mirror of https://github.com/gtank/ristretto255
internal/ed25519: implement MultiscalarMul
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@ -113,7 +113,52 @@ func (v *ProjP3) VartimeDoubleBaseMul(a, b *scalar.Scalar, A *ProjP3) *ProjP3 {
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//
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// The multiscalar multiplication is performed in constant time.
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func (v *ProjP3) MultiscalarMul(scalars []scalar.Scalar, points []*ProjP3) *ProjP3 {
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panic("unimplemented")
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if len(scalars) != len(points) {
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panic("called MultiscalarMul with different size inputs")
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}
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// Proceed as in the single-base case, but share doublings
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// between each point in the multiscalar equation.
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// Build lookup tables for each point
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tables := make([]ProjLookupTable, len(points))
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for i := range tables {
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tables[i].FromP3(points[i])
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}
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// Compute signed radix-16 digits for each scalar
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digits := make([][64]int8, len(scalars))
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for i := range digits {
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digits[i] = scalars[i].SignedRadix16()
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}
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// Unwrap first loop iteration to save computing 16*identity
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multiple := &ProjCached{}
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tmp1 := &ProjP1xP1{}
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tmp2 := &ProjP2{}
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// Lookup-and-add the appropriate multiple of each input point
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for j := range tables {
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tables[j].SelectInto(multiple, digits[j][63])
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tmp1.Add(v, multiple) // tmp1 = v + x_(j,63)*Q in P1xP1 coords
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v.FromP1xP1(tmp1) // update v
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}
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tmp2.FromP3(v) // set up tmp2 = v in P2 coords for next iteration
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for i := 62; i >= 0; i-- {
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tmp1.Double(tmp2) // tmp1 = 2*(prev) in P1xP1 coords
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tmp2.FromP1xP1(tmp1) // tmp2 = 2*(prev) in P2 coords
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tmp1.Double(tmp2) // tmp1 = 4*(prev) in P1xP1 coords
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tmp2.FromP1xP1(tmp1) // tmp2 = 4*(prev) in P2 coords
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tmp1.Double(tmp2) // tmp1 = 8*(prev) in P1xP1 coords
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tmp2.FromP1xP1(tmp1) // tmp2 = 8*(prev) in P2 coords
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tmp1.Double(tmp2) // tmp1 = 16*(prev) in P1xP1 coords
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v.FromP1xP1(tmp1) // v = 16*(prev) in P3 coords
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// Lookup-and-add the appropriate multiple of each input point
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for j := range tables {
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tables[j].SelectInto(multiple, digits[j][i])
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tmp1.Add(v, multiple) // tmp1 = v + x_(j,i)*Q in P1xP1 coords
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v.FromP1xP1(tmp1) // update v
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}
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tmp2.FromP3(v) // set up tmp2 = v in P2 coords for next iteration
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}
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return v
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}
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@ -122,3 +122,27 @@ func TestScalarMulMatchesBasepointMul(t *testing.T) {
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t.Error(err)
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}
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}
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func TestMultiScalarMulMatchesBasepointMul(t *testing.T) {
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multiScalarMulMatchesBasepointMul := func(x, y, z scalar.Scalar) bool {
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// FIXME opaque scalars
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x[31] &= 127
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y[31] &= 127
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z[31] &= 127
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var p, q1, q2, q3, check ProjP3
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p.MultiscalarMul([]scalar.Scalar{x, y, z}, []*ProjP3{&B, &B, &B})
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q1.BasepointMul(&x)
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q2.BasepointMul(&y)
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q3.BasepointMul(&z)
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check.Zero()
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check.Add(&q1, &q2).Add(&check, &q3)
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return p.Equal(&check) == 1
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}
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if err := quick.Check(multiScalarMulMatchesBasepointMul, quickCheckConfig); err != nil {
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t.Error(err)
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}
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}
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