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 #if defined(MBEDTLS_BIGNUM_C)
74 #include "mbedtls/bignum.h"
75 #endif
76
77 #include "constant_time_internal.h"
78
79 #define ciL (sizeof(mbedtls_mpi_uint)) /** chars in limb */
80 #define biL (ciL << 3) /** bits in limb */
81 #define biH (ciL << 2) /** half limb size */
82
83 /*
84 * Convert between bits/chars and number of limbs
85 * Divide first in order to avoid potential overflows
86 */
87 #define BITS_TO_LIMBS(i) ((i) / biL + ((i) % biL != 0))
88 #define CHARS_TO_LIMBS(i) ((i) / ciL + ((i) % ciL != 0))
89 /* Get a specific byte, without range checks. */
90 #define GET_BYTE(X, i) \
91 (((X)[(i) / ciL] >> (((i) % ciL) * 8)) & 0xff)
92
93 /* Constants to identify whether a value is public or secret. If a parameter is marked as secret by
94 * this constant, the function must be constant time with respect to the parameter.
95 *
96 * This is only needed for functions with the _optionally_safe postfix. All other functions have
97 * fixed behavior that can't be changed at runtime and are constant time with respect to their
98 * parameters as prescribed by their documentation or by conventions in their module's documentation.
99 *
100 * Parameters should be named X_public where X is the name of the
101 * corresponding input parameter.
102 *
103 * Implementation should always check using
104 * if (X_public == MBEDTLS_MPI_IS_PUBLIC) {
105 * // unsafe path
106 * } else {
107 * // safe path
108 * }
109 * not the other way round, in order to prevent misuse. (This is, if a value
110 * other than the two below is passed, default to the safe path.) */
111 #define MBEDTLS_MPI_IS_PUBLIC 0x2a2a2a2a
112 #define MBEDTLS_MPI_IS_SECRET 0
113
114 /** Count leading zero bits in a given integer.
115 *
116 * \warning The result is undefined if \p a == 0
117 *
118 * \param a Integer to count leading zero bits.
119 *
120 * \return The number of leading zero bits in \p a, if \p a != 0.
121 * If \p a == 0, the result is undefined.
122 */
123 size_t mbedtls_mpi_core_clz(mbedtls_mpi_uint a);
124
125 /** Return the minimum number of bits required to represent the value held
126 * in the MPI.
127 *
128 * \note This function returns 0 if all the limbs of \p A are 0.
129 *
130 * \param[in] A The address of the MPI.
131 * \param A_limbs The number of limbs of \p A.
132 *
133 * \return The number of bits in \p A.
134 */
135 size_t mbedtls_mpi_core_bitlen(const mbedtls_mpi_uint *A, size_t A_limbs);
136
137 /** Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
138 * into the storage form used by mbedtls_mpi.
139 *
140 * \param[in,out] A The address of the MPI.
141 * \param A_limbs The number of limbs of \p A.
142 */
143 void mbedtls_mpi_core_bigendian_to_host(mbedtls_mpi_uint *A,
144 size_t A_limbs);
145
146 /** \brief Compare a machine integer with an MPI.
147 *
148 * This function operates in constant time with respect
149 * to the values of \p min and \p A.
150 *
151 * \param min A machine integer.
152 * \param[in] A An MPI.
153 * \param A_limbs The number of limbs of \p A.
154 * This must be at least 1.
155 *
156 * \return MBEDTLS_CT_TRUE if \p min is less than or equal to \p A, otherwise MBEDTLS_CT_FALSE.
157 */
158 mbedtls_ct_condition_t mbedtls_mpi_core_uint_le_mpi(mbedtls_mpi_uint min,
159 const mbedtls_mpi_uint *A,
160 size_t A_limbs);
161
162 /**
163 * \brief Check if one unsigned MPI is less than another in constant
164 * time.
165 *
166 * \param A The left-hand MPI. This must point to an array of limbs
167 * with the same allocated length as \p B.
168 * \param B The right-hand MPI. This must point to an array of limbs
169 * with the same allocated length as \p A.
170 * \param limbs The number of limbs in \p A and \p B.
171 * This must not be 0.
172 *
173 * \return MBEDTLS_CT_TRUE if \p A is less than \p B.
174 * MBEDTLS_CT_FALSE if \p A is greater than or equal to \p B.
175 */
176 mbedtls_ct_condition_t mbedtls_mpi_core_lt_ct(const mbedtls_mpi_uint *A,
177 const mbedtls_mpi_uint *B,
178 size_t limbs);
179
180 /**
181 * \brief Perform a safe conditional copy of an MPI which doesn't reveal
182 * whether assignment was done or not.
183 *
184 * \param[out] X The address of the destination MPI.
185 * This must be initialized. Must have enough limbs to
186 * store the full value of \p A.
187 * \param[in] A The address of the source MPI. This must be initialized.
188 * \param limbs The number of limbs of \p A.
189 * \param assign The condition deciding whether to perform the
190 * assignment or not. Callers will need to use
191 * the constant time interface (e.g. `mbedtls_ct_bool()`)
192 * to construct this argument.
193 *
194 * \note This function avoids leaking any information about whether
195 * the assignment was done or not.
196 */
197 void mbedtls_mpi_core_cond_assign(mbedtls_mpi_uint *X,
198 const mbedtls_mpi_uint *A,
199 size_t limbs,
200 mbedtls_ct_condition_t assign);
201
202 /**
203 * \brief Perform a safe conditional swap of two MPIs which doesn't reveal
204 * whether the swap was done or not.
205 *
206 * \param[in,out] X The address of the first MPI.
207 * This must be initialized.
208 * \param[in,out] Y The address of the second MPI.
209 * This must be initialized.
210 * \param limbs The number of limbs of \p X and \p Y.
211 * \param swap The condition deciding whether to perform
212 * the swap or not.
213 *
214 * \note This function avoids leaking any information about whether
215 * the swap was done or not.
216 */
217 void mbedtls_mpi_core_cond_swap(mbedtls_mpi_uint *X,
218 mbedtls_mpi_uint *Y,
219 size_t limbs,
220 mbedtls_ct_condition_t swap);
221
222 /** Import X from unsigned binary data, little-endian.
223 *
224 * The MPI needs to have enough limbs to store the full value (including any
225 * most significant zero bytes in the input).
226 *
227 * \param[out] X The address of the MPI.
228 * \param X_limbs The number of limbs of \p X.
229 * \param[in] input The input buffer to import from.
230 * \param input_length The length bytes of \p input.
231 *
232 * \return \c 0 if successful.
233 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p X isn't
234 * large enough to hold the value in \p input.
235 */
236 int mbedtls_mpi_core_read_le(mbedtls_mpi_uint *X,
237 size_t X_limbs,
238 const unsigned char *input,
239 size_t input_length);
240
241 /** Import X from unsigned binary data, big-endian.
242 *
243 * The MPI needs to have enough limbs to store the full value (including any
244 * most significant zero bytes in the input).
245 *
246 * \param[out] X The address of the MPI.
247 * May only be #NULL if \p X_limbs is 0 and \p input_length
248 * is 0.
249 * \param X_limbs The number of limbs of \p X.
250 * \param[in] input The input buffer to import from.
251 * May only be #NULL if \p input_length is 0.
252 * \param input_length The length in bytes of \p input.
253 *
254 * \return \c 0 if successful.
255 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p X isn't
256 * large enough to hold the value in \p input.
257 */
258 int mbedtls_mpi_core_read_be(mbedtls_mpi_uint *X,
259 size_t X_limbs,
260 const unsigned char *input,
261 size_t input_length);
262
263 /** Export A into unsigned binary data, little-endian.
264 *
265 * \note If \p output is shorter than \p A the export is still successful if the
266 * value held in \p A fits in the buffer (that is, if enough of the most
267 * significant bytes of \p A are 0).
268 *
269 * \param[in] A The address of the MPI.
270 * \param A_limbs The number of limbs of \p A.
271 * \param[out] output The output buffer to export to.
272 * \param output_length The length in bytes of \p output.
273 *
274 * \return \c 0 if successful.
275 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p output isn't
276 * large enough to hold the value of \p A.
277 */
278 int mbedtls_mpi_core_write_le(const mbedtls_mpi_uint *A,
279 size_t A_limbs,
280 unsigned char *output,
281 size_t output_length);
282
283 /** Export A into unsigned binary data, big-endian.
284 *
285 * \note If \p output is shorter than \p A the export is still successful if the
286 * value held in \p A fits in the buffer (that is, if enough of the most
287 * significant bytes of \p A are 0).
288 *
289 * \param[in] A The address of the MPI.
290 * \param A_limbs The number of limbs of \p A.
291 * \param[out] output The output buffer to export to.
292 * \param output_length The length in bytes of \p output.
293 *
294 * \return \c 0 if successful.
295 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p output isn't
296 * large enough to hold the value of \p A.
297 */
298 int mbedtls_mpi_core_write_be(const mbedtls_mpi_uint *A,
299 size_t A_limbs,
300 unsigned char *output,
301 size_t output_length);
302
303 /** \brief Shift an MPI in-place right by a number of bits.
304 *
305 * Shifting by more bits than there are bit positions
306 * in \p X is valid and results in setting \p X to 0.
307 *
308 * This function's execution time depends on the value
309 * of \p count (and of course \p limbs).
310 *
311 * \param[in,out] X The number to shift.
312 * \param limbs The number of limbs of \p X. This must be at least 1.
313 * \param count The number of bits to shift by.
314 */
315 void mbedtls_mpi_core_shift_r(mbedtls_mpi_uint *X, size_t limbs,
316 size_t count);
317
318 /**
319 * \brief Shift an MPI in-place left by a number of bits.
320 *
321 * Shifting by more bits than there are bit positions
322 * in \p X will produce an unspecified result.
323 *
324 * This function's execution time depends on the value
325 * of \p count (and of course \p limbs).
326 * \param[in,out] X The number to shift.
327 * \param limbs The number of limbs of \p X. This must be at least 1.
328 * \param count The number of bits to shift by.
329 */
330 void mbedtls_mpi_core_shift_l(mbedtls_mpi_uint *X, size_t limbs,
331 size_t count);
332
333 /**
334 * \brief Add two fixed-size large unsigned integers, returning the carry.
335 *
336 * Calculates `A + B` where `A` and `B` have the same size.
337 *
338 * This function operates modulo `2^(biL*limbs)` and returns the carry
339 * (1 if there was a wraparound, and 0 otherwise).
340 *
341 * \p X may be aliased to \p A or \p B.
342 *
343 * \param[out] X The result of the addition.
344 * \param[in] A Little-endian presentation of the left operand.
345 * \param[in] B Little-endian presentation of the right operand.
346 * \param limbs Number of limbs of \p X, \p A and \p B.
347 *
348 * \return 1 if `A + B >= 2^(biL*limbs)`, 0 otherwise.
349 */
350 mbedtls_mpi_uint mbedtls_mpi_core_add(mbedtls_mpi_uint *X,
351 const mbedtls_mpi_uint *A,
352 const mbedtls_mpi_uint *B,
353 size_t limbs);
354
355 /**
356 * \brief Conditional addition of two fixed-size large unsigned integers,
357 * returning the carry.
358 *
359 * Functionally equivalent to
360 *
361 * ```
362 * if( cond )
363 * X += A;
364 * return carry;
365 * ```
366 *
367 * This function operates modulo `2^(biL*limbs)`.
368 *
369 * \param[in,out] X The pointer to the (little-endian) array
370 * representing the bignum to accumulate onto.
371 * \param[in] A The pointer to the (little-endian) array
372 * representing the bignum to conditionally add
373 * to \p X. This may be aliased to \p X but may not
374 * overlap otherwise.
375 * \param limbs Number of limbs of \p X and \p A.
376 * \param cond Condition bit dictating whether addition should
377 * happen or not. This must be \c 0 or \c 1.
378 *
379 * \warning If \p cond is neither 0 nor 1, the result of this function
380 * is unspecified, and the resulting value in \p X might be
381 * neither its original value nor \p X + \p A.
382 *
383 * \return 1 if `X + cond * A >= 2^(biL*limbs)`, 0 otherwise.
384 */
385 mbedtls_mpi_uint mbedtls_mpi_core_add_if(mbedtls_mpi_uint *X,
386 const mbedtls_mpi_uint *A,
387 size_t limbs,
388 unsigned cond);
389
390 /**
391 * \brief Subtract two fixed-size large unsigned integers, returning the borrow.
392 *
393 * Calculate `A - B` where \p A and \p B have the same size.
394 * This function operates modulo `2^(biL*limbs)` and returns the carry
395 * (1 if there was a wraparound, i.e. if `A < B`, and 0 otherwise).
396 *
397 * \p X may be aliased to \p A or \p B, or even both, but may not overlap
398 * either otherwise.
399 *
400 * \param[out] X The result of the subtraction.
401 * \param[in] A Little-endian presentation of left operand.
402 * \param[in] B Little-endian presentation of right operand.
403 * \param limbs Number of limbs of \p X, \p A and \p B.
404 *
405 * \return 1 if `A < B`.
406 * 0 if `A >= B`.
407 */
408 mbedtls_mpi_uint mbedtls_mpi_core_sub(mbedtls_mpi_uint *X,
409 const mbedtls_mpi_uint *A,
410 const mbedtls_mpi_uint *B,
411 size_t limbs);
412
413 /**
414 * \brief Perform a fixed-size multiply accumulate operation: X += b * A
415 *
416 * \p X may be aliased to \p A (when \p X_limbs == \p A_limbs), but may not
417 * otherwise overlap.
418 *
419 * This function operates modulo `2^(biL*X_limbs)`.
420 *
421 * \param[in,out] X The pointer to the (little-endian) array
422 * representing the bignum to accumulate onto.
423 * \param X_limbs The number of limbs of \p X. This must be
424 * at least \p A_limbs.
425 * \param[in] A The pointer to the (little-endian) array
426 * representing the bignum to multiply with.
427 * This may be aliased to \p X but may not overlap
428 * otherwise.
429 * \param A_limbs The number of limbs of \p A.
430 * \param b X scalar to multiply with.
431 *
432 * \return The carry at the end of the operation.
433 */
434 mbedtls_mpi_uint mbedtls_mpi_core_mla(mbedtls_mpi_uint *X, size_t X_limbs,
435 const mbedtls_mpi_uint *A, size_t A_limbs,
436 mbedtls_mpi_uint b);
437
438 /**
439 * \brief Perform a known-size multiplication
440 *
441 * \p X may not be aliased to any of the inputs for this function.
442 * \p A may be aliased to \p B.
443 *
444 * \param[out] X The pointer to the (little-endian) array to receive
445 * the product of \p A_limbs and \p B_limbs.
446 * This must be of length \p A_limbs + \p B_limbs.
447 * \param[in] A The pointer to the (little-endian) array
448 * representing the first factor.
449 * \param A_limbs The number of limbs in \p A.
450 * \param[in] B The pointer to the (little-endian) array
451 * representing the second factor.
452 * \param B_limbs The number of limbs in \p B.
453 */
454 void mbedtls_mpi_core_mul(mbedtls_mpi_uint *X,
455 const mbedtls_mpi_uint *A, size_t A_limbs,
456 const mbedtls_mpi_uint *B, size_t B_limbs);
457
458 /**
459 * \brief Calculate initialisation value for fast Montgomery modular
460 * multiplication
461 *
462 * \param[in] N Little-endian presentation of the modulus. This must have
463 * at least one limb.
464 *
465 * \return The initialisation value for fast Montgomery modular multiplication
466 */
467 mbedtls_mpi_uint mbedtls_mpi_core_montmul_init(const mbedtls_mpi_uint *N);
468
469 /**
470 * \brief Montgomery multiplication: X = A * B * R^-1 mod N (HAC 14.36)
471 *
472 * \p A and \p B must be in canonical form. That is, < \p N.
473 *
474 * \p X may be aliased to \p A or \p N, or even \p B (if \p AN_limbs ==
475 * \p B_limbs) but may not overlap any parameters otherwise.
476 *
477 * \p A and \p B may alias each other, if \p AN_limbs == \p B_limbs. They may
478 * not alias \p N (since they must be in canonical form, they cannot == \p N).
479 *
480 * \param[out] X The destination MPI, as a little-endian array of
481 * length \p AN_limbs.
482 * On successful completion, X contains the result of
483 * the multiplication `A * B * R^-1` mod N where
484 * `R = 2^(biL*AN_limbs)`.
485 * \param[in] A Little-endian presentation of first operand.
486 * Must have the same number of limbs as \p N.
487 * \param[in] B Little-endian presentation of second operand.
488 * \param[in] B_limbs The number of limbs in \p B.
489 * Must be <= \p AN_limbs.
490 * \param[in] N Little-endian presentation of the modulus.
491 * This must be odd, and have exactly the same number
492 * of limbs as \p A.
493 * It may alias \p X, but must not alias or otherwise
494 * overlap any of the other parameters.
495 * \param[in] AN_limbs The number of limbs in \p X, \p A and \p N.
496 * \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL.
497 * This can be calculated by `mbedtls_mpi_core_montmul_init()`.
498 * \param[in,out] T Temporary storage of size at least 2*AN_limbs+1 limbs.
499 * Its initial content is unused and
500 * its final content is indeterminate.
501 * It must not alias or otherwise overlap any of the
502 * other parameters.
503 */
504 void mbedtls_mpi_core_montmul(mbedtls_mpi_uint *X,
505 const mbedtls_mpi_uint *A,
506 const mbedtls_mpi_uint *B, size_t B_limbs,
507 const mbedtls_mpi_uint *N, size_t AN_limbs,
508 mbedtls_mpi_uint mm, mbedtls_mpi_uint *T);
509
510 /**
511 * \brief Calculate the square of the Montgomery constant. (Needed
512 * for conversion and operations in Montgomery form.)
513 *
514 * \param[out] X A pointer to the result of the calculation of
515 * the square of the Montgomery constant:
516 * 2^{2*n*biL} mod N.
517 * \param[in] N Little-endian presentation of the modulus, which must be odd.
518 *
519 * \return 0 if successful.
520 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if there is not enough space
521 * to store the value of Montgomery constant squared.
522 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p N modulus is zero.
523 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p N modulus is negative.
524 */
525 int mbedtls_mpi_core_get_mont_r2_unsafe(mbedtls_mpi *X,
526 const mbedtls_mpi *N);
527
528 #if defined(MBEDTLS_TEST_HOOKS)
529 /**
530 * Copy an MPI from a table without leaking the index.
531 *
532 * \param dest The destination buffer. This must point to a writable
533 * buffer of at least \p limbs limbs.
534 * \param table The address of the table. This must point to a readable
535 * array of \p count elements of \p limbs limbs each.
536 * \param limbs The number of limbs in each table entry.
537 * \param count The number of entries in \p table.
538 * \param index The (secret) table index to look up. This must be in the
539 * range `0 .. count-1`.
540 */
541 void mbedtls_mpi_core_ct_uint_table_lookup(mbedtls_mpi_uint *dest,
542 const mbedtls_mpi_uint *table,
543 size_t limbs,
544 size_t count,
545 size_t index);
546 #endif /* MBEDTLS_TEST_HOOKS */
547
548 /**
549 * \brief Fill an integer with a number of random bytes.
550 *
551 * \param X The destination MPI.
552 * \param X_limbs The number of limbs of \p X.
553 * \param bytes The number of random bytes to generate.
554 * \param f_rng The RNG function to use. This must not be \c NULL.
555 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be
556 * \c NULL if \p f_rng doesn't need a context argument.
557 *
558 * \return \c 0 if successful.
559 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p X does not have
560 * enough room for \p bytes bytes.
561 * \return A negative error code on RNG failure.
562 *
563 * \note The bytes obtained from the RNG are interpreted
564 * as a big-endian representation of an MPI; this can
565 * be relevant in applications like deterministic ECDSA.
566 */
567 int mbedtls_mpi_core_fill_random(mbedtls_mpi_uint *X, size_t X_limbs,
568 size_t bytes,
569 int (*f_rng)(void *, unsigned char *, size_t),
570 void *p_rng);
571
572 /** Generate a random number uniformly in a range.
573 *
574 * This function generates a random number between \p min inclusive and
575 * \p N exclusive.
576 *
577 * The procedure complies with RFC 6979 ยง3.3 (deterministic ECDSA)
578 * when the RNG is a suitably parametrized instance of HMAC_DRBG
579 * and \p min is \c 1.
580 *
581 * \note There are `N - min` possible outputs. The lower bound
582 * \p min can be reached, but the upper bound \p N cannot.
583 *
584 * \param X The destination MPI, with \p limbs limbs.
585 * It must not be aliased with \p N or otherwise overlap it.
586 * \param min The minimum value to return.
587 * \param N The upper bound of the range, exclusive, with \p limbs limbs.
588 * In other words, this is one plus the maximum value to return.
589 * \p N must be strictly larger than \p min.
590 * \param limbs The number of limbs of \p N and \p X.
591 * This must not be 0.
592 * \param f_rng The RNG function to use. This must not be \c NULL.
593 * \param p_rng The RNG parameter to be passed to \p f_rng.
594 *
595 * \return \c 0 if successful.
596 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was
597 * unable to find a suitable value within a limited number
598 * of attempts. This has a negligible probability if \p N
599 * is significantly larger than \p min, which is the case
600 * for all usual cryptographic applications.
601 */
602 int mbedtls_mpi_core_random(mbedtls_mpi_uint *X,
603 mbedtls_mpi_uint min,
604 const mbedtls_mpi_uint *N,
605 size_t limbs,
606 int (*f_rng)(void *, unsigned char *, size_t),
607 void *p_rng);
608
609 /**
610 * \brief Returns the number of limbs of working memory required for
611 * a call to `mbedtls_mpi_core_exp_mod()`.
612 *
613 * \note This will always be at least
614 * `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)`,
615 * i.e. sufficient for a call to `mbedtls_mpi_core_montmul()`.
616 *
617 * \param AN_limbs The number of limbs in the input `A` and the modulus `N`
618 * (they must be the same size) that will be given to
619 * `mbedtls_mpi_core_exp_mod()`.
620 * \param E_limbs The number of limbs in the exponent `E` that will be given
621 * to `mbedtls_mpi_core_exp_mod()`.
622 *
623 * \return The number of limbs of working memory required by
624 * `mbedtls_mpi_core_exp_mod()`.
625 */
626 size_t mbedtls_mpi_core_exp_mod_working_limbs(size_t AN_limbs, size_t E_limbs);
627
628 /**
629 * \brief Perform a modular exponentiation with public or secret exponent:
630 * X = A^E mod N, where \p A is already in Montgomery form.
631 *
632 * \warning This function is not constant time with respect to \p E (the exponent).
633 *
634 * \p X may be aliased to \p A, but not to \p RR or \p E, even if \p E_limbs ==
635 * \p AN_limbs.
636 *
637 * \param[out] X The destination MPI, as a little endian array of length
638 * \p AN_limbs.
639 * \param[in] A The base MPI, as a little endian array of length \p AN_limbs.
640 * Must be in Montgomery form.
641 * \param[in] N The modulus, as a little endian array of length \p AN_limbs.
642 * \param AN_limbs The number of limbs in \p X, \p A, \p N, \p RR.
643 * \param[in] E The exponent, as a little endian array of length \p E_limbs.
644 * \param E_limbs The number of limbs in \p E.
645 * \param[in] RR The precomputed residue of 2^{2*biL} modulo N, as a little
646 * endian array of length \p AN_limbs.
647 * \param[in,out] T Temporary storage of at least the number of limbs returned
648 * by `mbedtls_mpi_core_exp_mod_working_limbs()`.
649 * Its initial content is unused and its final content is
650 * indeterminate.
651 * It must not alias or otherwise overlap any of the other
652 * parameters.
653 * It is up to the caller to zeroize \p T when it is no
654 * longer needed, and before freeing it if it was dynamically
655 * allocated.
656 */
657 void mbedtls_mpi_core_exp_mod_unsafe(mbedtls_mpi_uint *X,
658 const mbedtls_mpi_uint *A,
659 const mbedtls_mpi_uint *N, size_t AN_limbs,
660 const mbedtls_mpi_uint *E, size_t E_limbs,
661 const mbedtls_mpi_uint *RR,
662 mbedtls_mpi_uint *T);
663
664 /**
665 * \brief Perform a modular exponentiation with secret exponent:
666 * X = A^E mod N, where \p A is already in Montgomery form.
667 *
668 * \p X may be aliased to \p A, but not to \p RR or \p E, even if \p E_limbs ==
669 * \p AN_limbs.
670 *
671 * \param[out] X The destination MPI, as a little endian array of length
672 * \p AN_limbs.
673 * \param[in] A The base MPI, as a little endian array of length \p AN_limbs.
674 * Must be in Montgomery form.
675 * \param[in] N The modulus, as a little endian array of length \p AN_limbs.
676 * \param AN_limbs The number of limbs in \p X, \p A, \p N, \p RR.
677 * \param[in] E The exponent, as a little endian array of length \p E_limbs.
678 * \param E_limbs The number of limbs in \p E.
679 * \param[in] RR The precomputed residue of 2^{2*biL} modulo N, as a little
680 * endian array of length \p AN_limbs.
681 * \param[in,out] T Temporary storage of at least the number of limbs returned
682 * by `mbedtls_mpi_core_exp_mod_working_limbs()`.
683 * Its initial content is unused and its final content is
684 * indeterminate.
685 * It must not alias or otherwise overlap any of the other
686 * parameters.
687 * It is up to the caller to zeroize \p T when it is no
688 * longer needed, and before freeing it if it was dynamically
689 * allocated.
690 */
691 void mbedtls_mpi_core_exp_mod(mbedtls_mpi_uint *X,
692 const mbedtls_mpi_uint *A,
693 const mbedtls_mpi_uint *N, size_t AN_limbs,
694 const mbedtls_mpi_uint *E, size_t E_limbs,
695 const mbedtls_mpi_uint *RR,
696 mbedtls_mpi_uint *T);
697
698 /**
699 * \brief Subtract unsigned integer from known-size large unsigned integers.
700 * Return the borrow.
701 *
702 * \param[out] X The result of the subtraction.
703 * \param[in] A The left operand.
704 * \param b The unsigned scalar to subtract.
705 * \param limbs Number of limbs of \p X and \p A.
706 *
707 * \return 1 if `A < b`.
708 * 0 if `A >= b`.
709 */
710 mbedtls_mpi_uint mbedtls_mpi_core_sub_int(mbedtls_mpi_uint *X,
711 const mbedtls_mpi_uint *A,
712 mbedtls_mpi_uint b,
713 size_t limbs);
714
715 /**
716 * \brief Determine if a given MPI has the value \c 0 in constant time with
717 * respect to the value (but not with respect to the number of limbs).
718 *
719 * \param[in] A The MPI to test.
720 * \param limbs Number of limbs in \p A.
721 *
722 * \return MBEDTLS_CT_FALSE if `A == 0`
723 * MBEDTLS_CT_TRUE if `A != 0`.
724 */
725 mbedtls_ct_condition_t mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A,
726 size_t limbs);
727
728 /**
729 * \brief Returns the number of limbs of working memory required for
730 * a call to `mbedtls_mpi_core_montmul()`.
731 *
732 * \param AN_limbs The number of limbs in the input `A` and the modulus `N`
733 * (they must be the same size) that will be given to
734 * `mbedtls_mpi_core_montmul()` or one of the other functions
735 * that specifies this as the amount of working memory needed.
736 *
737 * \return The number of limbs of working memory required by
738 * `mbedtls_mpi_core_montmul()` (or other similar function).
739 */
mbedtls_mpi_core_montmul_working_limbs(size_t AN_limbs)740 static inline size_t mbedtls_mpi_core_montmul_working_limbs(size_t AN_limbs)
741 {
742 return 2 * AN_limbs + 1;
743 }
744
745 /** Convert an MPI into Montgomery form.
746 *
747 * \p X may be aliased to \p A, but may not otherwise overlap it.
748 *
749 * \p X may not alias \p N (it is in canonical form, so must be strictly less
750 * than \p N). Nor may it alias or overlap \p rr (this is unlikely to be
751 * required in practice.)
752 *
753 * This function is a thin wrapper around `mbedtls_mpi_core_montmul()` that is
754 * an alternative to calling `mbedtls_mpi_mod_raw_to_mont_rep()` when we
755 * don't want to allocate memory.
756 *
757 * \param[out] X The result of the conversion.
758 * Must have the same number of limbs as \p A.
759 * \param[in] A The MPI to convert into Montgomery form.
760 * Must have the same number of limbs as the modulus.
761 * \param[in] N The address of the modulus, which gives the size of
762 * the base `R` = 2^(biL*N->limbs).
763 * \param[in] AN_limbs The number of limbs in \p X, \p A, \p N and \p rr.
764 * \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL.
765 * This can be determined by calling
766 * `mbedtls_mpi_core_montmul_init()`.
767 * \param[in] rr The residue for `2^{2*n*biL} mod N`.
768 * \param[in,out] T Temporary storage of size at least
769 * `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)`
770 * limbs.
771 * Its initial content is unused and
772 * its final content is indeterminate.
773 * It must not alias or otherwise overlap any of the
774 * other parameters.
775 */
776 void mbedtls_mpi_core_to_mont_rep(mbedtls_mpi_uint *X,
777 const mbedtls_mpi_uint *A,
778 const mbedtls_mpi_uint *N,
779 size_t AN_limbs,
780 mbedtls_mpi_uint mm,
781 const mbedtls_mpi_uint *rr,
782 mbedtls_mpi_uint *T);
783
784 /** Convert an MPI from Montgomery form.
785 *
786 * \p X may be aliased to \p A, but may not otherwise overlap it.
787 *
788 * \p X may not alias \p N (it is in canonical form, so must be strictly less
789 * than \p N).
790 *
791 * This function is a thin wrapper around `mbedtls_mpi_core_montmul()` that is
792 * an alternative to calling `mbedtls_mpi_mod_raw_from_mont_rep()` when we
793 * don't want to allocate memory.
794 *
795 * \param[out] X The result of the conversion.
796 * Must have the same number of limbs as \p A.
797 * \param[in] A The MPI to convert from Montgomery form.
798 * Must have the same number of limbs as the modulus.
799 * \param[in] N The address of the modulus, which gives the size of
800 * the base `R` = 2^(biL*N->limbs).
801 * \param[in] AN_limbs The number of limbs in \p X, \p A and \p N.
802 * \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL.
803 * This can be determined by calling
804 * `mbedtls_mpi_core_montmul_init()`.
805 * \param[in,out] T Temporary storage of size at least
806 * `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)`
807 * limbs.
808 * Its initial content is unused and
809 * its final content is indeterminate.
810 * It must not alias or otherwise overlap any of the
811 * other parameters.
812 */
813 void mbedtls_mpi_core_from_mont_rep(mbedtls_mpi_uint *X,
814 const mbedtls_mpi_uint *A,
815 const mbedtls_mpi_uint *N,
816 size_t AN_limbs,
817 mbedtls_mpi_uint mm,
818 mbedtls_mpi_uint *T);
819
820 /*
821 * Can't define thread local variables with our abstraction layer: do nothing if threading is on.
822 */
823 #if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
824 extern int mbedtls_mpi_optionally_safe_codepath;
825
mbedtls_mpi_optionally_safe_codepath_reset(void)826 static inline void mbedtls_mpi_optionally_safe_codepath_reset(void)
827 {
828 // Set to a default that is neither MBEDTLS_MPI_IS_PUBLIC nor MBEDTLS_MPI_IS_SECRET
829 mbedtls_mpi_optionally_safe_codepath = MBEDTLS_MPI_IS_PUBLIC + MBEDTLS_MPI_IS_SECRET + 1;
830 }
831 #endif
832
833 #endif /* MBEDTLS_BIGNUM_CORE_H */
834
