[331] | 1 | /*
|
---|
| 2 | * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
|
---|
| 3 | *
|
---|
| 4 | * Licensed under the OpenSSL license (the "License"). You may not use
|
---|
| 5 | * this file except in compliance with the License. You can obtain a copy
|
---|
| 6 | * in the file LICENSE in the source distribution or at
|
---|
| 7 | * https://www.openssl.org/source/license.html
|
---|
| 8 | */
|
---|
| 9 |
|
---|
| 10 | #include "internal/cryptlib.h"
|
---|
| 11 | #include "internal/constant_time_locl.h"
|
---|
| 12 | #include "bn_lcl.h"
|
---|
| 13 |
|
---|
| 14 | #include <stdlib.h>
|
---|
| 15 | #ifdef _WIN32
|
---|
| 16 | # include <malloc.h>
|
---|
| 17 | # ifndef alloca
|
---|
| 18 | # define alloca _alloca
|
---|
| 19 | # endif
|
---|
| 20 | #elif defined(__GNUC__)
|
---|
| 21 | # ifndef alloca
|
---|
| 22 | # define alloca(s) __builtin_alloca((s))
|
---|
| 23 | # endif
|
---|
| 24 | #elif defined(__sun)
|
---|
| 25 | # include <alloca.h>
|
---|
| 26 | #endif
|
---|
| 27 |
|
---|
| 28 | #include "rsaz_exp.h"
|
---|
| 29 |
|
---|
| 30 | #undef SPARC_T4_MONT
|
---|
| 31 | #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
|
---|
| 32 | # include "sparc_arch.h"
|
---|
| 33 | extern unsigned int OPENSSL_sparcv9cap_P[];
|
---|
| 34 | # define SPARC_T4_MONT
|
---|
| 35 | #endif
|
---|
| 36 |
|
---|
| 37 | /* maximum precomputation table size for *variable* sliding windows */
|
---|
| 38 | #define TABLE_SIZE 32
|
---|
| 39 |
|
---|
| 40 | /* this one works - simple but works */
|
---|
| 41 | int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
|
---|
| 42 | {
|
---|
| 43 | int i, bits, ret = 0;
|
---|
| 44 | BIGNUM *v, *rr;
|
---|
| 45 |
|
---|
| 46 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
---|
| 47 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
---|
| 48 | BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
---|
| 49 | return 0;
|
---|
| 50 | }
|
---|
| 51 |
|
---|
| 52 | BN_CTX_start(ctx);
|
---|
| 53 | if ((r == a) || (r == p))
|
---|
| 54 | rr = BN_CTX_get(ctx);
|
---|
| 55 | else
|
---|
| 56 | rr = r;
|
---|
| 57 | v = BN_CTX_get(ctx);
|
---|
| 58 | if (rr == NULL || v == NULL)
|
---|
| 59 | goto err;
|
---|
| 60 |
|
---|
| 61 | if (BN_copy(v, a) == NULL)
|
---|
| 62 | goto err;
|
---|
| 63 | bits = BN_num_bits(p);
|
---|
| 64 |
|
---|
| 65 | if (BN_is_odd(p)) {
|
---|
| 66 | if (BN_copy(rr, a) == NULL)
|
---|
| 67 | goto err;
|
---|
| 68 | } else {
|
---|
| 69 | if (!BN_one(rr))
|
---|
| 70 | goto err;
|
---|
| 71 | }
|
---|
| 72 |
|
---|
| 73 | for (i = 1; i < bits; i++) {
|
---|
| 74 | if (!BN_sqr(v, v, ctx))
|
---|
| 75 | goto err;
|
---|
| 76 | if (BN_is_bit_set(p, i)) {
|
---|
| 77 | if (!BN_mul(rr, rr, v, ctx))
|
---|
| 78 | goto err;
|
---|
| 79 | }
|
---|
| 80 | }
|
---|
| 81 | if (r != rr && BN_copy(r, rr) == NULL)
|
---|
| 82 | goto err;
|
---|
| 83 |
|
---|
| 84 | ret = 1;
|
---|
| 85 | err:
|
---|
| 86 | BN_CTX_end(ctx);
|
---|
| 87 | bn_check_top(r);
|
---|
| 88 | return (ret);
|
---|
| 89 | }
|
---|
| 90 |
|
---|
| 91 | int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
|
---|
| 92 | BN_CTX *ctx)
|
---|
| 93 | {
|
---|
| 94 | int ret;
|
---|
| 95 |
|
---|
| 96 | bn_check_top(a);
|
---|
| 97 | bn_check_top(p);
|
---|
| 98 | bn_check_top(m);
|
---|
| 99 |
|
---|
| 100 | /*-
|
---|
| 101 | * For even modulus m = 2^k*m_odd, it might make sense to compute
|
---|
| 102 | * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
|
---|
| 103 | * exponentiation for the odd part), using appropriate exponent
|
---|
| 104 | * reductions, and combine the results using the CRT.
|
---|
| 105 | *
|
---|
| 106 | * For now, we use Montgomery only if the modulus is odd; otherwise,
|
---|
| 107 | * exponentiation using the reciprocal-based quick remaindering
|
---|
| 108 | * algorithm is used.
|
---|
| 109 | *
|
---|
| 110 | * (Timing obtained with expspeed.c [computations a^p mod m
|
---|
| 111 | * where a, p, m are of the same length: 256, 512, 1024, 2048,
|
---|
| 112 | * 4096, 8192 bits], compared to the running time of the
|
---|
| 113 | * standard algorithm:
|
---|
| 114 | *
|
---|
| 115 | * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
|
---|
| 116 | * 55 .. 77 % [UltraSparc processor, but
|
---|
| 117 | * debug-solaris-sparcv8-gcc conf.]
|
---|
| 118 | *
|
---|
| 119 | * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
|
---|
| 120 | * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
|
---|
| 121 | *
|
---|
| 122 | * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
|
---|
| 123 | * at 2048 and more bits, but at 512 and 1024 bits, it was
|
---|
| 124 | * slower even than the standard algorithm!
|
---|
| 125 | *
|
---|
| 126 | * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
|
---|
| 127 | * should be obtained when the new Montgomery reduction code
|
---|
| 128 | * has been integrated into OpenSSL.)
|
---|
| 129 | */
|
---|
| 130 |
|
---|
| 131 | #define MONT_MUL_MOD
|
---|
| 132 | #define MONT_EXP_WORD
|
---|
| 133 | #define RECP_MUL_MOD
|
---|
| 134 |
|
---|
| 135 | #ifdef MONT_MUL_MOD
|
---|
| 136 | /*
|
---|
| 137 | * I have finally been able to take out this pre-condition of the top bit
|
---|
| 138 | * being set. It was caused by an error in BN_div with negatives. There
|
---|
| 139 | * was also another problem when for a^b%m a >= m. eay 07-May-97
|
---|
| 140 | */
|
---|
| 141 | /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
|
---|
| 142 |
|
---|
| 143 | if (BN_is_odd(m)) {
|
---|
| 144 | # ifdef MONT_EXP_WORD
|
---|
| 145 | if (a->top == 1 && !a->neg
|
---|
| 146 | && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
|
---|
| 147 | BN_ULONG A = a->d[0];
|
---|
| 148 | ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
|
---|
| 149 | } else
|
---|
| 150 | # endif
|
---|
| 151 | ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
|
---|
| 152 | } else
|
---|
| 153 | #endif
|
---|
| 154 | #ifdef RECP_MUL_MOD
|
---|
| 155 | {
|
---|
| 156 | ret = BN_mod_exp_recp(r, a, p, m, ctx);
|
---|
| 157 | }
|
---|
| 158 | #else
|
---|
| 159 | {
|
---|
| 160 | ret = BN_mod_exp_simple(r, a, p, m, ctx);
|
---|
| 161 | }
|
---|
| 162 | #endif
|
---|
| 163 |
|
---|
| 164 | bn_check_top(r);
|
---|
| 165 | return (ret);
|
---|
| 166 | }
|
---|
| 167 |
|
---|
| 168 | int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
|
---|
| 169 | const BIGNUM *m, BN_CTX *ctx)
|
---|
| 170 | {
|
---|
| 171 | int i, j, bits, ret = 0, wstart, wend, window, wvalue;
|
---|
| 172 | int start = 1;
|
---|
| 173 | BIGNUM *aa;
|
---|
| 174 | /* Table of variables obtained from 'ctx' */
|
---|
| 175 | BIGNUM *val[TABLE_SIZE];
|
---|
| 176 | BN_RECP_CTX recp;
|
---|
| 177 |
|
---|
| 178 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
---|
| 179 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
---|
| 180 | BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
---|
| 181 | return 0;
|
---|
| 182 | }
|
---|
| 183 |
|
---|
| 184 | bits = BN_num_bits(p);
|
---|
| 185 | if (bits == 0) {
|
---|
| 186 | /* x**0 mod 1 is still zero. */
|
---|
| 187 | if (BN_is_one(m)) {
|
---|
| 188 | ret = 1;
|
---|
| 189 | BN_zero(r);
|
---|
| 190 | } else {
|
---|
| 191 | ret = BN_one(r);
|
---|
| 192 | }
|
---|
| 193 | return ret;
|
---|
| 194 | }
|
---|
| 195 |
|
---|
| 196 | BN_CTX_start(ctx);
|
---|
| 197 | aa = BN_CTX_get(ctx);
|
---|
| 198 | val[0] = BN_CTX_get(ctx);
|
---|
| 199 | if (!aa || !val[0])
|
---|
| 200 | goto err;
|
---|
| 201 |
|
---|
| 202 | BN_RECP_CTX_init(&recp);
|
---|
| 203 | if (m->neg) {
|
---|
| 204 | /* ignore sign of 'm' */
|
---|
| 205 | if (!BN_copy(aa, m))
|
---|
| 206 | goto err;
|
---|
| 207 | aa->neg = 0;
|
---|
| 208 | if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
|
---|
| 209 | goto err;
|
---|
| 210 | } else {
|
---|
| 211 | if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
|
---|
| 212 | goto err;
|
---|
| 213 | }
|
---|
| 214 |
|
---|
| 215 | if (!BN_nnmod(val[0], a, m, ctx))
|
---|
| 216 | goto err; /* 1 */
|
---|
| 217 | if (BN_is_zero(val[0])) {
|
---|
| 218 | BN_zero(r);
|
---|
| 219 | ret = 1;
|
---|
| 220 | goto err;
|
---|
| 221 | }
|
---|
| 222 |
|
---|
| 223 | window = BN_window_bits_for_exponent_size(bits);
|
---|
| 224 | if (window > 1) {
|
---|
| 225 | if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
|
---|
| 226 | goto err; /* 2 */
|
---|
| 227 | j = 1 << (window - 1);
|
---|
| 228 | for (i = 1; i < j; i++) {
|
---|
| 229 | if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
|
---|
| 230 | !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
|
---|
| 231 | goto err;
|
---|
| 232 | }
|
---|
| 233 | }
|
---|
| 234 |
|
---|
| 235 | start = 1; /* This is used to avoid multiplication etc
|
---|
| 236 | * when there is only the value '1' in the
|
---|
| 237 | * buffer. */
|
---|
| 238 | wvalue = 0; /* The 'value' of the window */
|
---|
| 239 | wstart = bits - 1; /* The top bit of the window */
|
---|
| 240 | wend = 0; /* The bottom bit of the window */
|
---|
| 241 |
|
---|
| 242 | if (!BN_one(r))
|
---|
| 243 | goto err;
|
---|
| 244 |
|
---|
| 245 | for (;;) {
|
---|
| 246 | if (BN_is_bit_set(p, wstart) == 0) {
|
---|
| 247 | if (!start)
|
---|
| 248 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
|
---|
| 249 | goto err;
|
---|
| 250 | if (wstart == 0)
|
---|
| 251 | break;
|
---|
| 252 | wstart--;
|
---|
| 253 | continue;
|
---|
| 254 | }
|
---|
| 255 | /*
|
---|
| 256 | * We now have wstart on a 'set' bit, we now need to work out how bit
|
---|
| 257 | * a window to do. To do this we need to scan forward until the last
|
---|
| 258 | * set bit before the end of the window
|
---|
| 259 | */
|
---|
| 260 | j = wstart;
|
---|
| 261 | wvalue = 1;
|
---|
| 262 | wend = 0;
|
---|
| 263 | for (i = 1; i < window; i++) {
|
---|
| 264 | if (wstart - i < 0)
|
---|
| 265 | break;
|
---|
| 266 | if (BN_is_bit_set(p, wstart - i)) {
|
---|
| 267 | wvalue <<= (i - wend);
|
---|
| 268 | wvalue |= 1;
|
---|
| 269 | wend = i;
|
---|
| 270 | }
|
---|
| 271 | }
|
---|
| 272 |
|
---|
| 273 | /* wend is the size of the current window */
|
---|
| 274 | j = wend + 1;
|
---|
| 275 | /* add the 'bytes above' */
|
---|
| 276 | if (!start)
|
---|
| 277 | for (i = 0; i < j; i++) {
|
---|
| 278 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
|
---|
| 279 | goto err;
|
---|
| 280 | }
|
---|
| 281 |
|
---|
| 282 | /* wvalue will be an odd number < 2^window */
|
---|
| 283 | if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
|
---|
| 284 | goto err;
|
---|
| 285 |
|
---|
| 286 | /* move the 'window' down further */
|
---|
| 287 | wstart -= wend + 1;
|
---|
| 288 | wvalue = 0;
|
---|
| 289 | start = 0;
|
---|
| 290 | if (wstart < 0)
|
---|
| 291 | break;
|
---|
| 292 | }
|
---|
| 293 | ret = 1;
|
---|
| 294 | err:
|
---|
| 295 | BN_CTX_end(ctx);
|
---|
| 296 | BN_RECP_CTX_free(&recp);
|
---|
| 297 | bn_check_top(r);
|
---|
| 298 | return (ret);
|
---|
| 299 | }
|
---|
| 300 |
|
---|
| 301 | int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
|
---|
| 302 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
|
---|
| 303 | {
|
---|
| 304 | int i, j, bits, ret = 0, wstart, wend, window, wvalue;
|
---|
| 305 | int start = 1;
|
---|
| 306 | BIGNUM *d, *r;
|
---|
| 307 | const BIGNUM *aa;
|
---|
| 308 | /* Table of variables obtained from 'ctx' */
|
---|
| 309 | BIGNUM *val[TABLE_SIZE];
|
---|
| 310 | BN_MONT_CTX *mont = NULL;
|
---|
| 311 |
|
---|
| 312 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
---|
| 313 | return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
|
---|
| 314 | }
|
---|
| 315 |
|
---|
| 316 | bn_check_top(a);
|
---|
| 317 | bn_check_top(p);
|
---|
| 318 | bn_check_top(m);
|
---|
| 319 |
|
---|
| 320 | if (!BN_is_odd(m)) {
|
---|
| 321 | BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
|
---|
| 322 | return (0);
|
---|
| 323 | }
|
---|
| 324 | bits = BN_num_bits(p);
|
---|
| 325 | if (bits == 0) {
|
---|
| 326 | /* x**0 mod 1 is still zero. */
|
---|
| 327 | if (BN_is_one(m)) {
|
---|
| 328 | ret = 1;
|
---|
| 329 | BN_zero(rr);
|
---|
| 330 | } else {
|
---|
| 331 | ret = BN_one(rr);
|
---|
| 332 | }
|
---|
| 333 | return ret;
|
---|
| 334 | }
|
---|
| 335 |
|
---|
| 336 | BN_CTX_start(ctx);
|
---|
| 337 | d = BN_CTX_get(ctx);
|
---|
| 338 | r = BN_CTX_get(ctx);
|
---|
| 339 | val[0] = BN_CTX_get(ctx);
|
---|
| 340 | if (!d || !r || !val[0])
|
---|
| 341 | goto err;
|
---|
| 342 |
|
---|
| 343 | /*
|
---|
| 344 | * If this is not done, things will break in the montgomery part
|
---|
| 345 | */
|
---|
| 346 |
|
---|
| 347 | if (in_mont != NULL)
|
---|
| 348 | mont = in_mont;
|
---|
| 349 | else {
|
---|
| 350 | if ((mont = BN_MONT_CTX_new()) == NULL)
|
---|
| 351 | goto err;
|
---|
| 352 | if (!BN_MONT_CTX_set(mont, m, ctx))
|
---|
| 353 | goto err;
|
---|
| 354 | }
|
---|
| 355 |
|
---|
| 356 | if (a->neg || BN_ucmp(a, m) >= 0) {
|
---|
| 357 | if (!BN_nnmod(val[0], a, m, ctx))
|
---|
| 358 | goto err;
|
---|
| 359 | aa = val[0];
|
---|
| 360 | } else
|
---|
| 361 | aa = a;
|
---|
| 362 | if (BN_is_zero(aa)) {
|
---|
| 363 | BN_zero(rr);
|
---|
| 364 | ret = 1;
|
---|
| 365 | goto err;
|
---|
| 366 | }
|
---|
| 367 | if (!BN_to_montgomery(val[0], aa, mont, ctx))
|
---|
| 368 | goto err; /* 1 */
|
---|
| 369 |
|
---|
| 370 | window = BN_window_bits_for_exponent_size(bits);
|
---|
| 371 | if (window > 1) {
|
---|
| 372 | if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
|
---|
| 373 | goto err; /* 2 */
|
---|
| 374 | j = 1 << (window - 1);
|
---|
| 375 | for (i = 1; i < j; i++) {
|
---|
| 376 | if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
|
---|
| 377 | !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
|
---|
| 378 | goto err;
|
---|
| 379 | }
|
---|
| 380 | }
|
---|
| 381 |
|
---|
| 382 | start = 1; /* This is used to avoid multiplication etc
|
---|
| 383 | * when there is only the value '1' in the
|
---|
| 384 | * buffer. */
|
---|
| 385 | wvalue = 0; /* The 'value' of the window */
|
---|
| 386 | wstart = bits - 1; /* The top bit of the window */
|
---|
| 387 | wend = 0; /* The bottom bit of the window */
|
---|
| 388 |
|
---|
| 389 | #if 1 /* by Shay Gueron's suggestion */
|
---|
| 390 | j = m->top; /* borrow j */
|
---|
| 391 | if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
|
---|
| 392 | if (bn_wexpand(r, j) == NULL)
|
---|
| 393 | goto err;
|
---|
| 394 | /* 2^(top*BN_BITS2) - m */
|
---|
| 395 | r->d[0] = (0 - m->d[0]) & BN_MASK2;
|
---|
| 396 | for (i = 1; i < j; i++)
|
---|
| 397 | r->d[i] = (~m->d[i]) & BN_MASK2;
|
---|
| 398 | r->top = j;
|
---|
| 399 | /*
|
---|
| 400 | * Upper words will be zero if the corresponding words of 'm' were
|
---|
| 401 | * 0xfff[...], so decrement r->top accordingly.
|
---|
| 402 | */
|
---|
| 403 | bn_correct_top(r);
|
---|
| 404 | } else
|
---|
| 405 | #endif
|
---|
| 406 | if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
|
---|
| 407 | goto err;
|
---|
| 408 | for (;;) {
|
---|
| 409 | if (BN_is_bit_set(p, wstart) == 0) {
|
---|
| 410 | if (!start) {
|
---|
| 411 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
|
---|
| 412 | goto err;
|
---|
| 413 | }
|
---|
| 414 | if (wstart == 0)
|
---|
| 415 | break;
|
---|
| 416 | wstart--;
|
---|
| 417 | continue;
|
---|
| 418 | }
|
---|
| 419 | /*
|
---|
| 420 | * We now have wstart on a 'set' bit, we now need to work out how bit
|
---|
| 421 | * a window to do. To do this we need to scan forward until the last
|
---|
| 422 | * set bit before the end of the window
|
---|
| 423 | */
|
---|
| 424 | j = wstart;
|
---|
| 425 | wvalue = 1;
|
---|
| 426 | wend = 0;
|
---|
| 427 | for (i = 1; i < window; i++) {
|
---|
| 428 | if (wstart - i < 0)
|
---|
| 429 | break;
|
---|
| 430 | if (BN_is_bit_set(p, wstart - i)) {
|
---|
| 431 | wvalue <<= (i - wend);
|
---|
| 432 | wvalue |= 1;
|
---|
| 433 | wend = i;
|
---|
| 434 | }
|
---|
| 435 | }
|
---|
| 436 |
|
---|
| 437 | /* wend is the size of the current window */
|
---|
| 438 | j = wend + 1;
|
---|
| 439 | /* add the 'bytes above' */
|
---|
| 440 | if (!start)
|
---|
| 441 | for (i = 0; i < j; i++) {
|
---|
| 442 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
|
---|
| 443 | goto err;
|
---|
| 444 | }
|
---|
| 445 |
|
---|
| 446 | /* wvalue will be an odd number < 2^window */
|
---|
| 447 | if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
|
---|
| 448 | goto err;
|
---|
| 449 |
|
---|
| 450 | /* move the 'window' down further */
|
---|
| 451 | wstart -= wend + 1;
|
---|
| 452 | wvalue = 0;
|
---|
| 453 | start = 0;
|
---|
| 454 | if (wstart < 0)
|
---|
| 455 | break;
|
---|
| 456 | }
|
---|
| 457 | #if defined(SPARC_T4_MONT)
|
---|
| 458 | if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
|
---|
| 459 | j = mont->N.top; /* borrow j */
|
---|
| 460 | val[0]->d[0] = 1; /* borrow val[0] */
|
---|
| 461 | for (i = 1; i < j; i++)
|
---|
| 462 | val[0]->d[i] = 0;
|
---|
| 463 | val[0]->top = j;
|
---|
| 464 | if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
|
---|
| 465 | goto err;
|
---|
| 466 | } else
|
---|
| 467 | #endif
|
---|
| 468 | if (!BN_from_montgomery(rr, r, mont, ctx))
|
---|
| 469 | goto err;
|
---|
| 470 | ret = 1;
|
---|
| 471 | err:
|
---|
| 472 | if (in_mont == NULL)
|
---|
| 473 | BN_MONT_CTX_free(mont);
|
---|
| 474 | BN_CTX_end(ctx);
|
---|
| 475 | bn_check_top(rr);
|
---|
| 476 | return (ret);
|
---|
| 477 | }
|
---|
| 478 |
|
---|
| 479 | #if defined(SPARC_T4_MONT)
|
---|
| 480 | static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
|
---|
| 481 | {
|
---|
| 482 | BN_ULONG ret = 0;
|
---|
| 483 | int wordpos;
|
---|
| 484 |
|
---|
| 485 | wordpos = bitpos / BN_BITS2;
|
---|
| 486 | bitpos %= BN_BITS2;
|
---|
| 487 | if (wordpos >= 0 && wordpos < a->top) {
|
---|
| 488 | ret = a->d[wordpos] & BN_MASK2;
|
---|
| 489 | if (bitpos) {
|
---|
| 490 | ret >>= bitpos;
|
---|
| 491 | if (++wordpos < a->top)
|
---|
| 492 | ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
|
---|
| 493 | }
|
---|
| 494 | }
|
---|
| 495 |
|
---|
| 496 | return ret & BN_MASK2;
|
---|
| 497 | }
|
---|
| 498 | #endif
|
---|
| 499 |
|
---|
| 500 | /*
|
---|
| 501 | * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
|
---|
| 502 | * layout so that accessing any of these table values shows the same access
|
---|
| 503 | * pattern as far as cache lines are concerned. The following functions are
|
---|
| 504 | * used to transfer a BIGNUM from/to that table.
|
---|
| 505 | */
|
---|
| 506 |
|
---|
| 507 | static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
|
---|
| 508 | unsigned char *buf, int idx,
|
---|
| 509 | int window)
|
---|
| 510 | {
|
---|
| 511 | int i, j;
|
---|
| 512 | int width = 1 << window;
|
---|
| 513 | BN_ULONG *table = (BN_ULONG *)buf;
|
---|
| 514 |
|
---|
| 515 | if (top > b->top)
|
---|
| 516 | top = b->top; /* this works because 'buf' is explicitly
|
---|
| 517 | * zeroed */
|
---|
| 518 | for (i = 0, j = idx; i < top; i++, j += width) {
|
---|
| 519 | table[j] = b->d[i];
|
---|
| 520 | }
|
---|
| 521 |
|
---|
| 522 | return 1;
|
---|
| 523 | }
|
---|
| 524 |
|
---|
| 525 | static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
|
---|
| 526 | unsigned char *buf, int idx,
|
---|
| 527 | int window)
|
---|
| 528 | {
|
---|
| 529 | int i, j;
|
---|
| 530 | int width = 1 << window;
|
---|
| 531 | /*
|
---|
| 532 | * We declare table 'volatile' in order to discourage compiler
|
---|
| 533 | * from reordering loads from the table. Concern is that if
|
---|
| 534 | * reordered in specific manner loads might give away the
|
---|
| 535 | * information we are trying to conceal. Some would argue that
|
---|
| 536 | * compiler can reorder them anyway, but it can as well be
|
---|
| 537 | * argued that doing so would be violation of standard...
|
---|
| 538 | */
|
---|
| 539 | volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
|
---|
| 540 |
|
---|
| 541 | if (bn_wexpand(b, top) == NULL)
|
---|
| 542 | return 0;
|
---|
| 543 |
|
---|
| 544 | if (window <= 3) {
|
---|
| 545 | for (i = 0; i < top; i++, table += width) {
|
---|
| 546 | BN_ULONG acc = 0;
|
---|
| 547 |
|
---|
| 548 | for (j = 0; j < width; j++) {
|
---|
| 549 | acc |= table[j] &
|
---|
| 550 | ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
|
---|
| 551 | }
|
---|
| 552 |
|
---|
| 553 | b->d[i] = acc;
|
---|
| 554 | }
|
---|
| 555 | } else {
|
---|
| 556 | int xstride = 1 << (window - 2);
|
---|
| 557 | BN_ULONG y0, y1, y2, y3;
|
---|
| 558 |
|
---|
| 559 | i = idx >> (window - 2); /* equivalent of idx / xstride */
|
---|
| 560 | idx &= xstride - 1; /* equivalent of idx % xstride */
|
---|
| 561 |
|
---|
| 562 | y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
|
---|
| 563 | y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
|
---|
| 564 | y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
|
---|
| 565 | y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
|
---|
| 566 |
|
---|
| 567 | for (i = 0; i < top; i++, table += width) {
|
---|
| 568 | BN_ULONG acc = 0;
|
---|
| 569 |
|
---|
| 570 | for (j = 0; j < xstride; j++) {
|
---|
| 571 | acc |= ( (table[j + 0 * xstride] & y0) |
|
---|
| 572 | (table[j + 1 * xstride] & y1) |
|
---|
| 573 | (table[j + 2 * xstride] & y2) |
|
---|
| 574 | (table[j + 3 * xstride] & y3) )
|
---|
| 575 | & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
|
---|
| 576 | }
|
---|
| 577 |
|
---|
| 578 | b->d[i] = acc;
|
---|
| 579 | }
|
---|
| 580 | }
|
---|
| 581 |
|
---|
| 582 | b->top = top;
|
---|
| 583 | bn_correct_top(b);
|
---|
| 584 | return 1;
|
---|
| 585 | }
|
---|
| 586 |
|
---|
| 587 | /*
|
---|
| 588 | * Given a pointer value, compute the next address that is a cache line
|
---|
| 589 | * multiple.
|
---|
| 590 | */
|
---|
| 591 | #define MOD_EXP_CTIME_ALIGN(x_) \
|
---|
| 592 | ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
|
---|
| 593 |
|
---|
| 594 | /*
|
---|
| 595 | * This variant of BN_mod_exp_mont() uses fixed windows and the special
|
---|
| 596 | * precomputation memory layout to limit data-dependency to a minimum to
|
---|
| 597 | * protect secret exponents (cf. the hyper-threading timing attacks pointed
|
---|
| 598 | * out by Colin Percival,
|
---|
| 599 | * http://www.daemonology.net/hyperthreading-considered-harmful/)
|
---|
| 600 | */
|
---|
| 601 | int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
|
---|
| 602 | const BIGNUM *m, BN_CTX *ctx,
|
---|
| 603 | BN_MONT_CTX *in_mont)
|
---|
| 604 | {
|
---|
| 605 | int i, bits, ret = 0, window, wvalue;
|
---|
| 606 | int top;
|
---|
| 607 | BN_MONT_CTX *mont = NULL;
|
---|
| 608 |
|
---|
| 609 | int numPowers;
|
---|
| 610 | unsigned char *powerbufFree = NULL;
|
---|
| 611 | int powerbufLen = 0;
|
---|
| 612 | unsigned char *powerbuf = NULL;
|
---|
| 613 | BIGNUM tmp, am;
|
---|
| 614 | #if defined(SPARC_T4_MONT)
|
---|
| 615 | unsigned int t4 = 0;
|
---|
| 616 | #endif
|
---|
| 617 |
|
---|
| 618 | bn_check_top(a);
|
---|
| 619 | bn_check_top(p);
|
---|
| 620 | bn_check_top(m);
|
---|
| 621 |
|
---|
| 622 | if (!BN_is_odd(m)) {
|
---|
| 623 | BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
|
---|
| 624 | return (0);
|
---|
| 625 | }
|
---|
| 626 |
|
---|
| 627 | top = m->top;
|
---|
| 628 |
|
---|
| 629 | bits = BN_num_bits(p);
|
---|
| 630 | if (bits == 0) {
|
---|
| 631 | /* x**0 mod 1 is still zero. */
|
---|
| 632 | if (BN_is_one(m)) {
|
---|
| 633 | ret = 1;
|
---|
| 634 | BN_zero(rr);
|
---|
| 635 | } else {
|
---|
| 636 | ret = BN_one(rr);
|
---|
| 637 | }
|
---|
| 638 | return ret;
|
---|
| 639 | }
|
---|
| 640 |
|
---|
| 641 | BN_CTX_start(ctx);
|
---|
| 642 |
|
---|
| 643 | /*
|
---|
| 644 | * Allocate a montgomery context if it was not supplied by the caller. If
|
---|
| 645 | * this is not done, things will break in the montgomery part.
|
---|
| 646 | */
|
---|
| 647 | if (in_mont != NULL)
|
---|
| 648 | mont = in_mont;
|
---|
| 649 | else {
|
---|
| 650 | if ((mont = BN_MONT_CTX_new()) == NULL)
|
---|
| 651 | goto err;
|
---|
| 652 | if (!BN_MONT_CTX_set(mont, m, ctx))
|
---|
| 653 | goto err;
|
---|
| 654 | }
|
---|
| 655 |
|
---|
| 656 | #ifdef RSAZ_ENABLED
|
---|
| 657 | /*
|
---|
| 658 | * If the size of the operands allow it, perform the optimized
|
---|
| 659 | * RSAZ exponentiation. For further information see
|
---|
| 660 | * crypto/bn/rsaz_exp.c and accompanying assembly modules.
|
---|
| 661 | */
|
---|
| 662 | if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
|
---|
| 663 | && rsaz_avx2_eligible()) {
|
---|
| 664 | if (NULL == bn_wexpand(rr, 16))
|
---|
| 665 | goto err;
|
---|
| 666 | RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
|
---|
| 667 | mont->n0[0]);
|
---|
| 668 | rr->top = 16;
|
---|
| 669 | rr->neg = 0;
|
---|
| 670 | bn_correct_top(rr);
|
---|
| 671 | ret = 1;
|
---|
| 672 | goto err;
|
---|
| 673 | } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
|
---|
| 674 | if (NULL == bn_wexpand(rr, 8))
|
---|
| 675 | goto err;
|
---|
| 676 | RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
|
---|
| 677 | rr->top = 8;
|
---|
| 678 | rr->neg = 0;
|
---|
| 679 | bn_correct_top(rr);
|
---|
| 680 | ret = 1;
|
---|
| 681 | goto err;
|
---|
| 682 | }
|
---|
| 683 | #endif
|
---|
| 684 |
|
---|
| 685 | /* Get the window size to use with size of p. */
|
---|
| 686 | window = BN_window_bits_for_ctime_exponent_size(bits);
|
---|
| 687 | #if defined(SPARC_T4_MONT)
|
---|
| 688 | if (window >= 5 && (top & 15) == 0 && top <= 64 &&
|
---|
| 689 | (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
|
---|
| 690 | (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
|
---|
| 691 | window = 5;
|
---|
| 692 | else
|
---|
| 693 | #endif
|
---|
| 694 | #if defined(OPENSSL_BN_ASM_MONT5)
|
---|
| 695 | if (window >= 5) {
|
---|
| 696 | window = 5; /* ~5% improvement for RSA2048 sign, and even
|
---|
| 697 | * for RSA4096 */
|
---|
| 698 | /* reserve space for mont->N.d[] copy */
|
---|
| 699 | powerbufLen += top * sizeof(mont->N.d[0]);
|
---|
| 700 | }
|
---|
| 701 | #endif
|
---|
| 702 | (void)0;
|
---|
| 703 |
|
---|
| 704 | /*
|
---|
| 705 | * Allocate a buffer large enough to hold all of the pre-computed powers
|
---|
| 706 | * of am, am itself and tmp.
|
---|
| 707 | */
|
---|
| 708 | numPowers = 1 << window;
|
---|
| 709 | powerbufLen += sizeof(m->d[0]) * (top * numPowers +
|
---|
| 710 | ((2 * top) >
|
---|
| 711 | numPowers ? (2 * top) : numPowers));
|
---|
| 712 | #ifdef alloca
|
---|
| 713 | if (powerbufLen < 3072)
|
---|
| 714 | powerbufFree =
|
---|
| 715 | alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
|
---|
| 716 | else
|
---|
| 717 | #endif
|
---|
| 718 | if ((powerbufFree =
|
---|
| 719 | OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
|
---|
| 720 | == NULL)
|
---|
| 721 | goto err;
|
---|
| 722 |
|
---|
| 723 | powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
|
---|
| 724 | memset(powerbuf, 0, powerbufLen);
|
---|
| 725 |
|
---|
| 726 | #ifdef alloca
|
---|
| 727 | if (powerbufLen < 3072)
|
---|
| 728 | powerbufFree = NULL;
|
---|
| 729 | #endif
|
---|
| 730 |
|
---|
| 731 | /* lay down tmp and am right after powers table */
|
---|
| 732 | tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
|
---|
| 733 | am.d = tmp.d + top;
|
---|
| 734 | tmp.top = am.top = 0;
|
---|
| 735 | tmp.dmax = am.dmax = top;
|
---|
| 736 | tmp.neg = am.neg = 0;
|
---|
| 737 | tmp.flags = am.flags = BN_FLG_STATIC_DATA;
|
---|
| 738 |
|
---|
| 739 | /* prepare a^0 in Montgomery domain */
|
---|
| 740 | #if 1 /* by Shay Gueron's suggestion */
|
---|
| 741 | if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
|
---|
| 742 | /* 2^(top*BN_BITS2) - m */
|
---|
| 743 | tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
|
---|
| 744 | for (i = 1; i < top; i++)
|
---|
| 745 | tmp.d[i] = (~m->d[i]) & BN_MASK2;
|
---|
| 746 | tmp.top = top;
|
---|
| 747 | } else
|
---|
| 748 | #endif
|
---|
| 749 | if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
|
---|
| 750 | goto err;
|
---|
| 751 |
|
---|
| 752 | /* prepare a^1 in Montgomery domain */
|
---|
| 753 | if (a->neg || BN_ucmp(a, m) >= 0) {
|
---|
| 754 | if (!BN_mod(&am, a, m, ctx))
|
---|
| 755 | goto err;
|
---|
| 756 | if (!BN_to_montgomery(&am, &am, mont, ctx))
|
---|
| 757 | goto err;
|
---|
| 758 | } else if (!BN_to_montgomery(&am, a, mont, ctx))
|
---|
| 759 | goto err;
|
---|
| 760 |
|
---|
| 761 | #if defined(SPARC_T4_MONT)
|
---|
| 762 | if (t4) {
|
---|
| 763 | typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
|
---|
| 764 | const BN_ULONG *n0, const void *table,
|
---|
| 765 | int power, int bits);
|
---|
| 766 | int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
|
---|
| 767 | const BN_ULONG *n0, const void *table,
|
---|
| 768 | int power, int bits);
|
---|
| 769 | int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
|
---|
| 770 | const BN_ULONG *n0, const void *table,
|
---|
| 771 | int power, int bits);
|
---|
| 772 | int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
|
---|
| 773 | const BN_ULONG *n0, const void *table,
|
---|
| 774 | int power, int bits);
|
---|
| 775 | int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
|
---|
| 776 | const BN_ULONG *n0, const void *table,
|
---|
| 777 | int power, int bits);
|
---|
| 778 | static const bn_pwr5_mont_f pwr5_funcs[4] = {
|
---|
| 779 | bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
|
---|
| 780 | bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
|
---|
| 781 | };
|
---|
| 782 | bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
|
---|
| 783 |
|
---|
| 784 | typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 785 | const void *bp, const BN_ULONG *np,
|
---|
| 786 | const BN_ULONG *n0);
|
---|
| 787 | int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
|
---|
| 788 | const BN_ULONG *np, const BN_ULONG *n0);
|
---|
| 789 | int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 790 | const void *bp, const BN_ULONG *np,
|
---|
| 791 | const BN_ULONG *n0);
|
---|
| 792 | int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 793 | const void *bp, const BN_ULONG *np,
|
---|
| 794 | const BN_ULONG *n0);
|
---|
| 795 | int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 796 | const void *bp, const BN_ULONG *np,
|
---|
| 797 | const BN_ULONG *n0);
|
---|
| 798 | static const bn_mul_mont_f mul_funcs[4] = {
|
---|
| 799 | bn_mul_mont_t4_8, bn_mul_mont_t4_16,
|
---|
| 800 | bn_mul_mont_t4_24, bn_mul_mont_t4_32
|
---|
| 801 | };
|
---|
| 802 | bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
|
---|
| 803 |
|
---|
| 804 | void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 805 | const void *bp, const BN_ULONG *np,
|
---|
| 806 | const BN_ULONG *n0, int num);
|
---|
| 807 | void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 808 | const void *bp, const BN_ULONG *np,
|
---|
| 809 | const BN_ULONG *n0, int num);
|
---|
| 810 | void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 811 | const void *table, const BN_ULONG *np,
|
---|
| 812 | const BN_ULONG *n0, int num, int power);
|
---|
| 813 | void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
|
---|
| 814 | void *table, size_t power);
|
---|
| 815 | void bn_gather5_t4(BN_ULONG *out, size_t num,
|
---|
| 816 | void *table, size_t power);
|
---|
| 817 | void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
|
---|
| 818 |
|
---|
| 819 | BN_ULONG *np = mont->N.d, *n0 = mont->n0;
|
---|
| 820 | int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
|
---|
| 821 | * than 32 */
|
---|
| 822 |
|
---|
| 823 | /*
|
---|
| 824 | * BN_to_montgomery can contaminate words above .top [in
|
---|
| 825 | * BN_DEBUG[_DEBUG] build]...
|
---|
| 826 | */
|
---|
| 827 | for (i = am.top; i < top; i++)
|
---|
| 828 | am.d[i] = 0;
|
---|
| 829 | for (i = tmp.top; i < top; i++)
|
---|
| 830 | tmp.d[i] = 0;
|
---|
| 831 |
|
---|
| 832 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
|
---|
| 833 | bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
|
---|
| 834 | if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
|
---|
| 835 | !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
|
---|
| 836 | bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
|
---|
| 837 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
|
---|
| 838 |
|
---|
| 839 | for (i = 3; i < 32; i++) {
|
---|
| 840 | /* Calculate a^i = a^(i-1) * a */
|
---|
| 841 | if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
|
---|
| 842 | !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
|
---|
| 843 | bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
|
---|
| 844 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
|
---|
| 845 | }
|
---|
| 846 |
|
---|
| 847 | /* switch to 64-bit domain */
|
---|
| 848 | np = alloca(top * sizeof(BN_ULONG));
|
---|
| 849 | top /= 2;
|
---|
| 850 | bn_flip_t4(np, mont->N.d, top);
|
---|
| 851 |
|
---|
| 852 | bits--;
|
---|
| 853 | for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
|
---|
| 854 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
| 855 | bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
|
---|
| 856 |
|
---|
| 857 | /*
|
---|
| 858 | * Scan the exponent one window at a time starting from the most
|
---|
| 859 | * significant bits.
|
---|
| 860 | */
|
---|
| 861 | while (bits >= 0) {
|
---|
| 862 | if (bits < stride)
|
---|
| 863 | stride = bits + 1;
|
---|
| 864 | bits -= stride;
|
---|
| 865 | wvalue = bn_get_bits(p, bits + 1);
|
---|
| 866 |
|
---|
| 867 | if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
|
---|
| 868 | continue;
|
---|
| 869 | /* retry once and fall back */
|
---|
| 870 | if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
|
---|
| 871 | continue;
|
---|
| 872 |
|
---|
| 873 | bits += stride - 5;
|
---|
| 874 | wvalue >>= stride - 5;
|
---|
| 875 | wvalue &= 31;
|
---|
| 876 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 877 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 878 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 879 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 880 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 881 | bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
|
---|
| 882 | wvalue);
|
---|
| 883 | }
|
---|
| 884 |
|
---|
| 885 | bn_flip_t4(tmp.d, tmp.d, top);
|
---|
| 886 | top *= 2;
|
---|
| 887 | /* back to 32-bit domain */
|
---|
| 888 | tmp.top = top;
|
---|
| 889 | bn_correct_top(&tmp);
|
---|
| 890 | OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
|
---|
| 891 | } else
|
---|
| 892 | #endif
|
---|
| 893 | #if defined(OPENSSL_BN_ASM_MONT5)
|
---|
| 894 | if (window == 5 && top > 1) {
|
---|
| 895 | /*
|
---|
| 896 | * This optimization uses ideas from http://eprint.iacr.org/2011/239,
|
---|
| 897 | * specifically optimization of cache-timing attack countermeasures
|
---|
| 898 | * and pre-computation optimization.
|
---|
| 899 | */
|
---|
| 900 |
|
---|
| 901 | /*
|
---|
| 902 | * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
|
---|
| 903 | * 512-bit RSA is hardly relevant, we omit it to spare size...
|
---|
| 904 | */
|
---|
| 905 | void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 906 | const void *table, const BN_ULONG *np,
|
---|
| 907 | const BN_ULONG *n0, int num, int power);
|
---|
| 908 | void bn_scatter5(const BN_ULONG *inp, size_t num,
|
---|
| 909 | void *table, size_t power);
|
---|
| 910 | void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
|
---|
| 911 | void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 912 | const void *table, const BN_ULONG *np,
|
---|
| 913 | const BN_ULONG *n0, int num, int power);
|
---|
| 914 | int bn_get_bits5(const BN_ULONG *ap, int off);
|
---|
| 915 | int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
| 916 | const BN_ULONG *not_used, const BN_ULONG *np,
|
---|
| 917 | const BN_ULONG *n0, int num);
|
---|
| 918 |
|
---|
| 919 | BN_ULONG *n0 = mont->n0, *np;
|
---|
| 920 |
|
---|
| 921 | /*
|
---|
| 922 | * BN_to_montgomery can contaminate words above .top [in
|
---|
| 923 | * BN_DEBUG[_DEBUG] build]...
|
---|
| 924 | */
|
---|
| 925 | for (i = am.top; i < top; i++)
|
---|
| 926 | am.d[i] = 0;
|
---|
| 927 | for (i = tmp.top; i < top; i++)
|
---|
| 928 | tmp.d[i] = 0;
|
---|
| 929 |
|
---|
| 930 | /*
|
---|
| 931 | * copy mont->N.d[] to improve cache locality
|
---|
| 932 | */
|
---|
| 933 | for (np = am.d + top, i = 0; i < top; i++)
|
---|
| 934 | np[i] = mont->N.d[i];
|
---|
| 935 |
|
---|
| 936 | bn_scatter5(tmp.d, top, powerbuf, 0);
|
---|
| 937 | bn_scatter5(am.d, am.top, powerbuf, 1);
|
---|
| 938 | bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
|
---|
| 939 | bn_scatter5(tmp.d, top, powerbuf, 2);
|
---|
| 940 |
|
---|
| 941 | # if 0
|
---|
| 942 | for (i = 3; i < 32; i++) {
|
---|
| 943 | /* Calculate a^i = a^(i-1) * a */
|
---|
| 944 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
---|
| 945 | bn_scatter5(tmp.d, top, powerbuf, i);
|
---|
| 946 | }
|
---|
| 947 | # else
|
---|
| 948 | /* same as above, but uses squaring for 1/2 of operations */
|
---|
| 949 | for (i = 4; i < 32; i *= 2) {
|
---|
| 950 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 951 | bn_scatter5(tmp.d, top, powerbuf, i);
|
---|
| 952 | }
|
---|
| 953 | for (i = 3; i < 8; i += 2) {
|
---|
| 954 | int j;
|
---|
| 955 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
---|
| 956 | bn_scatter5(tmp.d, top, powerbuf, i);
|
---|
| 957 | for (j = 2 * i; j < 32; j *= 2) {
|
---|
| 958 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 959 | bn_scatter5(tmp.d, top, powerbuf, j);
|
---|
| 960 | }
|
---|
| 961 | }
|
---|
| 962 | for (; i < 16; i += 2) {
|
---|
| 963 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
---|
| 964 | bn_scatter5(tmp.d, top, powerbuf, i);
|
---|
| 965 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 966 | bn_scatter5(tmp.d, top, powerbuf, 2 * i);
|
---|
| 967 | }
|
---|
| 968 | for (; i < 32; i += 2) {
|
---|
| 969 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
---|
| 970 | bn_scatter5(tmp.d, top, powerbuf, i);
|
---|
| 971 | }
|
---|
| 972 | # endif
|
---|
| 973 | bits--;
|
---|
| 974 | for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
|
---|
| 975 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
| 976 | bn_gather5(tmp.d, top, powerbuf, wvalue);
|
---|
| 977 |
|
---|
| 978 | /*
|
---|
| 979 | * Scan the exponent one window at a time starting from the most
|
---|
| 980 | * significant bits.
|
---|
| 981 | */
|
---|
| 982 | if (top & 7)
|
---|
| 983 | while (bits >= 0) {
|
---|
| 984 | for (wvalue = 0, i = 0; i < 5; i++, bits--)
|
---|
| 985 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
| 986 |
|
---|
| 987 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 988 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 989 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 990 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 991 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
| 992 | bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
|
---|
| 993 | wvalue);
|
---|
| 994 | } else {
|
---|
| 995 | while (bits >= 0) {
|
---|
| 996 | wvalue = bn_get_bits5(p->d, bits - 4);
|
---|
| 997 | bits -= 5;
|
---|
| 998 | bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
|
---|
| 999 | }
|
---|
| 1000 | }
|
---|
| 1001 |
|
---|
| 1002 | ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
|
---|
| 1003 | tmp.top = top;
|
---|
| 1004 | bn_correct_top(&tmp);
|
---|
| 1005 | if (ret) {
|
---|
| 1006 | if (!BN_copy(rr, &tmp))
|
---|
| 1007 | ret = 0;
|
---|
| 1008 | goto err; /* non-zero ret means it's not error */
|
---|
| 1009 | }
|
---|
| 1010 | } else
|
---|
| 1011 | #endif
|
---|
| 1012 | {
|
---|
| 1013 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
|
---|
| 1014 | goto err;
|
---|
| 1015 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
|
---|
| 1016 | goto err;
|
---|
| 1017 |
|
---|
| 1018 | /*
|
---|
| 1019 | * If the window size is greater than 1, then calculate
|
---|
| 1020 | * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
|
---|
| 1021 | * powers could instead be computed as (a^(i/2))^2 to use the slight
|
---|
| 1022 | * performance advantage of sqr over mul).
|
---|
| 1023 | */
|
---|
| 1024 | if (window > 1) {
|
---|
| 1025 | if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
|
---|
| 1026 | goto err;
|
---|
| 1027 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
|
---|
| 1028 | window))
|
---|
| 1029 | goto err;
|
---|
| 1030 | for (i = 3; i < numPowers; i++) {
|
---|
| 1031 | /* Calculate a^i = a^(i-1) * a */
|
---|
| 1032 | if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
|
---|
| 1033 | goto err;
|
---|
| 1034 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
|
---|
| 1035 | window))
|
---|
| 1036 | goto err;
|
---|
| 1037 | }
|
---|
| 1038 | }
|
---|
| 1039 |
|
---|
| 1040 | bits--;
|
---|
| 1041 | for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
|
---|
| 1042 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
| 1043 | if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
|
---|
| 1044 | window))
|
---|
| 1045 | goto err;
|
---|
| 1046 |
|
---|
| 1047 | /*
|
---|
| 1048 | * Scan the exponent one window at a time starting from the most
|
---|
| 1049 | * significant bits.
|
---|
| 1050 | */
|
---|
| 1051 | while (bits >= 0) {
|
---|
| 1052 | wvalue = 0; /* The 'value' of the window */
|
---|
| 1053 |
|
---|
| 1054 | /* Scan the window, squaring the result as we go */
|
---|
| 1055 | for (i = 0; i < window; i++, bits--) {
|
---|
| 1056 | if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
|
---|
| 1057 | goto err;
|
---|
| 1058 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
| 1059 | }
|
---|
| 1060 |
|
---|
| 1061 | /*
|
---|
| 1062 | * Fetch the appropriate pre-computed value from the pre-buf
|
---|
| 1063 | */
|
---|
| 1064 | if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
|
---|
| 1065 | window))
|
---|
| 1066 | goto err;
|
---|
| 1067 |
|
---|
| 1068 | /* Multiply the result into the intermediate result */
|
---|
| 1069 | if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
|
---|
| 1070 | goto err;
|
---|
| 1071 | }
|
---|
| 1072 | }
|
---|
| 1073 |
|
---|
| 1074 | /* Convert the final result from montgomery to standard format */
|
---|
| 1075 | #if defined(SPARC_T4_MONT)
|
---|
| 1076 | if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
|
---|
| 1077 | am.d[0] = 1; /* borrow am */
|
---|
| 1078 | for (i = 1; i < top; i++)
|
---|
| 1079 | am.d[i] = 0;
|
---|
| 1080 | if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
|
---|
| 1081 | goto err;
|
---|
| 1082 | } else
|
---|
| 1083 | #endif
|
---|
| 1084 | if (!BN_from_montgomery(rr, &tmp, mont, ctx))
|
---|
| 1085 | goto err;
|
---|
| 1086 | ret = 1;
|
---|
| 1087 | err:
|
---|
| 1088 | if (in_mont == NULL)
|
---|
| 1089 | BN_MONT_CTX_free(mont);
|
---|
| 1090 | if (powerbuf != NULL) {
|
---|
| 1091 | OPENSSL_cleanse(powerbuf, powerbufLen);
|
---|
| 1092 | OPENSSL_free(powerbufFree);
|
---|
| 1093 | }
|
---|
| 1094 | BN_CTX_end(ctx);
|
---|
| 1095 | return (ret);
|
---|
| 1096 | }
|
---|
| 1097 |
|
---|
| 1098 | int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
|
---|
| 1099 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
|
---|
| 1100 | {
|
---|
| 1101 | BN_MONT_CTX *mont = NULL;
|
---|
| 1102 | int b, bits, ret = 0;
|
---|
| 1103 | int r_is_one;
|
---|
| 1104 | BN_ULONG w, next_w;
|
---|
| 1105 | BIGNUM *d, *r, *t;
|
---|
| 1106 | BIGNUM *swap_tmp;
|
---|
| 1107 | #define BN_MOD_MUL_WORD(r, w, m) \
|
---|
| 1108 | (BN_mul_word(r, (w)) && \
|
---|
| 1109 | (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
|
---|
| 1110 | (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
|
---|
| 1111 | /*
|
---|
| 1112 | * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
|
---|
| 1113 | * probably more overhead than always using BN_mod (which uses BN_copy if
|
---|
| 1114 | * a similar test returns true).
|
---|
| 1115 | */
|
---|
| 1116 | /*
|
---|
| 1117 | * We can use BN_mod and do not need BN_nnmod because our accumulator is
|
---|
| 1118 | * never negative (the result of BN_mod does not depend on the sign of
|
---|
| 1119 | * the modulus).
|
---|
| 1120 | */
|
---|
| 1121 | #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
|
---|
| 1122 | (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
|
---|
| 1123 |
|
---|
| 1124 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
---|
| 1125 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
---|
| 1126 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
---|
| 1127 | return 0;
|
---|
| 1128 | }
|
---|
| 1129 |
|
---|
| 1130 | bn_check_top(p);
|
---|
| 1131 | bn_check_top(m);
|
---|
| 1132 |
|
---|
| 1133 | if (!BN_is_odd(m)) {
|
---|
| 1134 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
|
---|
| 1135 | return (0);
|
---|
| 1136 | }
|
---|
| 1137 | if (m->top == 1)
|
---|
| 1138 | a %= m->d[0]; /* make sure that 'a' is reduced */
|
---|
| 1139 |
|
---|
| 1140 | bits = BN_num_bits(p);
|
---|
| 1141 | if (bits == 0) {
|
---|
| 1142 | /* x**0 mod 1 is still zero. */
|
---|
| 1143 | if (BN_is_one(m)) {
|
---|
| 1144 | ret = 1;
|
---|
| 1145 | BN_zero(rr);
|
---|
| 1146 | } else {
|
---|
| 1147 | ret = BN_one(rr);
|
---|
| 1148 | }
|
---|
| 1149 | return ret;
|
---|
| 1150 | }
|
---|
| 1151 | if (a == 0) {
|
---|
| 1152 | BN_zero(rr);
|
---|
| 1153 | ret = 1;
|
---|
| 1154 | return ret;
|
---|
| 1155 | }
|
---|
| 1156 |
|
---|
| 1157 | BN_CTX_start(ctx);
|
---|
| 1158 | d = BN_CTX_get(ctx);
|
---|
| 1159 | r = BN_CTX_get(ctx);
|
---|
| 1160 | t = BN_CTX_get(ctx);
|
---|
| 1161 | if (d == NULL || r == NULL || t == NULL)
|
---|
| 1162 | goto err;
|
---|
| 1163 |
|
---|
| 1164 | if (in_mont != NULL)
|
---|
| 1165 | mont = in_mont;
|
---|
| 1166 | else {
|
---|
| 1167 | if ((mont = BN_MONT_CTX_new()) == NULL)
|
---|
| 1168 | goto err;
|
---|
| 1169 | if (!BN_MONT_CTX_set(mont, m, ctx))
|
---|
| 1170 | goto err;
|
---|
| 1171 | }
|
---|
| 1172 |
|
---|
| 1173 | r_is_one = 1; /* except for Montgomery factor */
|
---|
| 1174 |
|
---|
| 1175 | /* bits-1 >= 0 */
|
---|
| 1176 |
|
---|
| 1177 | /* The result is accumulated in the product r*w. */
|
---|
| 1178 | w = a; /* bit 'bits-1' of 'p' is always set */
|
---|
| 1179 | for (b = bits - 2; b >= 0; b--) {
|
---|
| 1180 | /* First, square r*w. */
|
---|
| 1181 | next_w = w * w;
|
---|
| 1182 | if ((next_w / w) != w) { /* overflow */
|
---|
| 1183 | if (r_is_one) {
|
---|
| 1184 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
|
---|
| 1185 | goto err;
|
---|
| 1186 | r_is_one = 0;
|
---|
| 1187 | } else {
|
---|
| 1188 | if (!BN_MOD_MUL_WORD(r, w, m))
|
---|
| 1189 | goto err;
|
---|
| 1190 | }
|
---|
| 1191 | next_w = 1;
|
---|
| 1192 | }
|
---|
| 1193 | w = next_w;
|
---|
| 1194 | if (!r_is_one) {
|
---|
| 1195 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
|
---|
| 1196 | goto err;
|
---|
| 1197 | }
|
---|
| 1198 |
|
---|
| 1199 | /* Second, multiply r*w by 'a' if exponent bit is set. */
|
---|
| 1200 | if (BN_is_bit_set(p, b)) {
|
---|
| 1201 | next_w = w * a;
|
---|
| 1202 | if ((next_w / a) != w) { /* overflow */
|
---|
| 1203 | if (r_is_one) {
|
---|
| 1204 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
|
---|
| 1205 | goto err;
|
---|
| 1206 | r_is_one = 0;
|
---|
| 1207 | } else {
|
---|
| 1208 | if (!BN_MOD_MUL_WORD(r, w, m))
|
---|
| 1209 | goto err;
|
---|
| 1210 | }
|
---|
| 1211 | next_w = a;
|
---|
| 1212 | }
|
---|
| 1213 | w = next_w;
|
---|
| 1214 | }
|
---|
| 1215 | }
|
---|
| 1216 |
|
---|
| 1217 | /* Finally, set r:=r*w. */
|
---|
| 1218 | if (w != 1) {
|
---|
| 1219 | if (r_is_one) {
|
---|
| 1220 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
|
---|
| 1221 | goto err;
|
---|
| 1222 | r_is_one = 0;
|
---|
| 1223 | } else {
|
---|
| 1224 | if (!BN_MOD_MUL_WORD(r, w, m))
|
---|
| 1225 | goto err;
|
---|
| 1226 | }
|
---|
| 1227 | }
|
---|
| 1228 |
|
---|
| 1229 | if (r_is_one) { /* can happen only if a == 1 */
|
---|
| 1230 | if (!BN_one(rr))
|
---|
| 1231 | goto err;
|
---|
| 1232 | } else {
|
---|
| 1233 | if (!BN_from_montgomery(rr, r, mont, ctx))
|
---|
| 1234 | goto err;
|
---|
| 1235 | }
|
---|
| 1236 | ret = 1;
|
---|
| 1237 | err:
|
---|
| 1238 | if (in_mont == NULL)
|
---|
| 1239 | BN_MONT_CTX_free(mont);
|
---|
| 1240 | BN_CTX_end(ctx);
|
---|
| 1241 | bn_check_top(rr);
|
---|
| 1242 | return (ret);
|
---|
| 1243 | }
|
---|
| 1244 |
|
---|
| 1245 | /* The old fallback, simple version :-) */
|
---|
| 1246 | int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
|
---|
| 1247 | const BIGNUM *m, BN_CTX *ctx)
|
---|
| 1248 | {
|
---|
| 1249 | int i, j, bits, ret = 0, wstart, wend, window, wvalue;
|
---|
| 1250 | int start = 1;
|
---|
| 1251 | BIGNUM *d;
|
---|
| 1252 | /* Table of variables obtained from 'ctx' */
|
---|
| 1253 | BIGNUM *val[TABLE_SIZE];
|
---|
| 1254 |
|
---|
| 1255 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
---|
| 1256 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
---|
| 1257 | BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
---|
| 1258 | return 0;
|
---|
| 1259 | }
|
---|
| 1260 |
|
---|
| 1261 | bits = BN_num_bits(p);
|
---|
| 1262 | if (bits == 0) {
|
---|
| 1263 | /* x**0 mod 1 is still zero. */
|
---|
| 1264 | if (BN_is_one(m)) {
|
---|
| 1265 | ret = 1;
|
---|
| 1266 | BN_zero(r);
|
---|
| 1267 | } else {
|
---|
| 1268 | ret = BN_one(r);
|
---|
| 1269 | }
|
---|
| 1270 | return ret;
|
---|
| 1271 | }
|
---|
| 1272 |
|
---|
| 1273 | BN_CTX_start(ctx);
|
---|
| 1274 | d = BN_CTX_get(ctx);
|
---|
| 1275 | val[0] = BN_CTX_get(ctx);
|
---|
| 1276 | if (!d || !val[0])
|
---|
| 1277 | goto err;
|
---|
| 1278 |
|
---|
| 1279 | if (!BN_nnmod(val[0], a, m, ctx))
|
---|
| 1280 | goto err; /* 1 */
|
---|
| 1281 | if (BN_is_zero(val[0])) {
|
---|
| 1282 | BN_zero(r);
|
---|
| 1283 | ret = 1;
|
---|
| 1284 | goto err;
|
---|
| 1285 | }
|
---|
| 1286 |
|
---|
| 1287 | window = BN_window_bits_for_exponent_size(bits);
|
---|
| 1288 | if (window > 1) {
|
---|
| 1289 | if (!BN_mod_mul(d, val[0], val[0], m, ctx))
|
---|
| 1290 | goto err; /* 2 */
|
---|
| 1291 | j = 1 << (window - 1);
|
---|
| 1292 | for (i = 1; i < j; i++) {
|
---|
| 1293 | if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
|
---|
| 1294 | !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
|
---|
| 1295 | goto err;
|
---|
| 1296 | }
|
---|
| 1297 | }
|
---|
| 1298 |
|
---|
| 1299 | start = 1; /* This is used to avoid multiplication etc
|
---|
| 1300 | * when there is only the value '1' in the
|
---|
| 1301 | * buffer. */
|
---|
| 1302 | wvalue = 0; /* The 'value' of the window */
|
---|
| 1303 | wstart = bits - 1; /* The top bit of the window */
|
---|
| 1304 | wend = 0; /* The bottom bit of the window */
|
---|
| 1305 |
|
---|
| 1306 | if (!BN_one(r))
|
---|
| 1307 | goto err;
|
---|
| 1308 |
|
---|
| 1309 | for (;;) {
|
---|
| 1310 | if (BN_is_bit_set(p, wstart) == 0) {
|
---|
| 1311 | if (!start)
|
---|
| 1312 | if (!BN_mod_mul(r, r, r, m, ctx))
|
---|
| 1313 | goto err;
|
---|
| 1314 | if (wstart == 0)
|
---|
| 1315 | break;
|
---|
| 1316 | wstart--;
|
---|
| 1317 | continue;
|
---|
| 1318 | }
|
---|
| 1319 | /*
|
---|
| 1320 | * We now have wstart on a 'set' bit, we now need to work out how bit
|
---|
| 1321 | * a window to do. To do this we need to scan forward until the last
|
---|
| 1322 | * set bit before the end of the window
|
---|
| 1323 | */
|
---|
| 1324 | j = wstart;
|
---|
| 1325 | wvalue = 1;
|
---|
| 1326 | wend = 0;
|
---|
| 1327 | for (i = 1; i < window; i++) {
|
---|
| 1328 | if (wstart - i < 0)
|
---|
| 1329 | break;
|
---|
| 1330 | if (BN_is_bit_set(p, wstart - i)) {
|
---|
| 1331 | wvalue <<= (i - wend);
|
---|
| 1332 | wvalue |= 1;
|
---|
| 1333 | wend = i;
|
---|
| 1334 | }
|
---|
| 1335 | }
|
---|
| 1336 |
|
---|
| 1337 | /* wend is the size of the current window */
|
---|
| 1338 | j = wend + 1;
|
---|
| 1339 | /* add the 'bytes above' */
|
---|
| 1340 | if (!start)
|
---|
| 1341 | for (i = 0; i < j; i++) {
|
---|
| 1342 | if (!BN_mod_mul(r, r, r, m, ctx))
|
---|
| 1343 | goto err;
|
---|
| 1344 | }
|
---|
| 1345 |
|
---|
| 1346 | /* wvalue will be an odd number < 2^window */
|
---|
| 1347 | if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
|
---|
| 1348 | goto err;
|
---|
| 1349 |
|
---|
| 1350 | /* move the 'window' down further */
|
---|
| 1351 | wstart -= wend + 1;
|
---|
| 1352 | wvalue = 0;
|
---|
| 1353 | start = 0;
|
---|
| 1354 | if (wstart < 0)
|
---|
| 1355 | break;
|
---|
| 1356 | }
|
---|
| 1357 | ret = 1;
|
---|
| 1358 | err:
|
---|
| 1359 | BN_CTX_end(ctx);
|
---|
| 1360 | bn_check_top(r);
|
---|
| 1361 | return (ret);
|
---|
| 1362 | }
|
---|