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20f4d22055
ext-cryptopp/donna_32.cpp
Jeffrey Walton 20f4d22055
Fix compile on 32-bit MIPS (GH #761) 
Testing on a ci20 dev-board with Debian 5 and GCC 4
2018-12-13 04:21:38 -05:00

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// donna_32.cpp - written and placed in public domain by Jeffrey Walton
// This is a port of Adam Langley's curve25519-donna
// located at https://github.com/agl/curve25519-donna
/* Copyright 2008, Google Inc.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following disclaimer
* in the documentation and/or other materials provided with the
* distribution.
* * Neither the name of Google Inc. nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* curve25519-donna: Curve25519 elliptic curve, public key function
*
* http://code.google.com/p/curve25519-donna/
*
* Adam Langley <agl@imperialviolet.org>
*
* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
*
* More information about curve25519 can be found here
* http://cr.yp.to/ecdh.html
*
* djb's sample implementation of curve25519 is written in a special assembly
* language called qhasm and uses the floating point registers.
*
* This is, almost, a clean room reimplementation from the curve25519 paper. It
* uses many of the tricks described therein. Only the crecip function is taken
* from the sample implementation. */
#include "pch.h"
#include "config.h"
#include "donna.h"
#include "stdcpp.h"
#include "cpu.h"
// This macro is not in a header like config.h because we don't want it
// exposed to user code. We also need a standard header like <stdint.h>
// or <stdef.h>. Langley uses uint128_t in the 64-bit code paths so
// we further restrict 64-bit code.
#if (UINTPTR_MAX == 0xffffffff) || !defined(CRYPTOPP_WORD128_AVAILABLE)
# define CRYPTOPP_32BIT 1
#else
# define CRYPTOPP_64BIT 1
#endif
// Some compilers don't handle the code for the arithmetic shifts
// well. For compilers we know how to support we will issue the asm
// to sidestep the problem. We also switch to a slightly different
// pattern. We believe the pattern preserves the existing properties
// without a branch. The ASM uses one intruction, while the C statement
// use 2 to 6 instructions, depending on the compiler.
#if (__GNUC__ >= 3) || (__SUNPRO_CC >= 0x5100)
# define CRYPTOPP_ASR_ASM 1
#endif
// Squash MS LNK4221 and libtool warnings
extern const char DONNA32_FNAME[] = __FILE__;
#if defined(CRYPTOPP_32BIT)
ANONYMOUS_NAMESPACE_BEGIN
using std::memcpy;
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::word64;
using CryptoPP::sword32;
using CryptoPP::sword64;
typedef sword64 limb;
// Added by JW for SunCC. SignExtendShift is just an
// arithmetic shift. Easier said than done in C. Use
// inline ASM when available. Avoid the bit twiddling
// hacks. Also see the comments for CRYPTOPP_ASR_ASM.
template <unsigned int S>
inline int SignExtendShift(int val)
{
#if defined(CRYPTOPP_ASR_ASM) && (CRYPTOPP_BOOL_X86)
__asm__
(
"sar %1, %0 \n"
: "+g" (val) : "I" (S) : "cc"
);
return val;
#elif defined(CRYPTOPP_ASR_ASM) && (CRYPTOPP_BOOL_ARM32)
__asm__
(
"asr %0, %0, %1 \n"
: "+r" (val) : "I" (S) :
);
return val;
#elif defined(CRYPTOPP_ASR_ASM) && (CRYPTOPP_BOOL_MIPS32)
__asm__
(
"sra %0, %0, %1 \n"
: "+r" (val) : "I" (S) :
);
return val;
#else
const unsigned int v = ((unsigned int)val >> S);
return ((signed int)v * -1);
#endif
}
template <unsigned int S>
inline unsigned int SignExtendShift(unsigned int val)
{
#if defined(CRYPTOPP_ASR_ASM) && (CRYPTOPP_BOOL_X86)
__asm__
(
"sar %1, %0 \n"
: "+g" (val) : "I" (S) : "cc"
);
return val;
#elif defined(CRYPTOPP_ASR_ASM) && (CRYPTOPP_BOOL_ARM32)
__asm__
(
"asr %0, %0, %1 \n"
: "+r" (val) : "I" (S) :
);
return val;
#elif defined(CRYPTOPP_ASR_ASM) && (CRYPTOPP_BOOL_MIPS32)
__asm__
(
"sra %0, %0, %1 \n"
: "+r" (val) : "I" (S) :
);
return val;
#else
const signed int v = (signed int)(val >> S);
return (unsigned int)(v * -1);
#endif
}
/* Field element representation:
*
* Field elements are written as an array of signed, 64-bit limbs, least
* significant first. The value of the field element is:
* x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
*
* i.e. the limbs are 26, 25, 26, 25, ... bits wide. */
/* Sum two numbers: output += in */
void fsum(limb *output, const limb *in)
{
for (unsigned int i = 0; i < 10; i += 2) {
output[0+i] = output[0+i] + in[0+i];
output[1+i] = output[1+i] + in[1+i];
}
}
/* Find the difference of two numbers: output = in - output
* (note the order of the arguments!). */
void fdifference(limb *output, const limb *in)
{
for (unsigned int i = 0; i < 10; ++i) {
output[i] = in[i] - output[i];
}
}
/* Multiply a number by a scalar: output = in * scalar */
void fscalar_product(limb *output, const limb *in, const limb scalar)
{
for (unsigned int i = 0; i < 10; ++i) {
output[i] = in[i] * scalar;
}
}
/* Multiply two numbers: output = in2 * in
*
* output must be distinct to both inputs. The inputs are reduced coefficient
* form, the output is not.
*
* output[x] <= 14 * the largest product of the input limbs. */
void fproduct(limb *output, const limb *in2, const limb *in)
{
output[0] = ((limb) ((sword32) in2[0])) * ((sword32) in[0]);
output[1] = ((limb) ((sword32) in2[0])) * ((sword32) in[1]) +
((limb) ((sword32) in2[1])) * ((sword32) in[0]);
output[2] = 2 * ((limb) ((sword32) in2[1])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[2]) +
((limb) ((sword32) in2[2])) * ((sword32) in[0]);
output[3] = ((limb) ((sword32) in2[1])) * ((sword32) in[2]) +
((limb) ((sword32) in2[2])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[3]) +
((limb) ((sword32) in2[3])) * ((sword32) in[0]);
output[4] = ((limb) ((sword32) in2[2])) * ((sword32) in[2]) +
2 * (((limb) ((sword32) in2[1])) * ((sword32) in[3]) +
((limb) ((sword32) in2[3])) * ((sword32) in[1])) +
((limb) ((sword32) in2[0])) * ((sword32) in[4]) +
((limb) ((sword32) in2[4])) * ((sword32) in[0]);
output[5] = ((limb) ((sword32) in2[2])) * ((sword32) in[3]) +
((limb) ((sword32) in2[3])) * ((sword32) in[2]) +
((limb) ((sword32) in2[1])) * ((sword32) in[4]) +
((limb) ((sword32) in2[4])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[0]);
output[6] = 2 * (((limb) ((sword32) in2[3])) * ((sword32) in[3]) +
((limb) ((sword32) in2[1])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[1])) +
((limb) ((sword32) in2[2])) * ((sword32) in[4]) +
((limb) ((sword32) in2[4])) * ((sword32) in[2]) +
((limb) ((sword32) in2[0])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[0]);
output[7] = ((limb) ((sword32) in2[3])) * ((sword32) in[4]) +
((limb) ((sword32) in2[4])) * ((sword32) in[3]) +
((limb) ((sword32) in2[2])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[2]) +
((limb) ((sword32) in2[1])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[0]);
output[8] = ((limb) ((sword32) in2[4])) * ((sword32) in[4]) +
2 * (((limb) ((sword32) in2[3])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[3]) +
((limb) ((sword32) in2[1])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[1])) +
((limb) ((sword32) in2[2])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[2]) +
((limb) ((sword32) in2[0])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[0]);
output[9] = ((limb) ((sword32) in2[4])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[4]) +
((limb) ((sword32) in2[3])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[3]) +
((limb) ((sword32) in2[2])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[2]) +
((limb) ((sword32) in2[1])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[0]);
output[10] = 2 * (((limb) ((sword32) in2[5])) * ((sword32) in[5]) +
((limb) ((sword32) in2[3])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[3]) +
((limb) ((sword32) in2[1])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[1])) +
((limb) ((sword32) in2[4])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[4]) +
((limb) ((sword32) in2[2])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[2]);
output[11] = ((limb) ((sword32) in2[5])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[5]) +
((limb) ((sword32) in2[4])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[4]) +
((limb) ((sword32) in2[3])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[3]) +
((limb) ((sword32) in2[2])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[2]);
output[12] = ((limb) ((sword32) in2[6])) * ((sword32) in[6]) +
2 * (((limb) ((sword32) in2[5])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[5]) +
((limb) ((sword32) in2[3])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[3])) +
((limb) ((sword32) in2[4])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[4]);
output[13] = ((limb) ((sword32) in2[6])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[6]) +
((limb) ((sword32) in2[5])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[5]) +
((limb) ((sword32) in2[4])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[4]);
output[14] = 2 * (((limb) ((sword32) in2[7])) * ((sword32) in[7]) +
((limb) ((sword32) in2[5])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[5])) +
((limb) ((sword32) in2[6])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[6]);
output[15] = ((limb) ((sword32) in2[7])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[7]) +
((limb) ((sword32) in2[6])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[6]);
output[16] = ((limb) ((sword32) in2[8])) * ((sword32) in[8]) +
2 * (((limb) ((sword32) in2[7])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[7]));
output[17] = ((limb) ((sword32) in2[8])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[8]);
output[18] = 2 * ((limb) ((sword32) in2[9])) * ((sword32) in[9]);
}
/* Reduce a long form to a short form by taking the input mod 2^255 - 19.
*
* On entry: |output[i]| < 14*2^54
* On exit: |output[0..8]| < 280*2^54 */
void freduce_degree(limb *output)
{
/* Each of these shifts and adds ends up multiplying the value by 19.
*
* For output[0..8], the absolute entry value is < 14*2^54 and we add, at
* most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */
output[8] += output[18] << 4;
output[8] += output[18] << 1;
output[8] += output[18];
output[7] += output[17] << 4;
output[7] += output[17] << 1;
output[7] += output[17];
output[6] += output[16] << 4;
output[6] += output[16] << 1;
output[6] += output[16];
output[5] += output[15] << 4;
output[5] += output[15] << 1;
output[5] += output[15];
output[4] += output[14] << 4;
output[4] += output[14] << 1;
output[4] += output[14];
output[3] += output[13] << 4;
output[3] += output[13] << 1;
output[3] += output[13];
output[2] += output[12] << 4;
output[2] += output[12] << 1;
output[2] += output[12];
output[1] += output[11] << 4;
output[1] += output[11] << 1;
output[1] += output[11];
output[0] += output[10] << 4;
output[0] += output[10] << 1;
output[0] += output[10];
}
// Modified for SunCC. See comments for CRYPTOPP_ASR_ASM.
// #if (-1 & 3) != 3
// #error "This code only works on a two's complement system"
// #endif
/* return v / 2^26, using only shifts and adds.
*
* On entry: v can take any value. */
inline limb div_by_2_26(const limb v)
{
/* High word of v; no shift needed. */
const word32 highword = (word32) (((word64) v) >> 32);
// Modified for SunCC. See comments for CRYPTOPP_ASR_ASM.
/* Set to all 1s if v was negative; else set to 0s. */
/* const sword32 sign = ((sword32) highword) >> 31; */
const word32 sign = SignExtendShift<31>(highword);
/* Set to 0x3ffffff if v was negative; else set to 0. */
/* const sword32 roundoff = ((word32) sign) >> 6; */
const sword32 roundoff = (sword32)(sign >> 6);
/* Should return v / (1<<26) */
return (v + roundoff) >> 26;
}
/* return v / (2^25), using only shifts and adds.
*
* On entry: v can take any value. */
inline limb div_by_2_25(const limb v)
{
/* High word of v; no shift needed*/
const word32 highword = (word32) (((word64) v) >> 32);
// Modified for SunCC. See comments for CRYPTOPP_ASR_ASM.
/* Set to all 1s if v was negative; else set to 0s. */
/* const sword32 sign = ((sword32) highword) >> 31; */
const word32 sign = SignExtendShift<31>(highword);
/* Set to 0x1ffffff if v was negative; else set to 0. */
/* const sword32 roundoff = ((word32) sign) >> 7; */
const sword32 roundoff = (sword32)(sign >> 7);
/* Should return v / (1<<25) */
return (v + roundoff) >> 25;
}
/* Reduce all coefficients of the short form input so that |x| < 2^26.
*
* On entry: |output[i]| < 280*2^54 */
void freduce_coefficients(limb *output)
{
output[10] = 0;
for (unsigned int i = 0; i < 10; i += 2) {
limb over = div_by_2_26(output[i]);
/* The entry condition (that |output[i]| < 280*2^54) means that over is, at
* most, 280*2^28 in the first iteration of this loop. This is added to the
* next limb and we can approximate the resulting bound of that limb by
* 281*2^54. */
output[i] -= over << 26;
output[i+1] += over;
/* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
* 281*2^29. When this is added to the next limb, the resulting bound can
* be approximated as 281*2^54.
*
* For subsequent iterations of the loop, 281*2^54 remains a conservative
* bound and no overflow occurs. */
over = div_by_2_25(output[i+1]);
output[i+1] -= over << 25;
output[i+2] += over;
}
/* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
output[0] += output[10] << 4;
output[0] += output[10] << 1;
output[0] += output[10];
output[10] = 0;
/* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
* So |over| will be no more than 2^16. */
{
limb over = div_by_2_26(output[0]);
output[0] -= over << 26;
output[1] += over;
}
/* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
* bound on |output[1]| is sufficient to meet our needs. */
}
/* A helpful wrapper around fproduct: output = in * in2.
*
* On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.
*
* output must be distinct to both inputs. The output is reduced degree
* (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. */
void fmul(limb *output, const limb *in, const limb *in2)
{
limb t[19];
fproduct(t, in, in2);
/* |t[i]| < 14*2^54 */
freduce_degree(t);
freduce_coefficients(t);
/* |t[i]| < 2^26 */
memcpy(output, t, sizeof(limb) * 10);
}
/* Square a number: output = in**2
*
* output must be distinct from the input. The inputs are reduced coefficient
* form, the output is not.
*
* output[x] <= 14 * the largest product of the input limbs. */
void fsquare_inner(limb *output, const limb *in)
{
output[0] = ((limb) ((sword32) in[0])) * ((sword32) in[0]);
output[1] = 2 * ((limb) ((sword32) in[0])) * ((sword32) in[1]);
output[2] = 2 * (((limb) ((sword32) in[1])) * ((sword32) in[1]) +
((limb) ((sword32) in[0])) * ((sword32) in[2]));
output[3] = 2 * (((limb) ((sword32) in[1])) * ((sword32) in[2]) +
((limb) ((sword32) in[0])) * ((sword32) in[3]));
output[4] = ((limb) ((sword32) in[2])) * ((sword32) in[2]) +
4 * ((limb) ((sword32) in[1])) * ((sword32) in[3]) +
2 * ((limb) ((sword32) in[0])) * ((sword32) in[4]);
output[5] = 2 * (((limb) ((sword32) in[2])) * ((sword32) in[3]) +
((limb) ((sword32) in[1])) * ((sword32) in[4]) +
((limb) ((sword32) in[0])) * ((sword32) in[5]));
output[6] = 2 * (((limb) ((sword32) in[3])) * ((sword32) in[3]) +
((limb) ((sword32) in[2])) * ((sword32) in[4]) +
((limb) ((sword32) in[0])) * ((sword32) in[6]) +
2 * ((limb) ((sword32) in[1])) * ((sword32) in[5]));
output[7] = 2 * (((limb) ((sword32) in[3])) * ((sword32) in[4]) +
((limb) ((sword32) in[2])) * ((sword32) in[5]) +
((limb) ((sword32) in[1])) * ((sword32) in[6]) +
((limb) ((sword32) in[0])) * ((sword32) in[7]));
output[8] = ((limb) ((sword32) in[4])) * ((sword32) in[4]) +
2 * (((limb) ((sword32) in[2])) * ((sword32) in[6]) +
((limb) ((sword32) in[0])) * ((sword32) in[8]) +
2 * (((limb) ((sword32) in[1])) * ((sword32) in[7]) +
((limb) ((sword32) in[3])) * ((sword32) in[5])));
output[9] = 2 * (((limb) ((sword32) in[4])) * ((sword32) in[5]) +
((limb) ((sword32) in[3])) * ((sword32) in[6]) +
((limb) ((sword32) in[2])) * ((sword32) in[7]) +
((limb) ((sword32) in[1])) * ((sword32) in[8]) +
((limb) ((sword32) in[0])) * ((sword32) in[9]));
output[10] = 2 * (((limb) ((sword32) in[5])) * ((sword32) in[5]) +
((limb) ((sword32) in[4])) * ((sword32) in[6]) +
((limb) ((sword32) in[2])) * ((sword32) in[8]) +
2 * (((limb) ((sword32) in[3])) * ((sword32) in[7]) +
((limb) ((sword32) in[1])) * ((sword32) in[9])));
output[11] = 2 * (((limb) ((sword32) in[5])) * ((sword32) in[6]) +
((limb) ((sword32) in[4])) * ((sword32) in[7]) +
((limb) ((sword32) in[3])) * ((sword32) in[8]) +
((limb) ((sword32) in[2])) * ((sword32) in[9]));
output[12] = ((limb) ((sword32) in[6])) * ((sword32) in[6]) +
2 * (((limb) ((sword32) in[4])) * ((sword32) in[8]) +
2 * (((limb) ((sword32) in[5])) * ((sword32) in[7]) +
((limb) ((sword32) in[3])) * ((sword32) in[9])));
output[13] = 2 * (((limb) ((sword32) in[6])) * ((sword32) in[7]) +
((limb) ((sword32) in[5])) * ((sword32) in[8]) +
((limb) ((sword32) in[4])) * ((sword32) in[9]));
output[14] = 2 * (((limb) ((sword32) in[7])) * ((sword32) in[7]) +
((limb) ((sword32) in[6])) * ((sword32) in[8]) +
2 * ((limb) ((sword32) in[5])) * ((sword32) in[9]));
output[15] = 2 * (((limb) ((sword32) in[7])) * ((sword32) in[8]) +
((limb) ((sword32) in[6])) * ((sword32) in[9]));
output[16] = ((limb) ((sword32) in[8])) * ((sword32) in[8]) +
4 * ((limb) ((sword32) in[7])) * ((sword32) in[9]);
output[17] = 2 * ((limb) ((sword32) in[8])) * ((sword32) in[9]);
output[18] = 2 * ((limb) ((sword32) in[9])) * ((sword32) in[9]);
}
/* fsquare sets output = in^2.
*
* On entry: The |in| argument is in reduced coefficients form and |in[i]| <
* 2^27.
*
* On exit: The |output| argument is in reduced coefficients form (indeed, one
* need only provide storage for 10 limbs) and |out[i]| < 2^26. */
void
fsquare(limb *output, const limb *in)
{
limb t[19];
fsquare_inner(t, in);
/* |t[i]| < 14*2^54 because the largest product of two limbs will be <
* 2^(27+27) and fsquare_inner adds together, at most, 14 of those
* products. */
freduce_degree(t);
freduce_coefficients(t);
/* |t[i]| < 2^26 */
memcpy(output, t, sizeof(limb) * 10);
}
/* Take a little-endian, 32-byte number and expand it into polynomial form */
void fexpand(limb *output, const byte *input)
{
#define F(n,start,shift,mask) \
output[n] = ((((limb) input[start + 0]) | \
((limb) input[start + 1]) << 8 | \
((limb) input[start + 2]) << 16 | \
((limb) input[start + 3]) << 24) >> shift) & mask;
F(0, 0, 0, 0x3ffffff);
F(1, 3, 2, 0x1ffffff);
F(2, 6, 3, 0x3ffffff);
F(3, 9, 5, 0x1ffffff);
F(4, 12, 6, 0x3ffffff);
F(5, 16, 0, 0x1ffffff);
F(6, 19, 1, 0x3ffffff);
F(7, 22, 3, 0x1ffffff);
F(8, 25, 4, 0x3ffffff);
F(9, 28, 6, 0x1ffffff);
#undef F
}
// Modified for SunCC. See comments for CRYPTOPP_ASR_ASM.
// #if (-32 >> 1) != -16
// #error "This code only works when >> does sign-extension on negative numbers"
// #endif
/* sword32_eq returns 0xffffffff iff a == b and zero otherwise. */
sword32 sword32_eq(sword32 a, sword32 b)
{
// Modified for SunCC. See comments for CRYPTOPP_ASR_ASM.
a = ~(a ^ b);
a &= a << 16;
a &= a << 8;
a &= a << 4;
a &= a << 2;
a &= a << 1;
/* return a >> 31; */
return (sword32)SignExtendShift<31>(a);
}
/* sword32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
* both non-negative. */
sword32 sword32_gte(sword32 a, sword32 b)
{
// Modified for SunCC. See comments for CRYPTOPP_ASR_ASM.
a -= b;
/* a >= 0 iff a >= b. */
/* return ~(a >> 31); */
return ~(sword32)SignExtendShift<31>(a);
}
/* Take a fully reduced polynomial form number and contract it into a
* little-endian, 32-byte array.
*
* On entry: |input_limbs[i]| < 2^26 */
void fcontract(byte *output, limb *input_limbs)
{
int i, j;
sword32 input[10];
sword32 mask;
/* |input_limbs[i]| < 2^26, so it's valid to convert to an sword32. */
for (i = 0; i < 10; i++) {
input[i] = (sword32)input_limbs[i];
}
for (j = 0; j < 2; ++j) {
for (i = 0; i < 9; ++i) {
if ((i & 1) == 1) {
/* This calculation is a time-invariant way to make input[i]
* non-negative by borrowing from the next-larger limb. */
const sword32 mask = input[i] >> 31;
const sword32 carry = -((input[i] & mask) >> 25);
input[i] = input[i] + (carry << 25);
input[i+1] = input[i+1] - carry;
} else {
const sword32 mask = input[i] >> 31;
const sword32 carry = -((input[i] & mask) >> 26);
input[i] = input[i] + (carry << 26);
input[i+1] = input[i+1] - carry;
}
}
/* There's no greater limb for input[9] to borrow from, but we can multiply
* by 19 and borrow from input[0], which is valid mod 2^255-19. */
{
const sword32 mask = input[9] >> 31;
const sword32 carry = -((input[9] & mask) >> 25);
input[9] = input[9] + (carry << 25);
input[0] = input[0] - (carry * 19);
}
/* After the first iteration, input[1..9] are non-negative and fit within
* 25 or 26 bits, depending on position. However, input[0] may be
* negative. */
}
/* The first borrow-propagation pass above ended with every limb
except (possibly) input[0] non-negative.
If input[0] was negative after the first pass, then it was because of a
carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
In the second pass, each limb is decreased by at most one. Thus the second
borrow-propagation pass could only have wrapped around to decrease
input[0] again if the first pass left input[0] negative *and* input[1]
through input[9] were all zero. In that case, input[1] is now 2^25 - 1,
and this last borrow-propagation step will leave input[1] non-negative. */
{
const sword32 mask = input[0] >> 31;
const sword32 carry = -((input[0] & mask) >> 26);
input[0] = input[0] + (carry << 26);
input[1] = input[1] - carry;
}
/* All input[i] are now non-negative. However, there might be values between
* 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */
for (j = 0; j < 2; j++) {
for (i = 0; i < 9; i++) {
if ((i & 1) == 1) {
const sword32 carry = input[i] >> 25;
input[i] &= 0x1ffffff;
input[i+1] += carry;
} else {
const sword32 carry = input[i] >> 26;
input[i] &= 0x3ffffff;
input[i+1] += carry;
}
}
{
const sword32 carry = input[9] >> 25;
input[9] &= 0x1ffffff;
input[0] += 19*carry;
}
}
/* If the first carry-chain pass, just above, ended up with a carry from
* input[9], and that caused input[0] to be out-of-bounds, then input[0] was
* < 2^26 + 2*19, because the carry was, at most, two.
*
* If the second pass carried from input[9] again then input[0] is < 2*19 and
* the input[9] -> input[0] carry didn't push input[0] out of bounds. */
/* It still remains the case that input might be between 2^255-19 and 2^255.
* In this case, input[1..9] must take their maximum value and input[0] must
* be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */
mask = sword32_gte(input[0], 0x3ffffed);
for (i = 1; i < 10; i++) {
if ((i & 1) == 1) {
mask &= sword32_eq(input[i], 0x1ffffff);
} else {
mask &= sword32_eq(input[i], 0x3ffffff);
}
}
/* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
* this conditionally subtracts 2^255-19. */
input[0] -= mask & 0x3ffffed;
for (i = 1; i < 10; i++) {
if ((i & 1) == 1) {
input[i] -= mask & 0x1ffffff;
} else {
input[i] -= mask & 0x3ffffff;
}
}
input[1] <<= 2;
input[2] <<= 3;
input[3] <<= 5;
input[4] <<= 6;
input[6] <<= 1;
input[7] <<= 3;
input[8] <<= 4;
input[9] <<= 6;
#define F(i, s) \
output[s+0] |= input[i] & 0xff; \
output[s+1] = (input[i] >> 8) & 0xff; \
output[s+2] = (input[i] >> 16) & 0xff; \
output[s+3] = (input[i] >> 24) & 0xff;
output[0] = 0;
output[16] = 0;
F(0,0);
F(1,3);
F(2,6);
F(3,9);
F(4,12);
F(5,16);
F(6,19);
F(7,22);
F(8,25);
F(9,28);
#undef F
}
/* 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
*
* On entry and exit, the absolute value of the limbs of all inputs and outputs
* are < 2^26. */
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[10], origxprime[10], zzz[19], xx[19], zz[19];
limb xxprime[19], zzprime[19], zzzprime[19], xxxprime[19];
memcpy(origx, x, 10 * sizeof(limb));
fsum(x, z);
/* |x[i]| < 2^27 */
fdifference(z, origx); /* does x - z */
/* |z[i]| < 2^27 */
memcpy(origxprime, xprime, sizeof(limb) * 10);
fsum(xprime, zprime);
/* |xprime[i]| < 2^27 */
fdifference(zprime, origxprime);
/* |zprime[i]| < 2^27 */
fproduct(xxprime, xprime, z);
/* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <
* 2^(27+27) and fproduct adds together, at most, 14 of those products.
* (Approximating that to 2^58 doesn't work out.) */
fproduct(zzprime, x, zprime);
/* |zzprime[i]| < 14*2^54 */
freduce_degree(xxprime);
freduce_coefficients(xxprime);
/* |xxprime[i]| < 2^26 */
freduce_degree(zzprime);
freduce_coefficients(zzprime);
/* |zzprime[i]| < 2^26 */
memcpy(origxprime, xxprime, sizeof(limb) * 10);
fsum(xxprime, zzprime);
/* |xxprime[i]| < 2^27 */
fdifference(zzprime, origxprime);
/* |zzprime[i]| < 2^27 */
fsquare(xxxprime, xxprime);
/* |xxxprime[i]| < 2^26 */
fsquare(zzzprime, zzprime);
/* |zzzprime[i]| < 2^26 */
fproduct(zzprime, zzzprime, qmqp);
/* |zzprime[i]| < 14*2^52 */
freduce_degree(zzprime);
freduce_coefficients(zzprime);
/* |zzprime[i]| < 2^26 */
memcpy(x3, xxxprime, sizeof(limb) * 10);
memcpy(z3, zzprime, sizeof(limb) * 10);
fsquare(xx, x);
/* |xx[i]| < 2^26 */
fsquare(zz, z);
/* |zz[i]| < 2^26 */
fproduct(x2, xx, zz);
/* |x2[i]| < 14*2^52 */
freduce_degree(x2);
freduce_coefficients(x2);
/* |x2[i]| < 2^26 */
fdifference(zz, xx); // does zz = xx - zz
/* |zz[i]| < 2^27 */
memset(zzz + 10, 0, sizeof(limb) * 9);
fscalar_product(zzz, zz, 121665);
/* |zzz[i]| < 2^(27+17) */
/* No need to call freduce_degree here:
fscalar_product doesn't increase the degree of its input. */
freduce_coefficients(zzz);
/* |zzz[i]| < 2^26 */
fsum(zzz, xx);
/* |zzz[i]| < 2^27 */
fproduct(z2, zz, zzz);
/* |z2[i]| < 14*2^(26+27) */
freduce_degree(z2);
freduce_coefficients(z2);
/* |z2|i| < 2^26 */
}
/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
* them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
* side-channel attacks.
*
* NOTE that this function requires that 'iswap' be 1 or 0; other values give
* wrong results. Also, the two limb arrays must be in reduced-coefficient,
* reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
* and all all values in a[0..9],b[0..9] must have magnitude less than
* INT32_MAX. */
void swap_conditional(limb a[19], limb b[19], limb iswap)
{
const sword32 swap = (sword32) -iswap;
for (unsigned int i = 0; i < 10; ++i) {
const sword32 x = swap & ( ((sword32)a[i]) ^ ((sword32)b[i]) );
a[i] = ((sword32)a[i]) ^ x;
b[i] = ((sword32)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[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
memcpy(nqpqx, q, sizeof(limb) * 10);
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) * 10);
memcpy(resultz, nqz, sizeof(limb) * 10);
}
// -----------------------------------------------------------------------------
// Shamelessly copied from djb's code
// -----------------------------------------------------------------------------
void crecip(limb *out, const limb *z)
{
limb z2[10];
limb z9[10];
limb z11[10];
limb z2_5_0[10];
limb z2_10_0[10];
limb z2_20_0[10];
limb z2_50_0[10];
limb z2_100_0[10];
limb t0[10];
limb t1[10];
int i;
/* 2 */ fsquare(z2,z);
/* 4 */ fsquare(t1,z2);
/* 8 */ fsquare(t0,t1);
/* 9 */ fmul(z9,t0,z);
/* 11 */ fmul(z11,z9,z2);
/* 22 */ fsquare(t0,z11);
/* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9);
/* 2^6 - 2^1 */ fsquare(t0,z2_5_0);
/* 2^7 - 2^2 */ fsquare(t1,t0);
/* 2^8 - 2^3 */ fsquare(t0,t1);
/* 2^9 - 2^4 */ fsquare(t1,t0);
/* 2^10 - 2^5 */ fsquare(t0,t1);
/* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0);
/* 2^11 - 2^1 */ fsquare(t0,z2_10_0);
/* 2^12 - 2^2 */ fsquare(t1,t0);
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0);
/* 2^21 - 2^1 */ fsquare(t0,z2_20_0);
/* 2^22 - 2^2 */ fsquare(t1,t0);
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0);
/* 2^41 - 2^1 */ fsquare(t1,t0);
/* 2^42 - 2^2 */ fsquare(t0,t1);
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
/* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0);
/* 2^51 - 2^1 */ fsquare(t0,z2_50_0);
/* 2^52 - 2^2 */ fsquare(t1,t0);
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0);
/* 2^101 - 2^1 */ fsquare(t1,z2_100_0);
/* 2^102 - 2^2 */ fsquare(t0,t1);
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
/* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0);
/* 2^201 - 2^1 */ fsquare(t0,t1);
/* 2^202 - 2^2 */ fsquare(t1,t0);
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0);
/* 2^251 - 2^1 */ fsquare(t1,t0);
/* 2^252 - 2^2 */ fsquare(t0,t1);
/* 2^253 - 2^3 */ fsquare(t1,t0);
/* 2^254 - 2^4 */ fsquare(t0,t1);
/* 2^255 - 2^5 */ fsquare(t1,t0);
/* 2^255 - 21 */ fmul(out,t1,z11);
}
ANONYMOUS_NAMESPACE_END
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
int curve25519(byte publicKey[32], const byte secretKey[32])
{
const byte basePoint[32] = {9};
return curve25519(publicKey, secretKey, basePoint);
}
int curve25519(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
{
limb bp[10], x[10], z[11], zmone[10];
byte e[32];
for (unsigned int i = 0; i < 32; ++i)
e[i] = secretKey[i];
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;
}
NAMESPACE_END // Donna
NAMESPACE_END // CryptoPP
#endif // CRYPTOPP_32BIT
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