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Diffstat (limited to 'vendor/filippo.io/edwards25519/extra.go')
| -rw-r--r-- | vendor/filippo.io/edwards25519/extra.go | 349 |
1 files changed, 349 insertions, 0 deletions
diff --git a/vendor/filippo.io/edwards25519/extra.go b/vendor/filippo.io/edwards25519/extra.go new file mode 100644 index 0000000..d152d68 --- /dev/null +++ b/vendor/filippo.io/edwards25519/extra.go @@ -0,0 +1,349 @@ +// Copyright (c) 2021 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. + +package edwards25519 + +// This file contains additional functionality that is not included in the +// upstream crypto/internal/edwards25519 package. + +import ( + "errors" + + "filippo.io/edwards25519/field" +) + +// ExtendedCoordinates returns v in extended coordinates (X:Y:Z:T) where +// x = X/Z, y = Y/Z, and xy = T/Z as in https://eprint.iacr.org/2008/522. +func (v *Point) ExtendedCoordinates() (X, Y, Z, T *field.Element) { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. Don't change the style without making + // sure it doesn't increase the inliner cost. + var e [4]field.Element + X, Y, Z, T = v.extendedCoordinates(&e) + return +} + +func (v *Point) extendedCoordinates(e *[4]field.Element) (X, Y, Z, T *field.Element) { + checkInitialized(v) + X = e[0].Set(&v.x) + Y = e[1].Set(&v.y) + Z = e[2].Set(&v.z) + T = e[3].Set(&v.t) + return +} + +// SetExtendedCoordinates sets v = (X:Y:Z:T) in extended coordinates where +// x = X/Z, y = Y/Z, and xy = T/Z as in https://eprint.iacr.org/2008/522. +// +// If the coordinates are invalid or don't represent a valid point on the curve, +// SetExtendedCoordinates returns nil and an error and the receiver is +// unchanged. Otherwise, SetExtendedCoordinates returns v. +func (v *Point) SetExtendedCoordinates(X, Y, Z, T *field.Element) (*Point, error) { + if !isOnCurve(X, Y, Z, T) { + return nil, errors.New("edwards25519: invalid point coordinates") + } + v.x.Set(X) + v.y.Set(Y) + v.z.Set(Z) + v.t.Set(T) + return v, nil +} + +func isOnCurve(X, Y, Z, T *field.Element) bool { + var lhs, rhs field.Element + XX := new(field.Element).Square(X) + YY := new(field.Element).Square(Y) + ZZ := new(field.Element).Square(Z) + TT := new(field.Element).Square(T) + // -x² + y² = 1 + dx²y² + // -(X/Z)² + (Y/Z)² = 1 + d(T/Z)² + // -X² + Y² = Z² + dT² + lhs.Subtract(YY, XX) + rhs.Multiply(d, TT).Add(&rhs, ZZ) + if lhs.Equal(&rhs) != 1 { + return false + } + // xy = T/Z + // XY/Z² = T/Z + // XY = TZ + lhs.Multiply(X, Y) + rhs.Multiply(T, Z) + return lhs.Equal(&rhs) == 1 +} + +// BytesMontgomery converts v to a point on the birationally-equivalent +// Curve25519 Montgomery curve, and returns its canonical 32 bytes encoding +// according to RFC 7748. +// +// Note that BytesMontgomery only encodes the u-coordinate, so v and -v encode +// to the same value. If v is the identity point, BytesMontgomery returns 32 +// zero bytes, analogously to the X25519 function. +// +// The lack of an inverse operation (such as SetMontgomeryBytes) is deliberate: +// while every valid edwards25519 point has a unique u-coordinate Montgomery +// encoding, X25519 accepts inputs on the quadratic twist, which don't correspond +// to any edwards25519 point, and every other X25519 input corresponds to two +// edwards25519 points. +func (v *Point) BytesMontgomery() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var buf [32]byte + return v.bytesMontgomery(&buf) +} + +func (v *Point) bytesMontgomery(buf *[32]byte) []byte { + checkInitialized(v) + + // RFC 7748, Section 4.1 provides the bilinear map to calculate the + // Montgomery u-coordinate + // + // u = (1 + y) / (1 - y) + // + // where y = Y / Z. + + var y, recip, u field.Element + + y.Multiply(&v.y, y.Invert(&v.z)) // y = Y / Z + recip.Invert(recip.Subtract(feOne, &y)) // r = 1/(1 - y) + u.Multiply(u.Add(feOne, &y), &recip) // u = (1 + y)*r + + return copyFieldElement(buf, &u) +} + +// MultByCofactor sets v = 8 * p, and returns v. +func (v *Point) MultByCofactor(p *Point) *Point { + checkInitialized(p) + result := projP1xP1{} + pp := (&projP2{}).FromP3(p) + result.Double(pp) + pp.FromP1xP1(&result) + result.Double(pp) + pp.FromP1xP1(&result) + result.Double(pp) + return v.fromP1xP1(&result) +} + +// Given k > 0, set s = s**(2*i). +func (s *Scalar) pow2k(k int) { + for i := 0; i < k; i++ { + s.Multiply(s, s) + } +} + +// Invert sets s to the inverse of a nonzero scalar v, and returns s. +// +// If t is zero, Invert returns zero. +func (s *Scalar) Invert(t *Scalar) *Scalar { + // Uses a hardcoded sliding window of width 4. + var table [8]Scalar + var tt Scalar + tt.Multiply(t, t) + table[0] = *t + for i := 0; i < 7; i++ { + table[i+1].Multiply(&table[i], &tt) + } + // Now table = [t**1, t**3, t**5, t**7, t**9, t**11, t**13, t**15] + // so t**k = t[k/2] for odd k + + // To compute the sliding window digits, use the following Sage script: + + // sage: import itertools + // sage: def sliding_window(w,k): + // ....: digits = [] + // ....: while k > 0: + // ....: if k % 2 == 1: + // ....: kmod = k % (2**w) + // ....: digits.append(kmod) + // ....: k = k - kmod + // ....: else: + // ....: digits.append(0) + // ....: k = k // 2 + // ....: return digits + + // Now we can compute s roughly as follows: + + // sage: s = 1 + // sage: for coeff in reversed(sliding_window(4,l-2)): + // ....: s = s*s + // ....: if coeff > 0 : + // ....: s = s*t**coeff + + // This works on one bit at a time, with many runs of zeros. + // The digits can be collapsed into [(count, coeff)] as follows: + + // sage: [(len(list(group)),d) for d,group in itertools.groupby(sliding_window(4,l-2))] + + // Entries of the form (k, 0) turn into pow2k(k) + // Entries of the form (1, coeff) turn into a squaring and then a table lookup. + // We can fold the squaring into the previous pow2k(k) as pow2k(k+1). + + *s = table[1/2] + s.pow2k(127 + 1) + s.Multiply(s, &table[1/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[9/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[11/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[13/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[15/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[7/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[15/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[5/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[1/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[15/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[15/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[7/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[3/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[11/2]) + s.pow2k(5 + 1) + s.Multiply(s, &table[11/2]) + s.pow2k(9 + 1) + s.Multiply(s, &table[9/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[3/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[3/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[3/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[9/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[7/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[3/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[13/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[7/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[9/2]) + s.pow2k(3 + 1) + s.Multiply(s, &table[15/2]) + s.pow2k(4 + 1) + s.Multiply(s, &table[11/2]) + + return s +} + +// MultiScalarMult sets v = sum(scalars[i] * points[i]), and returns v. +// +// Execution time depends only on the lengths of the two slices, which must match. +func (v *Point) MultiScalarMult(scalars []*Scalar, points []*Point) *Point { + if len(scalars) != len(points) { + panic("edwards25519: called MultiScalarMult with different size inputs") + } + checkInitialized(points...) + + // Proceed as in the single-base case, but share doublings + // between each point in the multiscalar equation. + + // Build lookup tables for each point + tables := make([]projLookupTable, len(points)) + for i := range tables { + tables[i].FromP3(points[i]) + } + // Compute signed radix-16 digits for each scalar + digits := make([][64]int8, len(scalars)) + for i := range digits { + digits[i] = scalars[i].signedRadix16() + } + + // Unwrap first loop iteration to save computing 16*identity + multiple := &projCached{} + tmp1 := &projP1xP1{} + tmp2 := &projP2{} + // Lookup-and-add the appropriate multiple of each input point + for j := range tables { + tables[j].SelectInto(multiple, digits[j][63]) + tmp1.Add(v, multiple) // tmp1 = v + x_(j,63)*Q in P1xP1 coords + v.fromP1xP1(tmp1) // update v + } + tmp2.FromP3(v) // set up tmp2 = v in P2 coords for next iteration + for i := 62; i >= 0; i-- { + tmp1.Double(tmp2) // tmp1 = 2*(prev) in P1xP1 coords + tmp2.FromP1xP1(tmp1) // tmp2 = 2*(prev) in P2 coords + tmp1.Double(tmp2) // tmp1 = 4*(prev) in P1xP1 coords + tmp2.FromP1xP1(tmp1) // tmp2 = 4*(prev) in P2 coords + tmp1.Double(tmp2) // tmp1 = 8*(prev) in P1xP1 coords + tmp2.FromP1xP1(tmp1) // tmp2 = 8*(prev) in P2 coords + tmp1.Double(tmp2) // tmp1 = 16*(prev) in P1xP1 coords + v.fromP1xP1(tmp1) // v = 16*(prev) in P3 coords + // Lookup-and-add the appropriate multiple of each input point + for j := range tables { + tables[j].SelectInto(multiple, digits[j][i]) + tmp1.Add(v, multiple) // tmp1 = v + x_(j,i)*Q in P1xP1 coords + v.fromP1xP1(tmp1) // update v + } + tmp2.FromP3(v) // set up tmp2 = v in P2 coords for next iteration + } + return v +} + +// VarTimeMultiScalarMult sets v = sum(scalars[i] * points[i]), and returns v. +// +// Execution time depends on the inputs. +func (v *Point) VarTimeMultiScalarMult(scalars []*Scalar, points []*Point) *Point { + if len(scalars) != len(points) { + panic("edwards25519: called VarTimeMultiScalarMult with different size inputs") + } + checkInitialized(points...) + + // Generalize double-base NAF computation to arbitrary sizes. + // Here all the points are dynamic, so we only use the smaller + // tables. + + // Build lookup tables for each point + tables := make([]nafLookupTable5, len(points)) + for i := range tables { + tables[i].FromP3(points[i]) + } + // Compute a NAF for each scalar + nafs := make([][256]int8, len(scalars)) + for i := range nafs { + nafs[i] = scalars[i].nonAdjacentForm(5) + } + + multiple := &projCached{} + tmp1 := &projP1xP1{} + tmp2 := &projP2{} + tmp2.Zero() + + // Move from high to low bits, doubling the accumulator + // at each iteration and checking whether there is a nonzero + // coefficient to look up a multiple of. + // + // Skip trying to find the first nonzero coefficent, because + // searching might be more work than a few extra doublings. + for i := 255; i >= 0; i-- { + tmp1.Double(tmp2) + + for j := range nafs { + if nafs[j][i] > 0 { + v.fromP1xP1(tmp1) + tables[j].SelectInto(multiple, nafs[j][i]) + tmp1.Add(v, multiple) + } else if nafs[j][i] < 0 { + v.fromP1xP1(tmp1) + tables[j].SelectInto(multiple, -nafs[j][i]) + tmp1.Sub(v, multiple) + } + } + + tmp2.FromP1xP1(tmp1) + } + + v.fromP2(tmp2) + return v +} |
