1 /* Copyright (C) 1995-1997 Eric Young (eay (at) cryptsoft.com) 2 * All rights reserved. 3 * 4 * This package is an SSL implementation written 5 * by Eric Young (eay (at) cryptsoft.com). 6 * The implementation was written so as to conform with Netscapes SSL. 7 * 8 * This library is free for commercial and non-commercial use as long as 9 * the following conditions are aheared to. The following conditions 10 * apply to all code found in this distribution, be it the RC4, RSA, 11 * lhash, DES, etc., code; not just the SSL code. The SSL documentation 12 * included with this distribution is covered by the same copyright terms 13 * except that the holder is Tim Hudson (tjh (at) cryptsoft.com). 14 * 15 * Copyright remains Eric Young's, and as such any Copyright notices in 16 * the code are not to be removed. 17 * If this package is used in a product, Eric Young should be given attribution 18 * as the author of the parts of the library used. 19 * This can be in the form of a textual message at program startup or 20 * in documentation (online or textual) provided with the package. 21 * 22 * Redistribution and use in source and binary forms, with or without 23 * modification, are permitted provided that the following conditions 24 * are met: 25 * 1. Redistributions of source code must retain the copyright 26 * notice, this list of conditions and the following disclaimer. 27 * 2. Redistributions in binary form must reproduce the above copyright 28 * notice, this list of conditions and the following disclaimer in the 29 * documentation and/or other materials provided with the distribution. 30 * 3. All advertising materials mentioning features or use of this software 31 * must display the following acknowledgement: 32 * "This product includes cryptographic software written by 33 * Eric Young (eay (at) cryptsoft.com)" 34 * The word 'cryptographic' can be left out if the rouines from the library 35 * being used are not cryptographic related :-). 36 * 4. If you include any Windows specific code (or a derivative thereof) from 37 * the apps directory (application code) you must include an acknowledgement: 38 * "This product includes software written by Tim Hudson (tjh (at) cryptsoft.com)" 39 * 40 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND 41 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 43 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 44 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 45 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 46 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 48 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 49 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 50 * SUCH DAMAGE. 51 * 52 * The licence and distribution terms for any publically available version or 53 * derivative of this code cannot be changed. i.e. this code cannot simply be 54 * copied and put under another distribution licence 55 * [including the GNU Public Licence.] 56 */ 57 /* ==================================================================== 58 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved. 59 * 60 * Redistribution and use in source and binary forms, with or without 61 * modification, are permitted provided that the following conditions 62 * are met: 63 * 64 * 1. Redistributions of source code must retain the above copyright 65 * notice, this list of conditions and the following disclaimer. 66 * 67 * 2. Redistributions in binary form must reproduce the above copyright 68 * notice, this list of conditions and the following disclaimer in 69 * the documentation and/or other materials provided with the 70 * distribution. 71 * 72 * 3. All advertising materials mentioning features or use of this 73 * software must display the following acknowledgment: 74 * "This product includes software developed by the OpenSSL Project 75 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 76 * 77 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 78 * endorse or promote products derived from this software without 79 * prior written permission. For written permission, please contact 80 * openssl-core (at) openssl.org. 81 * 82 * 5. Products derived from this software may not be called "OpenSSL" 83 * nor may "OpenSSL" appear in their names without prior written 84 * permission of the OpenSSL Project. 85 * 86 * 6. Redistributions of any form whatsoever must retain the following 87 * acknowledgment: 88 * "This product includes software developed by the OpenSSL Project 89 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 90 * 91 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 92 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 93 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 94 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 95 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 96 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 97 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 98 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 99 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 100 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 101 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 102 * OF THE POSSIBILITY OF SUCH DAMAGE. 103 * ==================================================================== 104 * 105 * This product includes cryptographic software written by Eric Young 106 * (eay (at) cryptsoft.com). This product includes software written by Tim 107 * Hudson (tjh (at) cryptsoft.com). 108 * 109 */ 110 /* ==================================================================== 111 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. 112 * 113 * Portions of the attached software ("Contribution") are developed by 114 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. 115 * 116 * The Contribution is licensed pursuant to the Eric Young open source 117 * license provided above. 118 * 119 * The binary polynomial arithmetic software is originally written by 120 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems 121 * Laboratories. */ 122 123 #ifndef OPENSSL_HEADER_BN_INTERNAL_H 124 #define OPENSSL_HEADER_BN_INTERNAL_H 125 126 #include <openssl/base.h> 127 128 #if defined(OPENSSL_X86_64) && defined(_MSC_VER) 129 OPENSSL_MSVC_PRAGMA(warning(push, 3)) 130 #include <intrin.h> 131 OPENSSL_MSVC_PRAGMA(warning(pop)) 132 #pragma intrinsic(__umulh, _umul128) 133 #endif 134 135 #include "../../internal.h" 136 137 #if defined(__cplusplus) 138 extern "C" { 139 #endif 140 141 #if defined(OPENSSL_64_BIT) 142 143 #if defined(BORINGSSL_HAS_UINT128) 144 // MSVC doesn't support two-word integers on 64-bit. 145 #define BN_ULLONG uint128_t 146 #if defined(BORINGSSL_CAN_DIVIDE_UINT128) 147 #define BN_CAN_DIVIDE_ULLONG 148 #endif 149 #endif 150 151 #define BN_BITS2 64 152 #define BN_BYTES 8 153 #define BN_BITS4 32 154 #define BN_MASK2 (0xffffffffffffffffUL) 155 #define BN_MASK2l (0xffffffffUL) 156 #define BN_MASK2h (0xffffffff00000000UL) 157 #define BN_MASK2h1 (0xffffffff80000000UL) 158 #define BN_MONT_CTX_N0_LIMBS 1 159 #define BN_DEC_CONV (10000000000000000000UL) 160 #define BN_DEC_NUM 19 161 #define TOBN(hi, lo) ((BN_ULONG)(hi) << 32 | (lo)) 162 163 #elif defined(OPENSSL_32_BIT) 164 165 #define BN_ULLONG uint64_t 166 #define BN_CAN_DIVIDE_ULLONG 167 #define BN_BITS2 32 168 #define BN_BYTES 4 169 #define BN_BITS4 16 170 #define BN_MASK2 (0xffffffffUL) 171 #define BN_MASK2l (0xffffUL) 172 #define BN_MASK2h1 (0xffff8000UL) 173 #define BN_MASK2h (0xffff0000UL) 174 // On some 32-bit platforms, Montgomery multiplication is done using 64-bit 175 // arithmetic with SIMD instructions. On such platforms, |BN_MONT_CTX::n0| 176 // needs to be two words long. Only certain 32-bit platforms actually make use 177 // of n0[1] and shorter R value would suffice for the others. However, 178 // currently only the assembly files know which is which. 179 #define BN_MONT_CTX_N0_LIMBS 2 180 #define BN_DEC_CONV (1000000000UL) 181 #define BN_DEC_NUM 9 182 #define TOBN(hi, lo) (lo), (hi) 183 184 #else 185 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT" 186 #endif 187 188 #if !defined(OPENSSL_NO_ASM) && (defined(__GNUC__) || defined(__clang__)) 189 #define BN_CAN_USE_INLINE_ASM 190 #endif 191 192 // |BN_mod_exp_mont_consttime| is based on the assumption that the L1 data 193 // cache line width of the target processor is at least the following value. 194 #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH 64 195 196 // The number of |BN_ULONG|s needed for the |BN_mod_exp_mont_consttime| stack- 197 // allocated storage buffer. The buffer is just the right size for the RSAZ 198 // and is about ~1KB larger than what's necessary (4480 bytes) for 1024-bit 199 // inputs. 200 #define MOD_EXP_CTIME_STORAGE_LEN \ 201 (((320u * 3u) + (32u * 9u * 16u)) / sizeof(BN_ULONG)) 202 203 #define STATIC_BIGNUM(x) \ 204 { \ 205 (BN_ULONG *)(x), sizeof(x) / sizeof(BN_ULONG), \ 206 sizeof(x) / sizeof(BN_ULONG), 0, BN_FLG_STATIC_DATA \ 207 } 208 209 #if defined(BN_ULLONG) 210 #define Lw(t) ((BN_ULONG)(t)) 211 #define Hw(t) ((BN_ULONG)((t) >> BN_BITS2)) 212 #endif 213 214 // bn_minimal_width returns the minimal value of |bn->top| which fits the 215 // value of |bn|. 216 int bn_minimal_width(const BIGNUM *bn); 217 218 // bn_set_minimal_width sets |bn->width| to |bn_minimal_width(bn)|. If |bn| is 219 // zero, |bn->neg| is set to zero. 220 void bn_set_minimal_width(BIGNUM *bn); 221 222 // bn_wexpand ensures that |bn| has at least |words| works of space without 223 // altering its value. It returns one on success or zero on allocation 224 // failure. 225 int bn_wexpand(BIGNUM *bn, size_t words); 226 227 // bn_expand acts the same as |bn_wexpand|, but takes a number of bits rather 228 // than a number of words. 229 int bn_expand(BIGNUM *bn, size_t bits); 230 231 // bn_resize_words adjusts |bn->top| to be |words|. It returns one on success 232 // and zero on allocation error or if |bn|'s value is too large. 233 OPENSSL_EXPORT int bn_resize_words(BIGNUM *bn, size_t words); 234 235 // bn_select_words sets |r| to |a| if |mask| is all ones or |b| if |mask| is 236 // all zeros. 237 void bn_select_words(BN_ULONG *r, BN_ULONG mask, const BN_ULONG *a, 238 const BN_ULONG *b, size_t num); 239 240 // bn_set_words sets |bn| to the value encoded in the |num| words in |words|, 241 // least significant word first. 242 int bn_set_words(BIGNUM *bn, const BN_ULONG *words, size_t num); 243 244 // bn_fits_in_words returns one if |bn| may be represented in |num| words, plus 245 // a sign bit, and zero otherwise. 246 int bn_fits_in_words(const BIGNUM *bn, size_t num); 247 248 // bn_copy_words copies the value of |bn| to |out| and returns one if the value 249 // is representable in |num| words. Otherwise, it returns zero. 250 int bn_copy_words(BN_ULONG *out, size_t num, const BIGNUM *bn); 251 252 // bn_mul_add_words multiples |ap| by |w|, adds the result to |rp|, and places 253 // the result in |rp|. |ap| and |rp| must both be |num| words long. It returns 254 // the carry word of the operation. |ap| and |rp| may be equal but otherwise may 255 // not alias. 256 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num, 257 BN_ULONG w); 258 259 // bn_mul_words multiples |ap| by |w| and places the result in |rp|. |ap| and 260 // |rp| must both be |num| words long. It returns the carry word of the 261 // operation. |ap| and |rp| may be equal but otherwise may not alias. 262 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num, BN_ULONG w); 263 264 // bn_sqr_words sets |rp[2*i]| and |rp[2*i+1]| to |ap[i]|'s square, for all |i| 265 // up to |num|. |ap| is an array of |num| words and |rp| an array of |2*num| 266 // words. |ap| and |rp| may not alias. 267 // 268 // This gives the contribution of the |ap[i]*ap[i]| terms when squaring |ap|. 269 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num); 270 271 // bn_add_words adds |ap| to |bp| and places the result in |rp|, each of which 272 // are |num| words long. It returns the carry bit, which is one if the operation 273 // overflowed and zero otherwise. Any pair of |ap|, |bp|, and |rp| may be equal 274 // to each other but otherwise may not alias. 275 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 276 size_t num); 277 278 // bn_sub_words subtracts |bp| from |ap| and places the result in |rp|. It 279 // returns the borrow bit, which is one if the computation underflowed and zero 280 // otherwise. Any pair of |ap|, |bp|, and |rp| may be equal to each other but 281 // otherwise may not alias. 282 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 283 size_t num); 284 285 // bn_mul_comba4 sets |r| to the product of |a| and |b|. 286 void bn_mul_comba4(BN_ULONG r[8], const BN_ULONG a[4], const BN_ULONG b[4]); 287 288 // bn_mul_comba8 sets |r| to the product of |a| and |b|. 289 void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]); 290 291 // bn_sqr_comba8 sets |r| to |a|^2. 292 void bn_sqr_comba8(BN_ULONG r[16], const BN_ULONG a[4]); 293 294 // bn_sqr_comba4 sets |r| to |a|^2. 295 void bn_sqr_comba4(BN_ULONG r[8], const BN_ULONG a[4]); 296 297 // bn_less_than_words returns one if |a| < |b| and zero otherwise, where |a| 298 // and |b| both are |len| words long. It runs in constant time. 299 int bn_less_than_words(const BN_ULONG *a, const BN_ULONG *b, size_t len); 300 301 // bn_in_range_words returns one if |min_inclusive| <= |a| < |max_exclusive|, 302 // where |a| and |max_exclusive| both are |len| words long. |a| and 303 // |max_exclusive| are treated as secret. 304 int bn_in_range_words(const BN_ULONG *a, BN_ULONG min_inclusive, 305 const BN_ULONG *max_exclusive, size_t len); 306 307 // bn_rand_range_words sets |out| to a uniformly distributed random number from 308 // |min_inclusive| to |max_exclusive|. Both |out| and |max_exclusive| are |len| 309 // words long. 310 // 311 // This function runs in time independent of the result, but |min_inclusive| and 312 // |max_exclusive| are public data. (Information about the range is unavoidably 313 // leaked by how many iterations it took to select a number.) 314 int bn_rand_range_words(BN_ULONG *out, BN_ULONG min_inclusive, 315 const BN_ULONG *max_exclusive, size_t len, 316 const uint8_t additional_data[32]); 317 318 // bn_range_secret_range behaves like |BN_rand_range_ex|, but treats 319 // |max_exclusive| as secret. Because of this constraint, the distribution of 320 // values returned is more complex. 321 // 322 // Rather than repeatedly generating values until one is in range, which would 323 // leak information, it generates one value. If the value is in range, it sets 324 // |*out_is_uniform| to one. Otherwise, it sets |*out_is_uniform| to zero, 325 // fixing up the value to force it in range. 326 // 327 // The subset of calls to |bn_rand_secret_range| which set |*out_is_uniform| to 328 // one are uniformly distributed in the target range. Calls overall are not. 329 // This function is intended for use in situations where the extra values are 330 // still usable and where the number of iterations needed to reach the target 331 // number of uniform outputs may be blinded for negligible probabilities of 332 // timing leaks. 333 // 334 // Although this function treats |max_exclusive| as secret, it treats the number 335 // of bits in |max_exclusive| as public. 336 int bn_rand_secret_range(BIGNUM *r, int *out_is_uniform, BN_ULONG min_inclusive, 337 const BIGNUM *max_exclusive); 338 339 #if !defined(OPENSSL_NO_ASM) && \ 340 (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \ 341 defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64)) 342 #define OPENSSL_BN_ASM_MONT 343 // bn_mul_mont writes |ap| * |bp| mod |np| to |rp|, each |num| words 344 // long. Inputs and outputs are in Montgomery form. |n0| is a pointer to the 345 // corresponding field in |BN_MONT_CTX|. It returns one if |bn_mul_mont| handles 346 // inputs of this size and zero otherwise. 347 // 348 // TODO(davidben): The x86_64 implementation expects a 32-bit input and masks 349 // off upper bits. The aarch64 implementation expects a 64-bit input and does 350 // not. |size_t| is the safer option but not strictly correct for x86_64. But 351 // this function implicitly already has a bound on the size of |num| because it 352 // internally creates |num|-sized stack allocation. 353 // 354 // See also discussion in |ToWord| in abi_test.h for notes on smaller-than-word 355 // inputs. 356 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 357 const BN_ULONG *np, const BN_ULONG *n0, size_t num); 358 #endif 359 360 #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) 361 #define OPENSSL_BN_ASM_MONT5 362 363 // bn_mul_mont_gather5 multiples loads index |power| of |table|, multiplies it 364 // by |ap| modulo |np|, and stores the result in |rp|. The values are |num| 365 // words long and represented in Montgomery form. |n0| is a pointer to the 366 // corresponding field in |BN_MONT_CTX|. 367 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, 368 const BN_ULONG *table, const BN_ULONG *np, 369 const BN_ULONG *n0, int num, int power); 370 371 // bn_scatter5 stores |inp| to index |power| of |table|. |inp| and each entry of 372 // |table| are |num| words long. |power| must be less than 32. |table| must be 373 // 32*|num| words long. 374 void bn_scatter5(const BN_ULONG *inp, size_t num, BN_ULONG *table, 375 size_t power); 376 377 // bn_gather5 loads index |power| of |table| and stores it in |out|. |out| and 378 // each entry of |table| are |num| words long. |power| must be less than 32. 379 void bn_gather5(BN_ULONG *out, size_t num, BN_ULONG *table, size_t power); 380 381 // bn_power5 squares |ap| five times and multiplies it by the value stored at 382 // index |power| of |table|, modulo |np|. It stores the result in |rp|. The 383 // values are |num| words long and represented in Montgomery form. |n0| is a 384 // pointer to the corresponding field in |BN_MONT_CTX|. |num| must be divisible 385 // by 8. 386 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *table, 387 const BN_ULONG *np, const BN_ULONG *n0, int num, int power); 388 389 // bn_from_montgomery converts |ap| from Montgomery form modulo |np| and writes 390 // the result in |rp|, each of which is |num| words long. It returns one on 391 // success and zero if it cannot handle inputs of length |num|. |n0| is a 392 // pointer to the corresponding field in |BN_MONT_CTX|. 393 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, 394 const BN_ULONG *not_used, const BN_ULONG *np, 395 const BN_ULONG *n0, int num); 396 #endif // !OPENSSL_NO_ASM && OPENSSL_X86_64 397 398 uint64_t bn_mont_n0(const BIGNUM *n); 399 400 // bn_mod_exp_base_2_consttime calculates r = 2**p (mod n). |p| must be larger 401 // than log_2(n); i.e. 2**p must be larger than |n|. |n| must be positive and 402 // odd. |p| and the bit width of |n| are assumed public, but |n| is otherwise 403 // treated as secret. 404 int bn_mod_exp_base_2_consttime(BIGNUM *r, unsigned p, const BIGNUM *n, 405 BN_CTX *ctx); 406 407 #if defined(OPENSSL_X86_64) && defined(_MSC_VER) 408 #define BN_UMULT_LOHI(low, high, a, b) ((low) = _umul128((a), (b), &(high))) 409 #endif 410 411 #if !defined(BN_ULLONG) && !defined(BN_UMULT_LOHI) 412 #error "Either BN_ULLONG or BN_UMULT_LOHI must be defined on every platform." 413 #endif 414 415 // bn_jacobi returns the Jacobi symbol of |a| and |b| (which is -1, 0 or 1), or 416 // -2 on error. 417 int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); 418 419 // bn_is_bit_set_words returns one if bit |bit| is set in |a| and zero 420 // otherwise. 421 int bn_is_bit_set_words(const BN_ULONG *a, size_t num, unsigned bit); 422 423 // bn_one_to_montgomery sets |r| to one in Montgomery form. It returns one on 424 // success and zero on error. This function treats the bit width of the modulus 425 // as public. 426 int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx); 427 428 // bn_less_than_montgomery_R returns one if |bn| is less than the Montgomery R 429 // value for |mont| and zero otherwise. 430 int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont); 431 432 // bn_mod_u16_consttime returns |bn| mod |d|, ignoring |bn|'s sign bit. It runs 433 // in time independent of the value of |bn|, but it treats |d| as public. 434 OPENSSL_EXPORT uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d); 435 436 // bn_odd_number_is_obviously_composite returns one if |bn| is divisible by one 437 // of the first several odd primes and zero otherwise. 438 int bn_odd_number_is_obviously_composite(const BIGNUM *bn); 439 440 // bn_rshift1_words sets |r| to |a| >> 1, where both arrays are |num| bits wide. 441 void bn_rshift1_words(BN_ULONG *r, const BN_ULONG *a, size_t num); 442 443 // bn_rshift_words sets |r| to |a| >> |shift|, where both arrays are |num| bits 444 // wide. 445 void bn_rshift_words(BN_ULONG *r, const BN_ULONG *a, unsigned shift, 446 size_t num); 447 448 // bn_rshift_secret_shift behaves like |BN_rshift| but runs in time independent 449 // of both |a| and |n|. 450 OPENSSL_EXPORT int bn_rshift_secret_shift(BIGNUM *r, const BIGNUM *a, 451 unsigned n, BN_CTX *ctx); 452 453 // bn_reduce_once sets |r| to |a| mod |m| where 0 <= |a| < 2*|m|. It returns 454 // zero if |a| < |m| and a mask of all ones if |a| >= |m|. Each array is |num| 455 // words long, but |a| has an additional word specified by |carry|. |carry| must 456 // be zero or one, as implied by the bounds on |a|. 457 // 458 // |r|, |a|, and |m| may not alias. Use |bn_reduce_once_in_place| if |r| and |a| 459 // must alias. 460 BN_ULONG bn_reduce_once(BN_ULONG *r, const BN_ULONG *a, BN_ULONG carry, 461 const BN_ULONG *m, size_t num); 462 463 // bn_reduce_once_in_place behaves like |bn_reduce_once| but acts in-place on 464 // |r|, using |tmp| as scratch space. |r|, |tmp|, and |m| may not alias. 465 BN_ULONG bn_reduce_once_in_place(BN_ULONG *r, BN_ULONG carry, const BN_ULONG *m, 466 BN_ULONG *tmp, size_t num); 467 468 469 // Constant-time non-modular arithmetic. 470 // 471 // The following functions implement non-modular arithmetic in constant-time 472 // and pessimally set |r->width| to the largest possible word size. 473 // 474 // Note this means that, e.g., repeatedly multiplying by one will cause widths 475 // to increase without bound. The corresponding public API functions minimize 476 // their outputs to avoid regressing calculator consumers. 477 478 // bn_uadd_consttime behaves like |BN_uadd|, but it pessimally sets 479 // |r->width| = |a->width| + |b->width| + 1. 480 int bn_uadd_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 481 482 // bn_usub_consttime behaves like |BN_usub|, but it pessimally sets 483 // |r->width| = |a->width|. 484 int bn_usub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 485 486 // bn_abs_sub_consttime sets |r| to the absolute value of |a| - |b|, treating 487 // both inputs as secret. It returns one on success and zero on error. 488 OPENSSL_EXPORT int bn_abs_sub_consttime(BIGNUM *r, const BIGNUM *a, 489 const BIGNUM *b, BN_CTX *ctx); 490 491 // bn_mul_consttime behaves like |BN_mul|, but it rejects negative inputs and 492 // pessimally sets |r->width| to |a->width| + |b->width|, to avoid leaking 493 // information about |a| and |b|. 494 int bn_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); 495 496 // bn_sqrt_consttime behaves like |BN_sqrt|, but it pessimally sets |r->width| 497 // to 2*|a->width|, to avoid leaking information about |a| and |b|. 498 int bn_sqr_consttime(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); 499 500 // bn_div_consttime behaves like |BN_div|, but it rejects negative inputs and 501 // treats both inputs, including their magnitudes, as secret. It is, as a 502 // result, much slower than |BN_div| and should only be used for rare operations 503 // where Montgomery reduction is not available. 504 // 505 // Note that |quotient->width| will be set pessimally to |numerator->width|. 506 OPENSSL_EXPORT int bn_div_consttime(BIGNUM *quotient, BIGNUM *remainder, 507 const BIGNUM *numerator, 508 const BIGNUM *divisor, BN_CTX *ctx); 509 510 // bn_is_relatively_prime checks whether GCD(|x|, |y|) is one. On success, it 511 // returns one and sets |*out_relatively_prime| to one if the GCD was one and 512 // zero otherwise. On error, it returns zero. 513 OPENSSL_EXPORT int bn_is_relatively_prime(int *out_relatively_prime, 514 const BIGNUM *x, const BIGNUM *y, 515 BN_CTX *ctx); 516 517 // bn_lcm_consttime sets |r| to LCM(|a|, |b|). It returns one and success and 518 // zero on error. |a| and |b| are both treated as secret. 519 OPENSSL_EXPORT int bn_lcm_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 520 BN_CTX *ctx); 521 522 523 // Constant-time modular arithmetic. 524 // 525 // The following functions implement basic constant-time modular arithmetic. 526 527 // bn_mod_add_words sets |r| to |a| + |b| (mod |m|), using |tmp| as scratch 528 // space. Each array is |num| words long. |a| and |b| must be < |m|. Any pair of 529 // |r|, |a|, and |b| may alias. 530 void bn_mod_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 531 const BN_ULONG *m, BN_ULONG *tmp, size_t num); 532 533 // bn_mod_add_consttime acts like |BN_mod_add_quick| but takes a |BN_CTX|. 534 int bn_mod_add_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 535 const BIGNUM *m, BN_CTX *ctx); 536 537 // bn_mod_sub_words sets |r| to |a| - |b| (mod |m|), using |tmp| as scratch 538 // space. Each array is |num| words long. |a| and |b| must be < |m|. Any pair of 539 // |r|, |a|, and |b| may alias. 540 void bn_mod_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 541 const BN_ULONG *m, BN_ULONG *tmp, size_t num); 542 543 // bn_mod_sub_consttime acts like |BN_mod_sub_quick| but takes a |BN_CTX|. 544 int bn_mod_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 545 const BIGNUM *m, BN_CTX *ctx); 546 547 // bn_mod_lshift1_consttime acts like |BN_mod_lshift1_quick| but takes a 548 // |BN_CTX|. 549 int bn_mod_lshift1_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, 550 BN_CTX *ctx); 551 552 // bn_mod_lshift_consttime acts like |BN_mod_lshift_quick| but takes a |BN_CTX|. 553 int bn_mod_lshift_consttime(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, 554 BN_CTX *ctx); 555 556 // bn_mod_inverse_consttime sets |r| to |a|^-1, mod |n|. |a| must be non- 557 // negative and less than |n|. It returns one on success and zero on error. On 558 // failure, if the failure was caused by |a| having no inverse mod |n| then 559 // |*out_no_inverse| will be set to one; otherwise it will be set to zero. 560 // 561 // This function treats both |a| and |n| as secret, provided they are both non- 562 // zero and the inverse exists. It should only be used for even moduli where 563 // none of the less general implementations are applicable. 564 OPENSSL_EXPORT int bn_mod_inverse_consttime(BIGNUM *r, int *out_no_inverse, 565 const BIGNUM *a, const BIGNUM *n, 566 BN_CTX *ctx); 567 568 // bn_mod_inverse_prime sets |out| to the modular inverse of |a| modulo |p|, 569 // computed with Fermat's Little Theorem. It returns one on success and zero on 570 // error. If |mont_p| is NULL, one will be computed temporarily. 571 int bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p, 572 BN_CTX *ctx, const BN_MONT_CTX *mont_p); 573 574 // bn_mod_inverse_secret_prime behaves like |bn_mod_inverse_prime| but uses 575 // |BN_mod_exp_mont_consttime| instead of |BN_mod_exp_mont| in hopes of 576 // protecting the exponent. 577 int bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p, 578 BN_CTX *ctx, const BN_MONT_CTX *mont_p); 579 580 581 // Low-level operations for small numbers. 582 // 583 // The following functions implement algorithms suitable for use with scalars 584 // and field elements in elliptic curves. They rely on the number being small 585 // both to stack-allocate various temporaries and because they do not implement 586 // optimizations useful for the larger values used in RSA. 587 588 // BN_SMALL_MAX_WORDS is the largest size input these functions handle. This 589 // limit allows temporaries to be more easily stack-allocated. This limit is set 590 // to accommodate P-521. 591 #if defined(OPENSSL_32_BIT) 592 #define BN_SMALL_MAX_WORDS 17 593 #else 594 #define BN_SMALL_MAX_WORDS 9 595 #endif 596 597 // bn_mul_small sets |r| to |a|*|b|. |num_r| must be |num_a| + |num_b|. |r| may 598 // not alias with |a| or |b|. 599 void bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a, 600 const BN_ULONG *b, size_t num_b); 601 602 // bn_sqr_small sets |r| to |a|^2. |num_a| must be at most |BN_SMALL_MAX_WORDS|. 603 // |num_r| must be |num_a|*2. |r| and |a| may not alias. 604 void bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a); 605 606 // In the following functions, the modulus must be at most |BN_SMALL_MAX_WORDS| 607 // words long. 608 609 // bn_to_montgomery_small sets |r| to |a| translated to the Montgomery domain. 610 // |r| and |a| are |num| words long, which must be |mont->N.width|. |a| must be 611 // fully reduced and may alias |r|. 612 void bn_to_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num, 613 const BN_MONT_CTX *mont); 614 615 // bn_from_montgomery_small sets |r| to |a| translated out of the Montgomery 616 // domain. |r| and |a| are |num| words long, which must be |mont->N.width|. |a| 617 // must be fully-reduced and may alias |r|. 618 void bn_from_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num, 619 const BN_MONT_CTX *mont); 620 621 // bn_mod_mul_montgomery_small sets |r| to |a| * |b| mod |mont->N|. Both inputs 622 // and outputs are in the Montgomery domain. Each array is |num| words long, 623 // which must be |mont->N.width|. Any two of |r|, |a|, and |b| may alias. |a| 624 // and |b| must be reduced on input. 625 void bn_mod_mul_montgomery_small(BN_ULONG *r, const BN_ULONG *a, 626 const BN_ULONG *b, size_t num, 627 const BN_MONT_CTX *mont); 628 629 // bn_mod_exp_mont_small sets |r| to |a|^|p| mod |mont->N|. It returns one on 630 // success and zero on programmer or internal error. Both inputs and outputs are 631 // in the Montgomery domain. |r| and |a| are |num| words long, which must be 632 // |mont->N.width| and at most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced. 633 // This function runs in time independent of |a|, but |p| and |mont->N| are 634 // public values. |a| must be fully-reduced and may alias with |r|. 635 // 636 // Note this function differs from |BN_mod_exp_mont| which uses Montgomery 637 // reduction but takes input and output outside the Montgomery domain. Combine 638 // this function with |bn_from_montgomery_small| and |bn_to_montgomery_small| 639 // if necessary. 640 void bn_mod_exp_mont_small(BN_ULONG *r, const BN_ULONG *a, size_t num, 641 const BN_ULONG *p, size_t num_p, 642 const BN_MONT_CTX *mont); 643 644 // bn_mod_inverse_prime_mont_small sets |r| to |a|^-1 mod |mont->N|. |mont->N| 645 // must be a prime. |r| and |a| are |num| words long, which must be 646 // |mont->N.width| and at most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced 647 // and may alias |r|. This function runs in time independent of |a|, but 648 // |mont->N| is a public value. 649 void bn_mod_inverse_prime_mont_small(BN_ULONG *r, const BN_ULONG *a, size_t num, 650 const BN_MONT_CTX *mont); 651 652 653 #if defined(__cplusplus) 654 } // extern C 655 #endif 656 657 #endif // OPENSSL_HEADER_BN_INTERNAL_H 658
