| /* 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 <openssl/bn.h> |
| |
| #include <assert.h> |
| |
| #include <openssl/cpu.h> |
| #include <openssl/err.h> |
| #include <openssl/mem.h> |
| |
| #include "internal.h" |
| |
| |
| #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) |
| #define OPENSSL_BN_ASM_MONT5 |
| #define RSAZ_ENABLED |
| |
| #include "rsaz_exp.h" |
| #endif |
| |
| int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) { |
| int i, bits, ret = 0; |
| BIGNUM *v, *rr; |
| |
| if ((p->flags & BN_FLG_CONSTTIME) != 0) { |
| /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ |
| OPENSSL_PUT_ERROR(BN, BN_exp, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
| return 0; |
| } |
| |
| 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); |
| return ret; |
| } |
| |
| /* maximum precomputation table size for *variable* sliding windows */ |
| #define TABLE_SIZE 32 |
| |
| typedef struct bn_recp_ctx_st { |
| BIGNUM N; /* the divisor */ |
| BIGNUM Nr; /* the reciprocal */ |
| int num_bits; |
| int shift; |
| int flags; |
| } BN_RECP_CTX; |
| |
| static void BN_RECP_CTX_init(BN_RECP_CTX *recp) { |
| BN_init(&recp->N); |
| BN_init(&recp->Nr); |
| recp->num_bits = 0; |
| recp->flags = 0; |
| } |
| |
| static void BN_RECP_CTX_free(BN_RECP_CTX *recp) { |
| if (recp == NULL) { |
| return; |
| } |
| |
| BN_free(&recp->N); |
| BN_free(&recp->Nr); |
| } |
| |
| static int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx) { |
| if (!BN_copy(&(recp->N), d)) { |
| return 0; |
| } |
| BN_zero(&recp->Nr); |
| recp->num_bits = BN_num_bits(d); |
| recp->shift = 0; |
| |
| return 1; |
| } |
| |
| /* len is the expected size of the result We actually calculate with an extra |
| * word of precision, so we can do faster division if the remainder is not |
| * required. |
| * r := 2^len / m */ |
| static int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx) { |
| int ret = -1; |
| BIGNUM *t; |
| |
| BN_CTX_start(ctx); |
| t = BN_CTX_get(ctx); |
| if (t == NULL) { |
| goto err; |
| } |
| |
| if (!BN_set_bit(t, len)) { |
| goto err; |
| } |
| |
| if (!BN_div(r, NULL, t, m, ctx)) { |
| goto err; |
| } |
| |
| ret = len; |
| |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |
| |
| static int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, |
| BN_RECP_CTX *recp, BN_CTX *ctx) { |
| int i, j, ret = 0; |
| BIGNUM *a, *b, *d, *r; |
| |
| BN_CTX_start(ctx); |
| a = BN_CTX_get(ctx); |
| b = BN_CTX_get(ctx); |
| if (dv != NULL) { |
| d = dv; |
| } else { |
| d = BN_CTX_get(ctx); |
| } |
| |
| if (rem != NULL) { |
| r = rem; |
| } else { |
| r = BN_CTX_get(ctx); |
| } |
| |
| if (a == NULL || b == NULL || d == NULL || r == NULL) { |
| goto err; |
| } |
| |
| if (BN_ucmp(m, &(recp->N)) < 0) { |
| BN_zero(d); |
| if (!BN_copy(r, m)) { |
| return 0; |
| } |
| BN_CTX_end(ctx); |
| return 1; |
| } |
| |
| /* We want the remainder |
| * Given input of ABCDEF / ab |
| * we need multiply ABCDEF by 3 digests of the reciprocal of ab */ |
| |
| /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */ |
| i = BN_num_bits(m); |
| j = recp->num_bits << 1; |
| if (j > i) { |
| i = j; |
| } |
| |
| /* Nr := round(2^i / N) */ |
| if (i != recp->shift) { |
| recp->shift = |
| BN_reciprocal(&(recp->Nr), &(recp->N), i, |
| ctx); /* BN_reciprocal returns i, or -1 for an error */ |
| } |
| |
| if (recp->shift == -1) { |
| goto err; |
| } |
| |
| /* d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - |
| * BN_num_bits(N)))| |
| * = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - |
| * BN_num_bits(N)))| |
| * <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)| |
| * = |m/N| */ |
| if (!BN_rshift(a, m, recp->num_bits)) { |
| goto err; |
| } |
| if (!BN_mul(b, a, &(recp->Nr), ctx)) { |
| goto err; |
| } |
| if (!BN_rshift(d, b, i - recp->num_bits)) { |
| goto err; |
| } |
| d->neg = 0; |
| |
| if (!BN_mul(b, &(recp->N), d, ctx)) { |
| goto err; |
| } |
| if (!BN_usub(r, m, b)) { |
| goto err; |
| } |
| r->neg = 0; |
| |
| j = 0; |
| while (BN_ucmp(r, &(recp->N)) >= 0) { |
| if (j++ > 2) { |
| OPENSSL_PUT_ERROR(BN, BN_div_recp, BN_R_BAD_RECIPROCAL); |
| goto err; |
| } |
| if (!BN_usub(r, r, &(recp->N))) { |
| goto err; |
| } |
| if (!BN_add_word(d, 1)) { |
| goto err; |
| } |
| } |
| |
| r->neg = BN_is_zero(r) ? 0 : m->neg; |
| d->neg = m->neg ^ recp->N.neg; |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |
| |
| static int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, |
| BN_RECP_CTX *recp, BN_CTX *ctx) { |
| int ret = 0; |
| BIGNUM *a; |
| const BIGNUM *ca; |
| |
| BN_CTX_start(ctx); |
| a = BN_CTX_get(ctx); |
| if (a == NULL) { |
| goto err; |
| } |
| |
| if (y != NULL) { |
| if (x == y) { |
| if (!BN_sqr(a, x, ctx)) { |
| goto err; |
| } |
| } else { |
| if (!BN_mul(a, x, y, ctx)) { |
| goto err; |
| } |
| } |
| ca = a; |
| } else { |
| ca = x; /* Just do the mod */ |
| } |
| |
| ret = BN_div_recp(NULL, r, ca, recp, ctx); |
| |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |
| |
| /* BN_window_bits_for_exponent_size -- macro for sliding window mod_exp |
| * functions |
| * |
| * For window size 'w' (w >= 2) and a random 'b' bits exponent, the number of |
| * multiplications is a constant plus on average |
| * |
| * 2^(w-1) + (b-w)/(w+1); |
| * |
| * here 2^(w-1) is for precomputing the table (we actually need entries only |
| * for windows that have the lowest bit set), and (b-w)/(w+1) is an |
| * approximation for the expected number of w-bit windows, not counting the |
| * first one. |
| * |
| * Thus we should use |
| * |
| * w >= 6 if b > 671 |
| * w = 5 if 671 > b > 239 |
| * w = 4 if 239 > b > 79 |
| * w = 3 if 79 > b > 23 |
| * w <= 2 if 23 > b |
| * |
| * (with draws in between). Very small exponents are often selected |
| * with low Hamming weight, so we use w = 1 for b <= 23. */ |
| #define BN_window_bits_for_exponent_size(b) \ |
| ((b) > 671 ? 6 : \ |
| (b) > 239 ? 5 : \ |
| (b) > 79 ? 4 : \ |
| (b) > 23 ? 3 : 1) |
| |
| static int mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
| const BIGNUM *m, BN_CTX *ctx) { |
| int i, j, bits, ret = 0, wstart, window; |
| 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() */ |
| OPENSSL_PUT_ERROR(BN, mod_exp_recp, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
| return 0; |
| } |
| |
| 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. */ |
| wstart = bits - 1; /* The top bit of the window */ |
| |
| if (!BN_one(r)) { |
| goto err; |
| } |
| |
| for (;;) { |
| int wvalue; /* The 'value' of the window */ |
| int wend; /* The bottom bit of the window */ |
| |
| 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 */ |
| 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; |
| start = 0; |
| if (wstart < 0) { |
| break; |
| } |
| } |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| BN_RECP_CTX_free(&recp); |
| return ret; |
| } |
| |
| int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, |
| BN_CTX *ctx) { |
| /* 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.) */ |
| |
| if (BN_is_odd(m)) { |
| if (a->top == 1 && !a->neg && BN_get_flags(p, BN_FLG_CONSTTIME) == 0) { |
| BN_ULONG A = a->d[0]; |
| return BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); |
| } |
| |
| return BN_mod_exp_mont(r, a, p, m, ctx, NULL); |
| } |
| |
| return mod_exp_recp(r, a, p, m, ctx); |
| } |
| |
| 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, window; |
| 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); |
| } |
| |
| if (!BN_is_odd(m)) { |
| OPENSSL_PUT_ERROR(BN, 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 { |
| mont = BN_MONT_CTX_new(); |
| if (mont == 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. */ |
| wstart = bits - 1; /* The top bit of the window */ |
| |
| j = m->top; /* borrow j */ |
| if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { |
| if (bn_wexpand(r, j) == NULL) |
| goto err; |
| /* 2^(top*BN_BITS2) - m */ |
| r->d[0] = (0 - m->d[0]) & BN_MASK2; |
| for (i = 1; i < j; i++) |
| r->d[i] = (~m->d[i]) & BN_MASK2; |
| r->top = j; |
| /* Upper words will be zero if the corresponding words of 'm' |
| * were 0xfff[...], so decrement r->top accordingly. */ |
| bn_correct_top(r); |
| } else if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) { |
| goto err; |
| } |
| |
| for (;;) { |
| int wvalue; /* The 'value' of the window */ |
| int wend; /* The bottom bit of the window */ |
| |
| 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 */ |
| 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; |
| 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); |
| 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 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 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; |
| } |
| |
| /* BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache |
| * line width of the target processor is at least the following value. */ |
| #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH (64) |
| #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK \ |
| (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1) |
| |
| /* Window sizes optimized for fixed window size modular exponentiation |
| * algorithm (BN_mod_exp_mont_consttime). |
| * |
| * To achieve the security goals of BN_mode_exp_mont_consttime, the maximum |
| * size of the window must not exceed |
| * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). |
| * |
| * Window size thresholds are defined for cache line sizes of 32 and 64, cache |
| * line sizes where log_2(32)=5 and log_2(64)=6 respectively. A window size of |
| * 7 should only be used on processors that have a 128 byte or greater cache |
| * line size. */ |
| #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64 |
| |
| #define BN_window_bits_for_ctime_exponent_size(b) \ |
| ((b) > 937 ? 6 : (b) > 306 ? 5 : (b) > 89 ? 4 : (b) > 22 ? 3 : 1) |
| #define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6) |
| |
| #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32 |
| |
| #define BN_window_bits_for_ctime_exponent_size(b) \ |
| ((b) > 306 ? 5 : (b) > 89 ? 4 : (b) > 22 ? 3 : 1) |
| #define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5) |
| |
| #endif |
| |
| /* 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; |
| |
| top = m->top; |
| |
| if (!(m->d[0] & 1)) { |
| OPENSSL_PUT_ERROR(BN, 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; |
| } |
| |
| #ifdef RSAZ_ENABLED |
| /* If the size of the operands allow it, perform the optimized |
| * RSAZ exponentiation. For further information see |
| * crypto/bn/rsaz_exp.c and accompanying assembly modules. */ |
| if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) && |
| rsaz_avx2_eligible()) { |
| if (NULL == bn_wexpand(rr, 16)) |
| goto err; |
| RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, mont->n0[0]); |
| rr->top = 16; |
| rr->neg = 0; |
| bn_correct_top(rr); |
| ret = 1; |
| goto err; |
| } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { |
| if (NULL == bn_wexpand(rr, 8)) |
| goto err; |
| RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); |
| rr->top = 8; |
| rr->neg = 0; |
| bn_correct_top(rr); |
| ret = 1; |
| goto err; |
| } |
| #endif |
| |
| /* 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 >= 5) { |
| window = 5; /* ~5% improvement for RSA2048 sign, and even for RSA4096 */ |
| if ((top & 7) == 0) |
| powerbufLen += 2 * top * sizeof(m->d[0]); |
| } |
| #endif |
| (void)0; |
| |
| /* 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); |
| 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 */ |
| /* by Shay Gueron's suggestion */ |
| if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { |
| /* 2^(top*BN_BITS2) - m */ |
| tmp.d[0] = (0 - m->d[0]) & BN_MASK2; |
| for (i = 1; i < top; i++) |
| tmp.d[i] = (~m->d[i]) & BN_MASK2; |
| tmp.top = top; |
| } else if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx)) |
| goto err; |
| |
| /* 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 && top > 1) { |
| 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); |
| void bn_power5(BN_ULONG * rp, const BN_ULONG * ap, const void * table, |
| const BN_ULONG * np, const BN_ULONG * n0, int num, |
| int power); |
| int bn_from_montgomery(BN_ULONG * rp, const BN_ULONG * ap, |
| const BN_ULONG * not_used, const BN_ULONG * np, |
| const BN_ULONG * n0, int num); |
| |
| BN_ULONG *np = mont->N.d, *n0 = mont->n0, *np2; |
| |
| /* 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; |
| |
| if (top & 7) |
| np2 = np; |
| else |
| for (np2 = am.d + top, i = 0; i < top; i++) |
| np2[2 * i] = np[i]; |
| |
| 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); |
| |
| /* 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, np2, 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, np2, 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, np2, n0, top, i - 1); |
| bn_scatter5(tmp.d, top, powerbuf, i); |
| } |
| |
| 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); |
| |
| /* At this point |bits| is 4 mod 5 and at least -1. (|bits| is the first bit |
| * that has not been read yet.) */ |
| assert(bits >= -1 && (bits == -1 || bits % 5 == 4)); |
| |
| /* Scan the exponent one window at a time starting from the most |
| * significant bits. |
| */ |
| if (top & 7) { |
| 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); |
| } |
| } else { |
| const uint8_t *p_bytes = (const uint8_t *)p->d; |
| int max_bits = p->top * BN_BITS2; |
| assert(bits < max_bits); |
| /* |p = 0| has been handled as a special case, so |max_bits| is at least |
| * one word. */ |
| assert(max_bits >= 64); |
| |
| /* If the first bit to be read lands in the last byte, unroll the first |
| * iteration to avoid reading past the bounds of |p->d|. (After the first |
| * iteration, we are guaranteed to be past the last byte.) Note |bits| |
| * here is the top bit, inclusive. */ |
| if (bits - 4 >= max_bits - 8) { |
| /* Read five bits from |bits-4| through |bits|, inclusive. */ |
| wvalue = p_bytes[p->top * BN_BYTES - 1]; |
| wvalue >>= (bits - 4) & 7; |
| wvalue &= 0x1f; |
| bits -= 5; |
| bn_power5(tmp.d, tmp.d, powerbuf, np2, n0, top, wvalue); |
| } |
| while (bits >= 0) { |
| /* Read five bits from |bits-4| through |bits|, inclusive. */ |
| int first_bit = bits - 4; |
| wvalue = *(const uint16_t *) (p_bytes + (first_bit >> 3)); |
| wvalue >>= first_bit & 7; |
| wvalue &= 0x1f; |
| bits -= 5; |
| bn_power5(tmp.d, tmp.d, powerbuf, np2, n0, top, wvalue); |
| } |
| } |
| |
| ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np2, n0, top); |
| tmp.top = top; |
| bn_correct_top(&tmp); |
| if (ret) { |
| if (!BN_copy(rr, &tmp)) |
| ret = 0; |
| goto err; /* non-zero ret means it's not error */ |
| } |
| } else |
| #endif |
| { |
| if (!copy_to_prebuf(&tmp, top, powerbuf, 0, numPowers)) |
| goto err; |
| if (!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 (!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 (!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 (!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 (!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() */ |
| OPENSSL_PUT_ERROR(BN, BN_mod_exp_mont_word, |
| ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
| return 0; |
| } |
| |
| if (!BN_is_odd(m)) { |
| OPENSSL_PUT_ERROR(BN, 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); |
| return ret; |
| } |
| |
| #define TABLE_SIZE 32 |
| |
| int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1, |
| const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m, |
| BN_CTX *ctx, BN_MONT_CTX *in_mont) { |
| int i, j, bits, b, bits1, bits2, ret = 0, wpos1, wpos2, window1, window2, |
| wvalue1, wvalue2; |
| int r_is_one = 1; |
| BIGNUM *d, *r; |
| const BIGNUM *a_mod_m; |
| /* Tables of variables obtained from 'ctx' */ |
| BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE]; |
| BN_MONT_CTX *mont = NULL; |
| |
| if (!(m->d[0] & 1)) { |
| OPENSSL_PUT_ERROR(BN, BN_mod_exp2_mont, BN_R_CALLED_WITH_EVEN_MODULUS); |
| return 0; |
| } |
| bits1 = BN_num_bits(p1); |
| bits2 = BN_num_bits(p2); |
| if (bits1 == 0 && bits2 == 0) { |
| ret = BN_one(rr); |
| return ret; |
| } |
| |
| bits = (bits1 > bits2) ? bits1 : bits2; |
| |
| BN_CTX_start(ctx); |
| d = BN_CTX_get(ctx); |
| r = BN_CTX_get(ctx); |
| val1[0] = BN_CTX_get(ctx); |
| val2[0] = BN_CTX_get(ctx); |
| if (!d || !r || !val1[0] || !val2[0]) { |
| goto err; |
| } |
| |
| if (in_mont != NULL) { |
| mont = in_mont; |
| } else { |
| mont = BN_MONT_CTX_new(); |
| if (mont == NULL) { |
| goto err; |
| } |
| if (!BN_MONT_CTX_set(mont, m, ctx)) { |
| goto err; |
| } |
| } |
| |
| window1 = BN_window_bits_for_exponent_size(bits1); |
| window2 = BN_window_bits_for_exponent_size(bits2); |
| |
| /* Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. |
| * 2^(window1-1) */ |
| if (a1->neg || BN_ucmp(a1, m) >= 0) { |
| if (!BN_mod(val1[0], a1, m, ctx)) { |
| goto err; |
| } |
| a_mod_m = val1[0]; |
| } else { |
| a_mod_m = a1; |
| } |
| |
| if (BN_is_zero(a_mod_m)) { |
| BN_zero(rr); |
| ret = 1; |
| goto err; |
| } |
| |
| if (!BN_to_montgomery(val1[0], a_mod_m, mont, ctx)) { |
| goto err; |
| } |
| |
| if (window1 > 1) { |
| if (!BN_mod_mul_montgomery(d, val1[0], val1[0], mont, ctx)) { |
| goto err; |
| } |
| |
| j = 1 << (window1 - 1); |
| for (i = 1; i < j; i++) { |
| if (((val1[i] = BN_CTX_get(ctx)) == NULL) || |
| !BN_mod_mul_montgomery(val1[i], val1[i - 1], d, mont, ctx)) { |
| goto err; |
| } |
| } |
| } |
| |
| /* Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. |
| * 2^(window2-1) */ |
| if (a2->neg || BN_ucmp(a2, m) >= 0) { |
| if (!BN_mod(val2[0], a2, m, ctx)) { |
| goto err; |
| } |
| a_mod_m = val2[0]; |
| } else { |
| a_mod_m = a2; |
| } |
| |
| if (BN_is_zero(a_mod_m)) { |
| BN_zero(rr); |
| ret = 1; |
| goto err; |
| } |
| |
| if (!BN_to_montgomery(val2[0], a_mod_m, mont, ctx)) { |
| goto err; |
| } |
| |
| if (window2 > 1) { |
| if (!BN_mod_mul_montgomery(d, val2[0], val2[0], mont, ctx)) { |
| goto err; |
| } |
| |
| j = 1 << (window2 - 1); |
| for (i = 1; i < j; i++) { |
| if (((val2[i] = BN_CTX_get(ctx)) == NULL) || |
| !BN_mod_mul_montgomery(val2[i], val2[i - 1], d, mont, ctx)) { |
| goto err; |
| } |
| } |
| } |
| |
| /* Now compute the power product, using independent windows. */ |
| r_is_one = 1; |
| wvalue1 = 0; /* The 'value' of the first window */ |
| wvalue2 = 0; /* The 'value' of the second window */ |
| wpos1 = 0; /* If wvalue1 > 0, the bottom bit of the first window */ |
| wpos2 = 0; /* If wvalue2 > 0, the bottom bit of the second window */ |
| |
| if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) { |
| goto err; |
| } |
| |
| for (b = bits - 1; b >= 0; b--) { |
| if (!r_is_one) { |
| if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) { |
| goto err; |
| } |
| } |
| |
| if (!wvalue1 && BN_is_bit_set(p1, b)) { |
| /* consider bits b-window1+1 .. b for this window */ |
| i = b - window1 + 1; |
| while (!BN_is_bit_set(p1, i)) /* works for i<0 */ |
| i++; |
| wpos1 = i; |
| wvalue1 = 1; |
| for (i = b - 1; i >= wpos1; i--) { |
| wvalue1 <<= 1; |
| if (BN_is_bit_set(p1, i)) |
| wvalue1++; |
| } |
| } |
| |
| if (!wvalue2 && BN_is_bit_set(p2, b)) { |
| /* consider bits b-window2+1 .. b for this window */ |
| i = b - window2 + 1; |
| while (!BN_is_bit_set(p2, i)) |
| i++; |
| wpos2 = i; |
| wvalue2 = 1; |
| for (i = b - 1; i >= wpos2; i--) { |
| wvalue2 <<= 1; |
| if (BN_is_bit_set(p2, i)) |
| wvalue2++; |
| } |
| } |
| |
| if (wvalue1 && b == wpos1) { |
| /* wvalue1 is odd and < 2^window1 */ |
| if (!BN_mod_mul_montgomery(r, r, val1[wvalue1 >> 1], mont, ctx)) { |
| goto err; |
| } |
| wvalue1 = 0; |
| r_is_one = 0; |
| } |
| |
| if (wvalue2 && b == wpos2) { |
| /* wvalue2 is odd and < 2^window2 */ |
| if (!BN_mod_mul_montgomery(r, r, val2[wvalue2 >> 1], mont, ctx)) { |
| goto err; |
| } |
| wvalue2 = 0; |
| r_is_one = 0; |
| } |
| } |
| |
| 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); |
| return ret; |
| } |