| /* 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 <openssl/opensslconf.h> |
| #if !defined(OPENSSL_SYS_STARBOARD) |
| #include <stdlib.h> |
| #endif // !defined(OPENSSL_SYS_STARBOARD) |
| #ifdef _WIN32 |
| # include <malloc.h> |
| # ifndef alloca |
| # define alloca _alloca |
| # endif |
| #elif defined(__SNC__) |
| # include <alloca.h> |
| // The code below assumes alloca is a macro. |
| # define alloca alloca |
| #elif defined(__GNUC__) |
| # ifndef alloca |
| # define alloca(s) __builtin_alloca((s)) |
| # endif |
| #endif |
| |
| /* 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; |
| } |
| } |
| if (r != rr) |
| BN_copy(r, rr); |
| ret = 1; |
| err: |
| 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) { |
| /* x**0 mod 1 is still zero. */ |
| if (BN_is_one(m)) { |
| ret = 1; |
| BN_zero(r); |
| } else { |
| 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) { |
| /* x**0 mod 1 is still zero. */ |
| if (BN_is_one(m)) { |
| ret = 1; |
| BN_zero(rr); |
| } else { |
| 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); |
| |
| if (!BN_is_odd(m)) { |
| BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); |
| return (0); |
| } |
| |
| top = m->top; |
| |
| bits = BN_num_bits(p); |
| if (bits == 0) { |
| /* x**0 mod 1 is still zero. */ |
| if (BN_is_one(m)) { |
| ret = 1; |
| BN_zero(rr); |
| } else { |
| 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)); |
| #ifdef alloca |
| if (powerbufLen < 3072) |
| powerbufFree = |
| alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); |
| else |
| #endif |
| if ((powerbufFree = |
| (unsigned char *)OPENSSL_malloc(powerbufLen + |
| MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) |
| == NULL) |
| goto err; |
| |
| powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); |
| OPENSSL_port_memset(powerbuf, 0, powerbufLen); |
| |
| #ifdef alloca |
| if (powerbufLen < 3072) |
| powerbufFree = NULL; |
| #endif |
| |
| /* 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) |
| if (window == 5 && top > 1) { |
| /* |
| * 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... |
| */ |
| 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); |
| if (powerbufFree) |
| OPENSSL_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) { |
| /* x**0 mod 1 is still zero. */ |
| if (BN_is_one(m)) { |
| ret = 1; |
| BN_zero(rr); |
| } else { |
| 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) { |
| /* x**0 mod 1 is still zero. */ |
| if (BN_is_one(m)) { |
| ret = 1; |
| BN_zero(r); |
| } else { |
| 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); |
| } |