mirror of
https://github.com/cwinfo/matterbridge.git
synced 2024-11-25 01:51:35 +00:00
215 lines
6.3 KiB
Go
215 lines
6.3 KiB
Go
// Copyright (c) 2019 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 "sync"
|
|
|
|
// basepointTable is a set of 32 affineLookupTables, where table i is generated
|
|
// from 256i * basepoint. It is precomputed the first time it's used.
|
|
func basepointTable() *[32]affineLookupTable {
|
|
basepointTablePrecomp.initOnce.Do(func() {
|
|
p := NewGeneratorPoint()
|
|
for i := 0; i < 32; i++ {
|
|
basepointTablePrecomp.table[i].FromP3(p)
|
|
for j := 0; j < 8; j++ {
|
|
p.Add(p, p)
|
|
}
|
|
}
|
|
})
|
|
return &basepointTablePrecomp.table
|
|
}
|
|
|
|
var basepointTablePrecomp struct {
|
|
table [32]affineLookupTable
|
|
initOnce sync.Once
|
|
}
|
|
|
|
// ScalarBaseMult sets v = x * B, where B is the canonical generator, and
|
|
// returns v.
|
|
//
|
|
// The scalar multiplication is done in constant time.
|
|
func (v *Point) ScalarBaseMult(x *Scalar) *Point {
|
|
basepointTable := basepointTable()
|
|
|
|
// Write x = sum(x_i * 16^i) so x*B = sum( B*x_i*16^i )
|
|
// as described in the Ed25519 paper
|
|
//
|
|
// Group even and odd coefficients
|
|
// x*B = x_0*16^0*B + x_2*16^2*B + ... + x_62*16^62*B
|
|
// + x_1*16^1*B + x_3*16^3*B + ... + x_63*16^63*B
|
|
// x*B = x_0*16^0*B + x_2*16^2*B + ... + x_62*16^62*B
|
|
// + 16*( x_1*16^0*B + x_3*16^2*B + ... + x_63*16^62*B)
|
|
//
|
|
// We use a lookup table for each i to get x_i*16^(2*i)*B
|
|
// and do four doublings to multiply by 16.
|
|
digits := x.signedRadix16()
|
|
|
|
multiple := &affineCached{}
|
|
tmp1 := &projP1xP1{}
|
|
tmp2 := &projP2{}
|
|
|
|
// Accumulate the odd components first
|
|
v.Set(NewIdentityPoint())
|
|
for i := 1; i < 64; i += 2 {
|
|
basepointTable[i/2].SelectInto(multiple, digits[i])
|
|
tmp1.AddAffine(v, multiple)
|
|
v.fromP1xP1(tmp1)
|
|
}
|
|
|
|
// Multiply by 16
|
|
tmp2.FromP3(v) // tmp2 = v in P2 coords
|
|
tmp1.Double(tmp2) // tmp1 = 2*v in P1xP1 coords
|
|
tmp2.FromP1xP1(tmp1) // tmp2 = 2*v in P2 coords
|
|
tmp1.Double(tmp2) // tmp1 = 4*v in P1xP1 coords
|
|
tmp2.FromP1xP1(tmp1) // tmp2 = 4*v in P2 coords
|
|
tmp1.Double(tmp2) // tmp1 = 8*v in P1xP1 coords
|
|
tmp2.FromP1xP1(tmp1) // tmp2 = 8*v in P2 coords
|
|
tmp1.Double(tmp2) // tmp1 = 16*v in P1xP1 coords
|
|
v.fromP1xP1(tmp1) // now v = 16*(odd components)
|
|
|
|
// Accumulate the even components
|
|
for i := 0; i < 64; i += 2 {
|
|
basepointTable[i/2].SelectInto(multiple, digits[i])
|
|
tmp1.AddAffine(v, multiple)
|
|
v.fromP1xP1(tmp1)
|
|
}
|
|
|
|
return v
|
|
}
|
|
|
|
// ScalarMult sets v = x * q, and returns v.
|
|
//
|
|
// The scalar multiplication is done in constant time.
|
|
func (v *Point) ScalarMult(x *Scalar, q *Point) *Point {
|
|
checkInitialized(q)
|
|
|
|
var table projLookupTable
|
|
table.FromP3(q)
|
|
|
|
// Write x = sum(x_i * 16^i)
|
|
// so x*Q = sum( Q*x_i*16^i )
|
|
// = Q*x_0 + 16*(Q*x_1 + 16*( ... + Q*x_63) ... )
|
|
// <------compute inside out---------
|
|
//
|
|
// We use the lookup table to get the x_i*Q values
|
|
// and do four doublings to compute 16*Q
|
|
digits := x.signedRadix16()
|
|
|
|
// Unwrap first loop iteration to save computing 16*identity
|
|
multiple := &projCached{}
|
|
tmp1 := &projP1xP1{}
|
|
tmp2 := &projP2{}
|
|
table.SelectInto(multiple, digits[63])
|
|
|
|
v.Set(NewIdentityPoint())
|
|
tmp1.Add(v, multiple) // tmp1 = x_63*Q in P1xP1 coords
|
|
for i := 62; i >= 0; i-- {
|
|
tmp2.FromP1xP1(tmp1) // tmp2 = (prev) in P2 coords
|
|
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
|
|
table.SelectInto(multiple, digits[i])
|
|
tmp1.Add(v, multiple) // tmp1 = x_i*Q + 16*(prev) in P1xP1 coords
|
|
}
|
|
v.fromP1xP1(tmp1)
|
|
return v
|
|
}
|
|
|
|
// basepointNafTable is the nafLookupTable8 for the basepoint.
|
|
// It is precomputed the first time it's used.
|
|
func basepointNafTable() *nafLookupTable8 {
|
|
basepointNafTablePrecomp.initOnce.Do(func() {
|
|
basepointNafTablePrecomp.table.FromP3(NewGeneratorPoint())
|
|
})
|
|
return &basepointNafTablePrecomp.table
|
|
}
|
|
|
|
var basepointNafTablePrecomp struct {
|
|
table nafLookupTable8
|
|
initOnce sync.Once
|
|
}
|
|
|
|
// VarTimeDoubleScalarBaseMult sets v = a * A + b * B, where B is the canonical
|
|
// generator, and returns v.
|
|
//
|
|
// Execution time depends on the inputs.
|
|
func (v *Point) VarTimeDoubleScalarBaseMult(a *Scalar, A *Point, b *Scalar) *Point {
|
|
checkInitialized(A)
|
|
|
|
// Similarly to the single variable-base approach, we compute
|
|
// digits and use them with a lookup table. However, because
|
|
// we are allowed to do variable-time operations, we don't
|
|
// need constant-time lookups or constant-time digit
|
|
// computations.
|
|
//
|
|
// So we use a non-adjacent form of some width w instead of
|
|
// radix 16. This is like a binary representation (one digit
|
|
// for each binary place) but we allow the digits to grow in
|
|
// magnitude up to 2^{w-1} so that the nonzero digits are as
|
|
// sparse as possible. Intuitively, this "condenses" the
|
|
// "mass" of the scalar onto sparse coefficients (meaning
|
|
// fewer additions).
|
|
|
|
basepointNafTable := basepointNafTable()
|
|
var aTable nafLookupTable5
|
|
aTable.FromP3(A)
|
|
// Because the basepoint is fixed, we can use a wider NAF
|
|
// corresponding to a bigger table.
|
|
aNaf := a.nonAdjacentForm(5)
|
|
bNaf := b.nonAdjacentForm(8)
|
|
|
|
// Find the first nonzero coefficient.
|
|
i := 255
|
|
for j := i; j >= 0; j-- {
|
|
if aNaf[j] != 0 || bNaf[j] != 0 {
|
|
break
|
|
}
|
|
}
|
|
|
|
multA := &projCached{}
|
|
multB := &affineCached{}
|
|
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.
|
|
for ; i >= 0; i-- {
|
|
tmp1.Double(tmp2)
|
|
|
|
// Only update v if we have a nonzero coeff to add in.
|
|
if aNaf[i] > 0 {
|
|
v.fromP1xP1(tmp1)
|
|
aTable.SelectInto(multA, aNaf[i])
|
|
tmp1.Add(v, multA)
|
|
} else if aNaf[i] < 0 {
|
|
v.fromP1xP1(tmp1)
|
|
aTable.SelectInto(multA, -aNaf[i])
|
|
tmp1.Sub(v, multA)
|
|
}
|
|
|
|
if bNaf[i] > 0 {
|
|
v.fromP1xP1(tmp1)
|
|
basepointNafTable.SelectInto(multB, bNaf[i])
|
|
tmp1.AddAffine(v, multB)
|
|
} else if bNaf[i] < 0 {
|
|
v.fromP1xP1(tmp1)
|
|
basepointNafTable.SelectInto(multB, -bNaf[i])
|
|
tmp1.SubAffine(v, multB)
|
|
}
|
|
|
|
tmp2.FromP1xP1(tmp1)
|
|
}
|
|
|
|
v.fromP2(tmp2)
|
|
return v
|
|
}
|