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-rw-r--r-- | security/nss/lib/freebl/mpi/mpmontg.c | 1160 |
1 files changed, 1160 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/mpi/mpmontg.c b/security/nss/lib/freebl/mpi/mpmontg.c new file mode 100644 index 0000000000..63842c6314 --- /dev/null +++ b/security/nss/lib/freebl/mpi/mpmontg.c @@ -0,0 +1,1160 @@ +/* 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/. */ + +/* 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 */ +#include <assert.h> + +#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); */ + 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 + +mp_err +mp_to_mont(const mp_int *x, const mp_int *N, mp_int *xMont) +{ + mp_err res; + + /* xMont = x * R mod N where N is modulus */ + if (x != xMont) { + MP_CHECKOK(mp_copy(x, xMont)); + } + MP_CHECKOK(s_mp_lshd(xMont, MP_USED(N))); /* xMont = x << b */ + MP_CHECKOK(mp_div(xMont, N, 0, xMont)); /* mod N */ +CLEANUP: + return res; +} + +mp_digit +mp_calculate_mont_n0i(const mp_int *N) +{ + return 0 - s_mp_invmod_radix(MP_DIGIT(N, 0)); +} + +#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(mp_to_mont(&accum1, &(mmm->N), &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 = malloc(dSize); + if (!dBuf) { + res = MP_MEM; + goto CLEANUP; + } + 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_CHECKOK(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_CHECKOK(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(mp_to_mont(&accum1, &(mmm->N), &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 + +/* + * 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. + * + * This implementation treats each mp_int bignum as an array of mp_digits, + * It stores those bytes as a column of mp_digits in the output matrix. It + * doesn't care if the machine uses big-endian or little-endian byte ordering + * within mp_digits. + * + * "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, + mp_digit *weaved, + mp_size nDigits, /* in each mp_int of input */ + mp_size nBignums) /* in the entire source array */ +{ + mp_size i; + mp_digit *endDest = weaved + (nDigits * nBignums); + + for (i = 0; i < WEAVE_WORD_SIZE; i++) { + mp_size used = MP_USED(&bignums[i]); + mp_digit *pSrc = MP_DIGITS(&bignums[i]); + mp_digit *endSrc = pSrc + used; + mp_digit *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; +} + +/* + * These functions return 0xffffffff if the output is true, and 0 otherwise. + */ +#define CONST_TIME_MSB(x) (0L - ((x) >> (8 * sizeof(x) - 1))) +#define CONST_TIME_EQ_Z(x) CONST_TIME_MSB(~(x) & ((x)-1)) +#define CONST_TIME_EQ(a, b) CONST_TIME_EQ_Z((a) ^ (b)) + +/* Reverse the operation above for one mp_int. + * Reconstruct one mp_int from its column in the weaved array. + * Every read accesses every element of the weaved array, in order to + * avoid timing attacks based on patterns of memory accesses. + */ +mp_err +weave_to_mpi(mp_int *a, /* out, result */ + const mp_digit *weaved, /* in, byte matrix */ + mp_size index, /* which column to read */ + mp_size nDigits, /* number of mp_digits in each bignum */ + mp_size nBignums) /* width of the matrix */ +{ + /* these are indices, but need to be the same size as mp_digit + * because of the CONST_TIME operations */ + mp_digit i, j; + mp_digit d; + mp_digit *pDest = MP_DIGITS(a); + + MP_SIGN(a) = MP_ZPOS; + MP_USED(a) = nDigits; + + assert(weaved != NULL); + + /* Fetch the proper column in constant time, indexing over the whole array */ + for (i = 0; i < nDigits; ++i) { + d = 0; + for (j = 0; j < nBignums; ++j) { + d |= weaved[i * nBignums + j] & CONST_TIME_EQ(j, index); + } + pDest[i] = d; + } + + s_mp_clamp(a); + return MP_OKAY; +} + +#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; + mp_digit *powersArray = NULL; + mp_digit *powers = NULL; + + 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; + + /* 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)); + + /* 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(mp_to_mont(&accum[0], &(mmm->N), &accum[0])); + MP_CHECKOK(mp_copy(montBase, &accum[1])); + SQR(montBase, &accum[2]); + MUL_NOWEAVE(montBase, &accum[2], &accum[3]); + powersArray = (mp_digit *)malloc(num_powers * (nLen * sizeof(mp_digit) + 1)); + if (!powersArray) { + res = MP_MEM; + goto CLEANUP; + } + /* powers[i] = base ** (i); */ + powers = (mp_digit *)MP_ALIGN(powersArray, num_powers); + 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(mp_to_mont(&accum1, &(mmm->N), &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. + * Given the value of 4 for WEAVE_WORD_SIZE, this loop will only execute if + * num_powers > 2, in which case powers will have been allocated. + */ + 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; + + /* tmp is not used if window_bits == 1. */ + if (window_bits != 1) { + MP_CHECKOK(mp_init_size(&tmp, 3 * nLen + 2)); + } + + 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); + /* zero required by FIPS here, can't use PORT_ZFree + * because mpi doesn't link with util */ + if (powers) { + PORT_Memset(powers, 0, num_powers * 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); + + if (mp_cmp_z(inBase) == MP_LT) + return MP_RANGE; + 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 = mp_calculate_mont_n0i(modulus); + + MP_CHECKOK(mp_to_mont(base, modulus, &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; +} |