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Revert "crypto/internal/nistec: refactor scalar multiplication"
This reverts CL 471256, except for its new tests, which are expanded to cover the case in #60717. Updates #60717 Change-Id: I712bbcd05bf3ea4a2c9aecc9e0f02841b21aadfa Reviewed-on: https://go-review.googlesource.com/c/go/+/502477 TryBot-Result: Gopher Robot <gobot@golang.org> Reviewed-by: David Chase <drchase@google.com> Run-TryBot: Filippo Valsorda <filippo@golang.org> Auto-Submit: Filippo Valsorda <filippo@golang.org> Reviewed-by: Roland Shoemaker <roland@golang.org>
This commit is contained in:
Filippo Valsorda
Gopher Robot
parent
3367475e83
commit
a674c6376f
@ -184,6 +184,23 @@ func testScalarMult[P nistPoint[P]](t *testing.T, newPoint func() P, c elliptic.
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t.Error("[k]G != ScalarBaseMult(k)")
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}
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expectInfinity := new(big.Int).Mod(new(big.Int).SetBytes(scalar), c.Params().N).Sign() == 0
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if expectInfinity {
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if !bytes.Equal(p1.Bytes(), newPoint().Bytes()) {
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t.Error("ScalarBaseMult(k) != ∞")
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}
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if !bytes.Equal(p2.Bytes(), newPoint().Bytes()) {
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t.Error("[k]G != ∞")
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}
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} else {
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if bytes.Equal(p1.Bytes(), newPoint().Bytes()) {
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t.Error("ScalarBaseMult(k) == ∞")
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}
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if bytes.Equal(p2.Bytes(), newPoint().Bytes()) {
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t.Error("[k]G == ∞")
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}
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}
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d := new(big.Int).SetBytes(scalar)
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d.Sub(c.Params().N, d)
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d.Mod(d, c.Params().N)
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@ -222,9 +239,14 @@ func testScalarMult[P nistPoint[P]](t *testing.T, newPoint func() P, c elliptic.
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checkScalar(t, s.FillBytes(make([]byte, byteLen)))
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})
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}
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// Test N-32...N+32 since they risk overlapping with precomputed table values
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for i := 0; i <= 64; i++ {
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t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
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checkScalar(t, big.NewInt(int64(i)).FillBytes(make([]byte, byteLen)))
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})
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}
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// Test N-64...N+64 since they risk overlapping with precomputed table values
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// in the final additions.
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for i := int64(-32); i <= 32; i++ {
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for i := int64(-64); i <= 64; i++ {
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t.Run(fmt.Sprintf("N%+d", i), func(t *testing.T) {
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checkScalar(t, new(big.Int).Add(c.Params().N, big.NewInt(i)).Bytes())
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})
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@ -294,9 +294,8 @@ func p256OrdLittleToBig(res *[32]byte, in *p256OrdElement)
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// [0]P is the point at infinity and it's not stored.
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type p256Table [16]P256Point
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// p256Select sets res to the point at index idx - 1 in the table.
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// idx must be in [1, 16] or res will be set to an undefined value.
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// It executes in constant time.
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// p256Select sets res to the point at index idx in the table.
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// idx must be in [0, 15]. It executes in constant time.
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//
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//go:noescape
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func p256Select(res *P256Point, table *p256Table, idx int)
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@ -336,25 +335,22 @@ func init() {
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p256Precomputed = (*[43]p256AffineTable)(*p256PrecomputedPtr)
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}
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// p256SelectAffine sets res to the point at index idx - 1 in the table.
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// idx must be in [1, 32] or res will be set to an undefined value.
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// It executes in constant time.
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// p256SelectAffine sets res to the point at index idx in the table.
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// idx must be in [0, 31]. It executes in constant time.
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//
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//go:noescape
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func p256SelectAffine(res *p256AffinePoint, table *p256AffineTable, idx int)
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// Point addition with an affine point and constant time conditions.
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// If zero is 0, sets res = in2. If sel is 0, sets res = in1.
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// If sign is not 0, sets res = in1 + -in2. Otherwise, sets res = in1 + in2.
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// If neither sel nor zero are 0 and in1 = in2, or both zero and sel are 0,
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// or in1 is the infinity, res is undefined.
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// If sign is not 0, sets res = in1 + -in2. Otherwise, sets res = in1 + in2
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//
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//go:noescape
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func p256PointAddAffineAsm(res, in1 *P256Point, in2 *p256AffinePoint, sign, sel, zero int)
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// Point addition. Sets res = in1 + in2 and returns zero if in1 and in2 are not
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// equal. Otherwise, returns one and res is undefined. If in1 or in2 are the
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// point at infinity, res and the return value are undefined.
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// Point addition. Sets res = in1 + in2. Returns one if the two input points
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// were equal and zero otherwise. If in1 or in2 are the point at infinity, res
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// and the return value are undefined.
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//
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//go:noescape
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func p256PointAddAsm(res, in1, in2 *P256Point) int
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@ -607,93 +603,58 @@ func p256Inverse(out, in *p256Element) {
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p256Mul(out, in, z)
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}
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// p256OrdRsh returns the 64 least significant bits of x >> n. n must be lower
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// than 256. The value of n leaks through timing side-channels.
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func p256OrdRsh(x *p256OrdElement, n int) uint64 {
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i := n / 64
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n = n % 64
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res := x[i] >> n
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// Shift in the more significant limb, if present.
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if i := i + 1; i < len(x) {
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res |= x[i] << (64 - n)
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}
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return res
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}
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func boothW5(in uint64) (int, int) {
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s := ^((in >> 5) - 1)
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d := (1 << 6) - in - 1
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func boothW5(in uint) (int, int) {
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var s uint = ^((in >> 5) - 1)
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var d uint = (1 << 6) - in - 1
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d = (d & s) | (in & (^s))
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d = (d >> 1) + (d & 1)
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return int(d), int(s & 1)
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}
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func boothW6(in uint64) (int, int) {
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s := ^((in >> 6) - 1)
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d := (1 << 7) - in - 1
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func boothW6(in uint) (int, int) {
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var s uint = ^((in >> 6) - 1)
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var d uint = (1 << 7) - in - 1
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d = (d & s) | (in & (^s))
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d = (d >> 1) + (d & 1)
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return int(d), int(s & 1)
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}
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func (p *P256Point) p256BaseMult(scalar *p256OrdElement) {
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// This function works like p256ScalarMult below, but the table is fixed and
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// "pre-doubled" for each iteration, so instead of doubling we move to the
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// next table at each iteration.
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// Start scanning the window from the most significant bits. We move by
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// 6 bits at a time and need to finish at -1, so -1 + 6 * 42 = 251.
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index := 251
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sel, sign := boothW6(p256OrdRsh(scalar, index))
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// sign is always zero because the boothW6 input here is at
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// most five bits long, so the top bit is never set.
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_ = sign
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var t0 p256AffinePoint
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p256SelectAffine(&t0, &p256Precomputed[(index+1)/6], sel)
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wvalue := (scalar[0] << 1) & 0x7f
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sel, sign := boothW6(uint(wvalue))
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p256SelectAffine(&t0, &p256Precomputed[0], sel)
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p.x, p.y, p.z = t0.x, t0.y, p256One
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p256NegCond(&p.y, sign)
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index := uint(5)
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zero := sel
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for index >= 5 {
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index -= 6
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if index >= 0 {
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sel, sign = boothW6(p256OrdRsh(scalar, index) & 0b1111111)
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for i := 1; i < 43; i++ {
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if index < 192 {
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wvalue = ((scalar[index/64] >> (index % 64)) + (scalar[index/64+1] << (64 - (index % 64)))) & 0x7f
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} else {
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// Booth encoding considers a virtual zero bit at index -1,
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// so we shift left the least significant limb.
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wvalue := (scalar[0] << 1) & 0b1111111
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sel, sign = boothW6(wvalue)
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wvalue = (scalar[index/64] >> (index % 64)) & 0x7f
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}
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table := &p256Precomputed[(index+1)/6]
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p256SelectAffine(&t0, table, sel)
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// See p256ScalarMult for the behavior of sign, sel, and zero, that here
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// is all rolled into the p256PointAddAffineAsm function. We also know
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// that (if sel and zero are not 0) p != t0 for a similar reason.
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index += 6
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sel, sign = boothW6(uint(wvalue))
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p256SelectAffine(&t0, &p256Precomputed[i], sel)
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p256PointAddAffineAsm(p, p, &t0, sign, sel, zero)
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zero |= sel
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}
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// If zero is 0, the whole scalar was zero, p is undefined,
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// and the correct result is the infinity.
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infinity := NewP256Point()
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p256MovCond(p, p, infinity, zero)
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// If the whole scalar was zero, set to the point at infinity.
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p256MovCond(p, p, NewP256Point(), zero)
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}
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func (p *P256Point) p256ScalarMult(scalar *p256OrdElement) {
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// If p is the point at infinity, p256PointAddAsm's behavior below is
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// undefined. We'll just return the infinity at the end.
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isInfinity := p.isInfinity()
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// precomp is a table of precomputed points that stores
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// powers of p from p^1 to p^16.
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// precomp is a table of precomputed points that stores powers of p
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// from p^1 to p^16.
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var precomp p256Table
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var t0, t1, t2, t3 P256Point
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// Prepare the table by double and adding.
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// Prepare the table
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precomp[0] = *p // 1
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p256PointDoubleAsm(&t0, p)
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@ -732,56 +693,52 @@ func (p *P256Point) p256ScalarMult(scalar *p256OrdElement) {
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precomp[12] = t0 // 13
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precomp[14] = t2 // 15
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// Start scanning the window from the most significant bits. We move by
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// 5 bits at a time and need to finish at -1, so -1 + 5 * 51 = 254.
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index := 254
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// Start scanning the window from top bit
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index := uint(254)
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var sel, sign int
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sel, sign := boothW5(p256OrdRsh(scalar, index))
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// sign is always zero because the boothW5 input here is at
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// most two bits long, so the top bit is never set.
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_ = sign
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wvalue := (scalar[index/64] >> (index % 64)) & 0x3f
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sel, _ = boothW5(uint(wvalue))
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p256Select(p, &precomp, sel)
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zero := sel
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for index >= 4 {
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for index > 4 {
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index -= 5
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p256PointDoubleAsm(p, p)
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p256PointDoubleAsm(p, p)
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p256PointDoubleAsm(p, p)
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p256PointDoubleAsm(p, p)
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p256PointDoubleAsm(p, p)
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if index >= 0 {
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sel, sign = boothW5(p256OrdRsh(scalar, index) & 0b111111)
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if index < 192 {
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wvalue = ((scalar[index/64] >> (index % 64)) + (scalar[index/64+1] << (64 - (index % 64)))) & 0x3f
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} else {
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// Booth encoding considers a virtual zero bit at index -1,
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// so we shift left the least significant limb.
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wvalue := (scalar[0] << 1) & 0b111111
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sel, sign = boothW5(wvalue)
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wvalue = (scalar[index/64] >> (index % 64)) & 0x3f
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}
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sel, sign = boothW5(uint(wvalue))
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p256Select(&t0, &precomp, sel)
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p256NegCond(&t0.y, sign)
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// We don't check the return value of p256PointAddAsm because t0 is
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// [±1-16]P, while p was just doubled five times and can't have wrapped
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// around because scalar is less than the group order.
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p256PointAddAsm(&t1, p, &t0)
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// If sel is 0, t0 was undefined and the correct result is p unmodified.
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// If zero is 0, all previous sel were 0 and the correct result is t0.
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// If both are 0, the result doesn't matter as it will be thrown out.
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p256MovCond(&t1, &t1, p, sel)
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p256MovCond(p, &t1, &t0, zero)
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zero |= sel
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}
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// If zero is 0, the whole scalar was zero.
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// If isInfinity is 1, the input point was the infinity.
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// In both cases, p is undefined and the correct result is the infinity.
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infinity := NewP256Point()
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wantInfinity := zero & (isInfinity - 1)
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p256MovCond(p, p, infinity, wantInfinity)
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p256PointDoubleAsm(p, p)
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p256PointDoubleAsm(p, p)
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p256PointDoubleAsm(p, p)
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p256PointDoubleAsm(p, p)
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p256PointDoubleAsm(p, p)
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wvalue = (scalar[0] << 1) & 0x3f
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sel, sign = boothW5(uint(wvalue))
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p256Select(&t0, &precomp, sel)
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p256NegCond(&t0.y, sign)
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p256PointAddAsm(&t1, p, &t0)
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p256MovCond(&t1, &t1, p, sel)
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p256MovCond(p, &t1, &t0, zero)
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}
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