Line data Source code
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 38 : static inline size_t mbedtls_mpi_core_montmul_working_limbs(size_t AN_limbs)
746 : {
747 38 : 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 */
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