| Index: mozilla/security/nss/lib/freebl/mpi/mpmontg.c
|
| ===================================================================
|
| --- mozilla/security/nss/lib/freebl/mpi/mpmontg.c (revision 191424)
|
| +++ mozilla/security/nss/lib/freebl/mpi/mpmontg.c (working copy)
|
| @@ -1,1174 +0,0 @@
|
| -/* This Source Code Form is subject to the terms of the Mozilla Public
|
| - * License, v. 2.0. If a copy of the MPL was not distributed with this
|
| - * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
|
| -/* $Id: mpmontg.c,v 1.25 2012/11/14 01:14:11 wtc%google.com Exp $ */
|
| -
|
| -/* This file implements moduluar exponentiation using Montgomery's
|
| - * method for modular reduction. This file implements the method
|
| - * described as "Improvement 2" in the paper "A Cryptogrpahic Library for
|
| - * the Motorola DSP56000" by Stephen R. Dusse' and Burton S. Kaliski Jr.
|
| - * published in "Advances in Cryptology: Proceedings of EUROCRYPT '90"
|
| - * "Lecture Notes in Computer Science" volume 473, 1991, pg 230-244,
|
| - * published by Springer Verlag.
|
| - */
|
| -
|
| -#define MP_USING_CACHE_SAFE_MOD_EXP 1
|
| -#include <string.h>
|
| -#include "mpi-priv.h"
|
| -#include "mplogic.h"
|
| -#include "mpprime.h"
|
| -#ifdef MP_USING_MONT_MULF
|
| -#include "montmulf.h"
|
| -#endif
|
| -#include <stddef.h> /* ptrdiff_t */
|
| -
|
| -/* if MP_CHAR_STORE_SLOW is defined, we */
|
| -/* need to know endianness of this platform. */
|
| -#ifdef MP_CHAR_STORE_SLOW
|
| -#if !defined(MP_IS_BIG_ENDIAN) && !defined(MP_IS_LITTLE_ENDIAN)
|
| -#error "You must define MP_IS_BIG_ENDIAN or MP_IS_LITTLE_ENDIAN\n" \
|
| - " if you define MP_CHAR_STORE_SLOW."
|
| -#endif
|
| -#endif
|
| -
|
| -#define STATIC
|
| -
|
| -#define MAX_ODD_INTS 32 /* 2 ** (WINDOW_BITS - 1) */
|
| -
|
| -/*! computes T = REDC(T), 2^b == R
|
| - \param T < RN
|
| -*/
|
| -mp_err s_mp_redc(mp_int *T, mp_mont_modulus *mmm)
|
| -{
|
| - mp_err res;
|
| - mp_size i;
|
| -
|
| - i = (MP_USED(&mmm->N) << 1) + 1;
|
| - MP_CHECKOK( s_mp_pad(T, i) );
|
| - for (i = 0; i < MP_USED(&mmm->N); ++i ) {
|
| - mp_digit m_i = MP_DIGIT(T, i) * mmm->n0prime;
|
| - /* T += N * m_i * (MP_RADIX ** i); */
|
| - MP_CHECKOK( s_mp_mul_d_add_offset(&mmm->N, m_i, T, i) );
|
| - }
|
| - s_mp_clamp(T);
|
| -
|
| - /* T /= R */
|
| - s_mp_rshd( T, MP_USED(&mmm->N) );
|
| -
|
| - if ((res = s_mp_cmp(T, &mmm->N)) >= 0) {
|
| - /* T = T - N */
|
| - MP_CHECKOK( s_mp_sub(T, &mmm->N) );
|
| -#ifdef DEBUG
|
| - if ((res = mp_cmp(T, &mmm->N)) >= 0) {
|
| - res = MP_UNDEF;
|
| - goto CLEANUP;
|
| - }
|
| -#endif
|
| - }
|
| - res = MP_OKAY;
|
| -CLEANUP:
|
| - return res;
|
| -}
|
| -
|
| -#if !defined(MP_MONT_USE_MP_MUL)
|
| -
|
| -/*! c <- REDC( a * b ) mod N
|
| - \param a < N i.e. "reduced"
|
| - \param b < N i.e. "reduced"
|
| - \param mmm modulus N and n0' of N
|
| -*/
|
| -mp_err s_mp_mul_mont(const mp_int *a, const mp_int *b, mp_int *c,
|
| - mp_mont_modulus *mmm)
|
| -{
|
| - mp_digit *pb;
|
| - mp_digit m_i;
|
| - mp_err res;
|
| - mp_size ib; /* "index b": index of current digit of B */
|
| - mp_size useda, usedb;
|
| -
|
| - ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
|
| -
|
| - if (MP_USED(a) < MP_USED(b)) {
|
| - const mp_int *xch = b; /* switch a and b, to do fewer outer loops */
|
| - b = a;
|
| - a = xch;
|
| - }
|
| -
|
| - MP_USED(c) = 1; MP_DIGIT(c, 0) = 0;
|
| - ib = (MP_USED(&mmm->N) << 1) + 1;
|
| - if((res = s_mp_pad(c, ib)) != MP_OKAY)
|
| - goto CLEANUP;
|
| -
|
| - useda = MP_USED(a);
|
| - pb = MP_DIGITS(b);
|
| - s_mpv_mul_d(MP_DIGITS(a), useda, *pb++, MP_DIGITS(c));
|
| - s_mp_setz(MP_DIGITS(c) + useda + 1, ib - (useda + 1));
|
| - m_i = MP_DIGIT(c, 0) * mmm->n0prime;
|
| - s_mp_mul_d_add_offset(&mmm->N, m_i, c, 0);
|
| -
|
| - /* Outer loop: Digits of b */
|
| - usedb = MP_USED(b);
|
| - for (ib = 1; ib < usedb; ib++) {
|
| - mp_digit b_i = *pb++;
|
| -
|
| - /* Inner product: Digits of a */
|
| - if (b_i)
|
| - s_mpv_mul_d_add_prop(MP_DIGITS(a), useda, b_i, MP_DIGITS(c) + ib);
|
| - m_i = MP_DIGIT(c, ib) * mmm->n0prime;
|
| - s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
|
| - }
|
| - if (usedb < MP_USED(&mmm->N)) {
|
| - for (usedb = MP_USED(&mmm->N); ib < usedb; ++ib ) {
|
| - m_i = MP_DIGIT(c, ib) * mmm->n0prime;
|
| - s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
|
| - }
|
| - }
|
| - s_mp_clamp(c);
|
| - s_mp_rshd( c, MP_USED(&mmm->N) ); /* c /= R */
|
| - if (s_mp_cmp(c, &mmm->N) >= 0) {
|
| - MP_CHECKOK( s_mp_sub(c, &mmm->N) );
|
| - }
|
| - res = MP_OKAY;
|
| -
|
| -CLEANUP:
|
| - return res;
|
| -}
|
| -#endif
|
| -
|
| -STATIC
|
| -mp_err s_mp_to_mont(const mp_int *x, mp_mont_modulus *mmm, mp_int *xMont)
|
| -{
|
| - mp_err res;
|
| -
|
| - /* xMont = x * R mod N where N is modulus */
|
| - MP_CHECKOK( mp_copy( x, xMont ) );
|
| - MP_CHECKOK( s_mp_lshd( xMont, MP_USED(&mmm->N) ) ); /* xMont = x << b */
|
| - MP_CHECKOK( mp_div(xMont, &mmm->N, 0, xMont) ); /* mod N */
|
| -CLEANUP:
|
| - return res;
|
| -}
|
| -
|
| -#ifdef MP_USING_MONT_MULF
|
| -
|
| -/* the floating point multiply is already cache safe,
|
| - * don't turn on cache safe unless we specifically
|
| - * force it */
|
| -#ifndef MP_FORCE_CACHE_SAFE
|
| -#undef MP_USING_CACHE_SAFE_MOD_EXP
|
| -#endif
|
| -
|
| -unsigned int mp_using_mont_mulf = 1;
|
| -
|
| -/* computes montgomery square of the integer in mResult */
|
| -#define SQR \
|
| - conv_i32_to_d32_and_d16(dm1, d16Tmp, mResult, nLen); \
|
| - mont_mulf_noconv(mResult, dm1, d16Tmp, \
|
| - dTmp, dn, MP_DIGITS(modulus), nLen, dn0)
|
| -
|
| -/* computes montgomery product of x and the integer in mResult */
|
| -#define MUL(x) \
|
| - conv_i32_to_d32(dm1, mResult, nLen); \
|
| - mont_mulf_noconv(mResult, dm1, oddPowers[x], \
|
| - dTmp, dn, MP_DIGITS(modulus), nLen, dn0)
|
| -
|
| -/* Do modular exponentiation using floating point multiply code. */
|
| -mp_err mp_exptmod_f(const mp_int * montBase,
|
| - const mp_int * exponent,
|
| - const mp_int * modulus,
|
| - mp_int * result,
|
| - mp_mont_modulus *mmm,
|
| - int nLen,
|
| - mp_size bits_in_exponent,
|
| - mp_size window_bits,
|
| - mp_size odd_ints)
|
| -{
|
| - mp_digit *mResult;
|
| - double *dBuf = 0, *dm1, *dn, *dSqr, *d16Tmp, *dTmp;
|
| - double dn0;
|
| - mp_size i;
|
| - mp_err res;
|
| - int expOff;
|
| - int dSize = 0, oddPowSize, dTmpSize;
|
| - mp_int accum1;
|
| - double *oddPowers[MAX_ODD_INTS];
|
| -
|
| - /* function for computing n0prime only works if n0 is odd */
|
| -
|
| - MP_DIGITS(&accum1) = 0;
|
| -
|
| - for (i = 0; i < MAX_ODD_INTS; ++i)
|
| - oddPowers[i] = 0;
|
| -
|
| - MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
|
| -
|
| - mp_set(&accum1, 1);
|
| - MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
|
| - MP_CHECKOK( s_mp_pad(&accum1, nLen) );
|
| -
|
| - oddPowSize = 2 * nLen + 1;
|
| - dTmpSize = 2 * oddPowSize;
|
| - dSize = sizeof(double) * (nLen * 4 + 1 +
|
| - ((odd_ints + 1) * oddPowSize) + dTmpSize);
|
| - dBuf = (double *)malloc(dSize);
|
| - dm1 = dBuf; /* array of d32 */
|
| - dn = dBuf + nLen; /* array of d32 */
|
| - dSqr = dn + nLen; /* array of d32 */
|
| - d16Tmp = dSqr + nLen; /* array of d16 */
|
| - dTmp = d16Tmp + oddPowSize;
|
| -
|
| - for (i = 0; i < odd_ints; ++i) {
|
| - oddPowers[i] = dTmp;
|
| - dTmp += oddPowSize;
|
| - }
|
| - mResult = (mp_digit *)(dTmp + dTmpSize); /* size is nLen + 1 */
|
| -
|
| - /* Make dn and dn0 */
|
| - conv_i32_to_d32(dn, MP_DIGITS(modulus), nLen);
|
| - dn0 = (double)(mmm->n0prime & 0xffff);
|
| -
|
| - /* Make dSqr */
|
| - conv_i32_to_d32_and_d16(dm1, oddPowers[0], MP_DIGITS(montBase), nLen);
|
| - mont_mulf_noconv(mResult, dm1, oddPowers[0],
|
| - dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
|
| - conv_i32_to_d32(dSqr, mResult, nLen);
|
| -
|
| - for (i = 1; i < odd_ints; ++i) {
|
| - mont_mulf_noconv(mResult, dSqr, oddPowers[i - 1],
|
| - dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
|
| - conv_i32_to_d16(oddPowers[i], mResult, nLen);
|
| - }
|
| -
|
| - s_mp_copy(MP_DIGITS(&accum1), mResult, nLen); /* from, to, len */
|
| -
|
| - for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
|
| - mp_size smallExp;
|
| - MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
|
| - smallExp = (mp_size)res;
|
| -
|
| - if (window_bits == 1) {
|
| - if (!smallExp) {
|
| - SQR;
|
| - } else if (smallExp & 1) {
|
| - SQR; MUL(0);
|
| - } else {
|
| - abort();
|
| - }
|
| - } else if (window_bits == 4) {
|
| - if (!smallExp) {
|
| - SQR; SQR; SQR; SQR;
|
| - } else if (smallExp & 1) {
|
| - SQR; SQR; SQR; SQR; MUL(smallExp/2);
|
| - } else if (smallExp & 2) {
|
| - SQR; SQR; SQR; MUL(smallExp/4); SQR;
|
| - } else if (smallExp & 4) {
|
| - SQR; SQR; MUL(smallExp/8); SQR; SQR;
|
| - } else if (smallExp & 8) {
|
| - SQR; MUL(smallExp/16); SQR; SQR; SQR;
|
| - } else {
|
| - abort();
|
| - }
|
| - } else if (window_bits == 5) {
|
| - if (!smallExp) {
|
| - SQR; SQR; SQR; SQR; SQR;
|
| - } else if (smallExp & 1) {
|
| - SQR; SQR; SQR; SQR; SQR; MUL(smallExp/2);
|
| - } else if (smallExp & 2) {
|
| - SQR; SQR; SQR; SQR; MUL(smallExp/4); SQR;
|
| - } else if (smallExp & 4) {
|
| - SQR; SQR; SQR; MUL(smallExp/8); SQR; SQR;
|
| - } else if (smallExp & 8) {
|
| - SQR; SQR; MUL(smallExp/16); SQR; SQR; SQR;
|
| - } else if (smallExp & 0x10) {
|
| - SQR; MUL(smallExp/32); SQR; SQR; SQR; SQR;
|
| - } else {
|
| - abort();
|
| - }
|
| - } else if (window_bits == 6) {
|
| - if (!smallExp) {
|
| - SQR; SQR; SQR; SQR; SQR; SQR;
|
| - } else if (smallExp & 1) {
|
| - SQR; SQR; SQR; SQR; SQR; SQR; MUL(smallExp/2);
|
| - } else if (smallExp & 2) {
|
| - SQR; SQR; SQR; SQR; SQR; MUL(smallExp/4); SQR;
|
| - } else if (smallExp & 4) {
|
| - SQR; SQR; SQR; SQR; MUL(smallExp/8); SQR; SQR;
|
| - } else if (smallExp & 8) {
|
| - SQR; SQR; SQR; MUL(smallExp/16); SQR; SQR; SQR;
|
| - } else if (smallExp & 0x10) {
|
| - SQR; SQR; MUL(smallExp/32); SQR; SQR; SQR; SQR;
|
| - } else if (smallExp & 0x20) {
|
| - SQR; MUL(smallExp/64); SQR; SQR; SQR; SQR; SQR;
|
| - } else {
|
| - abort();
|
| - }
|
| - } else {
|
| - abort();
|
| - }
|
| - }
|
| -
|
| - s_mp_copy(mResult, MP_DIGITS(&accum1), nLen); /* from, to, len */
|
| -
|
| - res = s_mp_redc(&accum1, mmm);
|
| - mp_exch(&accum1, result);
|
| -
|
| -CLEANUP:
|
| - mp_clear(&accum1);
|
| - if (dBuf) {
|
| - if (dSize)
|
| - memset(dBuf, 0, dSize);
|
| - free(dBuf);
|
| - }
|
| -
|
| - return res;
|
| -}
|
| -#undef SQR
|
| -#undef MUL
|
| -#endif
|
| -
|
| -#define SQR(a,b) \
|
| - MP_CHECKOK( mp_sqr(a, b) );\
|
| - MP_CHECKOK( s_mp_redc(b, mmm) )
|
| -
|
| -#if defined(MP_MONT_USE_MP_MUL)
|
| -#define MUL(x,a,b) \
|
| - MP_CHECKOK( mp_mul(a, oddPowers + (x), b) ); \
|
| - MP_CHECKOK( s_mp_redc(b, mmm) )
|
| -#else
|
| -#define MUL(x,a,b) \
|
| - MP_CHECKOK( s_mp_mul_mont(a, oddPowers + (x), b, mmm) )
|
| -#endif
|
| -
|
| -#define SWAPPA ptmp = pa1; pa1 = pa2; pa2 = ptmp
|
| -
|
| -/* Do modular exponentiation using integer multiply code. */
|
| -mp_err mp_exptmod_i(const mp_int * montBase,
|
| - const mp_int * exponent,
|
| - const mp_int * modulus,
|
| - mp_int * result,
|
| - mp_mont_modulus *mmm,
|
| - int nLen,
|
| - mp_size bits_in_exponent,
|
| - mp_size window_bits,
|
| - mp_size odd_ints)
|
| -{
|
| - mp_int *pa1, *pa2, *ptmp;
|
| - mp_size i;
|
| - mp_err res;
|
| - int expOff;
|
| - mp_int accum1, accum2, power2, oddPowers[MAX_ODD_INTS];
|
| -
|
| - /* power2 = base ** 2; oddPowers[i] = base ** (2*i + 1); */
|
| - /* oddPowers[i] = base ** (2*i + 1); */
|
| -
|
| - MP_DIGITS(&accum1) = 0;
|
| - MP_DIGITS(&accum2) = 0;
|
| - MP_DIGITS(&power2) = 0;
|
| - for (i = 0; i < MAX_ODD_INTS; ++i) {
|
| - MP_DIGITS(oddPowers + i) = 0;
|
| - }
|
| -
|
| - MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
|
| - MP_CHECKOK( mp_init_size(&accum2, 3 * nLen + 2) );
|
| -
|
| - MP_CHECKOK( mp_init_copy(&oddPowers[0], montBase) );
|
| -
|
| - mp_init_size(&power2, nLen + 2 * MP_USED(montBase) + 2);
|
| - MP_CHECKOK( mp_sqr(montBase, &power2) ); /* power2 = montBase ** 2 */
|
| - MP_CHECKOK( s_mp_redc(&power2, mmm) );
|
| -
|
| - for (i = 1; i < odd_ints; ++i) {
|
| - mp_init_size(oddPowers + i, nLen + 2 * MP_USED(&power2) + 2);
|
| - MP_CHECKOK( mp_mul(oddPowers + (i - 1), &power2, oddPowers + i) );
|
| - MP_CHECKOK( s_mp_redc(oddPowers + i, mmm) );
|
| - }
|
| -
|
| - /* set accumulator to montgomery residue of 1 */
|
| - mp_set(&accum1, 1);
|
| - MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
|
| - pa1 = &accum1;
|
| - pa2 = &accum2;
|
| -
|
| - for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
|
| - mp_size smallExp;
|
| - MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
|
| - smallExp = (mp_size)res;
|
| -
|
| - if (window_bits == 1) {
|
| - if (!smallExp) {
|
| - SQR(pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 1) {
|
| - SQR(pa1,pa2); MUL(0,pa2,pa1);
|
| - } else {
|
| - abort();
|
| - }
|
| - } else if (window_bits == 4) {
|
| - if (!smallExp) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - } else if (smallExp & 1) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - MUL(smallExp/2, pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 2) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2);
|
| - MUL(smallExp/4,pa2,pa1); SQR(pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 4) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/8,pa1,pa2);
|
| - SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 8) {
|
| - SQR(pa1,pa2); MUL(smallExp/16,pa2,pa1); SQR(pa1,pa2);
|
| - SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
|
| - } else {
|
| - abort();
|
| - }
|
| - } else if (window_bits == 5) {
|
| - if (!smallExp) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - SQR(pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 1) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - SQR(pa1,pa2); MUL(smallExp/2,pa2,pa1);
|
| - } else if (smallExp & 2) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - MUL(smallExp/4,pa1,pa2); SQR(pa2,pa1);
|
| - } else if (smallExp & 4) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2);
|
| - MUL(smallExp/8,pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - } else if (smallExp & 8) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/16,pa1,pa2);
|
| - SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - } else if (smallExp & 0x10) {
|
| - SQR(pa1,pa2); MUL(smallExp/32,pa2,pa1); SQR(pa1,pa2);
|
| - SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - } else {
|
| - abort();
|
| - }
|
| - } else if (window_bits == 6) {
|
| - if (!smallExp) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - SQR(pa1,pa2); SQR(pa2,pa1);
|
| - } else if (smallExp & 1) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/2,pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 2) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - SQR(pa1,pa2); MUL(smallExp/4,pa2,pa1); SQR(pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 4) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - MUL(smallExp/8,pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 8) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2);
|
| - MUL(smallExp/16,pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - SQR(pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 0x10) {
|
| - SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/32,pa1,pa2);
|
| - SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 0x20) {
|
| - SQR(pa1,pa2); MUL(smallExp/64,pa2,pa1); SQR(pa1,pa2);
|
| - SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
|
| - } else {
|
| - abort();
|
| - }
|
| - } else {
|
| - abort();
|
| - }
|
| - }
|
| -
|
| - res = s_mp_redc(pa1, mmm);
|
| - mp_exch(pa1, result);
|
| -
|
| -CLEANUP:
|
| - mp_clear(&accum1);
|
| - mp_clear(&accum2);
|
| - mp_clear(&power2);
|
| - for (i = 0; i < odd_ints; ++i) {
|
| - mp_clear(oddPowers + i);
|
| - }
|
| - return res;
|
| -}
|
| -#undef SQR
|
| -#undef MUL
|
| -
|
| -#ifdef MP_USING_CACHE_SAFE_MOD_EXP
|
| -unsigned int mp_using_cache_safe_exp = 1;
|
| -#endif
|
| -
|
| -mp_err mp_set_safe_modexp(int value)
|
| -{
|
| -#ifdef MP_USING_CACHE_SAFE_MOD_EXP
|
| - mp_using_cache_safe_exp = value;
|
| - return MP_OKAY;
|
| -#else
|
| - if (value == 0) {
|
| - return MP_OKAY;
|
| - }
|
| - return MP_BADARG;
|
| -#endif
|
| -}
|
| -
|
| -#ifdef MP_USING_CACHE_SAFE_MOD_EXP
|
| -#define WEAVE_WORD_SIZE 4
|
| -
|
| -#ifndef MP_CHAR_STORE_SLOW
|
| -/*
|
| - * mpi_to_weave takes an array of bignums, a matrix in which each bignum
|
| - * occupies all the columns of a row, and transposes it into a matrix in
|
| - * which each bignum occupies a column of every row. The first row of the
|
| - * input matrix becomes the first column of the output matrix. The n'th
|
| - * row of input becomes the n'th column of output. The input data is said
|
| - * to be "interleaved" or "woven" into the output matrix.
|
| - *
|
| - * The array of bignums is left in this woven form. Each time a single
|
| - * bignum value is needed, it is recreated by fetching the n'th column,
|
| - * forming a single row which is the new bignum.
|
| - *
|
| - * The purpose of this interleaving is make it impossible to determine which
|
| - * of the bignums is being used in any one operation by examining the pattern
|
| - * of cache misses.
|
| - *
|
| - * The weaving function does not transpose the entire input matrix in one call.
|
| - * It transposes 4 rows of mp_ints into their respective columns of output.
|
| - *
|
| - * There are two different implementations of the weaving and unweaving code
|
| - * in this file. One uses byte loads and stores. The second uses loads and
|
| - * stores of mp_weave_word size values. The weaved forms of these two
|
| - * implementations differ. Consequently, each one has its own explanation.
|
| - *
|
| - * Here is the explanation for the byte-at-a-time implementation.
|
| - *
|
| - * This implementation treats each mp_int bignum as an array of bytes,
|
| - * rather than as an array of mp_digits. It stores those bytes as a
|
| - * column of bytes in the output matrix. It doesn't care if the machine
|
| - * uses big-endian or little-endian byte ordering within mp_digits.
|
| - * The first byte of the mp_digit array becomes the first byte in the output
|
| - * column, regardless of whether that byte is the MSB or LSB of the mp_digit.
|
| - *
|
| - * "bignums" is an array of mp_ints.
|
| - * It points to four rows, four mp_ints, a subset of a larger array of mp_ints.
|
| - *
|
| - * "weaved" is the weaved output matrix.
|
| - * The first byte of bignums[0] is stored in weaved[0].
|
| - *
|
| - * "nBignums" is the total number of bignums in the array of which "bignums"
|
| - * is a part.
|
| - *
|
| - * "nDigits" is the size in mp_digits of each mp_int in the "bignums" array.
|
| - * mp_ints that use less than nDigits digits are logically padded with zeros
|
| - * while being stored in the weaved array.
|
| - */
|
| -mp_err mpi_to_weave(const mp_int *bignums,
|
| - unsigned char *weaved,
|
| - mp_size nDigits, /* in each mp_int of input */
|
| - mp_size nBignums) /* in the entire source array */
|
| -{
|
| - mp_size i;
|
| - unsigned char * endDest = weaved + (nDigits * nBignums * sizeof(mp_digit));
|
| -
|
| - for (i=0; i < WEAVE_WORD_SIZE; i++) {
|
| - mp_size used = MP_USED(&bignums[i]);
|
| - unsigned char *pSrc = (unsigned char *)MP_DIGITS(&bignums[i]);
|
| - unsigned char *endSrc = pSrc + (used * sizeof(mp_digit));
|
| - unsigned char *pDest = weaved + i;
|
| -
|
| - ARGCHK(MP_SIGN(&bignums[i]) == MP_ZPOS, MP_BADARG);
|
| - ARGCHK(used <= nDigits, MP_BADARG);
|
| -
|
| - for (; pSrc < endSrc; pSrc++) {
|
| - *pDest = *pSrc;
|
| - pDest += nBignums;
|
| - }
|
| - while (pDest < endDest) {
|
| - *pDest = 0;
|
| - pDest += nBignums;
|
| - }
|
| - }
|
| -
|
| - return MP_OKAY;
|
| -}
|
| -
|
| -/* Reverse the operation above for one mp_int.
|
| - * Reconstruct one mp_int from its column in the weaved array.
|
| - * "pSrc" points to the offset into the weave array of the bignum we
|
| - * are going to reconstruct.
|
| - */
|
| -mp_err weave_to_mpi(mp_int *a, /* output, result */
|
| - const unsigned char *pSrc, /* input, byte matrix */
|
| - mp_size nDigits, /* per mp_int output */
|
| - mp_size nBignums) /* bignums in weaved matrix */
|
| -{
|
| - unsigned char *pDest = (unsigned char *)MP_DIGITS(a);
|
| - unsigned char *endDest = pDest + (nDigits * sizeof(mp_digit));
|
| -
|
| - MP_SIGN(a) = MP_ZPOS;
|
| - MP_USED(a) = nDigits;
|
| -
|
| - for (; pDest < endDest; pSrc += nBignums, pDest++) {
|
| - *pDest = *pSrc;
|
| - }
|
| - s_mp_clamp(a);
|
| - return MP_OKAY;
|
| -}
|
| -
|
| -#else
|
| -
|
| -/* Need a primitive that we know is 32 bits long... */
|
| -/* this is true on all modern processors we know of today*/
|
| -typedef unsigned int mp_weave_word;
|
| -
|
| -/*
|
| - * on some platforms character stores into memory is very expensive since they
|
| - * generate a read/modify/write operation on the bus. On those platforms
|
| - * we need to do integer writes to the bus. Because of some unrolled code,
|
| - * in this current code the size of mp_weave_word must be four. The code that
|
| - * makes this assumption explicity is called out. (on some platforms a write
|
| - * of 4 bytes still requires a single read-modify-write operation.
|
| - *
|
| - * This function is takes the identical parameters as the function above,
|
| - * however it lays out the final array differently. Where the previous function
|
| - * treats the mpi_int as an byte array, this function treats it as an array of
|
| - * mp_digits where each digit is stored in big endian order.
|
| - *
|
| - * since we need to interleave on a byte by byte basis, we need to collect
|
| - * several mpi structures together into a single uint32 before we write. We
|
| - * also need to make sure the uint32 is arranged so that the first value of
|
| - * the first array winds up in b[0]. This means construction of that uint32
|
| - * is endian specific (even though the layout of the mp_digits in the array
|
| - * is always big endian).
|
| - *
|
| - * The final data is stored as follows :
|
| - *
|
| - * Our same logical array p array, m is sizeof(mp_digit),
|
| - * N is still count and n is now b_size. If we define p[i].digit[j]0 as the
|
| - * most significant byte of the word p[i].digit[j], p[i].digit[j]1 as
|
| - * the next most significant byte of p[i].digit[j], ... and p[i].digit[j]m-1
|
| - * is the least significant byte.
|
| - * Our array would look like:
|
| - * p[0].digit[0]0 p[1].digit[0]0 ... p[N-2].digit[0]0 p[N-1].digit[0]0
|
| - * p[0].digit[0]1 p[1].digit[0]1 ... p[N-2].digit[0]1 p[N-1].digit[0]1
|
| - * . .
|
| - * p[0].digit[0]m-1 p[1].digit[0]m-1 ... p[N-2].digit[0]m-1 p[N-1].digit[0]m-1
|
| - * p[0].digit[1]0 p[1].digit[1]0 ... p[N-2].digit[1]0 p[N-1].digit[1]0
|
| - * . .
|
| - * . .
|
| - * p[0].digit[n-1]m-2 p[1].digit[n-1]m-2 ... p[N-2].digit[n-1]m-2 p[N-1].digit[n-1]m-2
|
| - * p[0].digit[n-1]m-1 p[1].digit[n-1]m-1 ... p[N-2].digit[n-1]m-1 p[N-1].digit[n-1]m-1
|
| - *
|
| - */
|
| -mp_err mpi_to_weave(const mp_int *a, unsigned char *b,
|
| - mp_size b_size, mp_size count)
|
| -{
|
| - mp_size i;
|
| - mp_digit *digitsa0;
|
| - mp_digit *digitsa1;
|
| - mp_digit *digitsa2;
|
| - mp_digit *digitsa3;
|
| - mp_size useda0;
|
| - mp_size useda1;
|
| - mp_size useda2;
|
| - mp_size useda3;
|
| - mp_weave_word *weaved = (mp_weave_word *)b;
|
| -
|
| - count = count/sizeof(mp_weave_word);
|
| -
|
| - /* this code pretty much depends on this ! */
|
| -#if MP_ARGCHK == 2
|
| - assert(WEAVE_WORD_SIZE == 4);
|
| - assert(sizeof(mp_weave_word) == 4);
|
| -#endif
|
| -
|
| - digitsa0 = MP_DIGITS(&a[0]);
|
| - digitsa1 = MP_DIGITS(&a[1]);
|
| - digitsa2 = MP_DIGITS(&a[2]);
|
| - digitsa3 = MP_DIGITS(&a[3]);
|
| - useda0 = MP_USED(&a[0]);
|
| - useda1 = MP_USED(&a[1]);
|
| - useda2 = MP_USED(&a[2]);
|
| - useda3 = MP_USED(&a[3]);
|
| -
|
| - ARGCHK(MP_SIGN(&a[0]) == MP_ZPOS, MP_BADARG);
|
| - ARGCHK(MP_SIGN(&a[1]) == MP_ZPOS, MP_BADARG);
|
| - ARGCHK(MP_SIGN(&a[2]) == MP_ZPOS, MP_BADARG);
|
| - ARGCHK(MP_SIGN(&a[3]) == MP_ZPOS, MP_BADARG);
|
| - ARGCHK(useda0 <= b_size, MP_BADARG);
|
| - ARGCHK(useda1 <= b_size, MP_BADARG);
|
| - ARGCHK(useda2 <= b_size, MP_BADARG);
|
| - ARGCHK(useda3 <= b_size, MP_BADARG);
|
| -
|
| -#define SAFE_FETCH(digit, used, word) ((word) < (used) ? (digit[word]) : 0)
|
| -
|
| - for (i=0; i < b_size; i++) {
|
| - mp_digit d0 = SAFE_FETCH(digitsa0,useda0,i);
|
| - mp_digit d1 = SAFE_FETCH(digitsa1,useda1,i);
|
| - mp_digit d2 = SAFE_FETCH(digitsa2,useda2,i);
|
| - mp_digit d3 = SAFE_FETCH(digitsa3,useda3,i);
|
| - register mp_weave_word acc;
|
| -
|
| -/*
|
| - * ONE_STEP takes the MSB of each of our current digits and places that
|
| - * byte in the appropriate position for writing to the weaved array.
|
| - * On little endian:
|
| - * b3 b2 b1 b0
|
| - * On big endian:
|
| - * b0 b1 b2 b3
|
| - * When the data is written it would always wind up:
|
| - * b[0] = b0
|
| - * b[1] = b1
|
| - * b[2] = b2
|
| - * b[3] = b3
|
| - *
|
| - * Once we've written the MSB, we shift the whole digit up left one
|
| - * byte, putting the Next Most Significant Byte in the MSB position,
|
| - * so we we repeat the next one step that byte will be written.
|
| - * NOTE: This code assumes sizeof(mp_weave_word) and MP_WEAVE_WORD_SIZE
|
| - * is 4.
|
| - */
|
| -#ifdef MP_IS_LITTLE_ENDIAN
|
| -#define MPI_WEAVE_ONE_STEP \
|
| - acc = (d0 >> (MP_DIGIT_BIT-8)) & 0x000000ff; d0 <<= 8; /*b0*/ \
|
| - acc |= (d1 >> (MP_DIGIT_BIT-16)) & 0x0000ff00; d1 <<= 8; /*b1*/ \
|
| - acc |= (d2 >> (MP_DIGIT_BIT-24)) & 0x00ff0000; d2 <<= 8; /*b2*/ \
|
| - acc |= (d3 >> (MP_DIGIT_BIT-32)) & 0xff000000; d3 <<= 8; /*b3*/ \
|
| - *weaved = acc; weaved += count;
|
| -#else
|
| -#define MPI_WEAVE_ONE_STEP \
|
| - acc = (d0 >> (MP_DIGIT_BIT-32)) & 0xff000000; d0 <<= 8; /*b0*/ \
|
| - acc |= (d1 >> (MP_DIGIT_BIT-24)) & 0x00ff0000; d1 <<= 8; /*b1*/ \
|
| - acc |= (d2 >> (MP_DIGIT_BIT-16)) & 0x0000ff00; d2 <<= 8; /*b2*/ \
|
| - acc |= (d3 >> (MP_DIGIT_BIT-8)) & 0x000000ff; d3 <<= 8; /*b3*/ \
|
| - *weaved = acc; weaved += count;
|
| -#endif
|
| - switch (sizeof(mp_digit)) {
|
| - case 32:
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - case 16:
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - case 8:
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - case 4:
|
| - MPI_WEAVE_ONE_STEP
|
| - MPI_WEAVE_ONE_STEP
|
| - case 2:
|
| - MPI_WEAVE_ONE_STEP
|
| - case 1:
|
| - MPI_WEAVE_ONE_STEP
|
| - break;
|
| - }
|
| - }
|
| -
|
| - return MP_OKAY;
|
| -}
|
| -
|
| -/* reverse the operation above for one entry.
|
| - * b points to the offset into the weave array of the power we are
|
| - * calculating */
|
| -mp_err weave_to_mpi(mp_int *a, const unsigned char *b,
|
| - mp_size b_size, mp_size count)
|
| -{
|
| - mp_digit *pb = MP_DIGITS(a);
|
| - mp_digit *end = &pb[b_size];
|
| -
|
| - MP_SIGN(a) = MP_ZPOS;
|
| - MP_USED(a) = b_size;
|
| -
|
| - for (; pb < end; pb++) {
|
| - register mp_digit digit;
|
| -
|
| - digit = *b << 8; b += count;
|
| -#define MPI_UNWEAVE_ONE_STEP digit |= *b; b += count; digit = digit << 8;
|
| - switch (sizeof(mp_digit)) {
|
| - case 32:
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - case 16:
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - case 8:
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - case 4:
|
| - MPI_UNWEAVE_ONE_STEP
|
| - MPI_UNWEAVE_ONE_STEP
|
| - case 2:
|
| - break;
|
| - }
|
| - digit |= *b; b += count;
|
| -
|
| - *pb = digit;
|
| - }
|
| - s_mp_clamp(a);
|
| - return MP_OKAY;
|
| -}
|
| -#endif
|
| -
|
| -
|
| -#define SQR(a,b) \
|
| - MP_CHECKOK( mp_sqr(a, b) );\
|
| - MP_CHECKOK( s_mp_redc(b, mmm) )
|
| -
|
| -#if defined(MP_MONT_USE_MP_MUL)
|
| -#define MUL_NOWEAVE(x,a,b) \
|
| - MP_CHECKOK( mp_mul(a, x, b) ); \
|
| - MP_CHECKOK( s_mp_redc(b, mmm) )
|
| -#else
|
| -#define MUL_NOWEAVE(x,a,b) \
|
| - MP_CHECKOK( s_mp_mul_mont(a, x, b, mmm) )
|
| -#endif
|
| -
|
| -#define MUL(x,a,b) \
|
| - MP_CHECKOK( weave_to_mpi(&tmp, powers + (x), nLen, num_powers) ); \
|
| - MUL_NOWEAVE(&tmp,a,b)
|
| -
|
| -#define SWAPPA ptmp = pa1; pa1 = pa2; pa2 = ptmp
|
| -#define MP_ALIGN(x,y) ((((ptrdiff_t)(x))+((y)-1))&(((ptrdiff_t)0)-(y)))
|
| -
|
| -/* Do modular exponentiation using integer multiply code. */
|
| -mp_err mp_exptmod_safe_i(const mp_int * montBase,
|
| - const mp_int * exponent,
|
| - const mp_int * modulus,
|
| - mp_int * result,
|
| - mp_mont_modulus *mmm,
|
| - int nLen,
|
| - mp_size bits_in_exponent,
|
| - mp_size window_bits,
|
| - mp_size num_powers)
|
| -{
|
| - mp_int *pa1, *pa2, *ptmp;
|
| - mp_size i;
|
| - mp_size first_window;
|
| - mp_err res;
|
| - int expOff;
|
| - mp_int accum1, accum2, accum[WEAVE_WORD_SIZE];
|
| - mp_int tmp;
|
| - unsigned char *powersArray;
|
| - unsigned char *powers;
|
| -
|
| - MP_DIGITS(&accum1) = 0;
|
| - MP_DIGITS(&accum2) = 0;
|
| - MP_DIGITS(&accum[0]) = 0;
|
| - MP_DIGITS(&accum[1]) = 0;
|
| - MP_DIGITS(&accum[2]) = 0;
|
| - MP_DIGITS(&accum[3]) = 0;
|
| - MP_DIGITS(&tmp) = 0;
|
| -
|
| - powersArray = (unsigned char *)malloc(num_powers*(nLen*sizeof(mp_digit)+1));
|
| - if (powersArray == NULL) {
|
| - res = MP_MEM;
|
| - goto CLEANUP;
|
| - }
|
| -
|
| - /* powers[i] = base ** (i); */
|
| - powers = (unsigned char *)MP_ALIGN(powersArray,num_powers);
|
| -
|
| - /* grab the first window value. This allows us to preload accumulator1
|
| - * and save a conversion, some squares and a multiple*/
|
| - MP_CHECKOK( mpl_get_bits(exponent,
|
| - bits_in_exponent-window_bits, window_bits) );
|
| - first_window = (mp_size)res;
|
| -
|
| - MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
|
| - MP_CHECKOK( mp_init_size(&accum2, 3 * nLen + 2) );
|
| - MP_CHECKOK( mp_init_size(&tmp, 3 * nLen + 2) );
|
| -
|
| - /* build the first WEAVE_WORD powers inline */
|
| - /* if WEAVE_WORD_SIZE is not 4, this code will have to change */
|
| - if (num_powers > 2) {
|
| - MP_CHECKOK( mp_init_size(&accum[0], 3 * nLen + 2) );
|
| - MP_CHECKOK( mp_init_size(&accum[1], 3 * nLen + 2) );
|
| - MP_CHECKOK( mp_init_size(&accum[2], 3 * nLen + 2) );
|
| - MP_CHECKOK( mp_init_size(&accum[3], 3 * nLen + 2) );
|
| - mp_set(&accum[0], 1);
|
| - MP_CHECKOK( s_mp_to_mont(&accum[0], mmm, &accum[0]) );
|
| - MP_CHECKOK( mp_copy(montBase, &accum[1]) );
|
| - SQR(montBase, &accum[2]);
|
| - MUL_NOWEAVE(montBase, &accum[2], &accum[3]);
|
| - MP_CHECKOK( mpi_to_weave(accum, powers, nLen, num_powers) );
|
| - if (first_window < 4) {
|
| - MP_CHECKOK( mp_copy(&accum[first_window], &accum1) );
|
| - first_window = num_powers;
|
| - }
|
| - } else {
|
| - if (first_window == 0) {
|
| - mp_set(&accum1, 1);
|
| - MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
|
| - } else {
|
| - /* assert first_window == 1? */
|
| - MP_CHECKOK( mp_copy(montBase, &accum1) );
|
| - }
|
| - }
|
| -
|
| - /*
|
| - * calculate all the powers in the powers array.
|
| - * this adds 2**(k-1)-2 square operations over just calculating the
|
| - * odd powers where k is the window size in the two other mp_modexpt
|
| - * implementations in this file. We will get some of that
|
| - * back by not needing the first 'k' squares and one multiply for the
|
| - * first window */
|
| - for (i = WEAVE_WORD_SIZE; i < num_powers; i++) {
|
| - int acc_index = i & (WEAVE_WORD_SIZE-1); /* i % WEAVE_WORD_SIZE */
|
| - if ( i & 1 ) {
|
| - MUL_NOWEAVE(montBase, &accum[acc_index-1] , &accum[acc_index]);
|
| - /* we've filled the array do our 'per array' processing */
|
| - if (acc_index == (WEAVE_WORD_SIZE-1)) {
|
| - MP_CHECKOK( mpi_to_weave(accum, powers + i - (WEAVE_WORD_SIZE-1),
|
| - nLen, num_powers) );
|
| -
|
| - if (first_window <= i) {
|
| - MP_CHECKOK( mp_copy(&accum[first_window & (WEAVE_WORD_SIZE-1)],
|
| - &accum1) );
|
| - first_window = num_powers;
|
| - }
|
| - }
|
| - } else {
|
| - /* up to 8 we can find 2^i-1 in the accum array, but at 8 we our source
|
| - * and target are the same so we need to copy.. After that, the
|
| - * value is overwritten, so we need to fetch it from the stored
|
| - * weave array */
|
| - if (i > 2* WEAVE_WORD_SIZE) {
|
| - MP_CHECKOK(weave_to_mpi(&accum2, powers+i/2, nLen, num_powers));
|
| - SQR(&accum2, &accum[acc_index]);
|
| - } else {
|
| - int half_power_index = (i/2) & (WEAVE_WORD_SIZE-1);
|
| - if (half_power_index == acc_index) {
|
| - /* copy is cheaper than weave_to_mpi */
|
| - MP_CHECKOK(mp_copy(&accum[half_power_index], &accum2));
|
| - SQR(&accum2,&accum[acc_index]);
|
| - } else {
|
| - SQR(&accum[half_power_index],&accum[acc_index]);
|
| - }
|
| - }
|
| - }
|
| - }
|
| - /* if the accum1 isn't set, Then there is something wrong with our logic
|
| - * above and is an internal programming error.
|
| - */
|
| -#if MP_ARGCHK == 2
|
| - assert(MP_USED(&accum1) != 0);
|
| -#endif
|
| -
|
| - /* set accumulator to montgomery residue of 1 */
|
| - pa1 = &accum1;
|
| - pa2 = &accum2;
|
| -
|
| - for (expOff = bits_in_exponent - window_bits*2; expOff >= 0; expOff -= window_bits) {
|
| - mp_size smallExp;
|
| - MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
|
| - smallExp = (mp_size)res;
|
| -
|
| - /* handle unroll the loops */
|
| - switch (window_bits) {
|
| - case 1:
|
| - if (!smallExp) {
|
| - SQR(pa1,pa2); SWAPPA;
|
| - } else if (smallExp & 1) {
|
| - SQR(pa1,pa2); MUL_NOWEAVE(montBase,pa2,pa1);
|
| - } else {
|
| - abort();
|
| - }
|
| - break;
|
| - case 6:
|
| - SQR(pa1,pa2); SQR(pa2,pa1);
|
| - /* fall through */
|
| - case 4:
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - MUL(smallExp, pa1,pa2); SWAPPA;
|
| - break;
|
| - case 5:
|
| - SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
|
| - SQR(pa1,pa2); MUL(smallExp,pa2,pa1);
|
| - break;
|
| - default:
|
| - abort(); /* could do a loop? */
|
| - }
|
| - }
|
| -
|
| - res = s_mp_redc(pa1, mmm);
|
| - mp_exch(pa1, result);
|
| -
|
| -CLEANUP:
|
| - mp_clear(&accum1);
|
| - mp_clear(&accum2);
|
| - mp_clear(&accum[0]);
|
| - mp_clear(&accum[1]);
|
| - mp_clear(&accum[2]);
|
| - mp_clear(&accum[3]);
|
| - mp_clear(&tmp);
|
| - /* PORT_Memset(powers,0,num_powers*nLen*sizeof(mp_digit)); */
|
| - free(powersArray);
|
| - return res;
|
| -}
|
| -#undef SQR
|
| -#undef MUL
|
| -#endif
|
| -
|
| -mp_err mp_exptmod(const mp_int *inBase, const mp_int *exponent,
|
| - const mp_int *modulus, mp_int *result)
|
| -{
|
| - const mp_int *base;
|
| - mp_size bits_in_exponent, i, window_bits, odd_ints;
|
| - mp_err res;
|
| - int nLen;
|
| - mp_int montBase, goodBase;
|
| - mp_mont_modulus mmm;
|
| -#ifdef MP_USING_CACHE_SAFE_MOD_EXP
|
| - static unsigned int max_window_bits;
|
| -#endif
|
| -
|
| - /* function for computing n0prime only works if n0 is odd */
|
| - if (!mp_isodd(modulus))
|
| - return s_mp_exptmod(inBase, exponent, modulus, result);
|
| -
|
| - MP_DIGITS(&montBase) = 0;
|
| - MP_DIGITS(&goodBase) = 0;
|
| -
|
| - if (mp_cmp(inBase, modulus) < 0) {
|
| - base = inBase;
|
| - } else {
|
| - MP_CHECKOK( mp_init(&goodBase) );
|
| - base = &goodBase;
|
| - MP_CHECKOK( mp_mod(inBase, modulus, &goodBase) );
|
| - }
|
| -
|
| - nLen = MP_USED(modulus);
|
| - MP_CHECKOK( mp_init_size(&montBase, 2 * nLen + 2) );
|
| -
|
| - mmm.N = *modulus; /* a copy of the mp_int struct */
|
| -
|
| - /* compute n0', given n0, n0' = -(n0 ** -1) mod MP_RADIX
|
| - ** where n0 = least significant mp_digit of N, the modulus.
|
| - */
|
| - mmm.n0prime = 0 - s_mp_invmod_radix( MP_DIGIT(modulus, 0) );
|
| -
|
| - MP_CHECKOK( s_mp_to_mont(base, &mmm, &montBase) );
|
| -
|
| - bits_in_exponent = mpl_significant_bits(exponent);
|
| -#ifdef MP_USING_CACHE_SAFE_MOD_EXP
|
| - if (mp_using_cache_safe_exp) {
|
| - if (bits_in_exponent > 780)
|
| - window_bits = 6;
|
| - else if (bits_in_exponent > 256)
|
| - window_bits = 5;
|
| - else if (bits_in_exponent > 20)
|
| - window_bits = 4;
|
| - /* RSA public key exponents are typically under 20 bits (common values
|
| - * are: 3, 17, 65537) and a 4-bit window is inefficient
|
| - */
|
| - else
|
| - window_bits = 1;
|
| - } else
|
| -#endif
|
| - if (bits_in_exponent > 480)
|
| - window_bits = 6;
|
| - else if (bits_in_exponent > 160)
|
| - window_bits = 5;
|
| - else if (bits_in_exponent > 20)
|
| - window_bits = 4;
|
| - /* RSA public key exponents are typically under 20 bits (common values
|
| - * are: 3, 17, 65537) and a 4-bit window is inefficient
|
| - */
|
| - else
|
| - window_bits = 1;
|
| -
|
| -#ifdef MP_USING_CACHE_SAFE_MOD_EXP
|
| - /*
|
| - * clamp the window size based on
|
| - * the cache line size.
|
| - */
|
| - if (!max_window_bits) {
|
| - unsigned long cache_size = s_mpi_getProcessorLineSize();
|
| - /* processor has no cache, use 'fast' code always */
|
| - if (cache_size == 0) {
|
| - mp_using_cache_safe_exp = 0;
|
| - }
|
| - if ((cache_size == 0) || (cache_size >= 64)) {
|
| - max_window_bits = 6;
|
| - } else if (cache_size >= 32) {
|
| - max_window_bits = 5;
|
| - } else if (cache_size >= 16) {
|
| - max_window_bits = 4;
|
| - } else max_window_bits = 1; /* should this be an assert? */
|
| - }
|
| -
|
| - /* clamp the window size down before we caclulate bits_in_exponent */
|
| - if (mp_using_cache_safe_exp) {
|
| - if (window_bits > max_window_bits) {
|
| - window_bits = max_window_bits;
|
| - }
|
| - }
|
| -#endif
|
| -
|
| - odd_ints = 1 << (window_bits - 1);
|
| - i = bits_in_exponent % window_bits;
|
| - if (i != 0) {
|
| - bits_in_exponent += window_bits - i;
|
| - }
|
| -
|
| -#ifdef MP_USING_MONT_MULF
|
| - if (mp_using_mont_mulf) {
|
| - MP_CHECKOK( s_mp_pad(&montBase, nLen) );
|
| - res = mp_exptmod_f(&montBase, exponent, modulus, result, &mmm, nLen,
|
| - bits_in_exponent, window_bits, odd_ints);
|
| - } else
|
| -#endif
|
| -#ifdef MP_USING_CACHE_SAFE_MOD_EXP
|
| - if (mp_using_cache_safe_exp) {
|
| - res = mp_exptmod_safe_i(&montBase, exponent, modulus, result, &mmm, nLen,
|
| - bits_in_exponent, window_bits, 1 << window_bits);
|
| - } else
|
| -#endif
|
| - res = mp_exptmod_i(&montBase, exponent, modulus, result, &mmm, nLen,
|
| - bits_in_exponent, window_bits, odd_ints);
|
| -
|
| -CLEANUP:
|
| - mp_clear(&montBase);
|
| - mp_clear(&goodBase);
|
| - /* Don't mp_clear mmm.N because it is merely a copy of modulus.
|
| - ** Just zap it.
|
| - */
|
| - memset(&mmm, 0, sizeof mmm);
|
| - return res;
|
| -}
|
|
|