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remove crapy x448
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The MIT License (MIT)
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Copyright (c) 2014-2015 Cryptography Research, Inc.
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Copyright (c) 2015 Yawning Angel.
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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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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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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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114
ec/x448/x448.go
114
ec/x448/x448.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 provides an implementation of scalar multiplication on the
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// elliptic curve known as curve448.
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//
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// See https://tools.ietf.org/html/draft-irtf-cfrg-curves-11
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package x448
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const (
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SharedSecretSize = 56
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edwardsD = -39081
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)
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var basePoint = [56]byte{
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5, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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}
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func ScalarMult(out, scalar, base *[56]byte) int {
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var x1, x2, z2, x3, z3, t1, t2 gf
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x1.deser(base)
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x2.cpy(&one)
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z2.cpy(&zero)
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x3.cpy(&x1)
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z3.cpy(&one)
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var swap limbUint
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for t := int(448 - 1); t >= 0; t-- {
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sb := scalar[t/8]
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// Scalar conditioning.
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if t/8 == 0 {
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sb &= 0xFC
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} else if t/8 == SharedSecretSize-1 {
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sb |= 0x80
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}
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kT := (limbUint)((sb >> ((uint)(t) % 8)) & 1)
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kT = -kT // Set to all 0s or all 1s
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swap ^= kT
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x2.condSwap(&x3, swap)
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z2.condSwap(&z3, swap)
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swap = kT
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t1.add(&x2, &z2) // A = x2 + z2
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t2.sub(&x2, &z2) // B = x2 - z2
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z2.sub(&x3, &z3) // D = x3 - z3
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x2.mul(&t1, &z2) // DA
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z2.add(&z3, &x3) // C = x3 + z3
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x3.mul(&t2, &z2) // CB
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z3.sub(&x2, &x3) // DA-CB
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z2.sqr(&z3) // (DA-CB)^2
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z3.mul(&x1, &z2) // z3 = x1(DA-CB)^2
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z2.add(&x2, &x3) // (DA+CB)
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x3.sqr(&z2) // x3 = (DA+CB)^2
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z2.sqr(&t1) // AA = A^2
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t1.sqr(&t2) // BB = B^2
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x2.mul(&z2, &t1) // x2 = AA*BB
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t2.sub(&z2, &t1) // E = AA-BB
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t1.mlw(&t2, -edwardsD) // E*-d = a24*E
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t1.add(&t1, &z2) // AA + a24*E
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z2.mul(&t2, &t1) // z2 = E(AA+a24*E)
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}
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// Finish
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x2.condSwap(&x3, swap)
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z2.condSwap(&x3, swap)
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z2.inv(&z2)
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x1.mul(&x2, &z2)
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x1.ser(out)
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// As with X25519, both sides MUST check, without leaking extra
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// information about the value of K, whether the resulting shared K is
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// the all-zero value and abort if so.
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var nz limbSint
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for _, v := range out {
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nz |= (limbSint)(v)
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}
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nz = (nz - 1) >> 8 // 0 = succ, -1 = fail
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// return value: 0 = succ, -1 = fail
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return (int)(nz)
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}
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func ScalarBaseMult(out, scalar *[56]byte) int {
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return ScalarMult(out, scalar, &basePoint)
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}
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@ -1,778 +0,0 @@
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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])
|
|
||||||
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")
|
|
||||||
}
|
|
||||||
}
|
|
||||||
@ -1,265 +0,0 @@
|
|||||||
// The MIT License (MIT)
|
|
||||||
//
|
|
||||||
// Copyright (c) 2011 Stanford University.
|
|
||||||
// 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
|
|
||||||
|
|
||||||
import (
|
|
||||||
"bytes"
|
|
||||||
"crypto/rand"
|
|
||||||
"encoding/hex"
|
|
||||||
"testing"
|
|
||||||
)
|
|
||||||
|
|
||||||
// Cowardly refuse to run the full slow test vector case unless this is set
|
|
||||||
// at compile time, because the timeout for the test harness needs to be
|
|
||||||
// adjusted at runtime.
|
|
||||||
var reallyRunSlowTest = false
|
|
||||||
|
|
||||||
func TestX448(t *testing.T) {
|
|
||||||
type KATVectors struct {
|
|
||||||
scalar [SharedSecretSize]byte
|
|
||||||
base [SharedSecretSize]byte
|
|
||||||
answer [SharedSecretSize]byte
|
|
||||||
}
|
|
||||||
|
|
||||||
vectors := []KATVectors{
|
|
||||||
{
|
|
||||||
[SharedSecretSize]byte{
|
|
||||||
0x3d, 0x26, 0x2f, 0xdd, 0xf9, 0xec, 0x8e, 0x88,
|
|
||||||
0x49, 0x52, 0x66, 0xfe, 0xa1, 0x9a, 0x34, 0xd2,
|
|
||||||
0x88, 0x82, 0xac, 0xef, 0x04, 0x51, 0x04, 0xd0,
|
|
||||||
0xd1, 0xaa, 0xe1, 0x21, 0x70, 0x0a, 0x77, 0x9c,
|
|
||||||
0x98, 0x4c, 0x24, 0xf8, 0xcd, 0xd7, 0x8f, 0xbf,
|
|
||||||
0xf4, 0x49, 0x43, 0xeb, 0xa3, 0x68, 0xf5, 0x4b,
|
|
||||||
0x29, 0x25, 0x9a, 0x4f, 0x1c, 0x60, 0x0a, 0xd3,
|
|
||||||
},
|
|
||||||
[SharedSecretSize]byte{
|
|
||||||
0x06, 0xfc, 0xe6, 0x40, 0xfa, 0x34, 0x87, 0xbf,
|
|
||||||
0xda, 0x5f, 0x6c, 0xf2, 0xd5, 0x26, 0x3f, 0x8a,
|
|
||||||
0xad, 0x88, 0x33, 0x4c, 0xbd, 0x07, 0x43, 0x7f,
|
|
||||||
0x02, 0x0f, 0x08, 0xf9, 0x81, 0x4d, 0xc0, 0x31,
|
|
||||||
0xdd, 0xbd, 0xc3, 0x8c, 0x19, 0xc6, 0xda, 0x25,
|
|
||||||
0x83, 0xfa, 0x54, 0x29, 0xdb, 0x94, 0xad, 0xa1,
|
|
||||||
0x8a, 0xa7, 0xa7, 0xfb, 0x4e, 0xf8, 0xa0, 0x86,
|
|
||||||
},
|
|
||||||
[SharedSecretSize]byte{
|
|
||||||
0xce, 0x3e, 0x4f, 0xf9, 0x5a, 0x60, 0xdc, 0x66,
|
|
||||||
0x97, 0xda, 0x1d, 0xb1, 0xd8, 0x5e, 0x6a, 0xfb,
|
|
||||||
0xdf, 0x79, 0xb5, 0x0a, 0x24, 0x12, 0xd7, 0x54,
|
|
||||||
0x6d, 0x5f, 0x23, 0x9f, 0xe1, 0x4f, 0xba, 0xad,
|
|
||||||
0xeb, 0x44, 0x5f, 0xc6, 0x6a, 0x01, 0xb0, 0x77,
|
|
||||||
0x9d, 0x98, 0x22, 0x39, 0x61, 0x11, 0x1e, 0x21,
|
|
||||||
0x76, 0x62, 0x82, 0xf7, 0x3d, 0xd9, 0x6b, 0x6f,
|
|
||||||
},
|
|
||||||
},
|
|
||||||
{
|
|
||||||
[SharedSecretSize]byte{
|
|
||||||
0x20, 0x3d, 0x49, 0x44, 0x28, 0xb8, 0x39, 0x93,
|
|
||||||
0x52, 0x66, 0x5d, 0xdc, 0xa4, 0x2f, 0x9d, 0xe8,
|
|
||||||
0xfe, 0xf6, 0x00, 0x90, 0x8e, 0x0d, 0x46, 0x1c,
|
|
||||||
0xb0, 0x21, 0xf8, 0xc5, 0x38, 0x34, 0x5d, 0xd7,
|
|
||||||
0x7c, 0x3e, 0x48, 0x06, 0xe2, 0x5f, 0x46, 0xd3,
|
|
||||||
0x31, 0x5c, 0x44, 0xe0, 0xa5, 0xb4, 0x37, 0x12,
|
|
||||||
0x82, 0xdd, 0x2c, 0x8d, 0x5b, 0xe3, 0x09, 0x5f,
|
|
||||||
},
|
|
||||||
[SharedSecretSize]byte{
|
|
||||||
0x0f, 0xbc, 0xc2, 0xf9, 0x93, 0xcd, 0x56, 0xd3,
|
|
||||||
0x30, 0x5b, 0x0b, 0x7d, 0x9e, 0x55, 0xd4, 0xc1,
|
|
||||||
0xa8, 0xfb, 0x5d, 0xbb, 0x52, 0xf8, 0xe9, 0xa1,
|
|
||||||
0xe9, 0xb6, 0x20, 0x1b, 0x16, 0x5d, 0x01, 0x58,
|
|
||||||
0x94, 0xe5, 0x6c, 0x4d, 0x35, 0x70, 0xbe, 0xe5,
|
|
||||||
0x2f, 0xe2, 0x05, 0xe2, 0x8a, 0x78, 0xb9, 0x1c,
|
|
||||||
0xdf, 0xbd, 0xe7, 0x1c, 0xe8, 0xd1, 0x57, 0xdb,
|
|
||||||
},
|
|
||||||
[SharedSecretSize]byte{
|
|
||||||
0x88, 0x4a, 0x02, 0x57, 0x62, 0x39, 0xff, 0x7a,
|
|
||||||
0x2f, 0x2f, 0x63, 0xb2, 0xdb, 0x6a, 0x9f, 0xf3,
|
|
||||||
0x70, 0x47, 0xac, 0x13, 0x56, 0x8e, 0x1e, 0x30,
|
|
||||||
0xfe, 0x63, 0xc4, 0xa7, 0xad, 0x1b, 0x3e, 0xe3,
|
|
||||||
0xa5, 0x70, 0x0d, 0xf3, 0x43, 0x21, 0xd6, 0x20,
|
|
||||||
0x77, 0xe6, 0x36, 0x33, 0xc5, 0x75, 0xc1, 0xc9,
|
|
||||||
0x54, 0x51, 0x4e, 0x99, 0xda, 0x7c, 0x17, 0x9d,
|
|
||||||
},
|
|
||||||
},
|
|
||||||
}
|
|
||||||
|
|
||||||
var out [SharedSecretSize]byte
|
|
||||||
for i, vec := range vectors {
|
|
||||||
ret := ScalarMult(&out, &vec.scalar, &vec.base)
|
|
||||||
if ret != 0 {
|
|
||||||
t.Errorf("KAT[%d]: ScalarMultiply failed", i)
|
|
||||||
}
|
|
||||||
if !bytes.Equal(out[:], vec.answer[:]) {
|
|
||||||
t.Errorf("KAT[%d]: Mismatch", i)
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func TestX448IETFDraft(t *testing.T) {
|
|
||||||
// Run the other test vectors from 5.2 of the IETF draft.
|
|
||||||
|
|
||||||
// WARNING: The full version of the test will easily take longer than the
|
|
||||||
// default 10 min test timeout, even on a moderately powerful box.
|
|
||||||
//
|
|
||||||
// Unless reallyRunSlowTest is set in the source code, it will cowardly
|
|
||||||
// refuse to run the full 1 million iterations, and the `go test`
|
|
||||||
// timeout will need to be increased (`go test -timeout 30m`).
|
|
||||||
|
|
||||||
var k, u, out [SharedSecretSize]byte
|
|
||||||
copy(k[:], basePoint[:])
|
|
||||||
copy(u[:], basePoint[:])
|
|
||||||
|
|
||||||
for i := 0; i < 1000000; i++ {
|
|
||||||
ret := ScalarMult(&out, &k, &u)
|
|
||||||
if ret != 0 {
|
|
||||||
t.Fatalf("Iterated[%d]: ScalarMultiply failed", i)
|
|
||||||
}
|
|
||||||
switch i + 1 {
|
|
||||||
case 1:
|
|
||||||
known, _ := hex.DecodeString("3f482c8a9f19b01e6c46ee9711d9dc14fd4bf67af30765c2ae2b846a4d23a8cd0db897086239492caf350b51f833868b9bc2b3bca9cf4113")
|
|
||||||
if !bytes.Equal(out[:], known) {
|
|
||||||
t.Fatalf("Iterated[%d]: Mismatch", i)
|
|
||||||
}
|
|
||||||
case 1000:
|
|
||||||
known, _ := hex.DecodeString("aa3b4749d55b9daf1e5b00288826c467274ce3ebbdd5c17b975e09d4af6c67cf10d087202db88286e2b79fceea3ec353ef54faa26e219f38")
|
|
||||||
if !bytes.Equal(out[:], known) {
|
|
||||||
t.Fatalf("Iterated[%d]: Mismatch", i)
|
|
||||||
}
|
|
||||||
if testing.Short() || !reallyRunSlowTest {
|
|
||||||
t.Skipf("Short test requested, skipping remaining, was correct at 1k")
|
|
||||||
}
|
|
||||||
}
|
|
||||||
copy(u[:], k[:])
|
|
||||||
copy(k[:], out[:])
|
|
||||||
}
|
|
||||||
known, _ := hex.DecodeString("077f453681caca3693198420bbe515cae0002472519b3e67661a7e89cab94695c8f4bcd66e61b9b9c946da8d524de3d69bd9d9d66b997e37")
|
|
||||||
if !bytes.Equal(k[:], known) {
|
|
||||||
t.Fatal("Final value mismatch")
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func TestCurve448(t *testing.T) {
|
|
||||||
alicePriv := [SharedSecretSize]byte{
|
|
||||||
0x9a, 0x8f, 0x49, 0x25, 0xd1, 0x51, 0x9f, 0x57,
|
|
||||||
0x75, 0xcf, 0x46, 0xb0, 0x4b, 0x58, 0x00, 0xd4,
|
|
||||||
0xee, 0x9e, 0xe8, 0xba, 0xe8, 0xbc, 0x55, 0x65,
|
|
||||||
0xd4, 0x98, 0xc2, 0x8d, 0xd9, 0xc9, 0xba, 0xf5,
|
|
||||||
0x74, 0xa9, 0x41, 0x97, 0x44, 0x89, 0x73, 0x91,
|
|
||||||
0x00, 0x63, 0x82, 0xa6, 0xf1, 0x27, 0xab, 0x1d,
|
|
||||||
0x9a, 0xc2, 0xd8, 0xc0, 0xa5, 0x98, 0x72, 0x6b,
|
|
||||||
}
|
|
||||||
|
|
||||||
alicePub := [SharedSecretSize]byte{
|
|
||||||
0x9b, 0x08, 0xf7, 0xcc, 0x31, 0xb7, 0xe3, 0xe6,
|
|
||||||
0x7d, 0x22, 0xd5, 0xae, 0xa1, 0x21, 0x07, 0x4a,
|
|
||||||
0x27, 0x3b, 0xd2, 0xb8, 0x3d, 0xe0, 0x9c, 0x63,
|
|
||||||
0xfa, 0xa7, 0x3d, 0x2c, 0x22, 0xc5, 0xd9, 0xbb,
|
|
||||||
0xc8, 0x36, 0x64, 0x72, 0x41, 0xd9, 0x53, 0xd4,
|
|
||||||
0x0c, 0x5b, 0x12, 0xda, 0x88, 0x12, 0x0d, 0x53,
|
|
||||||
0x17, 0x7f, 0x80, 0xe5, 0x32, 0xc4, 0x1f, 0xa0,
|
|
||||||
}
|
|
||||||
|
|
||||||
bobPriv := [SharedSecretSize]byte{
|
|
||||||
0x1c, 0x30, 0x6a, 0x7a, 0xc2, 0xa0, 0xe2, 0xe0,
|
|
||||||
0x99, 0x0b, 0x29, 0x44, 0x70, 0xcb, 0xa3, 0x39,
|
|
||||||
0xe6, 0x45, 0x37, 0x72, 0xb0, 0x75, 0x81, 0x1d,
|
|
||||||
0x8f, 0xad, 0x0d, 0x1d, 0x69, 0x27, 0xc1, 0x20,
|
|
||||||
0xbb, 0x5e, 0xe8, 0x97, 0x2b, 0x0d, 0x3e, 0x21,
|
|
||||||
0x37, 0x4c, 0x9c, 0x92, 0x1b, 0x09, 0xd1, 0xb0,
|
|
||||||
0x36, 0x6f, 0x10, 0xb6, 0x51, 0x73, 0x99, 0x2d,
|
|
||||||
}
|
|
||||||
|
|
||||||
bobPub := [SharedSecretSize]byte{
|
|
||||||
0x3e, 0xb7, 0xa8, 0x29, 0xb0, 0xcd, 0x20, 0xf5,
|
|
||||||
0xbc, 0xfc, 0x0b, 0x59, 0x9b, 0x6f, 0xec, 0xcf,
|
|
||||||
0x6d, 0xa4, 0x62, 0x71, 0x07, 0xbd, 0xb0, 0xd4,
|
|
||||||
0xf3, 0x45, 0xb4, 0x30, 0x27, 0xd8, 0xb9, 0x72,
|
|
||||||
0xfc, 0x3e, 0x34, 0xfb, 0x42, 0x32, 0xa1, 0x3c,
|
|
||||||
0xa7, 0x06, 0xdc, 0xb5, 0x7a, 0xec, 0x3d, 0xae,
|
|
||||||
0x07, 0xbd, 0xc1, 0xc6, 0x7b, 0xf3, 0x36, 0x09,
|
|
||||||
}
|
|
||||||
|
|
||||||
aliceBob := [SharedSecretSize]byte{
|
|
||||||
0x07, 0xff, 0xf4, 0x18, 0x1a, 0xc6, 0xcc, 0x95,
|
|
||||||
0xec, 0x1c, 0x16, 0xa9, 0x4a, 0x0f, 0x74, 0xd1,
|
|
||||||
0x2d, 0xa2, 0x32, 0xce, 0x40, 0xa7, 0x75, 0x52,
|
|
||||||
0x28, 0x1d, 0x28, 0x2b, 0xb6, 0x0c, 0x0b, 0x56,
|
|
||||||
0xfd, 0x24, 0x64, 0xc3, 0x35, 0x54, 0x39, 0x36,
|
|
||||||
0x52, 0x1c, 0x24, 0x40, 0x30, 0x85, 0xd5, 0x9a,
|
|
||||||
0x44, 0x9a, 0x50, 0x37, 0x51, 0x4a, 0x87, 0x9d,
|
|
||||||
}
|
|
||||||
|
|
||||||
var out [SharedSecretSize]byte
|
|
||||||
ret := ScalarBaseMult(&out, &alicePriv)
|
|
||||||
if ret != 0 {
|
|
||||||
t.Error("Alice: ScalarBaseMult failed")
|
|
||||||
}
|
|
||||||
if !bytes.Equal(out[:], alicePub[:]) {
|
|
||||||
t.Error("Alice: ScalarBaseMult Mismatch")
|
|
||||||
}
|
|
||||||
ret = ScalarBaseMult(&out, &bobPriv)
|
|
||||||
if ret != 0 {
|
|
||||||
t.Error("Bob: ScalarBaseMult failed")
|
|
||||||
}
|
|
||||||
if !bytes.Equal(out[:], bobPub[:]) {
|
|
||||||
t.Error("Bob: ScalarBaseMult Mismatch")
|
|
||||||
}
|
|
||||||
ret = ScalarMult(&out, &bobPriv, &alicePub)
|
|
||||||
if ret != 0 {
|
|
||||||
t.Error("Bob: ScalarMult failed")
|
|
||||||
}
|
|
||||||
if !bytes.Equal(out[:], aliceBob[:]) {
|
|
||||||
t.Error("Bob: ScalarMult Mismatch")
|
|
||||||
}
|
|
||||||
ret = ScalarMult(&out, &alicePriv, &bobPub)
|
|
||||||
if ret != 0 {
|
|
||||||
t.Error("Alice: ScalarMult failed")
|
|
||||||
}
|
|
||||||
if !bytes.Equal(out[:], aliceBob[:]) {
|
|
||||||
t.Error("Alice: ScalarMult Mismatch")
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func BenchmarkECDH(b *testing.B) {
|
|
||||||
var sa, sb, pa, pb, ab, ba [SharedSecretSize]byte
|
|
||||||
ret := 0
|
|
||||||
|
|
||||||
rand.Read(sa[:])
|
|
||||||
rand.Read(sb[:])
|
|
||||||
b.ResetTimer()
|
|
||||||
b.StopTimer()
|
|
||||||
for i := 0; i < b.N; i++ {
|
|
||||||
ret |= ScalarBaseMult(&pa, &sa)
|
|
||||||
ret |= ScalarBaseMult(&pb, &sb)
|
|
||||||
b.StartTimer()
|
|
||||||
ret |= ScalarMult(&ab, &sa, &pb)
|
|
||||||
b.StopTimer()
|
|
||||||
ret |= ScalarMult(&ba, &sb, &pa)
|
|
||||||
if !bytes.Equal(ab[:], ba[:]) {
|
|
||||||
b.Fatal("Alice/Bob: Mismatch")
|
|
||||||
}
|
|
||||||
copy(sa[:], pa[:])
|
|
||||||
copy(sb[:], pb[:])
|
|
||||||
}
|
|
||||||
}
|
|
||||||
Loading…
Reference in New Issue
Block a user