gmsm/sm2/p256_asm.go

// It is by standing on the shoulders of giants.

// 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
// +build amd64 arm64

package sm2

import (
	"crypto/elliptic"
	"math/big"
)

type (
	p256Curve struct {
		*elliptic.CurveParams
	}

	p256Point struct {
		xyz [12]uint64
	}
)

var (
	p256 p256Curve
)

func initP256() {
	// 2**256 - 2**224 - 2**96 + 2**64 - 1
	p256.CurveParams = &elliptic.CurveParams{Name: "sm2p256v1"}
	p256.P, _ = new(big.Int).SetString("FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF", 16)
	p256.N, _ = new(big.Int).SetString("FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123", 16)
	p256.B, _ = new(big.Int).SetString("28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93", 16)
	p256.Gx, _ = new(big.Int).SetString("32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7", 16)
	p256.Gy, _ = new(big.Int).SetString("BC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0", 16)
	p256.BitSize = 256
}

func (curve p256Curve) Params() *elliptic.CurveParams {
	return curve.CurveParams
}

// Functions implemented in p256_asm_*64.s
// Montgomery multiplication modulo P256
//go:noescape
func p256Mul(res, in1, in2 []uint64)

// Montgomery square modulo P256, repeated n times (n >= 1)
//go:noescape
func p256Sqr(res, in []uint64, n int)

// Montgomery multiplication by 1
//go:noescape
func p256FromMont(res, in []uint64)

// iff cond == 1  val <- -val
//go:noescape
func p256NegCond(val []uint64, cond int)

// if cond == 0 res <- b; else res <- a
//go:noescape
func p256MovCond(res, a, b []uint64, cond int)

// Endianness swap
//go:noescape
func p256BigToLittle(res []uint64, in []byte)

//go:noescape
func p256LittleToBig(res []byte, in []uint64)

// Constant time table access
//go:noescape
func p256Select(point, table []uint64, idx int)

//go:noescape
func p256SelectBase(point *[12]uint64, table string, idx int)

// Montgomery multiplication modulo Ord(G)
//go:noescape
func p256OrdMul(res, in1, in2 []uint64)

// Montgomery square modulo Ord(G), repeated n times
//go:noescape
func p256OrdSqr(res, in []uint64, n int)

// Point add with in2 being affine point
// If sign == 1 -> in2 = -in2
// If sel == 0 -> res = in1
// if zero == 0 -> res = in2
//go:noescape
func p256PointAddAffineAsm(res, in1, in2 []uint64, sign, sel, zero int)

// Point add. Returns one if the two input points were equal and zero
// otherwise. (Note that, due to the way that the equations work out, some
// representations of ∞ are considered equal to everything by this function.)
//go:noescape
func p256PointAddAsm(res, in1, in2 []uint64) int

// Point double
//go:noescape
func p256PointDoubleAsm(res, in []uint64)

var p256one = []uint64{0x0000000000000001, 0x00000000ffffffff, 0x0000000000000000, 0x0000000100000000}

// Inverse, implements invertible interface, used by Sign()
// n-2 =
// 1111111111111111111111111111111011111111111111111111111111111111
// 1111111111111111111111111111111111111111111111111111111111111111
// 0111001000000011110111110110101100100001110001100000010100101011
// 0101001110111011111101000000100100111001110101010100000100100001
//
func (curve p256Curve) Inverse(k *big.Int) *big.Int {
	if k.Sign() < 0 {
		// This should never happen.
		k = new(big.Int).Neg(k)
	}

	if k.Cmp(p256.N) >= 0 {
		// This should never happen.
		k = new(big.Int).Mod(k, p256.N)
	}

	// table will store precomputed powers of x.
	var table [4 * 10]uint64
	var (
		_1      = table[4*0 : 4*1]
		_11     = table[4*1 : 4*2]
		_101    = table[4*2 : 4*3]
		_111    = table[4*3 : 4*4]
		_1111   = table[4*4 : 4*5]
		_10101  = table[4*5 : 4*6]
		_101111 = table[4*6 : 4*7]
		x       = table[4*7 : 4*8]
		t       = table[4*8 : 4*9]
		m       = table[4*9 : 4*10]
	)

	fromBig(x[:], 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.
	// Window values borrowed from https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion
	RR := []uint64{0x901192af7c114f20, 0x3464504ade6fa2fa, 0x620fc84c3affe0d4, 0x1eb5e412a22b3d3b}

	p256OrdMul(_1, x, RR)      // _1 , 2^0
	p256OrdSqr(m, _1, 1)       // _10, 2^1
	p256OrdMul(_11, m, _1)     // _11, 2^1 + 2^0
	p256OrdMul(_101, m, _11)   // _101, 2^2 + 2^0
	p256OrdMul(_111, m, _101)  // _111, 2^2 + 2^1 + 2^0
	p256OrdSqr(x, _101, 1)     // _1010, 2^3 + 2^1
	p256OrdMul(_1111, _101, x) // _1111, 2^3 + 2^2 + 2^1 + 2^0

	p256OrdSqr(t, x, 1)          // _10100, 2^4 + 2^2
	p256OrdMul(_10101, t, _1)    // _10101, 2^4 + 2^2 + 2^0
	p256OrdSqr(x, _10101, 1)     // _101010, 2^5 + 2^3 + 2^1
	p256OrdMul(_101111, _101, x) // _101111, 2^5 + 2^3 + 2^2 + 2^1 + 2^0
	p256OrdMul(x, _10101, x)     // _111111 = x6, 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0
	p256OrdSqr(t, x, 2)          // _11111100, 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2

	p256OrdMul(m, t, m)   // _11111110 = x8, , 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1
	p256OrdMul(t, t, _11) // _11111111 = x8, , 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0
	p256OrdSqr(x, t, 8)   // _ff00, 2^15 + 2^14 + 2^13 + 2^12 + 2^11 + 2^10 + 2^9 + 2^8
	p256OrdMul(m, x, m)   //  _fffe
	p256OrdMul(x, x, t)   // _ffff = x16, 2^15 + 2^14 + 2^13 + 2^12 + 2^11 + 2^10 + 2^9 + 2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0

	p256OrdSqr(t, x, 16) // _ffff0000, 2^31 + 2^30 + 2^29 + 2^28 + 2^27 + 2^26 + 2^25 + 2^24 + 2^23 + 2^22 + 2^21 + 2^20 + 2^19 + 2^18 + 2^17 + 2^16
	p256OrdMul(m, t, m)  // _fffffffe
	p256OrdMul(t, t, x)  // _ffffffff = x32

	p256OrdSqr(x, m, 32) // _fffffffe00000000
	p256OrdMul(x, x, t)  // _fffffffeffffffff
	p256OrdSqr(x, x, 32) // _fffffffeffffffff00000000
	p256OrdMul(x, x, t)  // _fffffffeffffffffffffffff
	p256OrdSqr(x, x, 32) // _fffffffeffffffffffffffff00000000
	p256OrdMul(x, x, t)  // _fffffffeffffffffffffffffffffffff

	sqrs := []uint8{
		4, 3, 11, 5, 3, 5, 1,
		3, 7, 5, 9, 7, 5, 5,
		4, 5, 2, 2, 7, 3, 5,
		5, 6, 2, 6, 3, 5,
	}
	muls := [][]uint64{
		_111, _1, _1111, _1111, _101, _10101, _1,
		_1, _111, _11, _101, _10101, _10101, _111,
		_111, _1111, _11, _1, _1, _1, _111,
		_111, _10101, _1, _1, _1, _1}

	for i, s := range sqrs {
		p256OrdSqr(x, x, int(s))
		p256OrdMul(x, x, muls[i])
	}

	// Multiplying by one in the Montgomery domain converts a Montgomery
	// value out of the domain.
	one := []uint64{1, 0, 0, 0}
	p256OrdMul(x, x, one)

	xOut := make([]byte, 32)
	p256LittleToBig(xOut, x)
	return new(big.Int).SetBytes(xOut)
}

// fromBig converts a *big.Int into a format used by this code.
func fromBig(out []uint64, big *big.Int) {
	for i := range out {
		out[i] = 0
	}

	for i, v := range big.Bits() {
		out[i] = uint64(v)
	}
}

// p256GetScalar endian-swaps the big-endian scalar value from in and writes it
// to out. If the scalar is equal or greater than the order of the group, it's
// reduced modulo that order.
func p256GetScalar(out []uint64, in []byte) {
	n := new(big.Int).SetBytes(in)

	if n.Cmp(p256.N) >= 0 {
		n.Mod(n, p256.N)
	}
	fromBig(out, n)
}

// p256Mul 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 = []uint64{0x200000003, 0x2ffffffff, 0x100000001, 0x400000002}

func maybeReduceModP(in *big.Int) *big.Int {
	if in.Cmp(p256.P) < 0 {
		return in
	}
	return new(big.Int).Mod(in, p256.P)
}

func (curve p256Curve) CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int) {
	scalarReversed := make([]uint64, 4)
	var r1, r2 p256Point
	p256GetScalar(scalarReversed, baseScalar)
	r1IsInfinity := scalarIsZero(scalarReversed)
	r1.p256BaseMult(scalarReversed)

	p256GetScalar(scalarReversed, scalar)
	r2IsInfinity := scalarIsZero(scalarReversed)
	fromBig(r2.xyz[0:4], maybeReduceModP(bigX))
	fromBig(r2.xyz[4:8], maybeReduceModP(bigY))
	p256Mul(r2.xyz[0:4], r2.xyz[0:4], rr[:])
	p256Mul(r2.xyz[4:8], r2.xyz[4:8], rr[:])

	// This sets r2's Z value to 1, in the Montgomery domain.
	r2.xyz[8] = p256one[0]
	r2.xyz[9] = p256one[1]
	r2.xyz[10] = p256one[2]
	r2.xyz[11] = p256one[3]

	r2.p256ScalarMult(scalarReversed)

	var sum, double p256Point
	pointsEqual := p256PointAddAsm(sum.xyz[:], r1.xyz[:], r2.xyz[:])
	p256PointDoubleAsm(double.xyz[:], r1.xyz[:])
	sum.CopyConditional(&double, pointsEqual)
	sum.CopyConditional(&r1, r2IsInfinity)
	sum.CopyConditional(&r2, r1IsInfinity)

	return sum.p256PointToAffine()
}

func (curve p256Curve) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
	scalarReversed := make([]uint64, 4)
	p256GetScalar(scalarReversed, scalar)

	var r p256Point
	r.p256BaseMult(scalarReversed)
	return r.p256PointToAffine()
}

func (curve p256Curve) ScalarMult(bigX, bigY *big.Int, scalar []byte) (x, y *big.Int) {
	scalarReversed := make([]uint64, 4)
	p256GetScalar(scalarReversed, scalar)

	var r p256Point
	fromBig(r.xyz[0:4], maybeReduceModP(bigX))
	fromBig(r.xyz[4:8], maybeReduceModP(bigY))
	p256Mul(r.xyz[0:4], r.xyz[0:4], rr[:])
	p256Mul(r.xyz[4:8], r.xyz[4:8], rr[:])
	// This sets r2's Z value to 1, in the Montgomery domain.
	r.xyz[8] = p256one[0]
	r.xyz[9] = p256one[1]
	r.xyz[10] = p256one[2]
	r.xyz[11] = p256one[3]

	r.p256ScalarMult(scalarReversed)
	return r.p256PointToAffine()
}

// 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)
}

// scalarIsZero returns 1 if scalar represents the zero value, and zero
// otherwise.
func scalarIsZero(scalar []uint64) int {
	return uint64IsZero(scalar[0] | scalar[1] | scalar[2] | scalar[3])
}

func (p *p256Point) p256PointToAffine() (x, y *big.Int) {
	zInv := make([]uint64, 4)
	zInvSq := make([]uint64, 4)
	p256Inverse(zInv, p.xyz[8:12])
	p256Sqr(zInvSq, zInv, 1)
	p256Mul(zInv, zInv, zInvSq)

	p256Mul(zInvSq, p.xyz[0:4], zInvSq)
	p256Mul(zInv, p.xyz[4:8], zInv)

	p256FromMont(zInvSq, zInvSq)
	p256FromMont(zInv, zInv)

	xOut := make([]byte, 32)
	yOut := make([]byte, 32)
	p256LittleToBig(xOut, zInvSq)
	p256LittleToBig(yOut, zInv)

	return new(big.Int).SetBytes(xOut), new(big.Int).SetBytes(yOut)
}

// CopyConditional copies overwrites p with src if v == 1, and leaves p
// unchanged if v == 0.
func (p *p256Point) CopyConditional(src *p256Point, v int) {
	pMask := uint64(v) - 1
	srcMask := ^pMask

	for i, n := range p.xyz {
		p.xyz[i] = (n & pMask) | (src.xyz[i] & srcMask)
	}
}

// p256Inverse sets out to in^-1 mod p.
func p256Inverse(out, in []uint64) {
	var stack [8 * 4]uint64
	p2 := stack[4*0 : 4*0+4]
	p4 := stack[4*1 : 4*1+4]
	p8 := stack[4*2 : 4*2+4]
	p16 := stack[4*3 : 4*3+4]
	p32 := stack[4*4 : 4*4+4]
	p64 := stack[4*5 : 4*5+4]
	p32m2 := stack[4*6 : 4*6+4]
	ptmp := stack[4*7 : 4*7+4]

	p256Sqr(ptmp, in, 1)  // 2^1
	p256Mul(p2, ptmp, in) // 2^2 - 2^0

	p256Sqr(out, p2, 2)      // 2^4 - 2^2
	p256Mul(ptmp, out, ptmp) // 2^4 - 2^1
	p256Mul(p4, out, p2)     // 2^4 - 2^0

	p256Sqr(out, p4, 4)      // 2^8 - 2^4
	p256Mul(ptmp, out, ptmp) // 2^8 - 2^1
	p256Mul(p8, out, p4)     // 2^8 - 2^0

	p256Sqr(out, p8, 8)      // 2^16 - 2^8
	p256Mul(ptmp, out, ptmp) // 2^16 - 2^1
	p256Mul(p16, out, p8)    // 2^16 - 2^0

	p256Sqr(out, p16, 16)     // 2^32 - 2^16
	p256Mul(p32m2, out, ptmp) // 2^32 - 2^1
	p256Mul(p32, out, p16)    // 2^32 - 2^0

	p256Sqr(out, p32, 32)  //2^64 - 2^32
	p256Mul(p64, out, p32) // 2^64 - 2^0

	p256Sqr(out, p64, 64)  //2^128 - 2^64
	p256Mul(out, out, p64) // 2^128 - 2^0
	p256Sqr(ptmp, out, 96) // 2^224 - 2^96

	p256Sqr(out, p32m2, 224) //2^256 - 2^225
	p256Mul(ptmp, ptmp, out) //2^256 - 2^224 - 2^96

	p256Sqr(out, p32, 16)  // 2^48 - 2^16
	p256Mul(out, out, p16) // 2^48 - 2^0

	p256Sqr(out, out, 8)  // 2^56 - 2^8
	p256Mul(out, out, p8) // 2^56 - 2^0

	p256Sqr(out, out, 4)  // 2^60 - 2^4
	p256Mul(out, out, p4) // 2^60 - 2^0

	p256Sqr(out, out, 2)  // 2^62 - 2^2
	p256Mul(out, out, p2) // 2^62 - 2^0

	p256Sqr(out, out, 2)  // 2^64 - 2^2
	p256Mul(out, out, in) //2^64 - 2^2 + 2^0

	p256Mul(out, out, ptmp) //2^256 - 2^224 - 2^96 + 2^64 - 3
}

func (p *p256Point) p256StorePoint(r *[16 * 4 * 3]uint64, index int) {
	copy(r[index*12:], p.xyz[:])
}

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 []uint64) {
	wvalue := (scalar[0] << 1) & 0x7f
	sel, sign := boothW6(uint(wvalue))
	p256SelectBase(&p.xyz, p256Precomputed, sel)
	p256NegCond(p.xyz[4:8], sign)

	// (This is one, in the Montgomery domain.)
	p.xyz[8] = p256one[0]
	p.xyz[9] = p256one[1]
	p.xyz[10] = p256one[2]
	p.xyz[11] = p256one[3]

	var t0 p256Point
	// (This is one, in the Montgomery domain.)
	t0.xyz[8] = p256one[0]
	t0.xyz[9] = p256one[1]
	t0.xyz[10] = p256one[2]
	t0.xyz[11] = p256one[3]

	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))
		p256SelectBase(&t0.xyz, p256Precomputed[i*32*8*8:], sel)
		p256PointAddAffineAsm(p.xyz[0:12], p.xyz[0:12], t0.xyz[0:8], sign, sel, zero)
		zero |= sel
	}
}

func (p *p256Point) p256ScalarMult(scalar []uint64) {
	// precomp is a table of precomputed points that stores powers of p
	// from p^1 to p^16.
	var precomp [16 * 4 * 3]uint64
	var t0, t1, t2, t3 p256Point

	// Prepare the table
	p.p256StorePoint(&precomp, 0) // 1

	p256PointDoubleAsm(t0.xyz[:], p.xyz[:])
	p256PointDoubleAsm(t1.xyz[:], t0.xyz[:])
	p256PointDoubleAsm(t2.xyz[:], t1.xyz[:])
	p256PointDoubleAsm(t3.xyz[:], t2.xyz[:])
	t0.p256StorePoint(&precomp, 1)  // 2
	t1.p256StorePoint(&precomp, 3)  // 4
	t2.p256StorePoint(&precomp, 7)  // 8
	t3.p256StorePoint(&precomp, 15) // 16

	p256PointAddAsm(t0.xyz[:], t0.xyz[:], p.xyz[:])
	p256PointAddAsm(t1.xyz[:], t1.xyz[:], p.xyz[:])
	p256PointAddAsm(t2.xyz[:], t2.xyz[:], p.xyz[:])
	t0.p256StorePoint(&precomp, 2) // 3
	t1.p256StorePoint(&precomp, 4) // 5
	t2.p256StorePoint(&precomp, 8) // 9

	p256PointDoubleAsm(t0.xyz[:], t0.xyz[:])
	p256PointDoubleAsm(t1.xyz[:], t1.xyz[:])
	t0.p256StorePoint(&precomp, 5) // 6
	t1.p256StorePoint(&precomp, 9) // 10

	p256PointAddAsm(t2.xyz[:], t0.xyz[:], p.xyz[:])
	p256PointAddAsm(t1.xyz[:], t1.xyz[:], p.xyz[:])
	t2.p256StorePoint(&precomp, 6)  // 7
	t1.p256StorePoint(&precomp, 10) // 11

	p256PointDoubleAsm(t0.xyz[:], t0.xyz[:])
	p256PointDoubleAsm(t2.xyz[:], t2.xyz[:])
	t0.p256StorePoint(&precomp, 11) // 12
	t2.p256StorePoint(&precomp, 13) // 14

	p256PointAddAsm(t0.xyz[:], t0.xyz[:], p.xyz[:])
	p256PointAddAsm(t2.xyz[:], t2.xyz[:], p.xyz[:])
	t0.p256StorePoint(&precomp, 12) // 13
	t2.p256StorePoint(&precomp, 14) // 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.xyz[0:12], precomp[0:], sel)
	zero := sel

	for index > 4 {
		index -= 5
		p256PointDoubleAsm(p.xyz[:], p.xyz[:])
		p256PointDoubleAsm(p.xyz[:], p.xyz[:])
		p256PointDoubleAsm(p.xyz[:], p.xyz[:])
		p256PointDoubleAsm(p.xyz[:], p.xyz[:])
		p256PointDoubleAsm(p.xyz[:], p.xyz[:])

		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.xyz[0:], precomp[0:], sel)
		p256NegCond(t0.xyz[4:8], sign)
		p256PointAddAsm(t1.xyz[:], p.xyz[:], t0.xyz[:])
		p256MovCond(t1.xyz[0:12], t1.xyz[0:12], p.xyz[0:12], sel)
		p256MovCond(p.xyz[0:12], t1.xyz[0:12], t0.xyz[0:12], zero)
		zero |= sel
	}

	p256PointDoubleAsm(p.xyz[:], p.xyz[:])
	p256PointDoubleAsm(p.xyz[:], p.xyz[:])
	p256PointDoubleAsm(p.xyz[:], p.xyz[:])
	p256PointDoubleAsm(p.xyz[:], p.xyz[:])
	p256PointDoubleAsm(p.xyz[:], p.xyz[:])

	wvalue = (scalar[0] << 1) & 0x3f
	sel, sign = boothW5(uint(wvalue))

	p256Select(t0.xyz[0:], precomp[0:], sel)
	p256NegCond(t0.xyz[4:8], sign)
	p256PointAddAsm(t1.xyz[:], p.xyz[:], t0.xyz[:])
	p256MovCond(t1.xyz[0:12], t1.xyz[0:12], p.xyz[0:12], sel)
	p256MovCond(p.xyz[0:12], t1.xyz[0:12], t0.xyz[0:12], zero)
}