/* crypto/bn/bn_exp.c */ /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) * All rights reserved. * * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * "This product includes cryptographic software written by * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ /* ==================================================================== * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #include "cryptlib.h" #include "bn_lcl.h" #include /* maximum precomputation table size for *variable* sliding windows */ #define TABLE_SIZE 32 /* this one works - simple but works */ int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) { int i, bits, ret = 0; BIGNUM *v, *rr; if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return -1; } BN_CTX_start(ctx); if ((r == a) || (r == p)) rr = BN_CTX_get(ctx); else rr = r; v = BN_CTX_get(ctx); if (rr == NULL || v == NULL) goto err; if (BN_copy(v, a) == NULL) goto err; bits = BN_num_bits(p); if (BN_is_odd(p)) { if (BN_copy(rr, a) == NULL) goto err; } else { if (!BN_one(rr)) goto err; } for (i = 1; i < bits; i++) { if (!BN_sqr(v, v, ctx)) goto err; if (BN_is_bit_set(p, i)) { if (!BN_mul(rr, rr, v, ctx)) goto err; } } ret = 1; err: if (r != rr) BN_copy(r, rr); BN_CTX_end(ctx); bn_check_top(r); return (ret); } int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx) { int ret; bn_check_top(a); bn_check_top(p); bn_check_top(m); /* For even modulus m = 2^k*m_odd, it might make sense to compute * a^p mod m_odd and a^p mod 2^k separately (with Montgomery * exponentiation for the odd part), using appropriate exponent * reductions, and combine the results using the CRT. * * For now, we use Montgomery only if the modulus is odd; otherwise, * exponentiation using the reciprocal-based quick remaindering * algorithm is used. * * (Timing obtained with expspeed.c [computations a^p mod m * where a, p, m are of the same length: 256, 512, 1024, 2048, * 4096, 8192 bits], compared to the running time of the * standard algorithm: * * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] * 55 .. 77 % [UltraSparc processor, but * debug-solaris-sparcv8-gcc conf.] * * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] * * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont * at 2048 and more bits, but at 512 and 1024 bits, it was * slower even than the standard algorithm! * * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] * should be obtained when the new Montgomery reduction code * has been integrated into OpenSSL.) */ #define MONT_MUL_MOD #define MONT_EXP_WORD #define RECP_MUL_MOD #ifdef MONT_MUL_MOD /* I have finally been able to take out this pre-condition of * the top bit being set. It was caused by an error in BN_div * with negatives. There was also another problem when for a^b%m * a >= m. eay 07-May-97 */ /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ if (BN_is_odd(m)) { # ifdef MONT_EXP_WORD if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) { BN_ULONG A = a->d[0]; ret = BN_mod_exp_mont_word(r, A,p, m,ctx, NULL); } else # endif ret = BN_mod_exp_mont(r, a,p, m,ctx, NULL); } else #endif #ifdef RECP_MUL_MOD { ret = BN_mod_exp_recp(r, a,p, m, ctx); } #else { ret = BN_mod_exp_simple(r, a,p, m, ctx); } #endif bn_check_top(r); return (ret); } int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx) { int i, j, bits, ret = 0, wstart, wend, window, wvalue; int start = 1; BIGNUM *aa; /* Table of variables obtained from 'ctx' */ BIGNUM *val[TABLE_SIZE]; BN_RECP_CTX recp; if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return -1; } bits = BN_num_bits(p); if (bits == 0) { ret = BN_one(r); return ret; } BN_CTX_start(ctx); aa = BN_CTX_get(ctx); val[0] = BN_CTX_get(ctx); if (!aa || !val[0]) goto err; BN_RECP_CTX_init(&recp); if (m->neg) { /* ignore sign of 'm' */ if (!BN_copy(aa, m)) goto err; aa->neg = 0; if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) goto err; } else { if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) goto err; } if (!BN_nnmod(val[0], a, m, ctx)) goto err; /* 1 */ if (BN_is_zero(val[0])) { BN_zero(r); ret = 1; goto err; } window = BN_window_bits_for_exponent_size(bits); if (window > 1) { if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) goto err; /* 2 */ j = 1 << (window - 1); for (i = 1; i < j; i++) { if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) goto err; } } start = 1; /* This is used to avoid multiplication etc * when there is only the value '1' in the * buffer. */ wvalue = 0; /* The 'value' of the window */ wstart = bits - 1; /* The top bit of the window */ wend = 0; /* The bottom bit of the window */ if (!BN_one(r)) goto err; for (;;) { if (BN_is_bit_set(p, wstart) == 0) { if (!start) if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx)) goto err; if (wstart == 0) break; wstart--; continue; } /* We now have wstart on a 'set' bit, we now need to work out * how bit a window to do. To do this we need to scan * forward until the last set bit before the end of the * window */ j = wstart; wvalue = 1; wend = 0; for (i = 1; i < window; i++) { if (wstart - i < 0) break; if (BN_is_bit_set(p, wstart - i)) { wvalue <<= (i - wend); wvalue |= 1; wend = i; } } /* wend is the size of the current window */ j = wend + 1; /* add the 'bytes above' */ if (!start) for (i = 0; i < j; i++) { if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx)) goto err; } /* wvalue will be an odd number < 2^window */ if (!BN_mod_mul_reciprocal(r, r,val[wvalue >> 1], &recp, ctx)) goto err; /* move the 'window' down further */ wstart -= wend + 1; wvalue = 0; start = 0; if (wstart < 0) break; } ret = 1; err: BN_CTX_end(ctx); BN_RECP_CTX_free(&recp); bn_check_top(r); return (ret); } int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) { int i, j, bits, ret = 0, wstart, wend, window, wvalue; int start = 1; BIGNUM *d, *r; const BIGNUM *aa; /* Table of variables obtained from 'ctx' */ BIGNUM *val[TABLE_SIZE]; BN_MONT_CTX *mont = NULL; if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); } bn_check_top(a); bn_check_top(p); bn_check_top(m); if (!BN_is_odd(m)) { BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); return (0); } bits = BN_num_bits(p); if (bits == 0) { ret = BN_one(rr); return ret; } BN_CTX_start(ctx); d = BN_CTX_get(ctx); r = BN_CTX_get(ctx); val[0] = BN_CTX_get(ctx); if (!d || !r || !val[0]) goto err; /* If this is not done, things will break in the montgomery * part */ if (in_mont != NULL) mont = in_mont; else { if ((mont = BN_MONT_CTX_new()) == NULL) goto err; if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; } if (a->neg || BN_ucmp(a, m) >= 0) { if (!BN_nnmod(val[0], a,m, ctx)) goto err; aa = val[0]; } else aa = a; if (BN_is_zero(aa)) { BN_zero(rr); ret = 1; goto err; } if (!BN_to_montgomery(val[0], aa, mont, ctx)) goto err; /* 1 */ window = BN_window_bits_for_exponent_size(bits); if (window > 1) { if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx)) goto err; /* 2 */ j = 1 << (window - 1); for (i = 1; i < j; i++) { if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx)) goto err; } } start = 1; /* This is used to avoid multiplication etc * when there is only the value '1' in the * buffer. */ wvalue = 0; /* The 'value' of the window */ wstart = bits - 1; /* The top bit of the window */ wend = 0; /* The bottom bit of the window */ if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) goto err; for (;;) { if (BN_is_bit_set(p, wstart) == 0) { if (!start) { if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err; } if (wstart == 0) break; wstart--; continue; } /* We now have wstart on a 'set' bit, we now need to work out * how bit a window to do. To do this we need to scan * forward until the last set bit before the end of the * window */ j = wstart; wvalue = 1; wend = 0; for (i = 1; i < window; i++) { if (wstart - i < 0) break; if (BN_is_bit_set(p, wstart - i)) { wvalue <<= (i - wend); wvalue |= 1; wend = i; } } /* wend is the size of the current window */ j = wend + 1; /* add the 'bytes above' */ if (!start) for (i = 0; i < j; i++) { if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err; } /* wvalue will be an odd number < 2^window */ if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx)) goto err; /* move the 'window' down further */ wstart -= wend + 1; wvalue = 0; start = 0; if (wstart < 0) break; } if (!BN_from_montgomery(rr, r,mont, ctx)) goto err; ret = 1; err: if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); BN_CTX_end(ctx); bn_check_top(rr); return (ret); } /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout * so that accessing any of these table values shows the same access pattern as far * as cache lines are concerned. The following functions are used to transfer a BIGNUM * from/to that table. */ static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width) { size_t i, j; if (top > b->top) top = b->top; /* this works because 'buf' is explicitly zeroed */ for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) { buf[j] = ((unsigned char*)b->d)[i]; } return 1; } static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width) { size_t i, j; if (bn_wexpand(b, top) == NULL) return 0; for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) { ((unsigned char*)b->d)[i] = buf[j]; } b->top = top; bn_correct_top(b); return 1; } /* Given a pointer value, compute the next address that is a cache line multiple. */ #define MOD_EXP_CTIME_ALIGN(x_) \ ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) /* This variant of BN_mod_exp_mont() uses fixed windows and the special * precomputation memory layout to limit data-dependency to a minimum * to protect secret exponents (cf. the hyper-threading timing attacks * pointed out by Colin Percival, * http://www.daemonology.net/hyperthreading-considered-harmful/) */ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) { int i, bits, ret = 0, window, wvalue; int top; BN_MONT_CTX *mont = NULL; int numPowers; unsigned char *powerbufFree = NULL; int powerbufLen = 0; unsigned char *powerbuf = NULL; BIGNUM tmp, am; bn_check_top(a); bn_check_top(p); bn_check_top(m); top = m->top; if (!(m->d[0] & 1)) { BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); return (0); } bits = BN_num_bits(p); if (bits == 0) { ret = BN_one(rr); return ret; } BN_CTX_start(ctx); /* Allocate a montgomery context if it was not supplied by the caller. * If this is not done, things will break in the montgomery part. */ if (in_mont != NULL) mont = in_mont; else { if ((mont = BN_MONT_CTX_new()) == NULL) goto err; if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; } /* Get the window size to use with size of p. */ window = BN_window_bits_for_ctime_exponent_size(bits); #if defined(OPENSSL_BN_ASM_MONT5) if (window == 6 && bits <= 1024) window = 5; /* ~5% improvement of 2048-bit RSA sign */ #endif /* Allocate a buffer large enough to hold all of the pre-computed * powers of am, am itself and tmp. */ numPowers = 1 << window; powerbufLen = sizeof(m->d[0]) * (top * numPowers + ((2*top) > numPowers ? (2*top) : numPowers)); if ((powerbufFree = (unsigned char*)malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL) goto err; powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); memset(powerbuf, 0, powerbufLen); /* lay down tmp and am right after powers table */ tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); am.d = tmp.d + top; tmp.top = am.top = 0; tmp.dmax = am.dmax = top; tmp.neg = am.neg = 0; tmp.flags = am.flags = BN_FLG_STATIC_DATA; /* prepare a^0 in Montgomery domain */ #if 1 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx)) goto err; #else tmp.d[0] = (0 - m - >d[0]) & BN_MASK2; /* 2^(top*BN_BITS2) - m */ for (i = 1; i < top; i++) tmp.d[i] = (~m->d[i]) & BN_MASK2; tmp.top = top; #endif /* prepare a^1 in Montgomery domain */ if (a->neg || BN_ucmp(a, m) >= 0) { if (!BN_mod(&am, a,m, ctx)) goto err; if (!BN_to_montgomery(&am, &am, mont, ctx)) goto err; } else if (!BN_to_montgomery(&am, a,mont, ctx)) goto err; #if defined(OPENSSL_BN_ASM_MONT5) /* This optimization uses ideas from http://eprint.iacr.org/2011/239, * specifically optimization of cache-timing attack countermeasures * and pre-computation optimization. */ /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as * 512-bit RSA is hardly relevant, we omit it to spare size... */ if (window == 5) { void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, const void *table, const BN_ULONG *np, const BN_ULONG *n0, int num, int power); void bn_scatter5(const BN_ULONG *inp, size_t num, void *table, size_t power); void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); BN_ULONG *np = mont->N.d, *n0 = mont->n0; /* BN_to_montgomery can contaminate words above .top * [in BN_DEBUG[_DEBUG] build]... */ for (i = am.top; i < top; i++) am.d[i] = 0; for (i = tmp.top; i < top; i++) tmp.d[i] = 0; bn_scatter5(tmp.d, top, powerbuf, 0); bn_scatter5(am.d, am.top, powerbuf, 1); bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); bn_scatter5(tmp.d, top, powerbuf, 2); #if 0 for (i = 3; i < 32; i++) { /* Calculate a^i = a^(i-1) * a */ bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); bn_scatter5(tmp.d, top, powerbuf, i); } #else /* same as above, but uses squaring for 1/2 of operations */ for (i = 4; i < 32; i*=2) { bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_scatter5(tmp.d, top, powerbuf, i); } for (i = 3; i < 8; i += 2) { int j; bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); bn_scatter5(tmp.d, top, powerbuf, i); for (j = 2 * i; j < 32; j *= 2) { bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_scatter5(tmp.d, top, powerbuf, j); } } for (; i < 16; i += 2) { bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); bn_scatter5(tmp.d, top, powerbuf, i); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_scatter5(tmp.d, top, powerbuf, 2*i); } for (; i < 32; i += 2) { bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); bn_scatter5(tmp.d, top, powerbuf, i); } #endif bits--; for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); bn_gather5(tmp.d, top, powerbuf, wvalue); /* Scan the exponent one window at a time starting from the most * significant bits. */ while (bits >= 0) { for (wvalue = 0, i = 0; i < 5; i++, bits--) wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue); } tmp.top = top; bn_correct_top(&tmp); } else #endif { if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err; if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err; /* If the window size is greater than 1, then calculate * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) * (even powers could instead be computed as (a^(i/2))^2 * to use the slight performance advantage of sqr over mul). */ if (window > 1) { if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx)) goto err; if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err; for (i = 3; i < numPowers; i++) { /* Calculate a^i = a^(i-1) * a */ if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx)) goto err; if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err; } } bits--; for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, numPowers)) goto err; /* Scan the exponent one window at a time starting from the most * significant bits. */ while (bits >= 0) { wvalue = 0; /* The 'value' of the window */ /* Scan the window, squaring the result as we go */ for (i = 0; i < window; i++, bits--) { if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx)) goto err; wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); } /* Fetch the appropriate pre-computed value from the pre-buf */ if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err; /* Multiply the result into the intermediate result */ if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx)) goto err; } } /* Convert the final result from montgomery to standard format */ if (!BN_from_montgomery(rr, &tmp, mont, ctx)) goto err; ret = 1; err: if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); if (powerbuf != NULL) { OPENSSL_cleanse(powerbuf, powerbufLen); free(powerbufFree); } BN_CTX_end(ctx); return (ret); } int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) { BN_MONT_CTX *mont = NULL; int b, bits, ret = 0; int r_is_one; BN_ULONG w, next_w; BIGNUM *d, *r, *t; BIGNUM *swap_tmp; #define BN_MOD_MUL_WORD(r, w, m) \ (BN_mul_word(r, (w)) && \ (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) /* BN_MOD_MUL_WORD is only used with 'w' large, * so the BN_ucmp test is probably more overhead * than always using BN_mod (which uses BN_copy if * a similar test returns true). */ /* We can use BN_mod and do not need BN_nnmod because our * accumulator is never negative (the result of BN_mod does * not depend on the sign of the modulus). */ #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return -1; } bn_check_top(p); bn_check_top(m); if (!BN_is_odd(m)) { BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); return (0); } if (m->top == 1) a %= m->d[0]; /* make sure that 'a' is reduced */ bits = BN_num_bits(p); if (bits == 0) { ret = BN_one(rr); return ret; } if (a == 0) { BN_zero(rr); ret = 1; return ret; } BN_CTX_start(ctx); d = BN_CTX_get(ctx); r = BN_CTX_get(ctx); t = BN_CTX_get(ctx); if (d == NULL || r == NULL || t == NULL) goto err; if (in_mont != NULL) mont = in_mont; else { if ((mont = BN_MONT_CTX_new()) == NULL) goto err; if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; } r_is_one = 1; /* except for Montgomery factor */ /* bits-1 >= 0 */ /* The result is accumulated in the product r*w. */ w = a; /* bit 'bits-1' of 'p' is always set */ for (b = bits - 2; b >= 0; b--) { /* First, square r*w. */ next_w = w * w; if ((next_w / w) != w) /* overflow */ { if (r_is_one) { if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; r_is_one = 0; } else { if (!BN_MOD_MUL_WORD(r, w, m)) goto err; } next_w = 1; } w = next_w; if (!r_is_one) { if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err; } /* Second, multiply r*w by 'a' if exponent bit is set. */ if (BN_is_bit_set(p, b)) { next_w = w * a; if ((next_w / a) != w) /* overflow */ { if (r_is_one) { if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; r_is_one = 0; } else { if (!BN_MOD_MUL_WORD(r, w, m)) goto err; } next_w = a; } w = next_w; } } /* Finally, set r:=r*w. */ if (w != 1) { if (r_is_one) { if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; r_is_one = 0; } else { if (!BN_MOD_MUL_WORD(r, w, m)) goto err; } } if (r_is_one) /* can happen only if a == 1*/ { if (!BN_one(rr)) goto err; } else { if (!BN_from_montgomery(rr, r, mont, ctx)) goto err; } ret = 1; err: if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); BN_CTX_end(ctx); bn_check_top(rr); return (ret); } /* The old fallback, simple version :-) */ int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx) { int i, j,bits, ret = 0, wstart, wend, window, wvalue; int start = 1; BIGNUM *d; /* Table of variables obtained from 'ctx' */ BIGNUM *val[TABLE_SIZE]; if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return -1; } bits = BN_num_bits(p); if (bits == 0) { ret = BN_one(r); return ret; } BN_CTX_start(ctx); d = BN_CTX_get(ctx); val[0] = BN_CTX_get(ctx); if (!d || !val[0]) goto err; if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */ if (BN_is_zero(val[0])) { BN_zero(r); ret = 1; goto err; } window = BN_window_bits_for_exponent_size(bits); if (window > 1) { if (!BN_mod_mul(d, val[0], val[0], m, ctx)) goto err; /* 2 */ j = 1 << (window - 1); for (i = 1; i < j; i++) { if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul(val[i], val[i - 1], d,m, ctx)) goto err; } } start = 1; /* This is used to avoid multiplication etc * when there is only the value '1' in the * buffer. */ wvalue = 0; /* The 'value' of the window */ wstart = bits - 1; /* The top bit of the window */ wend = 0; /* The bottom bit of the window */ if (!BN_one(r)) goto err; for (;;) { if (BN_is_bit_set(p, wstart) == 0) { if (!start) if (!BN_mod_mul(r, r, r, m, ctx)) goto err; if (wstart == 0) break; wstart--; continue; } /* We now have wstart on a 'set' bit, we now need to work out * how bit a window to do. To do this we need to scan * forward until the last set bit before the end of the * window */ j = wstart; wvalue = 1; wend = 0; for (i = 1; i < window; i++) { if (wstart - i < 0) break; if (BN_is_bit_set(p, wstart - i)) { wvalue <<= (i - wend); wvalue |= 1; wend = i; } } /* wend is the size of the current window */ j = wend + 1; /* add the 'bytes above' */ if (!start) for (i = 0; i < j; i++) { if (!BN_mod_mul(r, r, r, m, ctx)) goto err; } /* wvalue will be an odd number < 2^window */ if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) goto err; /* move the 'window' down further */ wstart -= wend + 1; wvalue = 0; start = 0; if (wstart < 0) break; } ret = 1; err: BN_CTX_end(ctx); bn_check_top(r); return (ret); }