mirror of
https://github.com/42wim/matterbridge.git
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215 lines
6.3 KiB
Go
215 lines
6.3 KiB
Go
// Copyright (c) 2019 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package edwards25519
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import "sync"
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// basepointTable is a set of 32 affineLookupTables, where table i is generated
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// from 256i * basepoint. It is precomputed the first time it's used.
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func basepointTable() *[32]affineLookupTable {
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basepointTablePrecomp.initOnce.Do(func() {
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p := NewGeneratorPoint()
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for i := 0; i < 32; i++ {
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basepointTablePrecomp.table[i].FromP3(p)
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for j := 0; j < 8; j++ {
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p.Add(p, p)
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}
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}
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})
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return &basepointTablePrecomp.table
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}
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var basepointTablePrecomp struct {
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table [32]affineLookupTable
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initOnce sync.Once
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}
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// ScalarBaseMult sets v = x * B, where B is the canonical generator, and
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// returns v.
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//
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// The scalar multiplication is done in constant time.
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func (v *Point) ScalarBaseMult(x *Scalar) *Point {
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basepointTable := basepointTable()
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// Write x = sum(x_i * 16^i) so x*B = sum( B*x_i*16^i )
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// as described in the Ed25519 paper
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//
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// Group even and odd coefficients
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// x*B = x_0*16^0*B + x_2*16^2*B + ... + x_62*16^62*B
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// + x_1*16^1*B + x_3*16^3*B + ... + x_63*16^63*B
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// x*B = x_0*16^0*B + x_2*16^2*B + ... + x_62*16^62*B
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// + 16*( x_1*16^0*B + x_3*16^2*B + ... + x_63*16^62*B)
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//
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// We use a lookup table for each i to get x_i*16^(2*i)*B
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// and do four doublings to multiply by 16.
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digits := x.signedRadix16()
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multiple := &affineCached{}
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tmp1 := &projP1xP1{}
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tmp2 := &projP2{}
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// Accumulate the odd components first
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v.Set(NewIdentityPoint())
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for i := 1; i < 64; i += 2 {
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basepointTable[i/2].SelectInto(multiple, digits[i])
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tmp1.AddAffine(v, multiple)
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v.fromP1xP1(tmp1)
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}
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// Multiply by 16
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tmp2.FromP3(v) // tmp2 = v in P2 coords
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tmp1.Double(tmp2) // tmp1 = 2*v in P1xP1 coords
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tmp2.FromP1xP1(tmp1) // tmp2 = 2*v in P2 coords
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tmp1.Double(tmp2) // tmp1 = 4*v in P1xP1 coords
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tmp2.FromP1xP1(tmp1) // tmp2 = 4*v in P2 coords
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tmp1.Double(tmp2) // tmp1 = 8*v in P1xP1 coords
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tmp2.FromP1xP1(tmp1) // tmp2 = 8*v in P2 coords
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tmp1.Double(tmp2) // tmp1 = 16*v in P1xP1 coords
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v.fromP1xP1(tmp1) // now v = 16*(odd components)
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// Accumulate the even components
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for i := 0; i < 64; i += 2 {
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basepointTable[i/2].SelectInto(multiple, digits[i])
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tmp1.AddAffine(v, multiple)
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v.fromP1xP1(tmp1)
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}
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return v
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}
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// ScalarMult sets v = x * q, and returns v.
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//
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// The scalar multiplication is done in constant time.
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func (v *Point) ScalarMult(x *Scalar, q *Point) *Point {
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checkInitialized(q)
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var table projLookupTable
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table.FromP3(q)
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// Write x = sum(x_i * 16^i)
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// so x*Q = sum( Q*x_i*16^i )
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// = Q*x_0 + 16*(Q*x_1 + 16*( ... + Q*x_63) ... )
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// <------compute inside out---------
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//
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// We use the lookup table to get the x_i*Q values
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// and do four doublings to compute 16*Q
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digits := x.signedRadix16()
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// Unwrap first loop iteration to save computing 16*identity
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multiple := &projCached{}
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tmp1 := &projP1xP1{}
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tmp2 := &projP2{}
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table.SelectInto(multiple, digits[63])
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v.Set(NewIdentityPoint())
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tmp1.Add(v, multiple) // tmp1 = x_63*Q in P1xP1 coords
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for i := 62; i >= 0; i-- {
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tmp2.FromP1xP1(tmp1) // tmp2 = (prev) in P2 coords
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tmp1.Double(tmp2) // tmp1 = 2*(prev) in P1xP1 coords
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tmp2.FromP1xP1(tmp1) // tmp2 = 2*(prev) in P2 coords
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tmp1.Double(tmp2) // tmp1 = 4*(prev) in P1xP1 coords
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tmp2.FromP1xP1(tmp1) // tmp2 = 4*(prev) in P2 coords
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tmp1.Double(tmp2) // tmp1 = 8*(prev) in P1xP1 coords
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tmp2.FromP1xP1(tmp1) // tmp2 = 8*(prev) in P2 coords
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tmp1.Double(tmp2) // tmp1 = 16*(prev) in P1xP1 coords
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v.fromP1xP1(tmp1) // v = 16*(prev) in P3 coords
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table.SelectInto(multiple, digits[i])
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tmp1.Add(v, multiple) // tmp1 = x_i*Q + 16*(prev) in P1xP1 coords
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}
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v.fromP1xP1(tmp1)
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return v
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}
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// basepointNafTable is the nafLookupTable8 for the basepoint.
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// It is precomputed the first time it's used.
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func basepointNafTable() *nafLookupTable8 {
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basepointNafTablePrecomp.initOnce.Do(func() {
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basepointNafTablePrecomp.table.FromP3(NewGeneratorPoint())
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})
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return &basepointNafTablePrecomp.table
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}
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var basepointNafTablePrecomp struct {
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table nafLookupTable8
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initOnce sync.Once
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}
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// VarTimeDoubleScalarBaseMult sets v = a * A + b * B, where B is the canonical
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// generator, and returns v.
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//
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// Execution time depends on the inputs.
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func (v *Point) VarTimeDoubleScalarBaseMult(a *Scalar, A *Point, b *Scalar) *Point {
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checkInitialized(A)
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// Similarly to the single variable-base approach, we compute
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// digits and use them with a lookup table. However, because
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// we are allowed to do variable-time operations, we don't
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// need constant-time lookups or constant-time digit
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// computations.
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//
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// So we use a non-adjacent form of some width w instead of
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// radix 16. This is like a binary representation (one digit
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// for each binary place) but we allow the digits to grow in
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// magnitude up to 2^{w-1} so that the nonzero digits are as
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// sparse as possible. Intuitively, this "condenses" the
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// "mass" of the scalar onto sparse coefficients (meaning
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// fewer additions).
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basepointNafTable := basepointNafTable()
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var aTable nafLookupTable5
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aTable.FromP3(A)
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// Because the basepoint is fixed, we can use a wider NAF
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// corresponding to a bigger table.
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aNaf := a.nonAdjacentForm(5)
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bNaf := b.nonAdjacentForm(8)
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// Find the first nonzero coefficient.
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i := 255
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for j := i; j >= 0; j-- {
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if aNaf[j] != 0 || bNaf[j] != 0 {
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break
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}
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}
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multA := &projCached{}
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multB := &affineCached{}
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tmp1 := &projP1xP1{}
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tmp2 := &projP2{}
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tmp2.Zero()
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// Move from high to low bits, doubling the accumulator
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// at each iteration and checking whether there is a nonzero
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// coefficient to look up a multiple of.
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for ; i >= 0; i-- {
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tmp1.Double(tmp2)
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// Only update v if we have a nonzero coeff to add in.
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if aNaf[i] > 0 {
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v.fromP1xP1(tmp1)
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aTable.SelectInto(multA, aNaf[i])
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tmp1.Add(v, multA)
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} else if aNaf[i] < 0 {
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v.fromP1xP1(tmp1)
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aTable.SelectInto(multA, -aNaf[i])
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tmp1.Sub(v, multA)
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}
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if bNaf[i] > 0 {
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v.fromP1xP1(tmp1)
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basepointNafTable.SelectInto(multB, bNaf[i])
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tmp1.AddAffine(v, multB)
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} else if bNaf[i] < 0 {
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v.fromP1xP1(tmp1)
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basepointNafTable.SelectInto(multB, -bNaf[i])
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tmp1.SubAffine(v, multB)
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}
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tmp2.FromP1xP1(tmp1)
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}
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v.fromP2(tmp2)
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return v
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}
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