Cutover to Andrew Moon's 64-bit code (GH #761)
The code is public domain without license restrictions. It is also faster than Langley's original implementation.pull/765/head
Jeffrey Walton
parent
5f8dcbbb37
commit
560c332f19
734
donna_64.cpp
734
donna_64.cpp
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@ -1,66 +1,18 @@
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// donna_64.cpp - written and placed in public domain by Jeffrey Walton
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// This is a port of Adam Langley's curve25519-donna
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// located at https://github.com/agl/curve25519-donna
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/* Copyright 2008, Google Inc.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are
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* met:
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*
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above
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* copyright notice, this list of conditions and the following disclaimer
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* in the documentation and/or other materials provided with the
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* distribution.
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* * Neither the name of Google Inc. nor the names of its
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* contributors may be used to endorse or promote products derived from
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* this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* curve25519-donna: Curve25519 elliptic curve, public key function
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*
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* http://code.google.com/p/curve25519-donna/
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*
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* Adam Langley <agl@imperialviolet.org>
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*
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* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
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*
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* More information about curve25519 can be found here
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* http://cr.yp.to/ecdh.html
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*
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* djb's sample implementation of curve25519 is written in a special assembly
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* language called qhasm and uses the floating point registers.
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*
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* This is, almost, a clean room reimplementation from the curve25519 paper. It
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* uses many of the tricks described therein. Only the crecip function is taken
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* from the sample implementation. */
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// This is a integration of Andrew Moon's public domain code.
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// Also see curve25519-donna-64bit.h.
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#include "pch.h"
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#include "config.h"
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#include "donna.h"
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#include "stdcpp.h"
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#include "misc.h"
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#include "cpu.h"
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// This macro is not in a header like config.h because
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// we don't want it exposed to user code. We also need
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// a standard header like <stdint.h> or <stdef.h>.
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// Langley uses uint128_t in the 64-bit code paths so
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// we further restrict 64-bit code.
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// This macro is not in a header like config.h because we don't want it
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// exposed to user code. We also need a standard header like <stdint.h>
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// or <stdef.h>.
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#if (UINTPTR_MAX == 0xffffffff) || !defined(CRYPTOPP_WORD128_AVAILABLE)
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# define CRYPTOPP_32BIT 1
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#else
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@ -77,405 +29,331 @@ ANONYMOUS_NAMESPACE_BEGIN
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using std::memcpy;
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using CryptoPP::byte;
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using CryptoPP::word32;
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using CryptoPP::word64;
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using CryptoPP::sword32;
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using CryptoPP::word64;
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using CryptoPP::sword64;
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using CryptoPP::word128;
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typedef word64 limb;
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typedef limb felem[5];
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using CryptoPP::GetBlock;
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using CryptoPP::BigEndian;
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using CryptoPP::LittleEndian;
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// This is a special gcc mode for 128-bit integers. It's implemented on 64-bit
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// platforms only as far as I know.
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//typedef unsigned uint128_t __attribute__((mode(TI)));
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typedef word64 bignum25519[5];
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/* Sum two numbers: output += in */
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inline void fsum(limb *output, const limb *in)
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{
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output[0] += in[0];
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output[1] += in[1];
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output[2] += in[2];
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output[3] += in[3];
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output[4] += in[4];
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#define lo128(a) ((word64)a)
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#define hi128(a) ((word64)(a >> 64))
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#define add128(a,b) a += b;
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#define add128_64(a,b) a += (word64)b;
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#define mul64x64_128(out,a,b) out = (word128)a * b;
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#define shr128(out,in,shift) out = (word64)(in >> (shift));
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#define shl128(out,in,shift) out = (word64)((in << shift) >> 64);
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const word64 reduce_mask_40 = ((word64)1 << 40) - 1;
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const word64 reduce_mask_51 = ((word64)1 << 51) - 1;
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const word64 reduce_mask_56 = ((word64)1 << 56) - 1;
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/* out = in */
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inline void
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curve25519_copy(bignum25519 out, const bignum25519 in) {
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out[0] = in[0];
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out[1] = in[1];
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out[2] = in[2];
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out[3] = in[3];
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out[4] = in[4];
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}
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/* Find the difference of two numbers: output = in - output
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* (note the order of the arguments!)
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*
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* Assumes that out[i] < 2**52
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* On return, out[i] < 2**55
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*/
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inline void fdifference_backwards(felem out, const felem in)
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{
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/* 152 is 19 << 3 */
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const limb two54m152 = (((limb)1) << 54) - 152;
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const limb two54m8 = (((limb)1) << 54) - 8;
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out[0] = in[0] + two54m152 - out[0];
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out[1] = in[1] + two54m8 - out[1];
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out[2] = in[2] + two54m8 - out[2];
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out[3] = in[3] + two54m8 - out[3];
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out[4] = in[4] + two54m8 - out[4];
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/* out = a + b */
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inline void
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curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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out[0] = a[0] + b[0];
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out[1] = a[1] + b[1];
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out[2] = a[2] + b[2];
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out[3] = a[3] + b[3];
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out[4] = a[4] + b[4];
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}
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/* Multiply a number by a scalar: output = in * scalar */
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inline void fscalar_product(felem output, const felem in, const limb scalar)
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{
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word128 a;
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a = ((word128) in[0]) * scalar;
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output[0] = ((limb)a) & 0x7ffffffffffff;
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a = ((word128) in[1]) * scalar + ((limb) (a >> 51));
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output[1] = ((limb)a) & 0x7ffffffffffff;
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a = ((word128) in[2]) * scalar + ((limb) (a >> 51));
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output[2] = ((limb)a) & 0x7ffffffffffff;
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a = ((word128) in[3]) * scalar + ((limb) (a >> 51));
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output[3] = ((limb)a) & 0x7ffffffffffff;
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a = ((word128) in[4]) * scalar + ((limb) (a >> 51));
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output[4] = ((limb)a) & 0x7ffffffffffff;
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output[0] += (a >> 51) * 19;
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/* out = a + b, where a and/or b are the result of a basic op (add,sub) */
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inline void
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curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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out[0] = a[0] + b[0];
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out[1] = a[1] + b[1];
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out[2] = a[2] + b[2];
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out[3] = a[3] + b[3];
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out[4] = a[4] + b[4];
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}
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/* Multiply two numbers: output = in2 * in
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*
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* output must be distinct to both inputs. The inputs are reduced coefficient
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* form, the output is not.
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*
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* Assumes that in[i] < 2**55 and likewise for in2.
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* On return, output[i] < 2**52
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*/
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inline void fmul(felem output, const felem in2, const felem in)
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{
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word128 t[5];
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limb r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
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r0 = in[0];
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r1 = in[1];
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r2 = in[2];
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r3 = in[3];
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r4 = in[4];
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s0 = in2[0];
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s1 = in2[1];
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s2 = in2[2];
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s3 = in2[3];
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s4 = in2[4];
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t[0] = ((word128) r0) * s0;
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t[1] = ((word128) r0) * s1 + ((word128) r1) * s0;
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t[2] = ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
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t[3] = ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
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t[4] = ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
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r4 *= 19;
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r1 *= 19;
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r2 *= 19;
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r3 *= 19;
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t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
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t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
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t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
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t[3] += ((word128) r4) * s4;
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r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
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t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
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t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
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t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
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t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
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r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
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r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
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r2 += c;
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output[0] = r0;
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output[1] = r1;
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output[2] = r2;
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output[3] = r3;
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output[4] = r4;
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inline void
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curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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word64 c;
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out[0] = a[0] + b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
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out[1] = a[1] + b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
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out[2] = a[2] + b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
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out[3] = a[3] + b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
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out[4] = a[4] + b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
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out[0] += c * 19;
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}
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inline void fsquare_times(felem output, const felem in, limb count)
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{
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word128 t[5];
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limb r0,r1,r2,r3,r4,c;
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limb d0,d1,d2,d4,d419;
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/* multiples of p */
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const word64 twoP0 = 0x0fffffffffffda;
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const word64 twoP1234 = 0x0ffffffffffffe;
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const word64 fourP0 = 0x1fffffffffffb4;
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const word64 fourP1234 = 0x1ffffffffffffc;
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r0 = in[0];
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r1 = in[1];
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r2 = in[2];
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r3 = in[3];
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r4 = in[4];
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/* out = a - b */
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inline void
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curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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out[0] = a[0] + twoP0 - b[0];
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out[1] = a[1] + twoP1234 - b[1];
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out[2] = a[2] + twoP1234 - b[2];
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out[3] = a[3] + twoP1234 - b[3];
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out[4] = a[4] + twoP1234 - b[4];
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}
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do {
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d0 = r0 * 2;
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d1 = r1 * 2;
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/* out = a - b, where a and/or b are the result of a basic op (add,sub) */
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inline void
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curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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out[0] = a[0] + fourP0 - b[0];
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out[1] = a[1] + fourP1234 - b[1];
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out[2] = a[2] + fourP1234 - b[2];
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out[3] = a[3] + fourP1234 - b[3];
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out[4] = a[4] + fourP1234 - b[4];
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}
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inline void
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curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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word64 c;
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out[0] = a[0] + fourP0 - b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
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out[1] = a[1] + fourP1234 - b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
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out[2] = a[2] + fourP1234 - b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
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out[3] = a[3] + fourP1234 - b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
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out[4] = a[4] + fourP1234 - b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
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out[0] += c * 19;
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}
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/* out = -a */
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inline void
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curve25519_neg(bignum25519 out, const bignum25519 a) {
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word64 c;
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out[0] = twoP0 - a[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
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out[1] = twoP1234 - a[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
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out[2] = twoP1234 - a[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
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out[3] = twoP1234 - a[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
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out[4] = twoP1234 - a[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
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out[0] += c * 19;
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}
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/* out = a * b */
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inline void
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curve25519_mul(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
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#if !defined(CRYPTOPP_WORD128_AVAILABLE)
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word128 mul;
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#endif
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word128 t[5];
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word64 r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
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r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
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s0 = in2[0]; s1 = in2[1]; s2 = in2[2]; s3 = in2[3]; s4 = in2[4];
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#if defined(CRYPTOPP_WORD128_AVAILABLE)
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t[0] = ((word128) r0) * s0;
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t[1] = ((word128) r0) * s1 + ((word128) r1) * s0;
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t[2] = ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
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t[3] = ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
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t[4] = ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
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#else
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mul64x64_128(t[0], r0, s0)
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mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
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mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
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mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul)
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mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul)
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#endif
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r1 *= 19; r2 *= 19; r3 *= 19; r4 *= 19;
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#if defined(CRYPTOPP_WORD128_AVAILABLE)
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t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
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t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
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t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
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t[3] += ((word128) r4) * s4;
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#else
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mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul)
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mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul)
|
||||
mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
|
||||
mul64x64_128(mul, r4, s4) add128(t[3], mul)
|
||||
#endif
|
||||
|
||||
|
||||
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
|
||||
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
|
||||
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
|
||||
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
|
||||
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
|
||||
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
|
||||
r1 += c;
|
||||
|
||||
out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
|
||||
}
|
||||
|
||||
void
|
||||
curve25519_mul_noinline(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
|
||||
curve25519_mul(out, in2, in);
|
||||
}
|
||||
|
||||
/* out = in^(2 * count) */
|
||||
void
|
||||
curve25519_square_times(bignum25519 out, const bignum25519 in, word64 count) {
|
||||
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
|
||||
word128 mul;
|
||||
#endif
|
||||
word128 t[5];
|
||||
word64 r0,r1,r2,r3,r4,c;
|
||||
word64 d0,d1,d2,d4,d419;
|
||||
|
||||
r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
|
||||
|
||||
do {
|
||||
d0 = r0 * 2; d1 = r1 * 2;
|
||||
d2 = r2 * 2 * 19;
|
||||
d419 = r4 * 19;
|
||||
d4 = d419 * 2;
|
||||
|
||||
#if defined(CRYPTOPP_WORD128_AVAILABLE)
|
||||
t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
|
||||
t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
|
||||
t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
|
||||
t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
|
||||
t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
|
||||
#else
|
||||
mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
|
||||
mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
|
||||
mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
|
||||
mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
|
||||
mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
|
||||
#endif
|
||||
|
||||
r0 = lo128(t[0]) & reduce_mask_51;
|
||||
r1 = lo128(t[1]) & reduce_mask_51; shl128(c, t[0], 13); r1 += c;
|
||||
r2 = lo128(t[2]) & reduce_mask_51; shl128(c, t[1], 13); r2 += c;
|
||||
r3 = lo128(t[3]) & reduce_mask_51; shl128(c, t[2], 13); r3 += c;
|
||||
r4 = lo128(t[4]) & reduce_mask_51; shl128(c, t[3], 13); r4 += c;
|
||||
shl128(c, t[4], 13); r0 += c * 19;
|
||||
c = r0 >> 51; r0 &= reduce_mask_51;
|
||||
r1 += c ; c = r1 >> 51; r1 &= reduce_mask_51;
|
||||
r2 += c ; c = r2 >> 51; r2 &= reduce_mask_51;
|
||||
r3 += c ; c = r3 >> 51; r3 &= reduce_mask_51;
|
||||
r4 += c ; c = r4 >> 51; r4 &= reduce_mask_51;
|
||||
r0 += c * 19;
|
||||
} while(--count);
|
||||
|
||||
out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
|
||||
}
|
||||
|
||||
inline void
|
||||
curve25519_square(bignum25519 out, const bignum25519 in) {
|
||||
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
|
||||
word128 mul;
|
||||
#endif
|
||||
word128 t[5];
|
||||
word64 r0,r1,r2,r3,r4,c;
|
||||
word64 d0,d1,d2,d4,d419;
|
||||
|
||||
r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
|
||||
|
||||
d0 = r0 * 2; d1 = r1 * 2;
|
||||
d2 = r2 * 2 * 19;
|
||||
d419 = r4 * 19;
|
||||
d4 = d419 * 2;
|
||||
|
||||
#if defined(CRYPTOPP_WORD128_AVAILABLE)
|
||||
t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
|
||||
t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
|
||||
t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
|
||||
t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
|
||||
t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
|
||||
#else
|
||||
mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
|
||||
mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
|
||||
mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
|
||||
mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
|
||||
mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
|
||||
#endif
|
||||
|
||||
r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
|
||||
t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
|
||||
t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
|
||||
t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
|
||||
t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
|
||||
r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
|
||||
r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
|
||||
r2 += c;
|
||||
} while(--count);
|
||||
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
|
||||
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
|
||||
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
|
||||
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
|
||||
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
|
||||
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
|
||||
r1 += c;
|
||||
|
||||
output[0] = r0;
|
||||
output[1] = r1;
|
||||
output[2] = r2;
|
||||
output[3] = r3;
|
||||
output[4] = r4;
|
||||
}
|
||||
|
||||
/* Load a little-endian 64-bit number */
|
||||
limb load_limb(const byte *in)
|
||||
{
|
||||
return
|
||||
((limb)in[0]) |
|
||||
(((limb)in[1]) << 8) |
|
||||
(((limb)in[2]) << 16) |
|
||||
(((limb)in[3]) << 24) |
|
||||
(((limb)in[4]) << 32) |
|
||||
(((limb)in[5]) << 40) |
|
||||
(((limb)in[6]) << 48) |
|
||||
(((limb)in[7]) << 56);
|
||||
}
|
||||
|
||||
void store_limb(byte *out, limb in)
|
||||
{
|
||||
out[0] = in & 0xff;
|
||||
out[1] = (in >> 8) & 0xff;
|
||||
out[2] = (in >> 16) & 0xff;
|
||||
out[3] = (in >> 24) & 0xff;
|
||||
out[4] = (in >> 32) & 0xff;
|
||||
out[5] = (in >> 40) & 0xff;
|
||||
out[6] = (in >> 48) & 0xff;
|
||||
out[7] = (in >> 56) & 0xff;
|
||||
out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
|
||||
}
|
||||
|
||||
/* Take a little-endian, 32-byte number and expand it into polynomial form */
|
||||
void fexpand(limb *output, const byte *in)
|
||||
{
|
||||
output[0] = load_limb(in) & 0x7ffffffffffff;
|
||||
output[1] = (load_limb(in+6) >> 3) & 0x7ffffffffffff;
|
||||
output[2] = (load_limb(in+12) >> 6) & 0x7ffffffffffff;
|
||||
output[3] = (load_limb(in+19) >> 1) & 0x7ffffffffffff;
|
||||
output[4] = (load_limb(in+24) >> 12) & 0x7ffffffffffff;
|
||||
inline void
|
||||
curve25519_expand(bignum25519 out, const unsigned char *in) {
|
||||
word64 x0,x1,x2,x3;
|
||||
|
||||
GetBlock<word64, LittleEndian> block(in);
|
||||
block(x0)(x1)(x2)(x3);
|
||||
|
||||
out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
|
||||
out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
|
||||
out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
|
||||
out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
|
||||
out[4] = x3 & reduce_mask_51;
|
||||
}
|
||||
|
||||
/* Take a fully reduced polynomial form number and contract it into a
|
||||
* little-endian, 32-byte array
|
||||
*/
|
||||
void fcontract(byte *output, const felem input)
|
||||
{
|
||||
word128 t[5];
|
||||
inline void
|
||||
curve25519_contract(unsigned char *out, const bignum25519 input) {
|
||||
word64 t[5];
|
||||
word64 f, i;
|
||||
|
||||
t[0] = input[0];
|
||||
t[1] = input[1];
|
||||
t[2] = input[2];
|
||||
t[3] = input[3];
|
||||
t[4] = input[4];
|
||||
t[0] = input[0]; t[1] = input[1]; t[2] = input[2];
|
||||
t[3] = input[3]; t[4] = input[4];
|
||||
|
||||
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
|
||||
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
|
||||
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
|
||||
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
|
||||
t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
|
||||
#define curve25519_contract_carry() \
|
||||
t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \
|
||||
t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \
|
||||
t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \
|
||||
t[4] += t[3] >> 51; t[3] &= reduce_mask_51;
|
||||
|
||||
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
|
||||
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
|
||||
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
|
||||
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
|
||||
t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
|
||||
#define curve25519_contract_carry_full() curve25519_contract_carry() \
|
||||
t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51;
|
||||
|
||||
/* now t is between 0 and 2^255-1, properly carried. */
|
||||
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
|
||||
#define curve25519_contract_carry_final() curve25519_contract_carry() \
|
||||
t[4] &= reduce_mask_51;
|
||||
|
||||
t[0] += 19;
|
||||
curve25519_contract_carry_full()
|
||||
curve25519_contract_carry_full()
|
||||
|
||||
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
|
||||
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
|
||||
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
|
||||
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
|
||||
t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
|
||||
/* now t is between 0 and 2^255-1, properly carried. */
|
||||
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
|
||||
t[0] += 19;
|
||||
curve25519_contract_carry_full()
|
||||
|
||||
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
|
||||
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
|
||||
t[0] += (reduce_mask_51 + 1) - 19;
|
||||
t[1] += (reduce_mask_51 + 1) - 1;
|
||||
t[2] += (reduce_mask_51 + 1) - 1;
|
||||
t[3] += (reduce_mask_51 + 1) - 1;
|
||||
t[4] += (reduce_mask_51 + 1) - 1;
|
||||
|
||||
t[0] += 0x8000000000000 - 19;
|
||||
t[1] += 0x8000000000000 - 1;
|
||||
t[2] += 0x8000000000000 - 1;
|
||||
t[3] += 0x8000000000000 - 1;
|
||||
t[4] += 0x8000000000000 - 1;
|
||||
/* now between 2^255 and 2^256-20, and offset by 2^255. */
|
||||
curve25519_contract_carry_final()
|
||||
|
||||
/* now between 2^255 and 2^256-20, and offset by 2^255. */
|
||||
|
||||
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
|
||||
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
|
||||
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
|
||||
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
|
||||
t[4] &= 0x7ffffffffffff;
|
||||
|
||||
store_limb(output, t[0] | (t[1] << 51));
|
||||
store_limb(output+8, (t[1] >> 13) | (t[2] << 38));
|
||||
store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
|
||||
store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
|
||||
}
|
||||
|
||||
/* Input: Q, Q', Q-Q'
|
||||
* Output: 2Q, Q+Q'
|
||||
*
|
||||
* x2 z3: long form
|
||||
* x3 z3: long form
|
||||
* x z: short form, destroyed
|
||||
* xprime zprime: short form, destroyed
|
||||
* qmqp: short form, preserved
|
||||
*/
|
||||
void fmonty(limb *x2, limb *z2, /* output 2Q */
|
||||
limb *x3, limb *z3, /* output Q + Q' */
|
||||
limb *x, limb *z, /* input Q */
|
||||
limb *xprime, limb *zprime, /* input Q' */
|
||||
const limb *qmqp /* input Q - Q' */)
|
||||
{
|
||||
limb origx[5], origxprime[5], zzz[5], xx[5], zz[5];
|
||||
limb xxprime[5], zzprime[5], zzzprime[5];
|
||||
|
||||
memcpy(origx, x, 5 * sizeof(limb));
|
||||
fsum(x, z);
|
||||
fdifference_backwards(z, origx); // does x - z
|
||||
|
||||
memcpy(origxprime, xprime, sizeof(limb) * 5);
|
||||
fsum(xprime, zprime);
|
||||
fdifference_backwards(zprime, origxprime);
|
||||
fmul(xxprime, xprime, z);
|
||||
fmul(zzprime, x, zprime);
|
||||
memcpy(origxprime, xxprime, sizeof(limb) * 5);
|
||||
fsum(xxprime, zzprime);
|
||||
fdifference_backwards(zzprime, origxprime);
|
||||
fsquare_times(x3, xxprime, 1);
|
||||
fsquare_times(zzzprime, zzprime, 1);
|
||||
fmul(z3, zzzprime, qmqp);
|
||||
|
||||
fsquare_times(xx, x, 1);
|
||||
fsquare_times(zz, z, 1);
|
||||
fmul(x2, xx, zz);
|
||||
fdifference_backwards(zz, xx); // does zz = xx - zz
|
||||
fscalar_product(zzz, zz, 121665);
|
||||
fsum(zzz, xx);
|
||||
fmul(z2, zz, zzz);
|
||||
}
|
||||
|
||||
// -----------------------------------------------------------------------------
|
||||
// Maybe swap the contents of two limb arrays (@a and @b), each @len elements
|
||||
// long. Perform the swap iff @swap is non-zero.
|
||||
//
|
||||
// This function performs the swap without leaking any side-channel
|
||||
// information.
|
||||
// -----------------------------------------------------------------------------
|
||||
void swap_conditional(limb a[5], limb b[5], limb iswap)
|
||||
{
|
||||
const limb swap = -iswap;
|
||||
|
||||
for (unsigned int i = 0; i < 5; ++i) {
|
||||
const limb x = swap & (a[i] ^ b[i]);
|
||||
a[i] ^= x;
|
||||
b[i] ^= x;
|
||||
}
|
||||
}
|
||||
|
||||
/* Calculates nQ where Q is the x-coordinate of a point on the curve
|
||||
*
|
||||
* resultx/resultz: the x coordinate of the resulting curve point (short form)
|
||||
* n: a little endian, 32-byte number
|
||||
* q: a point of the curve (short form)
|
||||
*/
|
||||
void cmult(limb *resultx, limb *resultz, const byte *n, const limb *q)
|
||||
{
|
||||
limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
|
||||
limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
|
||||
limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
|
||||
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
|
||||
|
||||
memcpy(nqpqx, q, sizeof(limb) * 5);
|
||||
|
||||
for (unsigned int i = 0; i < 32; ++i) {
|
||||
byte b = n[31 - i];
|
||||
for (unsigned int j = 0; j < 8; ++j) {
|
||||
const limb bit = b >> 7;
|
||||
|
||||
swap_conditional(nqx, nqpqx, bit);
|
||||
swap_conditional(nqz, nqpqz, bit);
|
||||
fmonty(nqx2, nqz2,
|
||||
nqpqx2, nqpqz2,
|
||||
nqx, nqz,
|
||||
nqpqx, nqpqz,
|
||||
q);
|
||||
swap_conditional(nqx2, nqpqx2, bit);
|
||||
swap_conditional(nqz2, nqpqz2, bit);
|
||||
|
||||
t = nqx;
|
||||
nqx = nqx2;
|
||||
nqx2 = t;
|
||||
t = nqz;
|
||||
nqz = nqz2;
|
||||
nqz2 = t;
|
||||
t = nqpqx;
|
||||
nqpqx = nqpqx2;
|
||||
nqpqx2 = t;
|
||||
t = nqpqz;
|
||||
nqpqz = nqpqz2;
|
||||
nqpqz2 = t;
|
||||
|
||||
b <<= 1;
|
||||
}
|
||||
}
|
||||
|
||||
memcpy(resultx, nqx, sizeof(limb) * 5);
|
||||
memcpy(resultz, nqz, sizeof(limb) * 5);
|
||||
}
|
||||
|
||||
|
||||
// -----------------------------------------------------------------------------
|
||||
// Shamelessly copied from djb's code, tightened a little
|
||||
// -----------------------------------------------------------------------------
|
||||
void crecip(felem out, const felem z)
|
||||
{
|
||||
felem a,t0,b,c;
|
||||
|
||||
/* 2 */ fsquare_times(a, z, 1); // a = 2
|
||||
/* 8 */ fsquare_times(t0, a, 2);
|
||||
/* 9 */ fmul(b, t0, z); // b = 9
|
||||
/* 11 */ fmul(a, b, a); // a = 11
|
||||
/* 22 */ fsquare_times(t0, a, 1);
|
||||
/* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
|
||||
/* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
|
||||
/* 2^10 - 2^0 */ fmul(b, t0, b);
|
||||
/* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
|
||||
/* 2^20 - 2^0 */ fmul(c, t0, b);
|
||||
/* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
|
||||
/* 2^40 - 2^0 */ fmul(t0, t0, c);
|
||||
/* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
|
||||
/* 2^50 - 2^0 */ fmul(b, t0, b);
|
||||
/* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
|
||||
/* 2^100 - 2^0 */ fmul(c, t0, b);
|
||||
/* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
|
||||
/* 2^200 - 2^0 */ fmul(t0, t0, c);
|
||||
/* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
|
||||
/* 2^250 - 2^0 */ fmul(t0, t0, b);
|
||||
/* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
|
||||
/* 2^255 - 21 */ fmul(out, t0, a);
|
||||
#define write51full(n,shift) \
|
||||
f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \
|
||||
for (i = 0; i < 8; i++, f >>= 8) *out++ = (unsigned char)f;
|
||||
#define write51(n) write51full(n,13*n)
|
||||
write51(0)
|
||||
write51(1)
|
||||
write51(2)
|
||||
write51(3)
|
||||
}
|
||||
|
||||
ANONYMOUS_NAMESPACE_END
|
||||
|
|
@ -485,24 +363,14 @@ NAMESPACE_BEGIN(Donna)
|
|||
|
||||
int curve25519_CXX(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
|
||||
{
|
||||
limb bp[5], x[5], z[5], zmone[5];
|
||||
byte e[32];
|
||||
bignum25519 out, r, s;
|
||||
curve25519_expand(r, secretKey);
|
||||
curve25519_expand(s, othersKey);
|
||||
|
||||
for (unsigned int i = 0; i < 32; ++i)
|
||||
e[i] = secretKey[i];
|
||||
curve25519_mul(out, r, s);
|
||||
curve25519_contract(sharedKey, out);
|
||||
|
||||
// I'd like to remove this copy/clamp but I don't
|
||||
// know if an attacker can cause an information
|
||||
// leak if multiply is misused.
|
||||
e[0] &= 248; e[31] &= 127; e[31] |= 64;
|
||||
|
||||
fexpand(bp, othersKey);
|
||||
cmult(x, z, e, bp);
|
||||
crecip(zmone, z);
|
||||
fmul(z, x, zmone);
|
||||
fcontract(sharedKey, z);
|
||||
|
||||
return 0;
|
||||
return 0;
|
||||
}
|
||||
|
||||
int curve25519(byte publicKey[32], const byte secretKey[32])
|
||||
|
|
@ -510,23 +378,23 @@ int curve25519(byte publicKey[32], const byte secretKey[32])
|
|||
const byte basePoint[32] = {9};
|
||||
|
||||
#if (CRYPTOPP_SSE2_INTRIN_AVAILABLE)
|
||||
if (HasSSE2())
|
||||
return curve25519_SSE2(publicKey, secretKey, basePoint);
|
||||
else
|
||||
if (HasSSE2())
|
||||
return curve25519_SSE2(publicKey, secretKey, basePoint);
|
||||
else
|
||||
#endif
|
||||
|
||||
return curve25519_CXX(publicKey, secretKey, basePoint);
|
||||
return curve25519_CXX(publicKey, secretKey, basePoint);
|
||||
}
|
||||
|
||||
int curve25519(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
|
||||
{
|
||||
#if (CRYPTOPP_SSE2_INTRIN_AVAILABLE)
|
||||
if (HasSSE2())
|
||||
return curve25519_SSE2(sharedKey, secretKey, othersKey);
|
||||
else
|
||||
if (HasSSE2())
|
||||
return curve25519_SSE2(sharedKey, secretKey, othersKey);
|
||||
else
|
||||
#endif
|
||||
|
||||
return curve25519_CXX(sharedKey, secretKey, othersKey);
|
||||
return curve25519_CXX(sharedKey, secretKey, othersKey);
|
||||
}
|
||||
|
||||
NAMESPACE_END // Donna
|
||||
|
|
|
|||
Loading…
Reference in New Issue