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Diffstat (limited to 'src/crypto/internal/nistec/p256_asm.go')
| -rw-r--r-- | src/crypto/internal/nistec/p256_asm.go | 744 |
1 files changed, 744 insertions, 0 deletions
diff --git a/src/crypto/internal/nistec/p256_asm.go b/src/crypto/internal/nistec/p256_asm.go new file mode 100644 index 0000000..99a22b8 --- /dev/null +++ b/src/crypto/internal/nistec/p256_asm.go @@ -0,0 +1,744 @@ +// 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, + } +} + +// SetGenerator sets p to the canonical generator and returns p. +func (p *P256Point) SetGenerator() *P256Point { + p.x = p256Element{0x79e730d418a9143c, 0x75ba95fc5fedb601, + 0x79fb732b77622510, 0x18905f76a53755c6} + p.y = p256Element{0xddf25357ce95560a, 0x8b4ab8e4ba19e45c, + 0xd2e88688dd21f325, 0x8571ff1825885d85} + p.z = p256One + return p +} + +// 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) +} + +// BytesX returns the encoding of the x-coordinate of p, as specified in SEC 1, +// Version 2.0, Section 2.3.5, or an error if p is the point at infinity. +func (p *P256Point) BytesX() ([]byte, error) { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [p256ElementLength]byte + return p.bytesX(&out) +} + +func (p *P256Point) bytesX(out *[p256ElementLength]byte) ([]byte, error) { + if p.isInfinity() == 1 { + return nil, errors.New("P256 point is the point at infinity") + } + + x := new(p256Element) + p256Inverse(x, &p.z) + p256Sqr(x, x, 1) + p256Mul(x, &p.x, x) + p256FromMont(x, x) + p256LittleToBig((*[32]byte)(out[:]), x) + + return out[:], nil +} + +// 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) +} |