffineTable contains multiples of G. The second one
// multiples of [2⁶]G, the third one of [2¹²]G, and so on, where each successive
// table is the previous table doubled six times. Six is the width of the
// sliding window used in p256ScalarMult, and having each table already
// pre-doubled lets us avoid the doublings between windows entirely. This table
// MUST NOT be modified, as it aliases into p256PrecomputedEmbed below.
var p256Precomputed *[43]p256AffineTable
//go:embed p256_asm_table.bin
var p256PrecomputedEmbed string
func init() {
p256PrecomputedPtr := (*unsafe.Pointer)(unsafe.Pointer(&p256PrecomputedEmbed))
if runtime.GOARCH == "s390x" {
var newTable [43 * 32 * 2 * 4]uint64
for i, x := range (*[43 * 32 * 2 * 4][8]byte)(*p256PrecomputedPtr) {
newTable[i] = binary.LittleEndian.Uint64(x[:])
}
newTablePtr := unsafe.Pointer(&newTable)
p256PrecomputedPtr = &newTablePtr
}
p256Precomputed = (*[43]p256AffineTable)(*p256PrecomputedPtr)
}
// p256SelectAffine sets res to the point at index idx in the table.
// idx must be in [0, 31]. It executes in constant time.
//
//go:noescape
func p256SelectAffine(res *p256AffinePoint, table *p256AffineTable, idx int)
// Point addition with an affine point and constant time conditions.
// If zero is 0, sets res = in2. If sel is 0, sets res = in1.
// If sign is not 0, sets res = in1 + -in2. Otherwise, sets res = in1 + in2
//
//go:noescape
func p256PointAddAffineAsm(res, in1 *P256Point, in2 *p256AffinePoint, sign, sel, zero int)
// Point addition. Sets res = in1 + in2. Returns one if the two input points
// were equal and zero otherwise. If in1 or in2 are the point at infinity, res
// and the return value are undefined.
//
//go:noescape
func p256PointAddAsm(res, in1, in2 *P256Point) int
// Point doubling. Sets res = in + in. in can be the point at infinity.
//
//go:noescape
func p256PointDoubleAsm(res, in *P256Point)
// p256OrdElement is a P-256 scalar field element in [0, ord(G)-1] in the
// Montgomery domain (with R 2²⁵⁶) as four uint64 limbs in little-endian order.
type p256OrdElement [4]uint64
// p256OrdReduce ensures s is in the range [0, ord(G)-1].
func p256OrdReduce(s *p256OrdElement) {
// Since 2 * ord(G) > 2²⁵⁶, we can just conditionally subtract ord(G),
// keeping the result if it doesn't underflow.
t0, b := bits.Sub64(s[0], 0xf3b9cac2fc632551, 0)
t1, b := bits.Sub64(s[1], 0xbce6faada7179e84, b)
t2, b := bits.Sub64(s[2], 0xffffffffffffffff, b)
t3, b := bits.Sub64(s[3], 0xffffffff00000000, b)
tMask := b - 1 // zero if subtraction underflowed
s[0] ^= (t0 ^ s[0]) & tMask
s[1] ^= (t1 ^ s[1]) & tMask
s[2] ^= (t2 ^ s[2]) & tMask
s[3] ^= (t3 ^ s[3]) & tMask
}
// Add sets q = p1 + p2, and returns q. The points may overlap.
func (q *P256Point) Add(r1, r2 *P256Point) *P256Point {
var sum, double P256Point
r1IsInfinity := r1.isInfinity()
r2IsInfinity := r2.isInfinity()
pointsEqual := p256PointAddAsm(&sum, r1, r2)
p256PointDoubleAsm(&double, r1)
p256MovCond(&sum, &double, &sum, pointsEqual)
p256MovCond(&sum, r1, &sum, r2IsInfinity)
p256MovCond(&sum, r2, &sum, r1IsInfinity)
return q.Set(&sum)
}
// Double sets q = p + p, and returns q. The points may overlap.
func (q *P256Point) Double(p *P256Point) *P256Point {
var double P256Point
p256PointDoubleAsm(&double, p)
return q.Set(&double)
}
// ScalarBaseMult sets r = scalar * generator, where scalar is a 32-byte big
// endian value, and returns r. If scalar is not 32 bytes long, ScalarBaseMult
// returns an error and the receiver is unchanged.
func (r *P256Point) ScalarBaseMult(scalar []byte) (*P256Point, error) {
if len(scalar) != 32 {
return nil, errors.New("invalid scalar length")
}
scalarReversed := new(p256OrdElement)
p256OrdBigToLittle(scalarReversed, (*[32]byte)(scalar))
p256OrdReduce(scalarReversed)
r.p256BaseMult(scalarReversed)
return r, nil
}
// ScalarMult sets r = scalar * q, where scalar is a 32-byte big endian value,
// and returns r. If scalar is not 32 bytes long, ScalarBaseMult returns an
// error and the receiver is unchanged.
func (r *P256Point) ScalarMult(q *P256Point, scalar []byte) (*P256Point, error) {
if len(scalar) != 32 {
return nil, errors.New("invalid scalar length")
}
scalarReversed := new(p256OrdElement)
p256OrdBigToLittle(scalarReversed, (*[32]byte)(scalar))
p256OrdReduce(scalarReversed)
r.Set(q).p256ScalarMult(scalarReversed)
return r, nil
}
// uint64IsZero returns 1 if x is zero and zero otherwise.
func uint64IsZero(x uint64) int {
x = ^x
x &= x >> 32
x &= x >> 16
x &= x >> 8
x &= x >> 4
x &= x >> 2
x &= x >> 1
return int(x & 1)
}
// p256Equal returns 1 if a and b are equal and 0 otherwise.
func p256Equal(a, b *p256Element) int {
var acc uint64
for i := range a {
acc |= a[i] ^ b[i]
}
return uint64IsZero(acc)
}
// isInfinity returns 1 if p is the point at infinity and 0 otherwise.
func (p *P256Point) isInfinity() int {
return p256Equal(&p.z, &p256Zero)
}
// Bytes returns the uncompressed or infinity encoding of p, as specified in
// SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the point at
// infinity is shorter than all other encodings.
func (p *P256Point) Bytes() []byte {
// This function is outlined to make the allocations inline in the caller
// rather than happen on the heap.
var out [p256UncompressedLength]byte
return p.bytes(&out)
}
func (p *P256Point) bytes(out *[p256UncompressedLength]byte) []byte {
// The proper representation of the point at infinity is a single zero byte.
if p.isInfinity() == 1 {
return append(out[:0], 0)
}
x, y := new(p256Element), new(p256Element)
p.affineFromMont(x, y)
out[0] = 4 // Uncompressed form.
p256LittleToBig((*[32]byte)(out[1:33]), x)
p256LittleToBig((*[32]byte)(out[33:65]), y)
return out[:]
}
// affineFromMont sets (x, y) to the affine coordinates of p, converted out of the
// Montgomery domain.
func (p *P256Point) affineFromMont(x, y *p256Element) {
p256Inverse(y, &p.z)
p256Sqr(x, y, 1)
p256Mul(y, y, x)
p256Mul(x, &p.x, x)
p256Mul(y, &p.y, y)
p256FromMont(x, x)
p256FromMont(y, y)
}
// BytesCompressed returns the compressed or infinity encoding of p, as
// specified in SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the
// point at infinity is shorter than all other encodings.
func (p *P256Point) BytesCompressed() []byte {
// This function is outlined to make the allocations inline in the caller
// rather than happen on the heap.
var out [p256CompressedLength]byte
return p.bytesCompressed(&out)
}
func (p *P256Point) bytesCompressed(out *[p256CompressedLength]byte) []byte {
if p.isInfinity() == 1 {
return append(out[:0], 0)
}
x, y := new(p256Element), new(p256Element)
p.affineFromMont(x, y)
out[0] = 2 | byte(y[0]&1)
p256LittleToBig((*[32]byte)(out[1:33]), x)
return out[:]
}
// Select sets q to p1 if cond == 1, and to p2 if cond == 0.
func (q *P256Point) Select(p1, p2 *P256Point, cond int) *P256Point {
p256MovCond(q, p1, p2, cond)
return q
}
// p256Inverse sets out to in⁻¹ mod p. If in is zero, out will be zero.
func p256Inverse(out, in *p256Element) {
// Inversion is calculated through exponentiation by p - 2, per Fermat's
// little theorem.
//
// The sequence of 12 multiplications and 255 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain
// v0.4.0.
//
// _10 = 2*1
// _11 = 1 + _10
// _110 = 2*_11
// _111 = 1 + _110
// _111000 = _111 << 3
// _111111 = _111 + _111000
// x12 = _111111 << 6 + _111111
// x15 = x12 << 3 + _111
// x16 = 2*x15 + 1
// x32 = x16 << 16 + x16
// i53 = x32 << 15
// x47 = x15 + i53
// i263 = ((i53 << 17 + 1) << 143 + x47) << 47
// return (x47 + i263) << 2 + 1
//
var z = new(p256Element)
var t0 = new(p256Element)
var t1 = new(p256Element)
p256Sqr(z, in, 1)
p256Mul(z, in, z)
p256Sqr(z, z, 1)
p256Mul(z, in, z)
p256Sqr(t0, z, 3)
p256Mul(t0, z, t0)
p256Sqr(t1, t0, 6)
p256Mul(t0, t0, t1)
p256Sqr(t0, t0, 3)
p256Mul(z, z, t0)
p256Sqr(t0, z, 1)
p256Mul(t0, in, t0)
p256Sqr(t1, t0, 16)
p256Mul(t0, t0, t1)
p256Sqr(t0, t0, 15)
p256Mul(z, z, t0)
p256Sqr(t0, t0, 17)
p256Mul(t0, in, t0)
p256Sqr(t0, t0, 143)
p256Mul(t0, z, t0)
p256Sqr(t0, t0, 47)
p256Mul(z, z, t0)
p256Sqr(z, z, 2)
p256Mul(out, in, z)
}
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 boothW6(in uint) (int, int) {
var s uint = ^((in >> 6) - 1)
var d uint = (1 << 7) - in - 1
d = (d & s) | (in & (^s))
d = (d >> 1) + (d & 1)
return int(d), int(s & 1)
}
func (p *P256Point) p256BaseMult(scalar *p256OrdElement) {
var t0 p256AffinePoint
wvalue := (scalar[0] << 1) & 0x7f
sel, sign := boothW6(uint(wvalue))
p256SelectAffine(&t0, &p256Precomputed[0], sel)
p.x, p.y, p.z = t0.x, t0.y, p256One
p256NegCond(&p.y, sign)
index := uint(5)
zero := sel
for i := 1; i < 43; i++ {
if index < 192 {
wvalue = ((scalar[index/64] >> (index % 64)) + (scalar[index/64+1] << (64 - (index % 64)))) & 0x7f
} else {
wvalue = (scalar[index/64] >> (index % 64)) & 0x7f
}
index += 6
sel, sign = boothW6(uint(wvalue))
p256SelectAffine(&t0, &p256Precomputed[i], sel)
p256PointAddAffineAsm(p, p, &t0, sign, sel, zero)
zero |= sel
}
// If the whole scalar was zero, set to the point at infinity.
p256MovCond(p, p, NewP256Point(), zero)
}
func (p *P256Point) p256ScalarMult(scalar *p256OrdElement) {
// precomp is a table of precomputed points that stores powers of p
// from p^1 to p^16.
var precomp p256Table
var t0, t1, t2, t3 P256Point
// Prepare the table
precomp[0] = *p // 1
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 := (scalar[index/64] >> (index % 64)) & 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 < 192 {
wvalue = ((scalar[index/64] >> (index % 64)) + (scalar[index/64+1] << (64 - (index % 64)))) & 0x3f
} else {
wvalue = (scalar[index/64] >> (index % 64)) & 0x3f
}
sel, sign = boothW5(uint(wvalue))
p256Select(&t0, &precomp, sel)
p256NegCond(&t0.y, 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 = (scalar[0] << 1) & 0x3f
sel, sign = boothW5(uint(wvalue))
p256Select(&t0, &precomp, sel)
p256NegCond(&t0.y, sign)
p256PointAddAsm(&t1, p, &t0)
p256MovCond(&t1, &t1, p, sel)
p256MovCond(p, &t1, &t0, zero)
}
Mini Shell