/* ***** BEGIN LICENSE BLOCK ***** * Version: MPL 1.1/GPL 2.0/LGPL 2.1 * * The contents of this file are subject to the Mozilla Public License Version * 1.1 (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * http://www.mozilla.org/MPL/ * * Software distributed under the License is distributed on an "AS IS" basis, * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License * for the specific language governing rights and limitations under the * License. * * The Original Code is the Netscape security libraries. * * The Initial Developer of the Original Code is * Netscape Communications Corporation. * Portions created by the Initial Developer are Copyright (C) 2000 * the Initial Developer. All Rights Reserved. * * Contributor(s): * Sheueling Chang Shantz , * Stephen Fung , and * Douglas Stebila of Sun Laboratories. * * Alternatively, the contents of this file may be used under the terms of * either the GNU General Public License Version 2 or later (the "GPL"), or * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), * in which case the provisions of the GPL or the LGPL are applicable instead * of those above. If you wish to allow use of your version of this file only * under the terms of either the GPL or the LGPL, and not to allow others to * use your version of this file under the terms of the MPL, indicate your * decision by deleting the provisions above and replace them with the notice * and other provisions required by the GPL or the LGPL. If you do not delete * the provisions above, a recipient may use your version of this file under * the terms of any one of the MPL, the GPL or the LGPL. * * ***** END LICENSE BLOCK ***** */ /* $Id: mpmontg.c,v 1.20 2006/08/29 02:41:38 nelson%bolyard.com Exp $ */ /* This file implements moduluar exponentiation using Montgomery's * method for modular reduction. This file implements the method * described as "Improvement 1" 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 #include "mpi-priv.h" #include "mplogic.h" #include "mpprime.h" #ifdef MP_USING_MONT_MULF #include "montmulf.h" #endif #include /* 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) */ #if defined(_WIN32_WCE) #define ABORT res = MP_UNDEF; goto CLEANUP #else #define ABORT abort() #endif /* computes T = REDC(T), 2^b == R */ mp_err s_mp_redc(mp_int *T, mp_mont_modulus *mmm) { mp_err res; mp_size i; i = MP_USED(T) + MP_USED(&mmm->N) + 2; 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_div_2d(T, mmm->b); 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_ASSEMBLY_MUL_MONT) && !defined(MP_MONT_USE_MP_MUL) 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; 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(a) + MP_MAX(MP_USED(b), MP_USED(&mmm->N)) + 2; 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_div_2d(c, mmm->b); 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( mpl_lsh(x, xMont, mmm->b) ); /* 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 */ i = mpl_significant_bits(modulus); i += MP_DIGIT_BIT - 1; mmm.b = i - i % MP_DIGIT_BIT; /* 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; }