Add dependencies/vendor (whatsapp)

1 files changed, 343 insertions, 0 deletions

diff --git a/vendor/filippo.io/edwards25519/extra.go b/vendor/filippo.io/edwards25519/extra.go
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+// 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/ed25519/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.
+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**7, 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
+}