mirror of
https://github.com/42wim/matterbridge.git
synced 2024-12-20 16:02:01 -08:00
344 lines
11 KiB
Go
344 lines
11 KiB
Go
// Copyright (c) 2016 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
|
|
|
|
import (
|
|
"encoding/binary"
|
|
"errors"
|
|
)
|
|
|
|
// A Scalar is an integer modulo
|
|
//
|
|
// l = 2^252 + 27742317777372353535851937790883648493
|
|
//
|
|
// which is the prime order of the edwards25519 group.
|
|
//
|
|
// 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 Scalar struct {
|
|
// s is the scalar in the Montgomery domain, in the format of the
|
|
// fiat-crypto implementation.
|
|
s fiatScalarMontgomeryDomainFieldElement
|
|
}
|
|
|
|
// The field implementation in scalar_fiat.go is generated by the fiat-crypto
|
|
// project (https://github.com/mit-plv/fiat-crypto) at version v0.0.9 (23d2dbc)
|
|
// from a formally verified model.
|
|
//
|
|
// fiat-crypto code comes under the following license.
|
|
//
|
|
// Copyright (c) 2015-2020 The fiat-crypto Authors. All rights reserved.
|
|
//
|
|
// Redistribution and use in source and binary forms, with or without
|
|
// modification, are permitted provided that the following conditions are
|
|
// met:
|
|
//
|
|
// 1. Redistributions of source code must retain the above copyright
|
|
// notice, this list of conditions and the following disclaimer.
|
|
//
|
|
// THIS SOFTWARE IS PROVIDED BY the fiat-crypto authors "AS IS"
|
|
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
|
|
// THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
|
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL Berkeley Software Design,
|
|
// Inc. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
|
|
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
|
|
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
|
|
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
|
|
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
|
|
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
//
|
|
|
|
// NewScalar returns a new zero Scalar.
|
|
func NewScalar() *Scalar {
|
|
return &Scalar{}
|
|
}
|
|
|
|
// MultiplyAdd sets s = x * y + z mod l, and returns s. It is equivalent to
|
|
// using Multiply and then Add.
|
|
func (s *Scalar) MultiplyAdd(x, y, z *Scalar) *Scalar {
|
|
// Make a copy of z in case it aliases s.
|
|
zCopy := new(Scalar).Set(z)
|
|
return s.Multiply(x, y).Add(s, zCopy)
|
|
}
|
|
|
|
// Add sets s = x + y mod l, and returns s.
|
|
func (s *Scalar) Add(x, y *Scalar) *Scalar {
|
|
// s = 1 * x + y mod l
|
|
fiatScalarAdd(&s.s, &x.s, &y.s)
|
|
return s
|
|
}
|
|
|
|
// Subtract sets s = x - y mod l, and returns s.
|
|
func (s *Scalar) Subtract(x, y *Scalar) *Scalar {
|
|
// s = -1 * y + x mod l
|
|
fiatScalarSub(&s.s, &x.s, &y.s)
|
|
return s
|
|
}
|
|
|
|
// Negate sets s = -x mod l, and returns s.
|
|
func (s *Scalar) Negate(x *Scalar) *Scalar {
|
|
// s = -1 * x + 0 mod l
|
|
fiatScalarOpp(&s.s, &x.s)
|
|
return s
|
|
}
|
|
|
|
// Multiply sets s = x * y mod l, and returns s.
|
|
func (s *Scalar) Multiply(x, y *Scalar) *Scalar {
|
|
// s = x * y + 0 mod l
|
|
fiatScalarMul(&s.s, &x.s, &y.s)
|
|
return s
|
|
}
|
|
|
|
// Set sets s = x, and returns s.
|
|
func (s *Scalar) Set(x *Scalar) *Scalar {
|
|
*s = *x
|
|
return s
|
|
}
|
|
|
|
// SetUniformBytes sets s = x mod l, where x is a 64-byte little-endian integer.
|
|
// If x is not of the right length, SetUniformBytes returns nil and an error,
|
|
// and the receiver is unchanged.
|
|
//
|
|
// SetUniformBytes can be used to set s to a uniformly distributed value given
|
|
// 64 uniformly distributed random bytes.
|
|
func (s *Scalar) SetUniformBytes(x []byte) (*Scalar, error) {
|
|
if len(x) != 64 {
|
|
return nil, errors.New("edwards25519: invalid SetUniformBytes input length")
|
|
}
|
|
|
|
// We have a value x of 512 bits, but our fiatScalarFromBytes function
|
|
// expects an input lower than l, which is a little over 252 bits.
|
|
//
|
|
// Instead of writing a reduction function that operates on wider inputs, we
|
|
// can interpret x as the sum of three shorter values a, b, and c.
|
|
//
|
|
// x = a + b * 2^168 + c * 2^336 mod l
|
|
//
|
|
// We then precompute 2^168 and 2^336 modulo l, and perform the reduction
|
|
// with two multiplications and two additions.
|
|
|
|
s.setShortBytes(x[:21])
|
|
t := new(Scalar).setShortBytes(x[21:42])
|
|
s.Add(s, t.Multiply(t, scalarTwo168))
|
|
t.setShortBytes(x[42:])
|
|
s.Add(s, t.Multiply(t, scalarTwo336))
|
|
|
|
return s, nil
|
|
}
|
|
|
|
// scalarTwo168 and scalarTwo336 are 2^168 and 2^336 modulo l, encoded as a
|
|
// fiatScalarMontgomeryDomainFieldElement, which is a little-endian 4-limb value
|
|
// in the 2^256 Montgomery domain.
|
|
var scalarTwo168 = &Scalar{s: [4]uint64{0x5b8ab432eac74798, 0x38afddd6de59d5d7,
|
|
0xa2c131b399411b7c, 0x6329a7ed9ce5a30}}
|
|
var scalarTwo336 = &Scalar{s: [4]uint64{0xbd3d108e2b35ecc5, 0x5c3a3718bdf9c90b,
|
|
0x63aa97a331b4f2ee, 0x3d217f5be65cb5c}}
|
|
|
|
// setShortBytes sets s = x mod l, where x is a little-endian integer shorter
|
|
// than 32 bytes.
|
|
func (s *Scalar) setShortBytes(x []byte) *Scalar {
|
|
if len(x) >= 32 {
|
|
panic("edwards25519: internal error: setShortBytes called with a long string")
|
|
}
|
|
var buf [32]byte
|
|
copy(buf[:], x)
|
|
fiatScalarFromBytes((*[4]uint64)(&s.s), &buf)
|
|
fiatScalarToMontgomery(&s.s, (*fiatScalarNonMontgomeryDomainFieldElement)(&s.s))
|
|
return s
|
|
}
|
|
|
|
// SetCanonicalBytes sets s = x, where x is a 32-byte little-endian encoding of
|
|
// s, and returns s. If x is not a canonical encoding of s, SetCanonicalBytes
|
|
// returns nil and an error, and the receiver is unchanged.
|
|
func (s *Scalar) SetCanonicalBytes(x []byte) (*Scalar, error) {
|
|
if len(x) != 32 {
|
|
return nil, errors.New("invalid scalar length")
|
|
}
|
|
if !isReduced(x) {
|
|
return nil, errors.New("invalid scalar encoding")
|
|
}
|
|
|
|
fiatScalarFromBytes((*[4]uint64)(&s.s), (*[32]byte)(x))
|
|
fiatScalarToMontgomery(&s.s, (*fiatScalarNonMontgomeryDomainFieldElement)(&s.s))
|
|
|
|
return s, nil
|
|
}
|
|
|
|
// scalarMinusOneBytes is l - 1 in little endian.
|
|
var scalarMinusOneBytes = [32]byte{236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16}
|
|
|
|
// isReduced returns whether the given scalar in 32-byte little endian encoded
|
|
// form is reduced modulo l.
|
|
func isReduced(s []byte) bool {
|
|
if len(s) != 32 {
|
|
return false
|
|
}
|
|
|
|
for i := len(s) - 1; i >= 0; i-- {
|
|
switch {
|
|
case s[i] > scalarMinusOneBytes[i]:
|
|
return false
|
|
case s[i] < scalarMinusOneBytes[i]:
|
|
return true
|
|
}
|
|
}
|
|
return true
|
|
}
|
|
|
|
// SetBytesWithClamping applies the buffer pruning described in RFC 8032,
|
|
// Section 5.1.5 (also known as clamping) and sets s to the result. The input
|
|
// must be 32 bytes, and it is not modified. If x is not of the right length,
|
|
// SetBytesWithClamping returns nil and an error, and the receiver is unchanged.
|
|
//
|
|
// Note that since Scalar values are always reduced modulo the prime order of
|
|
// the curve, the resulting value will not preserve any of the cofactor-clearing
|
|
// properties that clamping is meant to provide. It will however work as
|
|
// expected as long as it is applied to points on the prime order subgroup, like
|
|
// in Ed25519. In fact, it is lost to history why RFC 8032 adopted the
|
|
// irrelevant RFC 7748 clamping, but it is now required for compatibility.
|
|
func (s *Scalar) SetBytesWithClamping(x []byte) (*Scalar, error) {
|
|
// The description above omits the purpose of the high bits of the clamping
|
|
// for brevity, but those are also lost to reductions, and are also
|
|
// irrelevant to edwards25519 as they protect against a specific
|
|
// implementation bug that was once observed in a generic Montgomery ladder.
|
|
if len(x) != 32 {
|
|
return nil, errors.New("edwards25519: invalid SetBytesWithClamping input length")
|
|
}
|
|
|
|
// We need to use the wide reduction from SetUniformBytes, since clamping
|
|
// sets the 2^254 bit, making the value higher than the order.
|
|
var wideBytes [64]byte
|
|
copy(wideBytes[:], x[:])
|
|
wideBytes[0] &= 248
|
|
wideBytes[31] &= 63
|
|
wideBytes[31] |= 64
|
|
return s.SetUniformBytes(wideBytes[:])
|
|
}
|
|
|
|
// Bytes returns the canonical 32-byte little-endian encoding of s.
|
|
func (s *Scalar) Bytes() []byte {
|
|
// This function is outlined to make the allocations inline in the caller
|
|
// rather than happen on the heap.
|
|
var encoded [32]byte
|
|
return s.bytes(&encoded)
|
|
}
|
|
|
|
func (s *Scalar) bytes(out *[32]byte) []byte {
|
|
var ss fiatScalarNonMontgomeryDomainFieldElement
|
|
fiatScalarFromMontgomery(&ss, &s.s)
|
|
fiatScalarToBytes(out, (*[4]uint64)(&ss))
|
|
return out[:]
|
|
}
|
|
|
|
// Equal returns 1 if s and t are equal, and 0 otherwise.
|
|
func (s *Scalar) Equal(t *Scalar) int {
|
|
var diff fiatScalarMontgomeryDomainFieldElement
|
|
fiatScalarSub(&diff, &s.s, &t.s)
|
|
var nonzero uint64
|
|
fiatScalarNonzero(&nonzero, (*[4]uint64)(&diff))
|
|
nonzero |= nonzero >> 32
|
|
nonzero |= nonzero >> 16
|
|
nonzero |= nonzero >> 8
|
|
nonzero |= nonzero >> 4
|
|
nonzero |= nonzero >> 2
|
|
nonzero |= nonzero >> 1
|
|
return int(^nonzero) & 1
|
|
}
|
|
|
|
// nonAdjacentForm computes a width-w non-adjacent form for this scalar.
|
|
//
|
|
// w must be between 2 and 8, or nonAdjacentForm will panic.
|
|
func (s *Scalar) nonAdjacentForm(w uint) [256]int8 {
|
|
// This implementation is adapted from the one
|
|
// in curve25519-dalek and is documented there:
|
|
// https://github.com/dalek-cryptography/curve25519-dalek/blob/f630041af28e9a405255f98a8a93adca18e4315b/src/scalar.rs#L800-L871
|
|
b := s.Bytes()
|
|
if b[31] > 127 {
|
|
panic("scalar has high bit set illegally")
|
|
}
|
|
if w < 2 {
|
|
panic("w must be at least 2 by the definition of NAF")
|
|
} else if w > 8 {
|
|
panic("NAF digits must fit in int8")
|
|
}
|
|
|
|
var naf [256]int8
|
|
var digits [5]uint64
|
|
|
|
for i := 0; i < 4; i++ {
|
|
digits[i] = binary.LittleEndian.Uint64(b[i*8:])
|
|
}
|
|
|
|
width := uint64(1 << w)
|
|
windowMask := uint64(width - 1)
|
|
|
|
pos := uint(0)
|
|
carry := uint64(0)
|
|
for pos < 256 {
|
|
indexU64 := pos / 64
|
|
indexBit := pos % 64
|
|
var bitBuf uint64
|
|
if indexBit < 64-w {
|
|
// This window's bits are contained in a single u64
|
|
bitBuf = digits[indexU64] >> indexBit
|
|
} else {
|
|
// Combine the current 64 bits with bits from the next 64
|
|
bitBuf = (digits[indexU64] >> indexBit) | (digits[1+indexU64] << (64 - indexBit))
|
|
}
|
|
|
|
// Add carry into the current window
|
|
window := carry + (bitBuf & windowMask)
|
|
|
|
if window&1 == 0 {
|
|
// If the window value is even, preserve the carry and continue.
|
|
// Why is the carry preserved?
|
|
// If carry == 0 and window & 1 == 0,
|
|
// then the next carry should be 0
|
|
// If carry == 1 and window & 1 == 0,
|
|
// then bit_buf & 1 == 1 so the next carry should be 1
|
|
pos += 1
|
|
continue
|
|
}
|
|
|
|
if window < width/2 {
|
|
carry = 0
|
|
naf[pos] = int8(window)
|
|
} else {
|
|
carry = 1
|
|
naf[pos] = int8(window) - int8(width)
|
|
}
|
|
|
|
pos += w
|
|
}
|
|
return naf
|
|
}
|
|
|
|
func (s *Scalar) signedRadix16() [64]int8 {
|
|
b := s.Bytes()
|
|
if b[31] > 127 {
|
|
panic("scalar has high bit set illegally")
|
|
}
|
|
|
|
var digits [64]int8
|
|
|
|
// Compute unsigned radix-16 digits:
|
|
for i := 0; i < 32; i++ {
|
|
digits[2*i] = int8(b[i] & 15)
|
|
digits[2*i+1] = int8((b[i] >> 4) & 15)
|
|
}
|
|
|
|
// Recenter coefficients:
|
|
for i := 0; i < 63; i++ {
|
|
carry := (digits[i] + 8) >> 4
|
|
digits[i] -= carry << 4
|
|
digits[i+1] += carry
|
|
}
|
|
|
|
return digits
|
|
}
|