diff options
Diffstat (limited to 'vendor/golang.org/x/crypto/curve25519/internal/field/fe.go')
| -rw-r--r-- | vendor/golang.org/x/crypto/curve25519/internal/field/fe.go | 416 |
1 files changed, 0 insertions, 416 deletions
diff --git a/vendor/golang.org/x/crypto/curve25519/internal/field/fe.go b/vendor/golang.org/x/crypto/curve25519/internal/field/fe.go deleted file mode 100644 index ca841ad99..000000000 --- a/vendor/golang.org/x/crypto/curve25519/internal/field/fe.go +++ /dev/null @@ -1,416 +0,0 @@ -// Copyright (c) 2017 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 field implements fast arithmetic modulo 2^255-19. -package field - -import ( - "crypto/subtle" - "encoding/binary" - "math/bits" -) - -// Element represents an element of the field GF(2^255-19). Note that this -// is not a cryptographically secure group, and should only be used to interact -// with edwards25519.Point coordinates. -// -// This type works similarly to math/big.Int, and all arguments and receivers -// are allowed to alias. -// -// The zero value is a valid zero element. -type Element struct { - // An element t represents the integer - // t.l0 + t.l1*2^51 + t.l2*2^102 + t.l3*2^153 + t.l4*2^204 - // - // Between operations, all limbs are expected to be lower than 2^52. - l0 uint64 - l1 uint64 - l2 uint64 - l3 uint64 - l4 uint64 -} - -const maskLow51Bits uint64 = (1 << 51) - 1 - -var feZero = &Element{0, 0, 0, 0, 0} - -// Zero sets v = 0, and returns v. -func (v *Element) Zero() *Element { - *v = *feZero - return v -} - -var feOne = &Element{1, 0, 0, 0, 0} - -// One sets v = 1, and returns v. -func (v *Element) One() *Element { - *v = *feOne - return v -} - -// reduce reduces v modulo 2^255 - 19 and returns it. -func (v *Element) reduce() *Element { - v.carryPropagate() - - // After the light reduction we now have a field element representation - // v < 2^255 + 2^13 * 19, but need v < 2^255 - 19. - - // If v >= 2^255 - 19, then v + 19 >= 2^255, which would overflow 2^255 - 1, - // generating a carry. That is, c will be 0 if v < 2^255 - 19, and 1 otherwise. - c := (v.l0 + 19) >> 51 - c = (v.l1 + c) >> 51 - c = (v.l2 + c) >> 51 - c = (v.l3 + c) >> 51 - c = (v.l4 + c) >> 51 - - // If v < 2^255 - 19 and c = 0, this will be a no-op. Otherwise, it's - // effectively applying the reduction identity to the carry. - v.l0 += 19 * c - - v.l1 += v.l0 >> 51 - v.l0 = v.l0 & maskLow51Bits - v.l2 += v.l1 >> 51 - v.l1 = v.l1 & maskLow51Bits - v.l3 += v.l2 >> 51 - v.l2 = v.l2 & maskLow51Bits - v.l4 += v.l3 >> 51 - v.l3 = v.l3 & maskLow51Bits - // no additional carry - v.l4 = v.l4 & maskLow51Bits - - return v -} - -// Add sets v = a + b, and returns v. -func (v *Element) Add(a, b *Element) *Element { - v.l0 = a.l0 + b.l0 - v.l1 = a.l1 + b.l1 - v.l2 = a.l2 + b.l2 - v.l3 = a.l3 + b.l3 - v.l4 = a.l4 + b.l4 - // Using the generic implementation here is actually faster than the - // assembly. Probably because the body of this function is so simple that - // the compiler can figure out better optimizations by inlining the carry - // propagation. TODO - return v.carryPropagateGeneric() -} - -// Subtract sets v = a - b, and returns v. -func (v *Element) Subtract(a, b *Element) *Element { - // We first add 2 * p, to guarantee the subtraction won't underflow, and - // then subtract b (which can be up to 2^255 + 2^13 * 19). - v.l0 = (a.l0 + 0xFFFFFFFFFFFDA) - b.l0 - v.l1 = (a.l1 + 0xFFFFFFFFFFFFE) - b.l1 - v.l2 = (a.l2 + 0xFFFFFFFFFFFFE) - b.l2 - v.l3 = (a.l3 + 0xFFFFFFFFFFFFE) - b.l3 - v.l4 = (a.l4 + 0xFFFFFFFFFFFFE) - b.l4 - return v.carryPropagate() -} - -// Negate sets v = -a, and returns v. -func (v *Element) Negate(a *Element) *Element { - return v.Subtract(feZero, a) -} - -// Invert sets v = 1/z mod p, and returns v. -// -// If z == 0, Invert returns v = 0. -func (v *Element) Invert(z *Element) *Element { - // Inversion is implemented as exponentiation with exponent p − 2. It uses the - // same sequence of 255 squarings and 11 multiplications as [Curve25519]. - var z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t Element - - z2.Square(z) // 2 - t.Square(&z2) // 4 - t.Square(&t) // 8 - z9.Multiply(&t, z) // 9 - z11.Multiply(&z9, &z2) // 11 - t.Square(&z11) // 22 - z2_5_0.Multiply(&t, &z9) // 31 = 2^5 - 2^0 - - t.Square(&z2_5_0) // 2^6 - 2^1 - for i := 0; i < 4; i++ { - t.Square(&t) // 2^10 - 2^5 - } - z2_10_0.Multiply(&t, &z2_5_0) // 2^10 - 2^0 - - t.Square(&z2_10_0) // 2^11 - 2^1 - for i := 0; i < 9; i++ { - t.Square(&t) // 2^20 - 2^10 - } - z2_20_0.Multiply(&t, &z2_10_0) // 2^20 - 2^0 - - t.Square(&z2_20_0) // 2^21 - 2^1 - for i := 0; i < 19; i++ { - t.Square(&t) // 2^40 - 2^20 - } - t.Multiply(&t, &z2_20_0) // 2^40 - 2^0 - - t.Square(&t) // 2^41 - 2^1 - for i := 0; i < 9; i++ { - t.Square(&t) // 2^50 - 2^10 - } - z2_50_0.Multiply(&t, &z2_10_0) // 2^50 - 2^0 - - t.Square(&z2_50_0) // 2^51 - 2^1 - for i := 0; i < 49; i++ { - t.Square(&t) // 2^100 - 2^50 - } - z2_100_0.Multiply(&t, &z2_50_0) // 2^100 - 2^0 - - t.Square(&z2_100_0) // 2^101 - 2^1 - for i := 0; i < 99; i++ { - t.Square(&t) // 2^200 - 2^100 - } - t.Multiply(&t, &z2_100_0) // 2^200 - 2^0 - - t.Square(&t) // 2^201 - 2^1 - for i := 0; i < 49; i++ { - t.Square(&t) // 2^250 - 2^50 - } - t.Multiply(&t, &z2_50_0) // 2^250 - 2^0 - - t.Square(&t) // 2^251 - 2^1 - t.Square(&t) // 2^252 - 2^2 - t.Square(&t) // 2^253 - 2^3 - t.Square(&t) // 2^254 - 2^4 - t.Square(&t) // 2^255 - 2^5 - - return v.Multiply(&t, &z11) // 2^255 - 21 -} - -// Set sets v = a, and returns v. -func (v *Element) Set(a *Element) *Element { - *v = *a - return v -} - -// SetBytes sets v to x, which must be a 32-byte little-endian encoding. -// -// Consistent with RFC 7748, the most significant bit (the high bit of the -// last byte) is ignored, and non-canonical values (2^255-19 through 2^255-1) -// are accepted. Note that this is laxer than specified by RFC 8032. -func (v *Element) SetBytes(x []byte) *Element { - if len(x) != 32 { - panic("edwards25519: invalid field element input size") - } - - // Bits 0:51 (bytes 0:8, bits 0:64, shift 0, mask 51). - v.l0 = binary.LittleEndian.Uint64(x[0:8]) - v.l0 &= maskLow51Bits - // Bits 51:102 (bytes 6:14, bits 48:112, shift 3, mask 51). - v.l1 = binary.LittleEndian.Uint64(x[6:14]) >> 3 - v.l1 &= maskLow51Bits - // Bits 102:153 (bytes 12:20, bits 96:160, shift 6, mask 51). - v.l2 = binary.LittleEndian.Uint64(x[12:20]) >> 6 - v.l2 &= maskLow51Bits - // Bits 153:204 (bytes 19:27, bits 152:216, shift 1, mask 51). - v.l3 = binary.LittleEndian.Uint64(x[19:27]) >> 1 - v.l3 &= maskLow51Bits - // Bits 204:251 (bytes 24:32, bits 192:256, shift 12, mask 51). - // Note: not bytes 25:33, shift 4, to avoid overread. - v.l4 = binary.LittleEndian.Uint64(x[24:32]) >> 12 - v.l4 &= maskLow51Bits - - return v -} - -// Bytes returns the canonical 32-byte little-endian encoding of v. -func (v *Element) Bytes() []byte { - // This function is outlined to make the allocations inline in the caller - // rather than happen on the heap. - var out [32]byte - return v.bytes(&out) -} - -func (v *Element) bytes(out *[32]byte) []byte { - t := *v - t.reduce() - - var buf [8]byte - for i, l := range [5]uint64{t.l0, t.l1, t.l2, t.l3, t.l4} { - bitsOffset := i * 51 - binary.LittleEndian.PutUint64(buf[:], l<<uint(bitsOffset%8)) - for i, bb := range buf { - off := bitsOffset/8 + i - if off >= len(out) { - break - } - out[off] |= bb - } - } - - return out[:] -} - -// Equal returns 1 if v and u are equal, and 0 otherwise. -func (v *Element) Equal(u *Element) int { - sa, sv := u.Bytes(), v.Bytes() - return subtle.ConstantTimeCompare(sa, sv) -} - -// mask64Bits returns 0xffffffff if cond is 1, and 0 otherwise. -func mask64Bits(cond int) uint64 { return ^(uint64(cond) - 1) } - -// Select sets v to a if cond == 1, and to b if cond == 0. -func (v *Element) Select(a, b *Element, cond int) *Element { - m := mask64Bits(cond) - v.l0 = (m & a.l0) | (^m & b.l0) - v.l1 = (m & a.l1) | (^m & b.l1) - v.l2 = (m & a.l2) | (^m & b.l2) - v.l3 = (m & a.l3) | (^m & b.l3) - v.l4 = (m & a.l4) | (^m & b.l4) - return v -} - -// Swap swaps v and u if cond == 1 or leaves them unchanged if cond == 0, and returns v. -func (v *Element) Swap(u *Element, cond int) { - m := mask64Bits(cond) - t := m & (v.l0 ^ u.l0) - v.l0 ^= t - u.l0 ^= t - t = m & (v.l1 ^ u.l1) - v.l1 ^= t - u.l1 ^= t - t = m & (v.l2 ^ u.l2) - v.l2 ^= t - u.l2 ^= t - t = m & (v.l3 ^ u.l3) - v.l3 ^= t - u.l3 ^= t - t = m & (v.l4 ^ u.l4) - v.l4 ^= t - u.l4 ^= t -} - -// IsNegative returns 1 if v is negative, and 0 otherwise. -func (v *Element) IsNegative() int { - return int(v.Bytes()[0] & 1) -} - -// Absolute sets v to |u|, and returns v. -func (v *Element) Absolute(u *Element) *Element { - return v.Select(new(Element).Negate(u), u, u.IsNegative()) -} - -// Multiply sets v = x * y, and returns v. -func (v *Element) Multiply(x, y *Element) *Element { - feMul(v, x, y) - return v -} - -// Square sets v = x * x, and returns v. -func (v *Element) Square(x *Element) *Element { - feSquare(v, x) - return v -} - -// Mult32 sets v = x * y, and returns v. -func (v *Element) Mult32(x *Element, y uint32) *Element { - x0lo, x0hi := mul51(x.l0, y) - x1lo, x1hi := mul51(x.l1, y) - x2lo, x2hi := mul51(x.l2, y) - x3lo, x3hi := mul51(x.l3, y) - x4lo, x4hi := mul51(x.l4, y) - v.l0 = x0lo + 19*x4hi // carried over per the reduction identity - v.l1 = x1lo + x0hi - v.l2 = x2lo + x1hi - v.l3 = x3lo + x2hi - v.l4 = x4lo + x3hi - // The hi portions are going to be only 32 bits, plus any previous excess, - // so we can skip the carry propagation. - return v -} - -// mul51 returns lo + hi * 2⁵¹ = a * b. -func mul51(a uint64, b uint32) (lo uint64, hi uint64) { - mh, ml := bits.Mul64(a, uint64(b)) - lo = ml & maskLow51Bits - hi = (mh << 13) | (ml >> 51) - return -} - -// Pow22523 set v = x^((p-5)/8), and returns v. (p-5)/8 is 2^252-3. -func (v *Element) Pow22523(x *Element) *Element { - var t0, t1, t2 Element - - t0.Square(x) // x^2 - t1.Square(&t0) // x^4 - t1.Square(&t1) // x^8 - t1.Multiply(x, &t1) // x^9 - t0.Multiply(&t0, &t1) // x^11 - t0.Square(&t0) // x^22 - t0.Multiply(&t1, &t0) // x^31 - t1.Square(&t0) // x^62 - for i := 1; i < 5; i++ { // x^992 - t1.Square(&t1) - } - t0.Multiply(&t1, &t0) // x^1023 -> 1023 = 2^10 - 1 - t1.Square(&t0) // 2^11 - 2 - for i := 1; i < 10; i++ { // 2^20 - 2^10 - t1.Square(&t1) - } - t1.Multiply(&t1, &t0) // 2^20 - 1 - t2.Square(&t1) // 2^21 - 2 - for i := 1; i < 20; i++ { // 2^40 - 2^20 - t2.Square(&t2) - } - t1.Multiply(&t2, &t1) // 2^40 - 1 - t1.Square(&t1) // 2^41 - 2 - for i := 1; i < 10; i++ { // 2^50 - 2^10 - t1.Square(&t1) - } - t0.Multiply(&t1, &t0) // 2^50 - 1 - t1.Square(&t0) // 2^51 - 2 - for i := 1; i < 50; i++ { // 2^100 - 2^50 - t1.Square(&t1) - } - t1.Multiply(&t1, &t0) // 2^100 - 1 - t2.Square(&t1) // 2^101 - 2 - for i := 1; i < 100; i++ { // 2^200 - 2^100 - t2.Square(&t2) - } - t1.Multiply(&t2, &t1) // 2^200 - 1 - t1.Square(&t1) // 2^201 - 2 - for i := 1; i < 50; i++ { // 2^250 - 2^50 - t1.Square(&t1) - } - t0.Multiply(&t1, &t0) // 2^250 - 1 - t0.Square(&t0) // 2^251 - 2 - t0.Square(&t0) // 2^252 - 4 - return v.Multiply(&t0, x) // 2^252 - 3 -> x^(2^252-3) -} - -// sqrtM1 is 2^((p-1)/4), which squared is equal to -1 by Euler's Criterion. -var sqrtM1 = &Element{1718705420411056, 234908883556509, - 2233514472574048, 2117202627021982, 765476049583133} - -// SqrtRatio sets r to the non-negative square root of the ratio of u and v. -// -// If u/v is square, SqrtRatio returns r and 1. If u/v is not square, SqrtRatio -// sets r according to Section 4.3 of draft-irtf-cfrg-ristretto255-decaf448-00, -// and returns r and 0. -func (r *Element) SqrtRatio(u, v *Element) (rr *Element, wasSquare int) { - var a, b Element - - // r = (u * v3) * (u * v7)^((p-5)/8) - v2 := a.Square(v) - uv3 := b.Multiply(u, b.Multiply(v2, v)) - uv7 := a.Multiply(uv3, a.Square(v2)) - r.Multiply(uv3, r.Pow22523(uv7)) - - check := a.Multiply(v, a.Square(r)) // check = v * r^2 - - uNeg := b.Negate(u) - correctSignSqrt := check.Equal(u) - flippedSignSqrt := check.Equal(uNeg) - flippedSignSqrtI := check.Equal(uNeg.Multiply(uNeg, sqrtM1)) - - rPrime := b.Multiply(r, sqrtM1) // r_prime = SQRT_M1 * r - // r = CT_SELECT(r_prime IF flipped_sign_sqrt | flipped_sign_sqrt_i ELSE r) - r.Select(rPrime, r, flippedSignSqrt|flippedSignSqrtI) - - r.Absolute(r) // Choose the nonnegative square root. - return r, correctSignSqrt | flippedSignSqrt -} |