bignum_core.h (38319B)
1 /** 2 * Core bignum functions 3 * 4 * This interface should only be used by the legacy bignum module (bignum.h) 5 * and the modular bignum modules (bignum_mod.c, bignum_mod_raw.c). All other 6 * modules should use the high-level modular bignum interface (bignum_mod.h) 7 * or the legacy bignum interface (bignum.h). 8 * 9 * This module is about processing non-negative integers with a fixed upper 10 * bound that's of the form 2^n-1 where n is a multiple of #biL. 11 * These can be thought of integers written in base 2^#biL with a fixed 12 * number of digits. Digits in this base are called *limbs*. 13 * Many operations treat these numbers as the principal representation of 14 * a number modulo 2^n or a smaller bound. 15 * 16 * The functions in this module obey the following conventions unless 17 * explicitly indicated otherwise: 18 * 19 * - **Overflow**: some functions indicate overflow from the range 20 * [0, 2^n-1] by returning carry parameters, while others operate 21 * modulo and so cannot overflow. This should be clear from the function 22 * documentation. 23 * - **Bignum parameters**: Bignums are passed as pointers to an array of 24 * limbs. A limb has the type #mbedtls_mpi_uint. Unless otherwise specified: 25 * - Bignum parameters called \p A, \p B, ... are inputs, and are 26 * not modified by the function. 27 * - For operations modulo some number, the modulus is called \p N 28 * and is input-only. 29 * - Bignum parameters called \p X, \p Y are outputs or input-output. 30 * The initial content of output-only parameters is ignored. 31 * - Some functions use different names that reflect traditional 32 * naming of operands of certain operations (e.g. 33 * divisor/dividend/quotient/remainder). 34 * - \p T is a temporary storage area. The initial content of such 35 * parameter is ignored and the final content is unspecified. 36 * - **Bignum sizes**: bignum sizes are always expressed in limbs. 37 * Most functions work on bignums of a given size and take a single 38 * \p limbs parameter that applies to all parameters that are limb arrays. 39 * All bignum sizes must be at least 1 and must be significantly less than 40 * #SIZE_MAX. The behavior if a size is 0 is undefined. The behavior if the 41 * total size of all parameters overflows #SIZE_MAX is undefined. 42 * - **Parameter ordering**: for bignum parameters, outputs come before inputs. 43 * Temporaries come last. 44 * - **Aliasing**: in general, output bignums may be aliased to one or more 45 * inputs. As an exception, parameters that are documented as a modulus value 46 * may not be aliased to an output. Outputs may not be aliased to one another. 47 * Temporaries may not be aliased to any other parameter. 48 * - **Overlap**: apart from aliasing of limb array pointers (where two 49 * arguments are equal pointers), overlap is not supported and may result 50 * in undefined behavior. 51 * - **Error handling**: This is a low-level module. Functions generally do not 52 * try to protect against invalid arguments such as nonsensical sizes or 53 * null pointers. Note that some functions that operate on bignums of 54 * different sizes have constraints about their size, and violating those 55 * constraints may lead to buffer overflows. 56 * - **Modular representatives**: functions that operate modulo \p N expect 57 * all modular inputs to be in the range [0, \p N - 1] and guarantee outputs 58 * in the range [0, \p N - 1]. If an input is out of range, outputs are 59 * fully unspecified, though bignum values out of range should not cause 60 * buffer overflows (beware that this is not extensively tested). 61 */ 62 63 /* 64 * Copyright The Mbed TLS Contributors 65 * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later 66 */ 67 68 #ifndef MBEDTLS_BIGNUM_CORE_H 69 #define MBEDTLS_BIGNUM_CORE_H 70 71 #include "common.h" 72 73 #include "mbedtls/bignum.h" 74 75 #include "constant_time_internal.h" 76 77 #define ciL (sizeof(mbedtls_mpi_uint)) /** chars in limb */ 78 #define biL (ciL << 3) /** bits in limb */ 79 #define biH (ciL << 2) /** half limb size */ 80 81 /* 82 * Convert between bits/chars and number of limbs 83 * Divide first in order to avoid potential overflows 84 */ 85 #define BITS_TO_LIMBS(i) ((i) / biL + ((i) % biL != 0)) 86 #define CHARS_TO_LIMBS(i) ((i) / ciL + ((i) % ciL != 0)) 87 /* Get a specific byte, without range checks. */ 88 #define GET_BYTE(X, i) \ 89 (((X)[(i) / ciL] >> (((i) % ciL) * 8)) & 0xff) 90 91 /* Constants to identify whether a value is public or secret. If a parameter is marked as secret by 92 * this constant, the function must be constant time with respect to the parameter. 93 * 94 * This is only needed for functions with the _optionally_safe postfix. All other functions have 95 * fixed behavior that can't be changed at runtime and are constant time with respect to their 96 * parameters as prescribed by their documentation or by conventions in their module's documentation. 97 * 98 * Parameters should be named X_public where X is the name of the 99 * corresponding input parameter. 100 * 101 * Implementation should always check using 102 * if (X_public == MBEDTLS_MPI_IS_PUBLIC) { 103 * // unsafe path 104 * } else { 105 * // safe path 106 * } 107 * not the other way round, in order to prevent misuse. (That is, if a value 108 * other than the two below is passed, default to the safe path.) 109 * 110 * The value of MBEDTLS_MPI_IS_PUBLIC is chosen in a way that is unlikely to happen by accident, but 111 * which can be used as an immediate value in a Thumb2 comparison (for code size). */ 112 #define MBEDTLS_MPI_IS_PUBLIC 0x2a2a2a2a 113 #define MBEDTLS_MPI_IS_SECRET 0 114 #if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C) 115 // Default value for testing that is neither MBEDTLS_MPI_IS_PUBLIC nor MBEDTLS_MPI_IS_SECRET 116 #define MBEDTLS_MPI_IS_TEST 1 117 #endif 118 119 /** Count leading zero bits in a given integer. 120 * 121 * \warning The result is undefined if \p a == 0 122 * 123 * \param a Integer to count leading zero bits. 124 * 125 * \return The number of leading zero bits in \p a, if \p a != 0. 126 * If \p a == 0, the result is undefined. 127 */ 128 size_t mbedtls_mpi_core_clz(mbedtls_mpi_uint a); 129 130 /** Return the minimum number of bits required to represent the value held 131 * in the MPI. 132 * 133 * \note This function returns 0 if all the limbs of \p A are 0. 134 * 135 * \param[in] A The address of the MPI. 136 * \param A_limbs The number of limbs of \p A. 137 * 138 * \return The number of bits in \p A. 139 */ 140 size_t mbedtls_mpi_core_bitlen(const mbedtls_mpi_uint *A, size_t A_limbs); 141 142 /** Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint 143 * into the storage form used by mbedtls_mpi. 144 * 145 * \param[in,out] A The address of the MPI. 146 * \param A_limbs The number of limbs of \p A. 147 */ 148 void mbedtls_mpi_core_bigendian_to_host(mbedtls_mpi_uint *A, 149 size_t A_limbs); 150 151 /** \brief Compare a machine integer with an MPI. 152 * 153 * This function operates in constant time with respect 154 * to the values of \p min and \p A. 155 * 156 * \param min A machine integer. 157 * \param[in] A An MPI. 158 * \param A_limbs The number of limbs of \p A. 159 * This must be at least 1. 160 * 161 * \return MBEDTLS_CT_TRUE if \p min is less than or equal to \p A, otherwise MBEDTLS_CT_FALSE. 162 */ 163 mbedtls_ct_condition_t mbedtls_mpi_core_uint_le_mpi(mbedtls_mpi_uint min, 164 const mbedtls_mpi_uint *A, 165 size_t A_limbs); 166 167 /** 168 * \brief Check if one unsigned MPI is less than another in constant 169 * time. 170 * 171 * \param A The left-hand MPI. This must point to an array of limbs 172 * with the same allocated length as \p B. 173 * \param B The right-hand MPI. This must point to an array of limbs 174 * with the same allocated length as \p A. 175 * \param limbs The number of limbs in \p A and \p B. 176 * This must not be 0. 177 * 178 * \return MBEDTLS_CT_TRUE if \p A is less than \p B. 179 * MBEDTLS_CT_FALSE if \p A is greater than or equal to \p B. 180 */ 181 mbedtls_ct_condition_t mbedtls_mpi_core_lt_ct(const mbedtls_mpi_uint *A, 182 const mbedtls_mpi_uint *B, 183 size_t limbs); 184 185 /** 186 * \brief Perform a safe conditional copy of an MPI which doesn't reveal 187 * whether assignment was done or not. 188 * 189 * \param[out] X The address of the destination MPI. 190 * This must be initialized. Must have enough limbs to 191 * store the full value of \p A. 192 * \param[in] A The address of the source MPI. This must be initialized. 193 * \param limbs The number of limbs of \p A. 194 * \param assign The condition deciding whether to perform the 195 * assignment or not. Callers will need to use 196 * the constant time interface (e.g. `mbedtls_ct_bool()`) 197 * to construct this argument. 198 * 199 * \note This function avoids leaking any information about whether 200 * the assignment was done or not. 201 */ 202 void mbedtls_mpi_core_cond_assign(mbedtls_mpi_uint *X, 203 const mbedtls_mpi_uint *A, 204 size_t limbs, 205 mbedtls_ct_condition_t assign); 206 207 /** 208 * \brief Perform a safe conditional swap of two MPIs which doesn't reveal 209 * whether the swap was done or not. 210 * 211 * \param[in,out] X The address of the first MPI. 212 * This must be initialized. 213 * \param[in,out] Y The address of the second MPI. 214 * This must be initialized. 215 * \param limbs The number of limbs of \p X and \p Y. 216 * \param swap The condition deciding whether to perform 217 * the swap or not. 218 * 219 * \note This function avoids leaking any information about whether 220 * the swap was done or not. 221 */ 222 void mbedtls_mpi_core_cond_swap(mbedtls_mpi_uint *X, 223 mbedtls_mpi_uint *Y, 224 size_t limbs, 225 mbedtls_ct_condition_t swap); 226 227 /** Import X from unsigned binary data, little-endian. 228 * 229 * The MPI needs to have enough limbs to store the full value (including any 230 * most significant zero bytes in the input). 231 * 232 * \param[out] X The address of the MPI. 233 * \param X_limbs The number of limbs of \p X. 234 * \param[in] input The input buffer to import from. 235 * \param input_length The length bytes of \p input. 236 * 237 * \return \c 0 if successful. 238 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p X isn't 239 * large enough to hold the value in \p input. 240 */ 241 int mbedtls_mpi_core_read_le(mbedtls_mpi_uint *X, 242 size_t X_limbs, 243 const unsigned char *input, 244 size_t input_length); 245 246 /** Import X from unsigned binary data, big-endian. 247 * 248 * The MPI needs to have enough limbs to store the full value (including any 249 * most significant zero bytes in the input). 250 * 251 * \param[out] X The address of the MPI. 252 * May only be #NULL if \p X_limbs is 0 and \p input_length 253 * is 0. 254 * \param X_limbs The number of limbs of \p X. 255 * \param[in] input The input buffer to import from. 256 * May only be #NULL if \p input_length is 0. 257 * \param input_length The length in bytes of \p input. 258 * 259 * \return \c 0 if successful. 260 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p X isn't 261 * large enough to hold the value in \p input. 262 */ 263 int mbedtls_mpi_core_read_be(mbedtls_mpi_uint *X, 264 size_t X_limbs, 265 const unsigned char *input, 266 size_t input_length); 267 268 /** Export A into unsigned binary data, little-endian. 269 * 270 * \note If \p output is shorter than \p A the export is still successful if the 271 * value held in \p A fits in the buffer (that is, if enough of the most 272 * significant bytes of \p A are 0). 273 * 274 * \param[in] A The address of the MPI. 275 * \param A_limbs The number of limbs of \p A. 276 * \param[out] output The output buffer to export to. 277 * \param output_length The length in bytes of \p output. 278 * 279 * \return \c 0 if successful. 280 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p output isn't 281 * large enough to hold the value of \p A. 282 */ 283 int mbedtls_mpi_core_write_le(const mbedtls_mpi_uint *A, 284 size_t A_limbs, 285 unsigned char *output, 286 size_t output_length); 287 288 /** Export A into unsigned binary data, big-endian. 289 * 290 * \note If \p output is shorter than \p A the export is still successful if the 291 * value held in \p A fits in the buffer (that is, if enough of the most 292 * significant bytes of \p A are 0). 293 * 294 * \param[in] A The address of the MPI. 295 * \param A_limbs The number of limbs of \p A. 296 * \param[out] output The output buffer to export to. 297 * \param output_length The length in bytes of \p output. 298 * 299 * \return \c 0 if successful. 300 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p output isn't 301 * large enough to hold the value of \p A. 302 */ 303 int mbedtls_mpi_core_write_be(const mbedtls_mpi_uint *A, 304 size_t A_limbs, 305 unsigned char *output, 306 size_t output_length); 307 308 /** \brief Shift an MPI in-place right by a number of bits. 309 * 310 * Shifting by more bits than there are bit positions 311 * in \p X is valid and results in setting \p X to 0. 312 * 313 * This function's execution time depends on the value 314 * of \p count (and of course \p limbs). 315 * 316 * \param[in,out] X The number to shift. 317 * \param limbs The number of limbs of \p X. This must be at least 1. 318 * \param count The number of bits to shift by. 319 */ 320 void mbedtls_mpi_core_shift_r(mbedtls_mpi_uint *X, size_t limbs, 321 size_t count); 322 323 /** 324 * \brief Shift an MPI in-place left by a number of bits. 325 * 326 * Shifting by more bits than there are bit positions 327 * in \p X will produce an unspecified result. 328 * 329 * This function's execution time depends on the value 330 * of \p count (and of course \p limbs). 331 * \param[in,out] X The number to shift. 332 * \param limbs The number of limbs of \p X. This must be at least 1. 333 * \param count The number of bits to shift by. 334 */ 335 void mbedtls_mpi_core_shift_l(mbedtls_mpi_uint *X, size_t limbs, 336 size_t count); 337 338 /** 339 * \brief Add two fixed-size large unsigned integers, returning the carry. 340 * 341 * Calculates `A + B` where `A` and `B` have the same size. 342 * 343 * This function operates modulo `2^(biL*limbs)` and returns the carry 344 * (1 if there was a wraparound, and 0 otherwise). 345 * 346 * \p X may be aliased to \p A or \p B. 347 * 348 * \param[out] X The result of the addition. 349 * \param[in] A Little-endian presentation of the left operand. 350 * \param[in] B Little-endian presentation of the right operand. 351 * \param limbs Number of limbs of \p X, \p A and \p B. 352 * 353 * \return 1 if `A + B >= 2^(biL*limbs)`, 0 otherwise. 354 */ 355 mbedtls_mpi_uint mbedtls_mpi_core_add(mbedtls_mpi_uint *X, 356 const mbedtls_mpi_uint *A, 357 const mbedtls_mpi_uint *B, 358 size_t limbs); 359 360 /** 361 * \brief Conditional addition of two fixed-size large unsigned integers, 362 * returning the carry. 363 * 364 * Functionally equivalent to 365 * 366 * ``` 367 * if( cond ) 368 * X += A; 369 * return carry; 370 * ``` 371 * 372 * This function operates modulo `2^(biL*limbs)`. 373 * 374 * \param[in,out] X The pointer to the (little-endian) array 375 * representing the bignum to accumulate onto. 376 * \param[in] A The pointer to the (little-endian) array 377 * representing the bignum to conditionally add 378 * to \p X. This may be aliased to \p X but may not 379 * overlap otherwise. 380 * \param limbs Number of limbs of \p X and \p A. 381 * \param cond Condition bit dictating whether addition should 382 * happen or not. This must be \c 0 or \c 1. 383 * 384 * \warning If \p cond is neither 0 nor 1, the result of this function 385 * is unspecified, and the resulting value in \p X might be 386 * neither its original value nor \p X + \p A. 387 * 388 * \return 1 if `X + cond * A >= 2^(biL*limbs)`, 0 otherwise. 389 */ 390 mbedtls_mpi_uint mbedtls_mpi_core_add_if(mbedtls_mpi_uint *X, 391 const mbedtls_mpi_uint *A, 392 size_t limbs, 393 unsigned cond); 394 395 /** 396 * \brief Subtract two fixed-size large unsigned integers, returning the borrow. 397 * 398 * Calculate `A - B` where \p A and \p B have the same size. 399 * This function operates modulo `2^(biL*limbs)` and returns the carry 400 * (1 if there was a wraparound, i.e. if `A < B`, and 0 otherwise). 401 * 402 * \p X may be aliased to \p A or \p B, or even both, but may not overlap 403 * either otherwise. 404 * 405 * \param[out] X The result of the subtraction. 406 * \param[in] A Little-endian presentation of left operand. 407 * \param[in] B Little-endian presentation of right operand. 408 * \param limbs Number of limbs of \p X, \p A and \p B. 409 * 410 * \return 1 if `A < B`. 411 * 0 if `A >= B`. 412 */ 413 mbedtls_mpi_uint mbedtls_mpi_core_sub(mbedtls_mpi_uint *X, 414 const mbedtls_mpi_uint *A, 415 const mbedtls_mpi_uint *B, 416 size_t limbs); 417 418 /** 419 * \brief Perform a fixed-size multiply accumulate operation: X += b * A 420 * 421 * \p X may be aliased to \p A (when \p X_limbs == \p A_limbs), but may not 422 * otherwise overlap. 423 * 424 * This function operates modulo `2^(biL*X_limbs)`. 425 * 426 * \param[in,out] X The pointer to the (little-endian) array 427 * representing the bignum to accumulate onto. 428 * \param X_limbs The number of limbs of \p X. This must be 429 * at least \p A_limbs. 430 * \param[in] A The pointer to the (little-endian) array 431 * representing the bignum to multiply with. 432 * This may be aliased to \p X but may not overlap 433 * otherwise. 434 * \param A_limbs The number of limbs of \p A. 435 * \param b X scalar to multiply with. 436 * 437 * \return The carry at the end of the operation. 438 */ 439 mbedtls_mpi_uint mbedtls_mpi_core_mla(mbedtls_mpi_uint *X, size_t X_limbs, 440 const mbedtls_mpi_uint *A, size_t A_limbs, 441 mbedtls_mpi_uint b); 442 443 /** 444 * \brief Perform a known-size multiplication 445 * 446 * \p X may not be aliased to any of the inputs for this function. 447 * \p A may be aliased to \p B. 448 * 449 * \param[out] X The pointer to the (little-endian) array to receive 450 * the product of \p A_limbs and \p B_limbs. 451 * This must be of length \p A_limbs + \p B_limbs. 452 * \param[in] A The pointer to the (little-endian) array 453 * representing the first factor. 454 * \param A_limbs The number of limbs in \p A. 455 * \param[in] B The pointer to the (little-endian) array 456 * representing the second factor. 457 * \param B_limbs The number of limbs in \p B. 458 */ 459 void mbedtls_mpi_core_mul(mbedtls_mpi_uint *X, 460 const mbedtls_mpi_uint *A, size_t A_limbs, 461 const mbedtls_mpi_uint *B, size_t B_limbs); 462 463 /** 464 * \brief Calculate initialisation value for fast Montgomery modular 465 * multiplication 466 * 467 * \param[in] N Little-endian presentation of the modulus. This must have 468 * at least one limb. 469 * 470 * \return The initialisation value for fast Montgomery modular multiplication 471 */ 472 mbedtls_mpi_uint mbedtls_mpi_core_montmul_init(const mbedtls_mpi_uint *N); 473 474 /** 475 * \brief Montgomery multiplication: X = A * B * R^-1 mod N (HAC 14.36) 476 * 477 * \p A and \p B must be in canonical form. That is, < \p N. 478 * 479 * \p X may be aliased to \p A or \p N, or even \p B (if \p AN_limbs == 480 * \p B_limbs) but may not overlap any parameters otherwise. 481 * 482 * \p A and \p B may alias each other, if \p AN_limbs == \p B_limbs. They may 483 * not alias \p N (since they must be in canonical form, they cannot == \p N). 484 * 485 * \param[out] X The destination MPI, as a little-endian array of 486 * length \p AN_limbs. 487 * On successful completion, X contains the result of 488 * the multiplication `A * B * R^-1` mod N where 489 * `R = 2^(biL*AN_limbs)`. 490 * \param[in] A Little-endian presentation of first operand. 491 * Must have the same number of limbs as \p N. 492 * \param[in] B Little-endian presentation of second operand. 493 * \param[in] B_limbs The number of limbs in \p B. 494 * Must be <= \p AN_limbs. 495 * \param[in] N Little-endian presentation of the modulus. 496 * This must be odd, and have exactly the same number 497 * of limbs as \p A. 498 * It may alias \p X, but must not alias or otherwise 499 * overlap any of the other parameters. 500 * \param[in] AN_limbs The number of limbs in \p X, \p A and \p N. 501 * \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL. 502 * This can be calculated by `mbedtls_mpi_core_montmul_init()`. 503 * \param[in,out] T Temporary storage of size at least 2*AN_limbs+1 limbs. 504 * Its initial content is unused and 505 * its final content is indeterminate. 506 * It must not alias or otherwise overlap any of the 507 * other parameters. 508 */ 509 void mbedtls_mpi_core_montmul(mbedtls_mpi_uint *X, 510 const mbedtls_mpi_uint *A, 511 const mbedtls_mpi_uint *B, size_t B_limbs, 512 const mbedtls_mpi_uint *N, size_t AN_limbs, 513 mbedtls_mpi_uint mm, mbedtls_mpi_uint *T); 514 515 /** 516 * \brief Calculate the square of the Montgomery constant. (Needed 517 * for conversion and operations in Montgomery form.) 518 * 519 * \param[out] X A pointer to the result of the calculation of 520 * the square of the Montgomery constant: 521 * 2^{2*n*biL} mod N. 522 * \param[in] N Little-endian presentation of the modulus, which must be odd. 523 * 524 * \return 0 if successful. 525 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if there is not enough space 526 * to store the value of Montgomery constant squared. 527 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p N modulus is zero. 528 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p N modulus is negative. 529 */ 530 int mbedtls_mpi_core_get_mont_r2_unsafe(mbedtls_mpi *X, 531 const mbedtls_mpi *N); 532 533 #if defined(MBEDTLS_TEST_HOOKS) 534 /** 535 * Copy an MPI from a table without leaking the index. 536 * 537 * \param dest The destination buffer. This must point to a writable 538 * buffer of at least \p limbs limbs. 539 * \param table The address of the table. This must point to a readable 540 * array of \p count elements of \p limbs limbs each. 541 * \param limbs The number of limbs in each table entry. 542 * \param count The number of entries in \p table. 543 * \param index The (secret) table index to look up. This must be in the 544 * range `0 .. count-1`. 545 */ 546 void mbedtls_mpi_core_ct_uint_table_lookup(mbedtls_mpi_uint *dest, 547 const mbedtls_mpi_uint *table, 548 size_t limbs, 549 size_t count, 550 size_t index); 551 #endif /* MBEDTLS_TEST_HOOKS */ 552 553 /** 554 * \brief Fill an integer with a number of random bytes. 555 * 556 * \param X The destination MPI. 557 * \param X_limbs The number of limbs of \p X. 558 * \param bytes The number of random bytes to generate. 559 * \param f_rng The RNG function to use. This must not be \c NULL. 560 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be 561 * \c NULL if \p f_rng doesn't need a context argument. 562 * 563 * \return \c 0 if successful. 564 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p X does not have 565 * enough room for \p bytes bytes. 566 * \return A negative error code on RNG failure. 567 * 568 * \note The bytes obtained from the RNG are interpreted 569 * as a big-endian representation of an MPI; this can 570 * be relevant in applications like deterministic ECDSA. 571 */ 572 int mbedtls_mpi_core_fill_random(mbedtls_mpi_uint *X, size_t X_limbs, 573 size_t bytes, 574 int (*f_rng)(void *, unsigned char *, size_t), 575 void *p_rng); 576 577 /** Generate a random number uniformly in a range. 578 * 579 * This function generates a random number between \p min inclusive and 580 * \p N exclusive. 581 * 582 * The procedure complies with RFC 6979 ยง3.3 (deterministic ECDSA) 583 * when the RNG is a suitably parametrized instance of HMAC_DRBG 584 * and \p min is \c 1. 585 * 586 * \note There are `N - min` possible outputs. The lower bound 587 * \p min can be reached, but the upper bound \p N cannot. 588 * 589 * \param X The destination MPI, with \p limbs limbs. 590 * It must not be aliased with \p N or otherwise overlap it. 591 * \param min The minimum value to return. 592 * \param N The upper bound of the range, exclusive, with \p limbs limbs. 593 * In other words, this is one plus the maximum value to return. 594 * \p N must be strictly larger than \p min. 595 * \param limbs The number of limbs of \p N and \p X. 596 * This must not be 0. 597 * \param f_rng The RNG function to use. This must not be \c NULL. 598 * \param p_rng The RNG parameter to be passed to \p f_rng. 599 * 600 * \return \c 0 if successful. 601 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was 602 * unable to find a suitable value within a limited number 603 * of attempts. This has a negligible probability if \p N 604 * is significantly larger than \p min, which is the case 605 * for all usual cryptographic applications. 606 */ 607 int mbedtls_mpi_core_random(mbedtls_mpi_uint *X, 608 mbedtls_mpi_uint min, 609 const mbedtls_mpi_uint *N, 610 size_t limbs, 611 int (*f_rng)(void *, unsigned char *, size_t), 612 void *p_rng); 613 614 /** 615 * \brief Returns the number of limbs of working memory required for 616 * a call to `mbedtls_mpi_core_exp_mod()`. 617 * 618 * \note This will always be at least 619 * `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)`, 620 * i.e. sufficient for a call to `mbedtls_mpi_core_montmul()`. 621 * 622 * \param AN_limbs The number of limbs in the input `A` and the modulus `N` 623 * (they must be the same size) that will be given to 624 * `mbedtls_mpi_core_exp_mod()`. 625 * \param E_limbs The number of limbs in the exponent `E` that will be given 626 * to `mbedtls_mpi_core_exp_mod()`. 627 * 628 * \return The number of limbs of working memory required by 629 * `mbedtls_mpi_core_exp_mod()`. 630 */ 631 size_t mbedtls_mpi_core_exp_mod_working_limbs(size_t AN_limbs, size_t E_limbs); 632 633 /** 634 * \brief Perform a modular exponentiation with public or secret exponent: 635 * X = A^E mod N, where \p A is already in Montgomery form. 636 * 637 * \warning This function is not constant time with respect to \p E (the exponent). 638 * 639 * \p X may be aliased to \p A, but not to \p RR or \p E, even if \p E_limbs == 640 * \p AN_limbs. 641 * 642 * \param[out] X The destination MPI, as a little endian array of length 643 * \p AN_limbs. 644 * \param[in] A The base MPI, as a little endian array of length \p AN_limbs. 645 * Must be in Montgomery form. 646 * \param[in] N The modulus, as a little endian array of length \p AN_limbs. 647 * \param AN_limbs The number of limbs in \p X, \p A, \p N, \p RR. 648 * \param[in] E The exponent, as a little endian array of length \p E_limbs. 649 * \param E_limbs The number of limbs in \p E. 650 * \param[in] RR The precomputed residue of 2^{2*biL} modulo N, as a little 651 * endian array of length \p AN_limbs. 652 * \param[in,out] T Temporary storage of at least the number of limbs returned 653 * by `mbedtls_mpi_core_exp_mod_working_limbs()`. 654 * Its initial content is unused and its final content is 655 * indeterminate. 656 * It must not alias or otherwise overlap any of the other 657 * parameters. 658 * It is up to the caller to zeroize \p T when it is no 659 * longer needed, and before freeing it if it was dynamically 660 * allocated. 661 */ 662 void mbedtls_mpi_core_exp_mod_unsafe(mbedtls_mpi_uint *X, 663 const mbedtls_mpi_uint *A, 664 const mbedtls_mpi_uint *N, size_t AN_limbs, 665 const mbedtls_mpi_uint *E, size_t E_limbs, 666 const mbedtls_mpi_uint *RR, 667 mbedtls_mpi_uint *T); 668 669 /** 670 * \brief Perform a modular exponentiation with secret exponent: 671 * X = A^E mod N, where \p A is already in Montgomery form. 672 * 673 * \p X may be aliased to \p A, but not to \p RR or \p E, even if \p E_limbs == 674 * \p AN_limbs. 675 * 676 * \param[out] X The destination MPI, as a little endian array of length 677 * \p AN_limbs. 678 * \param[in] A The base MPI, as a little endian array of length \p AN_limbs. 679 * Must be in Montgomery form. 680 * \param[in] N The modulus, as a little endian array of length \p AN_limbs. 681 * \param AN_limbs The number of limbs in \p X, \p A, \p N, \p RR. 682 * \param[in] E The exponent, as a little endian array of length \p E_limbs. 683 * \param E_limbs The number of limbs in \p E. 684 * \param[in] RR The precomputed residue of 2^{2*biL} modulo N, as a little 685 * endian array of length \p AN_limbs. 686 * \param[in,out] T Temporary storage of at least the number of limbs returned 687 * by `mbedtls_mpi_core_exp_mod_working_limbs()`. 688 * Its initial content is unused and its final content is 689 * indeterminate. 690 * It must not alias or otherwise overlap any of the other 691 * parameters. 692 * It is up to the caller to zeroize \p T when it is no 693 * longer needed, and before freeing it if it was dynamically 694 * allocated. 695 */ 696 void mbedtls_mpi_core_exp_mod(mbedtls_mpi_uint *X, 697 const mbedtls_mpi_uint *A, 698 const mbedtls_mpi_uint *N, size_t AN_limbs, 699 const mbedtls_mpi_uint *E, size_t E_limbs, 700 const mbedtls_mpi_uint *RR, 701 mbedtls_mpi_uint *T); 702 703 /** 704 * \brief Subtract unsigned integer from known-size large unsigned integers. 705 * Return the borrow. 706 * 707 * \param[out] X The result of the subtraction. 708 * \param[in] A The left operand. 709 * \param b The unsigned scalar to subtract. 710 * \param limbs Number of limbs of \p X and \p A. 711 * 712 * \return 1 if `A < b`. 713 * 0 if `A >= b`. 714 */ 715 mbedtls_mpi_uint mbedtls_mpi_core_sub_int(mbedtls_mpi_uint *X, 716 const mbedtls_mpi_uint *A, 717 mbedtls_mpi_uint b, 718 size_t limbs); 719 720 /** 721 * \brief Determine if a given MPI has the value \c 0 in constant time with 722 * respect to the value (but not with respect to the number of limbs). 723 * 724 * \param[in] A The MPI to test. 725 * \param limbs Number of limbs in \p A. 726 * 727 * \return MBEDTLS_CT_FALSE if `A == 0` 728 * MBEDTLS_CT_TRUE if `A != 0`. 729 */ 730 mbedtls_ct_condition_t mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A, 731 size_t limbs); 732 733 /** 734 * \brief Returns the number of limbs of working memory required for 735 * a call to `mbedtls_mpi_core_montmul()`. 736 * 737 * \param AN_limbs The number of limbs in the input `A` and the modulus `N` 738 * (they must be the same size) that will be given to 739 * `mbedtls_mpi_core_montmul()` or one of the other functions 740 * that specifies this as the amount of working memory needed. 741 * 742 * \return The number of limbs of working memory required by 743 * `mbedtls_mpi_core_montmul()` (or other similar function). 744 */ 745 static inline size_t mbedtls_mpi_core_montmul_working_limbs(size_t AN_limbs) 746 { 747 return 2 * AN_limbs + 1; 748 } 749 750 /** Convert an MPI into Montgomery form. 751 * 752 * \p X may be aliased to \p A, but may not otherwise overlap it. 753 * 754 * \p X may not alias \p N (it is in canonical form, so must be strictly less 755 * than \p N). Nor may it alias or overlap \p rr (this is unlikely to be 756 * required in practice.) 757 * 758 * This function is a thin wrapper around `mbedtls_mpi_core_montmul()` that is 759 * an alternative to calling `mbedtls_mpi_mod_raw_to_mont_rep()` when we 760 * don't want to allocate memory. 761 * 762 * \param[out] X The result of the conversion. 763 * Must have the same number of limbs as \p A. 764 * \param[in] A The MPI to convert into Montgomery form. 765 * Must have the same number of limbs as the modulus. 766 * \param[in] N The address of the modulus, which gives the size of 767 * the base `R` = 2^(biL*N->limbs). 768 * \param[in] AN_limbs The number of limbs in \p X, \p A, \p N and \p rr. 769 * \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL. 770 * This can be determined by calling 771 * `mbedtls_mpi_core_montmul_init()`. 772 * \param[in] rr The residue for `2^{2*n*biL} mod N`. 773 * \param[in,out] T Temporary storage of size at least 774 * `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)` 775 * limbs. 776 * Its initial content is unused and 777 * its final content is indeterminate. 778 * It must not alias or otherwise overlap any of the 779 * other parameters. 780 */ 781 void mbedtls_mpi_core_to_mont_rep(mbedtls_mpi_uint *X, 782 const mbedtls_mpi_uint *A, 783 const mbedtls_mpi_uint *N, 784 size_t AN_limbs, 785 mbedtls_mpi_uint mm, 786 const mbedtls_mpi_uint *rr, 787 mbedtls_mpi_uint *T); 788 789 /** Convert an MPI from Montgomery form. 790 * 791 * \p X may be aliased to \p A, but may not otherwise overlap it. 792 * 793 * \p X may not alias \p N (it is in canonical form, so must be strictly less 794 * than \p N). 795 * 796 * This function is a thin wrapper around `mbedtls_mpi_core_montmul()` that is 797 * an alternative to calling `mbedtls_mpi_mod_raw_from_mont_rep()` when we 798 * don't want to allocate memory. 799 * 800 * \param[out] X The result of the conversion. 801 * Must have the same number of limbs as \p A. 802 * \param[in] A The MPI to convert from Montgomery form. 803 * Must have the same number of limbs as the modulus. 804 * \param[in] N The address of the modulus, which gives the size of 805 * the base `R` = 2^(biL*N->limbs). 806 * \param[in] AN_limbs The number of limbs in \p X, \p A and \p N. 807 * \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL. 808 * This can be determined by calling 809 * `mbedtls_mpi_core_montmul_init()`. 810 * \param[in,out] T Temporary storage of size at least 811 * `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)` 812 * limbs. 813 * Its initial content is unused and 814 * its final content is indeterminate. 815 * It must not alias or otherwise overlap any of the 816 * other parameters. 817 */ 818 void mbedtls_mpi_core_from_mont_rep(mbedtls_mpi_uint *X, 819 const mbedtls_mpi_uint *A, 820 const mbedtls_mpi_uint *N, 821 size_t AN_limbs, 822 mbedtls_mpi_uint mm, 823 mbedtls_mpi_uint *T); 824 825 #endif /* MBEDTLS_BIGNUM_CORE_H */