mirror of
https://github.com/henrydcase/nobs.git
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779 lines
22 KiB
Go
779 lines
22 KiB
Go
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// The MIT License (MIT)
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//
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// Copyright (c) 2014-2015 Cryptography Research, Inc.
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// Copyright (c) 2015 Yawning Angel.
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to deal
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// in the Software without restriction, including without limitation the rights
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included in
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// all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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// THE SOFTWARE.
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package x448
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// This should really use 64 bit limbs, but Go is fucking retarded and doesn't
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// have __(u)int128_t, so the 32 bit code it is, at a hefty performance
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// penalty. Fuck my life, I'm going to have to bust out PeachPy to get this
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// to go fast aren't I.
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const (
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wBits = 32
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lBits = (wBits * 7 / 8)
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x448Limbs = (448 / lBits)
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lMask = (1 << lBits) - 1
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)
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type limbUint uint32
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type limbSint int32
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type gf struct {
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limb [x448Limbs]uint32
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}
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var zero = gf{[x448Limbs]uint32{0}}
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var one = gf{[x448Limbs]uint32{1}}
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var p = gf{[x448Limbs]uint32{
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lMask, lMask, lMask, lMask, lMask, lMask, lMask, lMask,
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lMask - 1, lMask, lMask, lMask, lMask, lMask, lMask, lMask,
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}}
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// cpy copies x = y.
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func (x *gf) cpy(y *gf) {
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// for i, v := range y.limb {
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// x.limb[i] = v
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// }
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copy(x.limb[:], y.limb[:])
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}
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// mul multiplies c = a * b. (PERF)
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func (c *gf) mul(a, b *gf) {
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var aa gf
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aa.cpy(a)
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//
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// This is *by far* the most CPU intesive routine in the code.
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//
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// var accum [x448Limbs]uint64
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// for i, bv := range b.limb {
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// for j, aav := range aa.limb {
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// accum[(i+j)%x448Limbs] += (uint64)(bv) * (uint64)(aav)
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// }
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// aa.limb[(x448Limbs-1-i)^(x448Limbs/2)] += aa.limb[x448Limbs-1-i]
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// }
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// So fucking stupid that this is actually a fairly massive gain.
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var accum0, accum1, accum2, accum3, accum4, accum5, accum6, accum7, accum8, accum9, accum10, accum11, accum12, accum13, accum14, accum15 uint64
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var bv uint64
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bv = (uint64)(b.limb[0])
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accum0 += bv * (uint64)(aa.limb[0])
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accum1 += bv * (uint64)(aa.limb[1])
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accum2 += bv * (uint64)(aa.limb[2])
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accum3 += bv * (uint64)(aa.limb[3])
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accum4 += bv * (uint64)(aa.limb[4])
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accum5 += bv * (uint64)(aa.limb[5])
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accum6 += bv * (uint64)(aa.limb[6])
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accum7 += bv * (uint64)(aa.limb[7])
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accum8 += bv * (uint64)(aa.limb[8])
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accum9 += bv * (uint64)(aa.limb[9])
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accum10 += bv * (uint64)(aa.limb[10])
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accum11 += bv * (uint64)(aa.limb[11])
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accum12 += bv * (uint64)(aa.limb[12])
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accum13 += bv * (uint64)(aa.limb[13])
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accum14 += bv * (uint64)(aa.limb[14])
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accum15 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-0)^(x448Limbs/2)] += aa.limb[x448Limbs-1-0]
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bv = (uint64)(b.limb[1])
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accum1 += bv * (uint64)(aa.limb[0])
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accum2 += bv * (uint64)(aa.limb[1])
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accum3 += bv * (uint64)(aa.limb[2])
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accum4 += bv * (uint64)(aa.limb[3])
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accum5 += bv * (uint64)(aa.limb[4])
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accum6 += bv * (uint64)(aa.limb[5])
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accum7 += bv * (uint64)(aa.limb[6])
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accum8 += bv * (uint64)(aa.limb[7])
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accum9 += bv * (uint64)(aa.limb[8])
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accum10 += bv * (uint64)(aa.limb[9])
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accum11 += bv * (uint64)(aa.limb[10])
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accum12 += bv * (uint64)(aa.limb[11])
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accum13 += bv * (uint64)(aa.limb[12])
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accum14 += bv * (uint64)(aa.limb[13])
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accum15 += bv * (uint64)(aa.limb[14])
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accum0 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-1)^(x448Limbs/2)] += aa.limb[x448Limbs-1-1]
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bv = (uint64)(b.limb[2])
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accum2 += bv * (uint64)(aa.limb[0])
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accum3 += bv * (uint64)(aa.limb[1])
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accum4 += bv * (uint64)(aa.limb[2])
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accum5 += bv * (uint64)(aa.limb[3])
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accum6 += bv * (uint64)(aa.limb[4])
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accum7 += bv * (uint64)(aa.limb[5])
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accum8 += bv * (uint64)(aa.limb[6])
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accum9 += bv * (uint64)(aa.limb[7])
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accum10 += bv * (uint64)(aa.limb[8])
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accum11 += bv * (uint64)(aa.limb[9])
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accum12 += bv * (uint64)(aa.limb[10])
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accum13 += bv * (uint64)(aa.limb[11])
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accum14 += bv * (uint64)(aa.limb[12])
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accum15 += bv * (uint64)(aa.limb[13])
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accum0 += bv * (uint64)(aa.limb[14])
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accum1 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-2)^(x448Limbs/2)] += aa.limb[x448Limbs-1-2]
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bv = (uint64)(b.limb[3])
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accum3 += bv * (uint64)(aa.limb[0])
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accum4 += bv * (uint64)(aa.limb[1])
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accum5 += bv * (uint64)(aa.limb[2])
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accum6 += bv * (uint64)(aa.limb[3])
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accum7 += bv * (uint64)(aa.limb[4])
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accum8 += bv * (uint64)(aa.limb[5])
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accum9 += bv * (uint64)(aa.limb[6])
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accum10 += bv * (uint64)(aa.limb[7])
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accum11 += bv * (uint64)(aa.limb[8])
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accum12 += bv * (uint64)(aa.limb[9])
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accum13 += bv * (uint64)(aa.limb[10])
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accum14 += bv * (uint64)(aa.limb[11])
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accum15 += bv * (uint64)(aa.limb[12])
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accum0 += bv * (uint64)(aa.limb[13])
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accum1 += bv * (uint64)(aa.limb[14])
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accum2 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-3)^(x448Limbs/2)] += aa.limb[x448Limbs-1-3]
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bv = (uint64)(b.limb[4])
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accum4 += bv * (uint64)(aa.limb[0])
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accum5 += bv * (uint64)(aa.limb[1])
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accum6 += bv * (uint64)(aa.limb[2])
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accum7 += bv * (uint64)(aa.limb[3])
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accum8 += bv * (uint64)(aa.limb[4])
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accum9 += bv * (uint64)(aa.limb[5])
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accum10 += bv * (uint64)(aa.limb[6])
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accum11 += bv * (uint64)(aa.limb[7])
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accum12 += bv * (uint64)(aa.limb[8])
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accum13 += bv * (uint64)(aa.limb[9])
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accum14 += bv * (uint64)(aa.limb[10])
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accum15 += bv * (uint64)(aa.limb[11])
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accum0 += bv * (uint64)(aa.limb[12])
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accum1 += bv * (uint64)(aa.limb[13])
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accum2 += bv * (uint64)(aa.limb[14])
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accum3 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-4)^(x448Limbs/2)] += aa.limb[x448Limbs-1-4]
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bv = (uint64)(b.limb[5])
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accum5 += bv * (uint64)(aa.limb[0])
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accum6 += bv * (uint64)(aa.limb[1])
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accum7 += bv * (uint64)(aa.limb[2])
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accum8 += bv * (uint64)(aa.limb[3])
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accum9 += bv * (uint64)(aa.limb[4])
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accum10 += bv * (uint64)(aa.limb[5])
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accum11 += bv * (uint64)(aa.limb[6])
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accum12 += bv * (uint64)(aa.limb[7])
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accum13 += bv * (uint64)(aa.limb[8])
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accum14 += bv * (uint64)(aa.limb[9])
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accum15 += bv * (uint64)(aa.limb[10])
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accum0 += bv * (uint64)(aa.limb[11])
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accum1 += bv * (uint64)(aa.limb[12])
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accum2 += bv * (uint64)(aa.limb[13])
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accum3 += bv * (uint64)(aa.limb[14])
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accum4 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-5)^(x448Limbs/2)] += aa.limb[x448Limbs-1-5]
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bv = (uint64)(b.limb[6])
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accum6 += bv * (uint64)(aa.limb[0])
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accum7 += bv * (uint64)(aa.limb[1])
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accum8 += bv * (uint64)(aa.limb[2])
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accum9 += bv * (uint64)(aa.limb[3])
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accum10 += bv * (uint64)(aa.limb[4])
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accum11 += bv * (uint64)(aa.limb[5])
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accum12 += bv * (uint64)(aa.limb[6])
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accum13 += bv * (uint64)(aa.limb[7])
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accum14 += bv * (uint64)(aa.limb[8])
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accum15 += bv * (uint64)(aa.limb[9])
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accum0 += bv * (uint64)(aa.limb[10])
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accum1 += bv * (uint64)(aa.limb[11])
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accum2 += bv * (uint64)(aa.limb[12])
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accum3 += bv * (uint64)(aa.limb[13])
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accum4 += bv * (uint64)(aa.limb[14])
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accum5 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-6)^(x448Limbs/2)] += aa.limb[x448Limbs-1-6]
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bv = (uint64)(b.limb[7])
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accum7 += bv * (uint64)(aa.limb[0])
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accum8 += bv * (uint64)(aa.limb[1])
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accum9 += bv * (uint64)(aa.limb[2])
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accum10 += bv * (uint64)(aa.limb[3])
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accum11 += bv * (uint64)(aa.limb[4])
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accum12 += bv * (uint64)(aa.limb[5])
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accum13 += bv * (uint64)(aa.limb[6])
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accum14 += bv * (uint64)(aa.limb[7])
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accum15 += bv * (uint64)(aa.limb[8])
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accum0 += bv * (uint64)(aa.limb[9])
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accum1 += bv * (uint64)(aa.limb[10])
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accum2 += bv * (uint64)(aa.limb[11])
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accum3 += bv * (uint64)(aa.limb[12])
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accum4 += bv * (uint64)(aa.limb[13])
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accum5 += bv * (uint64)(aa.limb[14])
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accum6 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-7)^(x448Limbs/2)] += aa.limb[x448Limbs-1-7]
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bv = (uint64)(b.limb[8])
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accum8 += bv * (uint64)(aa.limb[0])
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accum9 += bv * (uint64)(aa.limb[1])
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accum10 += bv * (uint64)(aa.limb[2])
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accum11 += bv * (uint64)(aa.limb[3])
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accum12 += bv * (uint64)(aa.limb[4])
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accum13 += bv * (uint64)(aa.limb[5])
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accum14 += bv * (uint64)(aa.limb[6])
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accum15 += bv * (uint64)(aa.limb[7])
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accum0 += bv * (uint64)(aa.limb[8])
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accum1 += bv * (uint64)(aa.limb[9])
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accum2 += bv * (uint64)(aa.limb[10])
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accum3 += bv * (uint64)(aa.limb[11])
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accum4 += bv * (uint64)(aa.limb[12])
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accum5 += bv * (uint64)(aa.limb[13])
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accum6 += bv * (uint64)(aa.limb[14])
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accum7 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-8)^(x448Limbs/2)] += aa.limb[x448Limbs-1-8]
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bv = (uint64)(b.limb[9])
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accum9 += bv * (uint64)(aa.limb[0])
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accum10 += bv * (uint64)(aa.limb[1])
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accum11 += bv * (uint64)(aa.limb[2])
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accum12 += bv * (uint64)(aa.limb[3])
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accum13 += bv * (uint64)(aa.limb[4])
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accum14 += bv * (uint64)(aa.limb[5])
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accum15 += bv * (uint64)(aa.limb[6])
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accum0 += bv * (uint64)(aa.limb[7])
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accum1 += bv * (uint64)(aa.limb[8])
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accum2 += bv * (uint64)(aa.limb[9])
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accum3 += bv * (uint64)(aa.limb[10])
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accum4 += bv * (uint64)(aa.limb[11])
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accum5 += bv * (uint64)(aa.limb[12])
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accum6 += bv * (uint64)(aa.limb[13])
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accum7 += bv * (uint64)(aa.limb[14])
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accum8 += bv * (uint64)(aa.limb[15])
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aa.limb[(x448Limbs-1-9)^(x448Limbs/2)] += aa.limb[x448Limbs-1-9]
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bv = (uint64)(b.limb[10])
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accum10 += bv * (uint64)(aa.limb[0])
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accum11 += bv * (uint64)(aa.limb[1])
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accum12 += bv * (uint64)(aa.limb[2])
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accum13 += bv * (uint64)(aa.limb[3])
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accum14 += bv * (uint64)(aa.limb[4])
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accum15 += bv * (uint64)(aa.limb[5])
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accum0 += bv * (uint64)(aa.limb[6])
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accum1 += bv * (uint64)(aa.limb[7])
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accum2 += bv * (uint64)(aa.limb[8])
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accum3 += bv * (uint64)(aa.limb[9])
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accum4 += bv * (uint64)(aa.limb[10])
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accum5 += bv * (uint64)(aa.limb[11])
|
||
|
|
accum6 += bv * (uint64)(aa.limb[12])
|
||
|
|
accum7 += bv * (uint64)(aa.limb[13])
|
||
|
|
accum8 += bv * (uint64)(aa.limb[14])
|
||
|
|
accum9 += bv * (uint64)(aa.limb[15])
|
||
|
|
aa.limb[(x448Limbs-1-10)^(x448Limbs/2)] += aa.limb[x448Limbs-1-10]
|
||
|
|
|
||
|
|
bv = (uint64)(b.limb[11])
|
||
|
|
accum11 += bv * (uint64)(aa.limb[0])
|
||
|
|
accum12 += bv * (uint64)(aa.limb[1])
|
||
|
|
accum13 += bv * (uint64)(aa.limb[2])
|
||
|
|
accum14 += bv * (uint64)(aa.limb[3])
|
||
|
|
accum15 += bv * (uint64)(aa.limb[4])
|
||
|
|
accum0 += bv * (uint64)(aa.limb[5])
|
||
|
|
accum1 += bv * (uint64)(aa.limb[6])
|
||
|
|
accum2 += bv * (uint64)(aa.limb[7])
|
||
|
|
accum3 += bv * (uint64)(aa.limb[8])
|
||
|
|
accum4 += bv * (uint64)(aa.limb[9])
|
||
|
|
accum5 += bv * (uint64)(aa.limb[10])
|
||
|
|
accum6 += bv * (uint64)(aa.limb[11])
|
||
|
|
accum7 += bv * (uint64)(aa.limb[12])
|
||
|
|
accum8 += bv * (uint64)(aa.limb[13])
|
||
|
|
accum9 += bv * (uint64)(aa.limb[14])
|
||
|
|
accum10 += bv * (uint64)(aa.limb[15])
|
||
|
|
aa.limb[(x448Limbs-1-11)^(x448Limbs/2)] += aa.limb[x448Limbs-1-11]
|
||
|
|
|
||
|
|
bv = (uint64)(b.limb[12])
|
||
|
|
accum12 += bv * (uint64)(aa.limb[0])
|
||
|
|
accum13 += bv * (uint64)(aa.limb[1])
|
||
|
|
accum14 += bv * (uint64)(aa.limb[2])
|
||
|
|
accum15 += bv * (uint64)(aa.limb[3])
|
||
|
|
accum0 += bv * (uint64)(aa.limb[4])
|
||
|
|
accum1 += bv * (uint64)(aa.limb[5])
|
||
|
|
accum2 += bv * (uint64)(aa.limb[6])
|
||
|
|
accum3 += bv * (uint64)(aa.limb[7])
|
||
|
|
accum4 += bv * (uint64)(aa.limb[8])
|
||
|
|
accum5 += bv * (uint64)(aa.limb[9])
|
||
|
|
accum6 += bv * (uint64)(aa.limb[10])
|
||
|
|
accum7 += bv * (uint64)(aa.limb[11])
|
||
|
|
accum8 += bv * (uint64)(aa.limb[12])
|
||
|
|
accum9 += bv * (uint64)(aa.limb[13])
|
||
|
|
accum10 += bv * (uint64)(aa.limb[14])
|
||
|
|
accum11 += bv * (uint64)(aa.limb[15])
|
||
|
|
aa.limb[(x448Limbs-1-12)^(x448Limbs/2)] += aa.limb[x448Limbs-1-12]
|
||
|
|
|
||
|
|
bv = (uint64)(b.limb[13])
|
||
|
|
accum13 += bv * (uint64)(aa.limb[0])
|
||
|
|
accum14 += bv * (uint64)(aa.limb[1])
|
||
|
|
accum15 += bv * (uint64)(aa.limb[2])
|
||
|
|
accum0 += bv * (uint64)(aa.limb[3])
|
||
|
|
accum1 += bv * (uint64)(aa.limb[4])
|
||
|
|
accum2 += bv * (uint64)(aa.limb[5])
|
||
|
|
accum3 += bv * (uint64)(aa.limb[6])
|
||
|
|
accum4 += bv * (uint64)(aa.limb[7])
|
||
|
|
accum5 += bv * (uint64)(aa.limb[8])
|
||
|
|
accum6 += bv * (uint64)(aa.limb[9])
|
||
|
|
accum7 += bv * (uint64)(aa.limb[10])
|
||
|
|
accum8 += bv * (uint64)(aa.limb[11])
|
||
|
|
accum9 += bv * (uint64)(aa.limb[12])
|
||
|
|
accum10 += bv * (uint64)(aa.limb[13])
|
||
|
|
accum11 += bv * (uint64)(aa.limb[14])
|
||
|
|
accum12 += bv * (uint64)(aa.limb[15])
|
||
|
|
aa.limb[(x448Limbs-1-13)^(x448Limbs/2)] += aa.limb[x448Limbs-1-13]
|
||
|
|
|
||
|
|
bv = (uint64)(b.limb[14])
|
||
|
|
accum14 += bv * (uint64)(aa.limb[0])
|
||
|
|
accum15 += bv * (uint64)(aa.limb[1])
|
||
|
|
accum0 += bv * (uint64)(aa.limb[2])
|
||
|
|
accum1 += bv * (uint64)(aa.limb[3])
|
||
|
|
accum2 += bv * (uint64)(aa.limb[4])
|
||
|
|
accum3 += bv * (uint64)(aa.limb[5])
|
||
|
|
accum4 += bv * (uint64)(aa.limb[6])
|
||
|
|
accum5 += bv * (uint64)(aa.limb[7])
|
||
|
|
accum6 += bv * (uint64)(aa.limb[8])
|
||
|
|
accum7 += bv * (uint64)(aa.limb[9])
|
||
|
|
accum8 += bv * (uint64)(aa.limb[10])
|
||
|
|
accum9 += bv * (uint64)(aa.limb[11])
|
||
|
|
accum10 += bv * (uint64)(aa.limb[12])
|
||
|
|
accum11 += bv * (uint64)(aa.limb[13])
|
||
|
|
accum12 += bv * (uint64)(aa.limb[14])
|
||
|
|
accum13 += bv * (uint64)(aa.limb[15])
|
||
|
|
aa.limb[(x448Limbs-1-14)^(x448Limbs/2)] += aa.limb[x448Limbs-1-14]
|
||
|
|
|
||
|
|
bv = (uint64)(b.limb[15])
|
||
|
|
accum15 += bv * (uint64)(aa.limb[0])
|
||
|
|
accum0 += bv * (uint64)(aa.limb[1])
|
||
|
|
accum1 += bv * (uint64)(aa.limb[2])
|
||
|
|
accum2 += bv * (uint64)(aa.limb[3])
|
||
|
|
accum3 += bv * (uint64)(aa.limb[4])
|
||
|
|
accum4 += bv * (uint64)(aa.limb[5])
|
||
|
|
accum5 += bv * (uint64)(aa.limb[6])
|
||
|
|
accum6 += bv * (uint64)(aa.limb[7])
|
||
|
|
accum7 += bv * (uint64)(aa.limb[8])
|
||
|
|
accum8 += bv * (uint64)(aa.limb[9])
|
||
|
|
accum9 += bv * (uint64)(aa.limb[10])
|
||
|
|
accum10 += bv * (uint64)(aa.limb[11])
|
||
|
|
accum11 += bv * (uint64)(aa.limb[12])
|
||
|
|
accum12 += bv * (uint64)(aa.limb[13])
|
||
|
|
accum13 += bv * (uint64)(aa.limb[14])
|
||
|
|
accum14 += bv * (uint64)(aa.limb[15])
|
||
|
|
aa.limb[(x448Limbs-1-15)^(x448Limbs/2)] += aa.limb[x448Limbs-1-15]
|
||
|
|
|
||
|
|
// accum[x448Limbs-1] += accum[x448Limbs-2] >> lBits
|
||
|
|
// accum[x448Limbs-2] &= lMask
|
||
|
|
// accum[x448Limbs/2] += accum[x448Limbs-1] >> lBits
|
||
|
|
accum15 += accum14 >> lBits
|
||
|
|
accum14 &= lMask
|
||
|
|
accum8 += accum15 >> lBits
|
||
|
|
|
||
|
|
// for j := uint(0); j < x448Limbs; j++ {
|
||
|
|
// accum[j] += accum[(j-1)%x448Limbs] >> lBits
|
||
|
|
// accum[(j-1)%x448Limbs] &= lMask
|
||
|
|
// }
|
||
|
|
accum0 += accum15 >> lBits
|
||
|
|
accum15 &= lMask
|
||
|
|
accum1 += accum0 >> lBits
|
||
|
|
accum0 &= lMask
|
||
|
|
accum2 += accum1 >> lBits
|
||
|
|
accum1 &= lMask
|
||
|
|
accum3 += accum2 >> lBits
|
||
|
|
accum2 &= lMask
|
||
|
|
accum4 += accum3 >> lBits
|
||
|
|
accum3 &= lMask
|
||
|
|
accum5 += accum4 >> lBits
|
||
|
|
accum4 &= lMask
|
||
|
|
accum6 += accum5 >> lBits
|
||
|
|
accum5 &= lMask
|
||
|
|
accum7 += accum6 >> lBits
|
||
|
|
accum6 &= lMask
|
||
|
|
accum8 += accum7 >> lBits
|
||
|
|
accum7 &= lMask
|
||
|
|
accum9 += accum8 >> lBits
|
||
|
|
accum8 &= lMask
|
||
|
|
accum10 += accum9 >> lBits
|
||
|
|
accum9 &= lMask
|
||
|
|
accum11 += accum10 >> lBits
|
||
|
|
accum10 &= lMask
|
||
|
|
accum12 += accum11 >> lBits
|
||
|
|
accum11 &= lMask
|
||
|
|
accum13 += accum12 >> lBits
|
||
|
|
accum12 &= lMask
|
||
|
|
accum14 += accum13 >> lBits
|
||
|
|
accum13 &= lMask
|
||
|
|
accum15 += accum14 >> lBits
|
||
|
|
accum14 &= lMask
|
||
|
|
|
||
|
|
// for j, accv := range accum {
|
||
|
|
// c.limb[j] = (uint32)(accv)
|
||
|
|
// }
|
||
|
|
c.limb[0] = (uint32)(accum0)
|
||
|
|
c.limb[1] = (uint32)(accum1)
|
||
|
|
c.limb[2] = (uint32)(accum2)
|
||
|
|
c.limb[3] = (uint32)(accum3)
|
||
|
|
c.limb[4] = (uint32)(accum4)
|
||
|
|
c.limb[5] = (uint32)(accum5)
|
||
|
|
c.limb[6] = (uint32)(accum6)
|
||
|
|
c.limb[7] = (uint32)(accum7)
|
||
|
|
c.limb[8] = (uint32)(accum8)
|
||
|
|
c.limb[9] = (uint32)(accum9)
|
||
|
|
c.limb[10] = (uint32)(accum10)
|
||
|
|
c.limb[11] = (uint32)(accum11)
|
||
|
|
c.limb[12] = (uint32)(accum12)
|
||
|
|
c.limb[13] = (uint32)(accum13)
|
||
|
|
c.limb[14] = (uint32)(accum14)
|
||
|
|
c.limb[15] = (uint32)(accum15)
|
||
|
|
}
|
||
|
|
|
||
|
|
// sqr squares (c = x * x). Just calls multiply. (PERF)
|
||
|
|
func (c *gf) sqr(x *gf) {
|
||
|
|
c.mul(x, x)
|
||
|
|
}
|
||
|
|
|
||
|
|
// isqrt inverse square roots (y = 1/sqrt(x)), using an addition chain.
|
||
|
|
func (y *gf) isqrt(x *gf) {
|
||
|
|
var a, b, c gf
|
||
|
|
c.sqr(x)
|
||
|
|
|
||
|
|
// XXX/Yawning, could unroll, but this is called only once.
|
||
|
|
|
||
|
|
// STEP(b,x,1);
|
||
|
|
b.mul(x, &c)
|
||
|
|
c.cpy(&b)
|
||
|
|
for i := 0; i < 1; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// STEP(b,x,3);
|
||
|
|
b.mul(x, &c)
|
||
|
|
c.cpy(&b)
|
||
|
|
for i := 0; i < 3; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
//STEP(a,b,3);
|
||
|
|
a.mul(&b, &c)
|
||
|
|
c.cpy(&a)
|
||
|
|
for i := 0; i < 3; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// STEP(a,b,9);
|
||
|
|
a.mul(&b, &c)
|
||
|
|
c.cpy(&a)
|
||
|
|
for i := 0; i < 9; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// STEP(b,a,1);
|
||
|
|
b.mul(&a, &c)
|
||
|
|
c.cpy(&b)
|
||
|
|
for i := 0; i < 1; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// STEP(a,x,18);
|
||
|
|
a.mul(x, &c)
|
||
|
|
c.cpy(&a)
|
||
|
|
for i := 0; i < 18; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// STEP(a,b,37);
|
||
|
|
a.mul(&b, &c)
|
||
|
|
c.cpy(&a)
|
||
|
|
for i := 0; i < 37; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// STEP(b,a,37);
|
||
|
|
b.mul(&a, &c)
|
||
|
|
c.cpy(&b)
|
||
|
|
for i := 0; i < 37; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// STEP(b,a,111);
|
||
|
|
b.mul(&a, &c)
|
||
|
|
c.cpy(&b)
|
||
|
|
for i := 0; i < 111; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// STEP(a,b,1);
|
||
|
|
a.mul(&b, &c)
|
||
|
|
c.cpy(&a)
|
||
|
|
for i := 0; i < 1; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// STEP(b,x,223);
|
||
|
|
b.mul(x, &c)
|
||
|
|
c.cpy(&b)
|
||
|
|
for i := 0; i < 223; i++ {
|
||
|
|
c.sqr(&c)
|
||
|
|
}
|
||
|
|
|
||
|
|
y.mul(&a, &c)
|
||
|
|
}
|
||
|
|
|
||
|
|
// inv inverses (y = 1/x).
|
||
|
|
func (y *gf) inv(x *gf) {
|
||
|
|
var z, w gf
|
||
|
|
z.sqr(x) // x^2
|
||
|
|
w.isqrt(&z) // +- 1/sqrt(x^2) = +- 1/x
|
||
|
|
z.sqr(&w) // 1/x^2
|
||
|
|
w.mul(x, &z) // 1/x
|
||
|
|
y.cpy(&w)
|
||
|
|
}
|
||
|
|
|
||
|
|
// reduce weakly reduces mod p
|
||
|
|
func (x *gf) reduce() {
|
||
|
|
x.limb[x448Limbs/2] += x.limb[x448Limbs-1] >> lBits
|
||
|
|
|
||
|
|
// for j := uint(0); j < x448Limbs; j++ {
|
||
|
|
// x.limb[j] += x.limb[(j-1)%x448Limbs] >> lBits
|
||
|
|
// x.limb[(j-1)%x448Limbs] &= lMask
|
||
|
|
// }
|
||
|
|
x.limb[0] += x.limb[15] >> lBits
|
||
|
|
x.limb[15] &= lMask
|
||
|
|
x.limb[1] += x.limb[0] >> lBits
|
||
|
|
x.limb[0] &= lMask
|
||
|
|
x.limb[2] += x.limb[1] >> lBits
|
||
|
|
x.limb[1] &= lMask
|
||
|
|
x.limb[3] += x.limb[2] >> lBits
|
||
|
|
x.limb[2] &= lMask
|
||
|
|
x.limb[4] += x.limb[3] >> lBits
|
||
|
|
x.limb[3] &= lMask
|
||
|
|
x.limb[5] += x.limb[4] >> lBits
|
||
|
|
x.limb[4] &= lMask
|
||
|
|
x.limb[6] += x.limb[5] >> lBits
|
||
|
|
x.limb[5] &= lMask
|
||
|
|
x.limb[7] += x.limb[6] >> lBits
|
||
|
|
x.limb[6] &= lMask
|
||
|
|
x.limb[8] += x.limb[7] >> lBits
|
||
|
|
x.limb[7] &= lMask
|
||
|
|
x.limb[9] += x.limb[8] >> lBits
|
||
|
|
x.limb[8] &= lMask
|
||
|
|
x.limb[10] += x.limb[9] >> lBits
|
||
|
|
x.limb[9] &= lMask
|
||
|
|
x.limb[11] += x.limb[10] >> lBits
|
||
|
|
x.limb[10] &= lMask
|
||
|
|
x.limb[12] += x.limb[11] >> lBits
|
||
|
|
x.limb[11] &= lMask
|
||
|
|
x.limb[13] += x.limb[12] >> lBits
|
||
|
|
x.limb[12] &= lMask
|
||
|
|
x.limb[14] += x.limb[13] >> lBits
|
||
|
|
x.limb[13] &= lMask
|
||
|
|
x.limb[15] += x.limb[14] >> lBits
|
||
|
|
x.limb[14] &= lMask
|
||
|
|
}
|
||
|
|
|
||
|
|
// add adds mod p. Conservatively always weak-reduces. (PERF)
|
||
|
|
func (x *gf) add(y, z *gf) {
|
||
|
|
// for i, yv := range y.limb {
|
||
|
|
// x.limb[i] = yv + z.limb[i]
|
||
|
|
// }
|
||
|
|
x.limb[0] = y.limb[0] + z.limb[0]
|
||
|
|
x.limb[1] = y.limb[1] + z.limb[1]
|
||
|
|
x.limb[2] = y.limb[2] + z.limb[2]
|
||
|
|
x.limb[3] = y.limb[3] + z.limb[3]
|
||
|
|
x.limb[4] = y.limb[4] + z.limb[4]
|
||
|
|
x.limb[5] = y.limb[5] + z.limb[5]
|
||
|
|
x.limb[6] = y.limb[6] + z.limb[6]
|
||
|
|
x.limb[7] = y.limb[7] + z.limb[7]
|
||
|
|
x.limb[8] = y.limb[8] + z.limb[8]
|
||
|
|
x.limb[9] = y.limb[9] + z.limb[9]
|
||
|
|
x.limb[10] = y.limb[10] + z.limb[10]
|
||
|
|
x.limb[11] = y.limb[11] + z.limb[11]
|
||
|
|
x.limb[12] = y.limb[12] + z.limb[12]
|
||
|
|
x.limb[13] = y.limb[13] + z.limb[13]
|
||
|
|
x.limb[14] = y.limb[14] + z.limb[14]
|
||
|
|
x.limb[15] = y.limb[15] + z.limb[15]
|
||
|
|
|
||
|
|
x.reduce()
|
||
|
|
}
|
||
|
|
|
||
|
|
// sub subtracts mod p. Conservatively always weak-reduces. (PERF)
|
||
|
|
func (x *gf) sub(y, z *gf) {
|
||
|
|
// for i, yv := range y.limb {
|
||
|
|
// x.limb[i] = yv - z.limb[i] + 2*p.limb[i]
|
||
|
|
// }
|
||
|
|
x.limb[0] = y.limb[0] - z.limb[0] + 2*lMask
|
||
|
|
x.limb[1] = y.limb[1] - z.limb[1] + 2*lMask
|
||
|
|
x.limb[2] = y.limb[2] - z.limb[2] + 2*lMask
|
||
|
|
x.limb[3] = y.limb[3] - z.limb[3] + 2*lMask
|
||
|
|
x.limb[4] = y.limb[4] - z.limb[4] + 2*lMask
|
||
|
|
x.limb[5] = y.limb[5] - z.limb[5] + 2*lMask
|
||
|
|
x.limb[6] = y.limb[6] - z.limb[6] + 2*lMask
|
||
|
|
x.limb[7] = y.limb[7] - z.limb[7] + 2*lMask
|
||
|
|
x.limb[8] = y.limb[8] - z.limb[8] + 2*(lMask-1)
|
||
|
|
x.limb[9] = y.limb[9] - z.limb[9] + 2*lMask
|
||
|
|
x.limb[10] = y.limb[10] - z.limb[10] + 2*lMask
|
||
|
|
x.limb[11] = y.limb[11] - z.limb[11] + 2*lMask
|
||
|
|
x.limb[12] = y.limb[12] - z.limb[12] + 2*lMask
|
||
|
|
x.limb[13] = y.limb[13] - z.limb[13] + 2*lMask
|
||
|
|
x.limb[14] = y.limb[14] - z.limb[14] + 2*lMask
|
||
|
|
x.limb[15] = y.limb[15] - z.limb[15] + 2*lMask
|
||
|
|
|
||
|
|
x.reduce()
|
||
|
|
}
|
||
|
|
|
||
|
|
// condSwap swaps x and y in constant time.
|
||
|
|
func (x *gf) condSwap(y *gf, swap limbUint) {
|
||
|
|
// for i, xv := range x.limb {
|
||
|
|
// s := (xv ^ y.limb[i]) & (uint32)(swap) // Sort of dumb, oh well.
|
||
|
|
// x.limb[i] ^= s
|
||
|
|
// y.limb[i] ^= s
|
||
|
|
// }
|
||
|
|
|
||
|
|
var s uint32
|
||
|
|
|
||
|
|
s = (x.limb[0] ^ y.limb[0]) & (uint32)(swap)
|
||
|
|
x.limb[0] ^= s
|
||
|
|
y.limb[0] ^= s
|
||
|
|
s = (x.limb[1] ^ y.limb[1]) & (uint32)(swap)
|
||
|
|
x.limb[1] ^= s
|
||
|
|
y.limb[1] ^= s
|
||
|
|
s = (x.limb[2] ^ y.limb[2]) & (uint32)(swap)
|
||
|
|
x.limb[2] ^= s
|
||
|
|
y.limb[2] ^= s
|
||
|
|
s = (x.limb[3] ^ y.limb[3]) & (uint32)(swap)
|
||
|
|
x.limb[3] ^= s
|
||
|
|
y.limb[3] ^= s
|
||
|
|
s = (x.limb[4] ^ y.limb[4]) & (uint32)(swap)
|
||
|
|
x.limb[4] ^= s
|
||
|
|
y.limb[4] ^= s
|
||
|
|
s = (x.limb[5] ^ y.limb[5]) & (uint32)(swap)
|
||
|
|
x.limb[5] ^= s
|
||
|
|
y.limb[5] ^= s
|
||
|
|
s = (x.limb[6] ^ y.limb[6]) & (uint32)(swap)
|
||
|
|
x.limb[6] ^= s
|
||
|
|
y.limb[6] ^= s
|
||
|
|
s = (x.limb[7] ^ y.limb[7]) & (uint32)(swap)
|
||
|
|
x.limb[7] ^= s
|
||
|
|
y.limb[7] ^= s
|
||
|
|
s = (x.limb[8] ^ y.limb[8]) & (uint32)(swap)
|
||
|
|
x.limb[8] ^= s
|
||
|
|
y.limb[8] ^= s
|
||
|
|
s = (x.limb[9] ^ y.limb[9]) & (uint32)(swap)
|
||
|
|
x.limb[9] ^= s
|
||
|
|
y.limb[9] ^= s
|
||
|
|
s = (x.limb[10] ^ y.limb[10]) & (uint32)(swap)
|
||
|
|
x.limb[10] ^= s
|
||
|
|
y.limb[10] ^= s
|
||
|
|
s = (x.limb[11] ^ y.limb[11]) & (uint32)(swap)
|
||
|
|
x.limb[11] ^= s
|
||
|
|
y.limb[11] ^= s
|
||
|
|
s = (x.limb[12] ^ y.limb[12]) & (uint32)(swap)
|
||
|
|
x.limb[12] ^= s
|
||
|
|
y.limb[12] ^= s
|
||
|
|
s = (x.limb[13] ^ y.limb[13]) & (uint32)(swap)
|
||
|
|
x.limb[13] ^= s
|
||
|
|
y.limb[13] ^= s
|
||
|
|
s = (x.limb[14] ^ y.limb[14]) & (uint32)(swap)
|
||
|
|
x.limb[14] ^= s
|
||
|
|
y.limb[14] ^= s
|
||
|
|
s = (x.limb[15] ^ y.limb[15]) & (uint32)(swap)
|
||
|
|
x.limb[15] ^= s
|
||
|
|
y.limb[15] ^= s
|
||
|
|
}
|
||
|
|
|
||
|
|
// mlw multiplies by a signed int. NOT CONSTANT TIME wrt the sign of the int,
|
||
|
|
// but that's ok because it's only ever called with w = -edwardsD. Just uses
|
||
|
|
// a full multiply. (PERF)
|
||
|
|
func (a *gf) mlw(b *gf, w int) {
|
||
|
|
if w > 0 {
|
||
|
|
ww := gf{[x448Limbs]uint32{(uint32)(w)}}
|
||
|
|
a.mul(b, &ww)
|
||
|
|
} else {
|
||
|
|
// This branch is *NEVER* taken with the current code.
|
||
|
|
panic("mul called with negative w")
|
||
|
|
ww := gf{[x448Limbs]uint32{(uint32)(-w)}}
|
||
|
|
a.mul(b, &ww)
|
||
|
|
a.sub(&zero, a)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// canon canonicalizes.
|
||
|
|
func (a *gf) canon() {
|
||
|
|
a.reduce()
|
||
|
|
|
||
|
|
// Subtract p with borrow.
|
||
|
|
var carry int64
|
||
|
|
for i, v := range a.limb {
|
||
|
|
carry = carry + (int64)(v) - (int64)(p.limb[i])
|
||
|
|
a.limb[i] = (uint32)(carry & lMask)
|
||
|
|
carry >>= lBits
|
||
|
|
}
|
||
|
|
|
||
|
|
addback := carry
|
||
|
|
carry = 0
|
||
|
|
|
||
|
|
// Add it back.
|
||
|
|
for i, v := range a.limb {
|
||
|
|
carry = carry + (int64)(v) + (int64)(p.limb[i]&(uint32)(addback))
|
||
|
|
a.limb[i] = uint32(carry & lMask)
|
||
|
|
carry >>= lBits
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// deser deserializes into the limb representation.
|
||
|
|
func (s *gf) deser(ser *[x448Bytes]byte) {
|
||
|
|
var buf uint64
|
||
|
|
bits := uint(0)
|
||
|
|
k := 0
|
||
|
|
|
||
|
|
for i, v := range ser {
|
||
|
|
buf |= (uint64)(v) << bits
|
||
|
|
for bits += 8; (bits >= lBits || i == x448Bytes-1) && k < x448Limbs; bits, buf = bits-lBits, buf>>lBits {
|
||
|
|
s.limb[k] = (uint32)(buf & lMask)
|
||
|
|
k++
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// ser serializes into byte representation.
|
||
|
|
func (a *gf) ser(ser *[x448Bytes]byte) {
|
||
|
|
a.canon()
|
||
|
|
k := 0
|
||
|
|
bits := uint(0)
|
||
|
|
var buf uint64
|
||
|
|
for i, v := range a.limb {
|
||
|
|
buf |= (uint64)(v) << bits
|
||
|
|
for bits += lBits; (bits >= 8 || i == x448Limbs-1) && k < x448Bytes; bits, buf = bits-8, buf>>8 {
|
||
|
|
ser[k] = (byte)(buf)
|
||
|
|
k++
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func init() {
|
||
|
|
if x448Limbs != 16 {
|
||
|
|
panic("x448Limbs != 16, unrolled loops likely broken")
|
||
|
|
}
|
||
|
|
}
|