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nobs/ec/x448/x448_ref.go
Kris Kwiatkowski c88bbf0f75
x448: Export shared secret size (#3) 
Changes x448Bytes variable to SharedSecretSize
2018-08-03 14:36:45 +01:00

779 lines
22 KiB
Go
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// The MIT License (MIT)
//
// Copyright (c) 2014-2015 Cryptography Research, Inc.
// Copyright (c) 2015 Yawning Angel.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
package x448
// This should really use 64 bit limbs, but Go is fucking retarded and doesn't
// have __(u)int128_t, so the 32 bit code it is, at a hefty performance
// penalty. Fuck my life, I'm going to have to bust out PeachPy to get this
// to go fast aren't I.
const (
wBits = 32
lBits = (wBits * 7 / 8)
x448Limbs = (448 / lBits)
lMask = (1 << lBits) - 1
)
type limbUint uint32
type limbSint int32
type gf struct {
limb [x448Limbs]uint32
}
var zero = gf{[x448Limbs]uint32{0}}
var one = gf{[x448Limbs]uint32{1}}
var p = gf{[x448Limbs]uint32{
lMask, lMask, lMask, lMask, lMask, lMask, lMask, lMask,
lMask - 1, lMask, lMask, lMask, lMask, lMask, lMask, lMask,
}}
// cpy copies x = y.
func (x *gf) cpy(y *gf) {
// for i, v := range y.limb {
// x.limb[i] = v
// }
copy(x.limb[:], y.limb[:])
}
// mul multiplies c = a * b. (PERF)
func (c *gf) mul(a, b *gf) {
var aa gf
aa.cpy(a)
//
// This is *by far* the most CPU intesive routine in the code.
//
// var accum [x448Limbs]uint64
// for i, bv := range b.limb {
// for j, aav := range aa.limb {
// accum[(i+j)%x448Limbs] += (uint64)(bv) * (uint64)(aav)
// }
// aa.limb[(x448Limbs-1-i)^(x448Limbs/2)] += aa.limb[x448Limbs-1-i]
// }
// So fucking stupid that this is actually a fairly massive gain.
var accum0, accum1, accum2, accum3, accum4, accum5, accum6, accum7, accum8, accum9, accum10, accum11, accum12, accum13, accum14, accum15 uint64
var bv uint64
bv = (uint64)(b.limb[0])
accum0 += bv * (uint64)(aa.limb[0])
accum1 += bv * (uint64)(aa.limb[1])
accum2 += bv * (uint64)(aa.limb[2])
accum3 += bv * (uint64)(aa.limb[3])
accum4 += bv * (uint64)(aa.limb[4])
accum5 += bv * (uint64)(aa.limb[5])
accum6 += bv * (uint64)(aa.limb[6])
accum7 += bv * (uint64)(aa.limb[7])
accum8 += bv * (uint64)(aa.limb[8])
accum9 += bv * (uint64)(aa.limb[9])
accum10 += bv * (uint64)(aa.limb[10])
accum11 += bv * (uint64)(aa.limb[11])
accum12 += bv * (uint64)(aa.limb[12])
accum13 += bv * (uint64)(aa.limb[13])
accum14 += bv * (uint64)(aa.limb[14])
accum15 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-0)^(x448Limbs/2)] += aa.limb[x448Limbs-1-0]
bv = (uint64)(b.limb[1])
accum1 += bv * (uint64)(aa.limb[0])
accum2 += bv * (uint64)(aa.limb[1])
accum3 += bv * (uint64)(aa.limb[2])
accum4 += bv * (uint64)(aa.limb[3])
accum5 += bv * (uint64)(aa.limb[4])
accum6 += bv * (uint64)(aa.limb[5])
accum7 += bv * (uint64)(aa.limb[6])
accum8 += bv * (uint64)(aa.limb[7])
accum9 += bv * (uint64)(aa.limb[8])
accum10 += bv * (uint64)(aa.limb[9])
accum11 += bv * (uint64)(aa.limb[10])
accum12 += bv * (uint64)(aa.limb[11])
accum13 += bv * (uint64)(aa.limb[12])
accum14 += bv * (uint64)(aa.limb[13])
accum15 += bv * (uint64)(aa.limb[14])
accum0 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-1)^(x448Limbs/2)] += aa.limb[x448Limbs-1-1]
bv = (uint64)(b.limb[2])
accum2 += bv * (uint64)(aa.limb[0])
accum3 += bv * (uint64)(aa.limb[1])
accum4 += bv * (uint64)(aa.limb[2])
accum5 += bv * (uint64)(aa.limb[3])
accum6 += bv * (uint64)(aa.limb[4])
accum7 += bv * (uint64)(aa.limb[5])
accum8 += bv * (uint64)(aa.limb[6])
accum9 += bv * (uint64)(aa.limb[7])
accum10 += bv * (uint64)(aa.limb[8])
accum11 += bv * (uint64)(aa.limb[9])
accum12 += bv * (uint64)(aa.limb[10])
accum13 += bv * (uint64)(aa.limb[11])
accum14 += bv * (uint64)(aa.limb[12])
accum15 += bv * (uint64)(aa.limb[13])
accum0 += bv * (uint64)(aa.limb[14])
accum1 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-2)^(x448Limbs/2)] += aa.limb[x448Limbs-1-2]
bv = (uint64)(b.limb[3])
accum3 += bv * (uint64)(aa.limb[0])
accum4 += bv * (uint64)(aa.limb[1])
accum5 += bv * (uint64)(aa.limb[2])
accum6 += bv * (uint64)(aa.limb[3])
accum7 += bv * (uint64)(aa.limb[4])
accum8 += bv * (uint64)(aa.limb[5])
accum9 += bv * (uint64)(aa.limb[6])
accum10 += bv * (uint64)(aa.limb[7])
accum11 += bv * (uint64)(aa.limb[8])
accum12 += bv * (uint64)(aa.limb[9])
accum13 += bv * (uint64)(aa.limb[10])
accum14 += bv * (uint64)(aa.limb[11])
accum15 += bv * (uint64)(aa.limb[12])
accum0 += bv * (uint64)(aa.limb[13])
accum1 += bv * (uint64)(aa.limb[14])
accum2 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-3)^(x448Limbs/2)] += aa.limb[x448Limbs-1-3]
bv = (uint64)(b.limb[4])
accum4 += bv * (uint64)(aa.limb[0])
accum5 += bv * (uint64)(aa.limb[1])
accum6 += bv * (uint64)(aa.limb[2])
accum7 += bv * (uint64)(aa.limb[3])
accum8 += bv * (uint64)(aa.limb[4])
accum9 += bv * (uint64)(aa.limb[5])
accum10 += bv * (uint64)(aa.limb[6])
accum11 += bv * (uint64)(aa.limb[7])
accum12 += bv * (uint64)(aa.limb[8])
accum13 += bv * (uint64)(aa.limb[9])
accum14 += bv * (uint64)(aa.limb[10])
accum15 += bv * (uint64)(aa.limb[11])
accum0 += bv * (uint64)(aa.limb[12])
accum1 += bv * (uint64)(aa.limb[13])
accum2 += bv * (uint64)(aa.limb[14])
accum3 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-4)^(x448Limbs/2)] += aa.limb[x448Limbs-1-4]
bv = (uint64)(b.limb[5])
accum5 += bv * (uint64)(aa.limb[0])
accum6 += bv * (uint64)(aa.limb[1])
accum7 += bv * (uint64)(aa.limb[2])
accum8 += bv * (uint64)(aa.limb[3])
accum9 += bv * (uint64)(aa.limb[4])
accum10 += bv * (uint64)(aa.limb[5])
accum11 += bv * (uint64)(aa.limb[6])
accum12 += bv * (uint64)(aa.limb[7])
accum13 += bv * (uint64)(aa.limb[8])
accum14 += bv * (uint64)(aa.limb[9])
accum15 += bv * (uint64)(aa.limb[10])
accum0 += bv * (uint64)(aa.limb[11])
accum1 += bv * (uint64)(aa.limb[12])
accum2 += bv * (uint64)(aa.limb[13])
accum3 += bv * (uint64)(aa.limb[14])
accum4 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-5)^(x448Limbs/2)] += aa.limb[x448Limbs-1-5]
bv = (uint64)(b.limb[6])
accum6 += bv * (uint64)(aa.limb[0])
accum7 += bv * (uint64)(aa.limb[1])
accum8 += bv * (uint64)(aa.limb[2])
accum9 += bv * (uint64)(aa.limb[3])
accum10 += bv * (uint64)(aa.limb[4])
accum11 += bv * (uint64)(aa.limb[5])
accum12 += bv * (uint64)(aa.limb[6])
accum13 += bv * (uint64)(aa.limb[7])
accum14 += bv * (uint64)(aa.limb[8])
accum15 += bv * (uint64)(aa.limb[9])
accum0 += bv * (uint64)(aa.limb[10])
accum1 += bv * (uint64)(aa.limb[11])
accum2 += bv * (uint64)(aa.limb[12])
accum3 += bv * (uint64)(aa.limb[13])
accum4 += bv * (uint64)(aa.limb[14])
accum5 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-6)^(x448Limbs/2)] += aa.limb[x448Limbs-1-6]
bv = (uint64)(b.limb[7])
accum7 += bv * (uint64)(aa.limb[0])
accum8 += bv * (uint64)(aa.limb[1])
accum9 += bv * (uint64)(aa.limb[2])
accum10 += bv * (uint64)(aa.limb[3])
accum11 += bv * (uint64)(aa.limb[4])
accum12 += bv * (uint64)(aa.limb[5])
accum13 += bv * (uint64)(aa.limb[6])
accum14 += bv * (uint64)(aa.limb[7])
accum15 += bv * (uint64)(aa.limb[8])
accum0 += bv * (uint64)(aa.limb[9])
accum1 += bv * (uint64)(aa.limb[10])
accum2 += bv * (uint64)(aa.limb[11])
accum3 += bv * (uint64)(aa.limb[12])
accum4 += bv * (uint64)(aa.limb[13])
accum5 += bv * (uint64)(aa.limb[14])
accum6 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-7)^(x448Limbs/2)] += aa.limb[x448Limbs-1-7]
bv = (uint64)(b.limb[8])
accum8 += bv * (uint64)(aa.limb[0])
accum9 += bv * (uint64)(aa.limb[1])
accum10 += bv * (uint64)(aa.limb[2])
accum11 += bv * (uint64)(aa.limb[3])
accum12 += bv * (uint64)(aa.limb[4])
accum13 += bv * (uint64)(aa.limb[5])
accum14 += bv * (uint64)(aa.limb[6])
accum15 += bv * (uint64)(aa.limb[7])
accum0 += bv * (uint64)(aa.limb[8])
accum1 += bv * (uint64)(aa.limb[9])
accum2 += bv * (uint64)(aa.limb[10])
accum3 += bv * (uint64)(aa.limb[11])
accum4 += bv * (uint64)(aa.limb[12])
accum5 += bv * (uint64)(aa.limb[13])
accum6 += bv * (uint64)(aa.limb[14])
accum7 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-8)^(x448Limbs/2)] += aa.limb[x448Limbs-1-8]
bv = (uint64)(b.limb[9])
accum9 += bv * (uint64)(aa.limb[0])
accum10 += bv * (uint64)(aa.limb[1])
accum11 += bv * (uint64)(aa.limb[2])
accum12 += bv * (uint64)(aa.limb[3])
accum13 += bv * (uint64)(aa.limb[4])
accum14 += bv * (uint64)(aa.limb[5])
accum15 += bv * (uint64)(aa.limb[6])
accum0 += bv * (uint64)(aa.limb[7])
accum1 += bv * (uint64)(aa.limb[8])
accum2 += bv * (uint64)(aa.limb[9])
accum3 += bv * (uint64)(aa.limb[10])
accum4 += bv * (uint64)(aa.limb[11])
accum5 += bv * (uint64)(aa.limb[12])
accum6 += bv * (uint64)(aa.limb[13])
accum7 += bv * (uint64)(aa.limb[14])
accum8 += bv * (uint64)(aa.limb[15])
aa.limb[(x448Limbs-1-9)^(x448Limbs/2)] += aa.limb[x448Limbs-1-9]
bv = (uint64)(b.limb[10])
accum10 += bv * (uint64)(aa.limb[0])
accum11 += bv * (uint64)(aa.limb[1])
accum12 += bv * (uint64)(aa.limb[2])
accum13 += bv * (uint64)(aa.limb[3])
accum14 += bv * (uint64)(aa.limb[4])
accum15 += bv * (uint64)(aa.limb[5])
accum0 += bv * (uint64)(aa.limb[6])
accum1 += bv * (uint64)(aa.limb[7])
accum2 += bv * (uint64)(aa.limb[8])
accum3 += bv * (uint64)(aa.limb[9])
accum4 += bv * (uint64)(aa.limb[10])
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 *[SharedSecretSize]byte) {
var buf uint64
bits := uint(0)
k := 0
for i, v := range ser {
buf |= (uint64)(v) << bits
for bits += 8; (bits >= lBits || i == SharedSecretSize-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 *[SharedSecretSize]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 < SharedSecretSize; bits, buf = bits-8, buf>>8 {
ser[k] = (byte)(buf)
k++
}
}
}
func init() {
if x448Limbs != 16 {
panic("x448Limbs != 16, unrolled loops likely broken")
}
}
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