src/crypto/internal/nistec/p256_asm.go - go - Git at Google

 // 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

 // 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))

 	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))

 	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)
 }
	// 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

	// 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))

	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))

	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)
	}