xref: /aosp_15_r20/external/cronet/third_party/boringssl/src/include/openssl/bn.h (revision 6777b5387eb2ff775bb5750e3f5d96f37fb7352b)
1 /* Copyright (C) 1995-1997 Eric Young ([email protected])
2  * All rights reserved.
3  *
4  * This package is an SSL implementation written
5  * by Eric Young ([email protected]).
6  * The implementation was written so as to conform with Netscapes SSL.
7  *
8  * This library is free for commercial and non-commercial use as long as
9  * the following conditions are aheared to.  The following conditions
10  * apply to all code found in this distribution, be it the RC4, RSA,
11  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
12  * included with this distribution is covered by the same copyright terms
13  * except that the holder is Tim Hudson ([email protected]).
14  *
15  * Copyright remains Eric Young's, and as such any Copyright notices in
16  * the code are not to be removed.
17  * If this package is used in a product, Eric Young should be given attribution
18  * as the author of the parts of the library used.
19  * This can be in the form of a textual message at program startup or
20  * in documentation (online or textual) provided with the package.
21  *
22  * Redistribution and use in source and binary forms, with or without
23  * modification, are permitted provided that the following conditions
24  * are met:
25  * 1. Redistributions of source code must retain the copyright
26  *    notice, this list of conditions and the following disclaimer.
27  * 2. Redistributions in binary form must reproduce the above copyright
28  *    notice, this list of conditions and the following disclaimer in the
29  *    documentation and/or other materials provided with the distribution.
30  * 3. All advertising materials mentioning features or use of this software
31  *    must display the following acknowledgement:
32  *    "This product includes cryptographic software written by
33  *     Eric Young ([email protected])"
34  *    The word 'cryptographic' can be left out if the rouines from the library
35  *    being used are not cryptographic related :-).
36  * 4. If you include any Windows specific code (or a derivative thereof) from
37  *    the apps directory (application code) you must include an acknowledgement:
38  *    "This product includes software written by Tim Hudson ([email protected])"
39  *
40  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
41  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
43  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
44  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
45  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
46  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
48  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
49  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
50  * SUCH DAMAGE.
51  *
52  * The licence and distribution terms for any publically available version or
53  * derivative of this code cannot be changed.  i.e. this code cannot simply be
54  * copied and put under another distribution licence
55  * [including the GNU Public Licence.]
56  */
57 /* ====================================================================
58  * Copyright (c) 1998-2006 The OpenSSL Project.  All rights reserved.
59  *
60  * Redistribution and use in source and binary forms, with or without
61  * modification, are permitted provided that the following conditions
62  * are met:
63  *
64  * 1. Redistributions of source code must retain the above copyright
65  *    notice, this list of conditions and the following disclaimer.
66  *
67  * 2. Redistributions in binary form must reproduce the above copyright
68  *    notice, this list of conditions and the following disclaimer in
69  *    the documentation and/or other materials provided with the
70  *    distribution.
71  *
72  * 3. All advertising materials mentioning features or use of this
73  *    software must display the following acknowledgment:
74  *    "This product includes software developed by the OpenSSL Project
75  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
76  *
77  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
78  *    endorse or promote products derived from this software without
79  *    prior written permission. For written permission, please contact
80  *    [email protected].
81  *
82  * 5. Products derived from this software may not be called "OpenSSL"
83  *    nor may "OpenSSL" appear in their names without prior written
84  *    permission of the OpenSSL Project.
85  *
86  * 6. Redistributions of any form whatsoever must retain the following
87  *    acknowledgment:
88  *    "This product includes software developed by the OpenSSL Project
89  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
90  *
91  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
92  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
93  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
94  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
95  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
96  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
97  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
98  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
99  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
100  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
101  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
102  * OF THE POSSIBILITY OF SUCH DAMAGE.
103  * ====================================================================
104  *
105  * This product includes cryptographic software written by Eric Young
106  * ([email protected]).  This product includes software written by Tim
107  * Hudson ([email protected]).
108  *
109  */
110 /* ====================================================================
111  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
112  *
113  * Portions of the attached software ("Contribution") are developed by
114  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
115  *
116  * The Contribution is licensed pursuant to the Eric Young open source
117  * license provided above.
118  *
119  * The binary polynomial arithmetic software is originally written by
120  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
121  * Laboratories. */
122 
123 #ifndef OPENSSL_HEADER_BN_H
124 #define OPENSSL_HEADER_BN_H
125 
126 #include <openssl/base.h>
127 #include <openssl/thread.h>
128 
129 #include <inttypes.h>  // for PRIu64 and friends
130 #include <stdio.h>  // for FILE*
131 
132 #if defined(__cplusplus)
133 extern "C" {
134 #endif
135 
136 
137 // BN provides support for working with arbitrary sized integers. For example,
138 // although the largest integer supported by the compiler might be 64 bits, BN
139 // will allow you to work with much larger numbers.
140 //
141 // This library is developed for use inside BoringSSL, and uses implementation
142 // strategies that may not be ideal for other applications. Non-cryptographic
143 // uses should use a more general-purpose integer library, especially if
144 // performance-sensitive.
145 //
146 // Many functions in BN scale quadratically or higher in the bit length of their
147 // input. Callers at this layer are assumed to have capped input sizes within
148 // their performance tolerances.
149 
150 
151 // BN_ULONG is the native word size when working with big integers.
152 //
153 // Note: on some platforms, inttypes.h does not define print format macros in
154 // C++ unless |__STDC_FORMAT_MACROS| defined. This is due to text in C99 which
155 // was never adopted in any C++ standard and explicitly overruled in C++11. As
156 // this is a public header, bn.h does not define |__STDC_FORMAT_MACROS| itself.
157 // Projects which use |BN_*_FMT*| with outdated C headers may need to define it
158 // externally.
159 #if defined(OPENSSL_64_BIT)
160 typedef uint64_t BN_ULONG;
161 #define BN_BITS2 64
162 #define BN_DEC_FMT1 "%" PRIu64
163 #define BN_HEX_FMT1 "%" PRIx64
164 #define BN_HEX_FMT2 "%016" PRIx64
165 #elif defined(OPENSSL_32_BIT)
166 typedef uint32_t BN_ULONG;
167 #define BN_BITS2 32
168 #define BN_DEC_FMT1 "%" PRIu32
169 #define BN_HEX_FMT1 "%" PRIx32
170 #define BN_HEX_FMT2 "%08" PRIx32
171 #else
172 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
173 #endif
174 
175 
176 // Allocation and freeing.
177 
178 // BN_new creates a new, allocated BIGNUM and initialises it.
179 OPENSSL_EXPORT BIGNUM *BN_new(void);
180 
181 // BN_init initialises a stack allocated |BIGNUM|.
182 OPENSSL_EXPORT void BN_init(BIGNUM *bn);
183 
184 // BN_free frees the data referenced by |bn| and, if |bn| was originally
185 // allocated on the heap, frees |bn| also.
186 OPENSSL_EXPORT void BN_free(BIGNUM *bn);
187 
188 // BN_clear_free erases and frees the data referenced by |bn| and, if |bn| was
189 // originally allocated on the heap, frees |bn| also.
190 OPENSSL_EXPORT void BN_clear_free(BIGNUM *bn);
191 
192 // BN_dup allocates a new BIGNUM and sets it equal to |src|. It returns the
193 // allocated BIGNUM on success or NULL otherwise.
194 OPENSSL_EXPORT BIGNUM *BN_dup(const BIGNUM *src);
195 
196 // BN_copy sets |dest| equal to |src| and returns |dest| or NULL on allocation
197 // failure.
198 OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src);
199 
200 // BN_clear sets |bn| to zero and erases the old data.
201 OPENSSL_EXPORT void BN_clear(BIGNUM *bn);
202 
203 // BN_value_one returns a static BIGNUM with value 1.
204 OPENSSL_EXPORT const BIGNUM *BN_value_one(void);
205 
206 
207 // Basic functions.
208 
209 // BN_num_bits returns the minimum number of bits needed to represent the
210 // absolute value of |bn|.
211 OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn);
212 
213 // BN_num_bytes returns the minimum number of bytes needed to represent the
214 // absolute value of |bn|.
215 //
216 // While |size_t| is the preferred type for byte counts, callers can assume that
217 // |BIGNUM|s are bounded such that this value, and its corresponding bit count,
218 // will always fit in |int|.
219 OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn);
220 
221 // BN_zero sets |bn| to zero.
222 OPENSSL_EXPORT void BN_zero(BIGNUM *bn);
223 
224 // BN_one sets |bn| to one. It returns one on success or zero on allocation
225 // failure.
226 OPENSSL_EXPORT int BN_one(BIGNUM *bn);
227 
228 // BN_set_word sets |bn| to |value|. It returns one on success or zero on
229 // allocation failure.
230 OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value);
231 
232 // BN_set_u64 sets |bn| to |value|. It returns one on success or zero on
233 // allocation failure.
234 OPENSSL_EXPORT int BN_set_u64(BIGNUM *bn, uint64_t value);
235 
236 // BN_set_negative sets the sign of |bn|.
237 OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign);
238 
239 // BN_is_negative returns one if |bn| is negative and zero otherwise.
240 OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn);
241 
242 
243 // Conversion functions.
244 
245 // BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as
246 // a big-endian number, and returns |ret|. If |ret| is NULL then a fresh
247 // |BIGNUM| is allocated and returned. It returns NULL on allocation
248 // failure.
249 OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret);
250 
251 // BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian
252 // integer, which must have |BN_num_bytes| of space available. It returns the
253 // number of bytes written. Note this function leaks the magnitude of |in|. If
254 // |in| is secret, use |BN_bn2bin_padded| instead.
255 OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out);
256 
257 // BN_lebin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as
258 // a little-endian number, and returns |ret|. If |ret| is NULL then a fresh
259 // |BIGNUM| is allocated and returned. It returns NULL on allocation
260 // failure.
261 OPENSSL_EXPORT BIGNUM *BN_lebin2bn(const uint8_t *in, size_t len, BIGNUM *ret);
262 
263 // BN_bn2le_padded serialises the absolute value of |in| to |out| as a
264 // little-endian integer, which must have |len| of space available, padding
265 // out the remainder of out with zeros. If |len| is smaller than |BN_num_bytes|,
266 // the function fails and returns 0. Otherwise, it returns 1.
267 OPENSSL_EXPORT int BN_bn2le_padded(uint8_t *out, size_t len, const BIGNUM *in);
268 
269 // BN_bn2bin_padded serialises the absolute value of |in| to |out| as a
270 // big-endian integer. The integer is padded with leading zeros up to size
271 // |len|. If |len| is smaller than |BN_num_bytes|, the function fails and
272 // returns 0. Otherwise, it returns 1.
273 OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in);
274 
275 // BN_bn2cbb_padded behaves like |BN_bn2bin_padded| but writes to a |CBB|.
276 OPENSSL_EXPORT int BN_bn2cbb_padded(CBB *out, size_t len, const BIGNUM *in);
277 
278 // BN_bn2hex returns an allocated string that contains a NUL-terminated, hex
279 // representation of |bn|. If |bn| is negative, the first char in the resulting
280 // string will be '-'. Returns NULL on allocation failure.
281 OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn);
282 
283 // BN_hex2bn parses the leading hex number from |in|, which may be proceeded by
284 // a '-' to indicate a negative number and may contain trailing, non-hex data.
285 // If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and
286 // stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and
287 // updates |*outp|. It returns the number of bytes of |in| processed or zero on
288 // error.
289 OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in);
290 
291 // BN_bn2dec returns an allocated string that contains a NUL-terminated,
292 // decimal representation of |bn|. If |bn| is negative, the first char in the
293 // resulting string will be '-'. Returns NULL on allocation failure.
294 //
295 // Converting an arbitrarily large integer to decimal is quadratic in the bit
296 // length of |a|. This function assumes the caller has capped the input within
297 // performance tolerances.
298 OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a);
299 
300 // BN_dec2bn parses the leading decimal number from |in|, which may be
301 // proceeded by a '-' to indicate a negative number and may contain trailing,
302 // non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the
303 // decimal number and stores it in |*outp|. If |*outp| is NULL then it
304 // allocates a new BIGNUM and updates |*outp|. It returns the number of bytes
305 // of |in| processed or zero on error.
306 //
307 // Converting an arbitrarily large integer to decimal is quadratic in the bit
308 // length of |a|. This function assumes the caller has capped the input within
309 // performance tolerances.
310 OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in);
311 
312 // BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in|
313 // begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A
314 // leading '-' is still permitted and comes before the optional 0X/0x. It
315 // returns one on success or zero on error.
316 OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in);
317 
318 // BN_print writes a hex encoding of |a| to |bio|. It returns one on success
319 // and zero on error.
320 OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a);
321 
322 // BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first.
323 OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a);
324 
325 // BN_get_word returns the absolute value of |bn| as a single word. If |bn| is
326 // too large to be represented as a single word, the maximum possible value
327 // will be returned.
328 OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn);
329 
330 // BN_get_u64 sets |*out| to the absolute value of |bn| as a |uint64_t| and
331 // returns one. If |bn| is too large to be represented as a |uint64_t|, it
332 // returns zero.
333 OPENSSL_EXPORT int BN_get_u64(const BIGNUM *bn, uint64_t *out);
334 
335 
336 // ASN.1 functions.
337 
338 // BN_parse_asn1_unsigned parses a non-negative DER INTEGER from |cbs| writes
339 // the result to |ret|. It returns one on success and zero on failure.
340 OPENSSL_EXPORT int BN_parse_asn1_unsigned(CBS *cbs, BIGNUM *ret);
341 
342 // BN_marshal_asn1 marshals |bn| as a non-negative DER INTEGER and appends the
343 // result to |cbb|. It returns one on success and zero on failure.
344 OPENSSL_EXPORT int BN_marshal_asn1(CBB *cbb, const BIGNUM *bn);
345 
346 
347 // BIGNUM pools.
348 //
349 // Certain BIGNUM operations need to use many temporary variables and
350 // allocating and freeing them can be quite slow. Thus such operations typically
351 // take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx|
352 // argument to a public function may be NULL, in which case a local |BN_CTX|
353 // will be created just for the lifetime of that call.
354 //
355 // A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called
356 // repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made
357 // before calling any other functions that use the |ctx| as an argument.
358 //
359 // Finally, |BN_CTX_end| must be called before returning from the function.
360 // When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from
361 // |BN_CTX_get| become invalid.
362 
363 // BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure.
364 OPENSSL_EXPORT BN_CTX *BN_CTX_new(void);
365 
366 // BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx|
367 // itself.
368 OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx);
369 
370 // BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future
371 // calls to |BN_CTX_get|.
372 OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx);
373 
374 // BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once
375 // |BN_CTX_get| has returned NULL, all future calls will also return NULL until
376 // |BN_CTX_end| is called.
377 OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx);
378 
379 // BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the
380 // matching |BN_CTX_start| call.
381 OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx);
382 
383 
384 // Simple arithmetic
385 
386 // BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a|
387 // or |b|. It returns one on success and zero on allocation failure.
388 OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
389 
390 // BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may
391 // be the same pointer as either |a| or |b|. It returns one on success and zero
392 // on allocation failure.
393 OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
394 
395 // BN_add_word adds |w| to |a|. It returns one on success and zero otherwise.
396 OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w);
397 
398 // BN_sub sets |r| = |a| - |b|, where |r| may be the same pointer as either |a|
399 // or |b|. It returns one on success and zero on allocation failure.
400 OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
401 
402 // BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers,
403 // |b| < |a| and |r| may be the same pointer as either |a| or |b|. It returns
404 // one on success and zero on allocation failure.
405 OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
406 
407 // BN_sub_word subtracts |w| from |a|. It returns one on success and zero on
408 // allocation failure.
409 OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w);
410 
411 // BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or
412 // |b|. Returns one on success and zero otherwise.
413 OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
414                           BN_CTX *ctx);
415 
416 // BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on
417 // allocation failure.
418 OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w);
419 
420 // BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as
421 // |a|. Returns one on success and zero otherwise. This is more efficient than
422 // BN_mul(r, a, a, ctx).
423 OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
424 
425 // BN_div divides |numerator| by |divisor| and places the result in |quotient|
426 // and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in
427 // which case the respective value is not returned. The result is rounded
428 // towards zero; thus if |numerator| is negative, the remainder will be zero or
429 // negative. It returns one on success or zero on error.
430 OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem,
431                           const BIGNUM *numerator, const BIGNUM *divisor,
432                           BN_CTX *ctx);
433 
434 // BN_div_word sets |numerator| = |numerator|/|divisor| and returns the
435 // remainder or (BN_ULONG)-1 on error.
436 OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor);
437 
438 // BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the
439 // square root of |in|, using |ctx|. It returns one on success or zero on
440 // error. Negative numbers and non-square numbers will result in an error with
441 // appropriate errors on the error queue.
442 OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx);
443 
444 
445 // Comparison functions
446 
447 // BN_cmp returns a value less than, equal to or greater than zero if |a| is
448 // less than, equal to or greater than |b|, respectively.
449 OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b);
450 
451 // BN_cmp_word is like |BN_cmp| except it takes its second argument as a
452 // |BN_ULONG| instead of a |BIGNUM|.
453 OPENSSL_EXPORT int BN_cmp_word(const BIGNUM *a, BN_ULONG b);
454 
455 // BN_ucmp returns a value less than, equal to or greater than zero if the
456 // absolute value of |a| is less than, equal to or greater than the absolute
457 // value of |b|, respectively.
458 OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
459 
460 // BN_equal_consttime returns one if |a| is equal to |b|, and zero otherwise.
461 // It takes an amount of time dependent on the sizes of |a| and |b|, but
462 // independent of the contents (including the signs) of |a| and |b|.
463 OPENSSL_EXPORT int BN_equal_consttime(const BIGNUM *a, const BIGNUM *b);
464 
465 // BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero
466 // otherwise.
467 OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w);
468 
469 // BN_is_zero returns one if |bn| is zero and zero otherwise.
470 OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn);
471 
472 // BN_is_one returns one if |bn| equals one and zero otherwise.
473 OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn);
474 
475 // BN_is_word returns one if |bn| is exactly |w| and zero otherwise.
476 OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w);
477 
478 // BN_is_odd returns one if |bn| is odd and zero otherwise.
479 OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn);
480 
481 // BN_is_pow2 returns 1 if |a| is a power of two, and 0 otherwise.
482 OPENSSL_EXPORT int BN_is_pow2(const BIGNUM *a);
483 
484 
485 // Bitwise operations.
486 
487 // BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the
488 // same |BIGNUM|. It returns one on success and zero on allocation failure.
489 OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
490 
491 // BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same
492 // pointer. It returns one on success and zero on allocation failure.
493 OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a);
494 
495 // BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same
496 // pointer. It returns one on success and zero on allocation failure.
497 OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
498 
499 // BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same
500 // pointer. It returns one on success and zero on allocation failure.
501 OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a);
502 
503 // BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a|
504 // is 2 then setting bit zero will make it 3. It returns one on success or zero
505 // on allocation failure.
506 OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n);
507 
508 // BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if
509 // |a| is 3, clearing bit zero will make it two. It returns one on success or
510 // zero on allocation failure.
511 OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n);
512 
513 // BN_is_bit_set returns one if the |n|th least-significant bit in |a| exists
514 // and is set. Otherwise, it returns zero.
515 OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n);
516 
517 // BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one
518 // on success or zero if |n| is negative.
519 //
520 // This differs from OpenSSL which additionally returns zero if |a|'s word
521 // length is less than or equal to |n|, rounded down to a number of words. Note
522 // word size is platform-dependent, so this behavior is also difficult to rely
523 // on in OpenSSL and not very useful.
524 OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n);
525 
526 // BN_count_low_zero_bits returns the number of low-order zero bits in |bn|, or
527 // the number of factors of two which divide it. It returns zero if |bn| is
528 // zero.
529 OPENSSL_EXPORT int BN_count_low_zero_bits(const BIGNUM *bn);
530 
531 
532 // Modulo arithmetic.
533 
534 // BN_mod_word returns |a| mod |w| or (BN_ULONG)-1 on error.
535 OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
536 
537 // BN_mod_pow2 sets |r| = |a| mod 2^|e|. It returns 1 on success and
538 // 0 on error.
539 OPENSSL_EXPORT int BN_mod_pow2(BIGNUM *r, const BIGNUM *a, size_t e);
540 
541 // BN_nnmod_pow2 sets |r| = |a| mod 2^|e| where |r| is always positive.
542 // It returns 1 on success and 0 on error.
543 OPENSSL_EXPORT int BN_nnmod_pow2(BIGNUM *r, const BIGNUM *a, size_t e);
544 
545 // BN_mod is a helper macro that calls |BN_div| and discards the quotient.
546 #define BN_mod(rem, numerator, divisor, ctx) \
547   BN_div(NULL, (rem), (numerator), (divisor), (ctx))
548 
549 // BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <=
550 // |rem| < |divisor| is always true. It returns one on success and zero on
551 // error.
552 OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator,
553                             const BIGNUM *divisor, BN_CTX *ctx);
554 
555 // BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero
556 // on error.
557 OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
558                               const BIGNUM *m, BN_CTX *ctx);
559 
560 // BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be
561 // non-negative and less than |m|.
562 OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
563                                     const BIGNUM *m);
564 
565 // BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero
566 // on error.
567 OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
568                               const BIGNUM *m, BN_CTX *ctx);
569 
570 // BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be
571 // non-negative and less than |m|.
572 OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
573                                     const BIGNUM *m);
574 
575 // BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero
576 // on error.
577 OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
578                               const BIGNUM *m, BN_CTX *ctx);
579 
580 // BN_mod_sqr sets |r| = |a|^2 mod |m|. It returns one on success and zero
581 // on error.
582 OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
583                               BN_CTX *ctx);
584 
585 // BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the
586 // same pointer. It returns one on success and zero on error.
587 OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n,
588                                  const BIGNUM *m, BN_CTX *ctx);
589 
590 // BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be
591 // non-negative and less than |m|.
592 OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n,
593                                        const BIGNUM *m);
594 
595 // BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the
596 // same pointer. It returns one on success and zero on error.
597 OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
598                                   BN_CTX *ctx);
599 
600 // BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be
601 // non-negative and less than |m|.
602 OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a,
603                                         const BIGNUM *m);
604 
605 // BN_mod_sqrt returns a newly-allocated |BIGNUM|, r, such that
606 // r^2 == a (mod p). It returns NULL on error or if |a| is not a square mod |p|.
607 // In the latter case, it will add |BN_R_NOT_A_SQUARE| to the error queue.
608 // If |a| is a square and |p| > 2, there are two possible square roots. This
609 // function may return either and may even select one non-deterministically.
610 //
611 // This function only works if |p| is a prime. If |p| is composite, it may fail
612 // or return an arbitrary value. Callers should not pass attacker-controlled
613 // values of |p|.
614 OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p,
615                                    BN_CTX *ctx);
616 
617 
618 // Random and prime number generation.
619 
620 // The following are values for the |top| parameter of |BN_rand|.
621 #define BN_RAND_TOP_ANY    (-1)
622 #define BN_RAND_TOP_ONE     0
623 #define BN_RAND_TOP_TWO     1
624 
625 // The following are values for the |bottom| parameter of |BN_rand|.
626 #define BN_RAND_BOTTOM_ANY  0
627 #define BN_RAND_BOTTOM_ODD  1
628 
629 // BN_rand sets |rnd| to a random number of length |bits|. It returns one on
630 // success and zero otherwise.
631 //
632 // |top| must be one of the |BN_RAND_TOP_*| values. If |BN_RAND_TOP_ONE|, the
633 // most-significant bit, if any, will be set. If |BN_RAND_TOP_TWO|, the two
634 // most significant bits, if any, will be set. If |BN_RAND_TOP_ANY|, no extra
635 // action will be taken and |BN_num_bits(rnd)| may not equal |bits| if the most
636 // significant bits randomly ended up as zeros.
637 //
638 // |bottom| must be one of the |BN_RAND_BOTTOM_*| values. If
639 // |BN_RAND_BOTTOM_ODD|, the least-significant bit, if any, will be set. If
640 // |BN_RAND_BOTTOM_ANY|, no extra action will be taken.
641 OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
642 
643 // BN_pseudo_rand is an alias for |BN_rand|.
644 OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
645 
646 // BN_rand_range is equivalent to |BN_rand_range_ex| with |min_inclusive| set
647 // to zero and |max_exclusive| set to |range|.
648 OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
649 
650 // BN_rand_range_ex sets |rnd| to a random value in
651 // [min_inclusive..max_exclusive). It returns one on success and zero
652 // otherwise.
653 OPENSSL_EXPORT int BN_rand_range_ex(BIGNUM *r, BN_ULONG min_inclusive,
654                                     const BIGNUM *max_exclusive);
655 
656 // BN_pseudo_rand_range is an alias for BN_rand_range.
657 OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
658 
659 #define BN_GENCB_GENERATED 0
660 #define BN_GENCB_PRIME_TEST 1
661 
662 // bn_gencb_st, or |BN_GENCB|, holds a callback function that is used by
663 // generation functions that can take a very long time to complete. Use
664 // |BN_GENCB_set| to initialise a |BN_GENCB| structure.
665 //
666 // The callback receives the address of that |BN_GENCB| structure as its last
667 // argument and the user is free to put an arbitrary pointer in |arg|. The other
668 // arguments are set as follows:
669 // - event=BN_GENCB_GENERATED, n=i:   after generating the i'th possible prime
670 //                                    number.
671 // - event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality
672 //                                    checks.
673 // - event=BN_GENCB_PRIME_TEST, n=i:  when the i'th primality test has finished.
674 //
675 // The callback can return zero to abort the generation progress or one to
676 // allow it to continue.
677 //
678 // When other code needs to call a BN generation function it will often take a
679 // BN_GENCB argument and may call the function with other argument values.
680 struct bn_gencb_st {
681   void *arg;        // callback-specific data
682   int (*callback)(int event, int n, struct bn_gencb_st *);
683 };
684 
685 // BN_GENCB_new returns a newly-allocated |BN_GENCB| object, or NULL on
686 // allocation failure. The result must be released with |BN_GENCB_free| when
687 // done.
688 OPENSSL_EXPORT BN_GENCB *BN_GENCB_new(void);
689 
690 // BN_GENCB_free releases memory associated with |callback|.
691 OPENSSL_EXPORT void BN_GENCB_free(BN_GENCB *callback);
692 
693 // BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to
694 // |arg|.
695 OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback,
696                                  int (*f)(int event, int n, BN_GENCB *),
697                                  void *arg);
698 
699 // BN_GENCB_call calls |callback|, if not NULL, and returns the return value of
700 // the callback, or 1 if |callback| is NULL.
701 OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n);
702 
703 // BN_GENCB_get_arg returns |callback->arg|.
704 OPENSSL_EXPORT void *BN_GENCB_get_arg(const BN_GENCB *callback);
705 
706 // BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe
707 // is non-zero then the prime will be such that (ret-1)/2 is also a prime.
708 // (This is needed for Diffie-Hellman groups to ensure that the only subgroups
709 // are of size 2 and (p-1)/2.).
710 //
711 // If |add| is not NULL, the prime will fulfill the condition |ret| % |add| ==
712 // |rem| in order to suit a given generator. (If |rem| is NULL then |ret| %
713 // |add| == 1.)
714 //
715 // If |cb| is not NULL, it will be called during processing to give an
716 // indication of progress. See the comments for |BN_GENCB|. It returns one on
717 // success and zero otherwise.
718 OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
719                                         const BIGNUM *add, const BIGNUM *rem,
720                                         BN_GENCB *cb);
721 
722 // BN_prime_checks_for_validation can be used as the |checks| argument to the
723 // primarily testing functions when validating an externally-supplied candidate
724 // prime. It gives a false positive rate of at most 2^{-128}. (The worst case
725 // false positive rate for a single iteration is 1/4 per
726 // https://eprint.iacr.org/2018/749. (1/4)^64 = 2^{-128}.)
727 #define BN_prime_checks_for_validation 64
728 
729 // BN_prime_checks_for_generation can be used as the |checks| argument to the
730 // primality testing functions when generating random primes. It gives a false
731 // positive rate at most the security level of the corresponding RSA key size.
732 //
733 // Note this value only performs enough checks if the candidate prime was
734 // selected randomly. If validating an externally-supplied candidate, especially
735 // one that may be selected adversarially, use |BN_prime_checks_for_validation|
736 // instead.
737 #define BN_prime_checks_for_generation 0
738 
739 // bn_primality_result_t enumerates the outcomes of primality-testing.
740 enum bn_primality_result_t {
741   bn_probably_prime,
742   bn_composite,
743   bn_non_prime_power_composite,
744 };
745 
746 // BN_enhanced_miller_rabin_primality_test tests whether |w| is probably a prime
747 // number using the Enhanced Miller-Rabin Test (FIPS 186-4 C.3.2) with
748 // |checks| iterations and returns the result in |out_result|. Enhanced
749 // Miller-Rabin tests primality for odd integers greater than 3, returning
750 // |bn_probably_prime| if the number is probably prime,
751 // |bn_non_prime_power_composite| if the number is a composite that is not the
752 // power of a single prime, and |bn_composite| otherwise. It returns one on
753 // success and zero on failure. If |cb| is not NULL, then it is called during
754 // each iteration of the primality test.
755 //
756 // See |BN_prime_checks_for_validation| and |BN_prime_checks_for_generation| for
757 // recommended values of |checks|.
758 OPENSSL_EXPORT int BN_enhanced_miller_rabin_primality_test(
759     enum bn_primality_result_t *out_result, const BIGNUM *w, int checks,
760     BN_CTX *ctx, BN_GENCB *cb);
761 
762 // BN_primality_test sets |*is_probably_prime| to one if |candidate| is
763 // probably a prime number by the Miller-Rabin test or zero if it's certainly
764 // not.
765 //
766 // If |do_trial_division| is non-zero then |candidate| will be tested against a
767 // list of small primes before Miller-Rabin tests. The probability of this
768 // function returning a false positive is at most 2^{2*checks}. See
769 // |BN_prime_checks_for_validation| and |BN_prime_checks_for_generation| for
770 // recommended values of |checks|.
771 //
772 // If |cb| is not NULL then it is called during the checking process. See the
773 // comment above |BN_GENCB|.
774 //
775 // The function returns one on success and zero on error.
776 OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime,
777                                      const BIGNUM *candidate, int checks,
778                                      BN_CTX *ctx, int do_trial_division,
779                                      BN_GENCB *cb);
780 
781 // BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime
782 // number by the Miller-Rabin test, zero if it's certainly not and -1 on error.
783 //
784 // If |do_trial_division| is non-zero then |candidate| will be tested against a
785 // list of small primes before Miller-Rabin tests. The probability of this
786 // function returning one when |candidate| is composite is at most 2^{2*checks}.
787 // See |BN_prime_checks_for_validation| and |BN_prime_checks_for_generation| for
788 // recommended values of |checks|.
789 //
790 // If |cb| is not NULL then it is called during the checking process. See the
791 // comment above |BN_GENCB|.
792 //
793 // WARNING: deprecated. Use |BN_primality_test|.
794 OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks,
795                                            BN_CTX *ctx, int do_trial_division,
796                                            BN_GENCB *cb);
797 
798 // BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with
799 // |do_trial_division| set to zero.
800 //
801 // WARNING: deprecated: Use |BN_primality_test|.
802 OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks,
803                                   BN_CTX *ctx, BN_GENCB *cb);
804 
805 
806 // Number theory functions
807 
808 // BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero
809 // otherwise.
810 OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
811                           BN_CTX *ctx);
812 
813 // BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If |out| is NULL, a
814 // fresh BIGNUM is allocated. It returns the result or NULL on error.
815 //
816 // If |n| is even then the operation is performed using an algorithm that avoids
817 // some branches but which isn't constant-time. This function shouldn't be used
818 // for secret values; use |BN_mod_inverse_blinded| instead. Or, if |n| is
819 // guaranteed to be prime, use
820 // |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking
821 // advantage of Fermat's Little Theorem.
822 OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a,
823                                       const BIGNUM *n, BN_CTX *ctx);
824 
825 // BN_mod_inverse_blinded sets |out| equal to |a|^-1, mod |n|, where |n| is the
826 // Montgomery modulus for |mont|. |a| must be non-negative and must be less
827 // than |n|. |n| must be greater than 1. |a| is blinded (masked by a random
828 // value) to protect it against side-channel attacks. On failure, if the failure
829 // was caused by |a| having no inverse mod |n| then |*out_no_inverse| will be
830 // set to one; otherwise it will be set to zero.
831 //
832 // Note this function may incorrectly report |a| has no inverse if the random
833 // blinding value has no inverse. It should only be used when |n| has few
834 // non-invertible elements, such as an RSA modulus.
835 OPENSSL_EXPORT int BN_mod_inverse_blinded(BIGNUM *out, int *out_no_inverse,
836                                           const BIGNUM *a,
837                                           const BN_MONT_CTX *mont, BN_CTX *ctx);
838 
839 // BN_mod_inverse_odd sets |out| equal to |a|^-1, mod |n|. |a| must be
840 // non-negative and must be less than |n|. |n| must be odd. This function
841 // shouldn't be used for secret values; use |BN_mod_inverse_blinded| instead.
842 // Or, if |n| is guaranteed to be prime, use
843 // |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking
844 // advantage of Fermat's Little Theorem. It returns one on success or zero on
845 // failure. On failure, if the failure was caused by |a| having no inverse mod
846 // |n| then |*out_no_inverse| will be set to one; otherwise it will be set to
847 // zero.
848 int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
849                        const BIGNUM *n, BN_CTX *ctx);
850 
851 
852 // Montgomery arithmetic.
853 
854 // BN_MONT_CTX contains the precomputed values needed to work in a specific
855 // Montgomery domain.
856 
857 // BN_MONT_CTX_new_for_modulus returns a fresh |BN_MONT_CTX| given the modulus,
858 // |mod| or NULL on error. Note this function assumes |mod| is public.
859 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod,
860                                                         BN_CTX *ctx);
861 
862 // BN_MONT_CTX_new_consttime behaves like |BN_MONT_CTX_new_for_modulus| but
863 // treats |mod| as secret.
864 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new_consttime(const BIGNUM *mod,
865                                                       BN_CTX *ctx);
866 
867 // BN_MONT_CTX_free frees memory associated with |mont|.
868 OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont);
869 
870 // BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or
871 // NULL on error.
872 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,
873                                              const BN_MONT_CTX *from);
874 
875 // BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. |a| is
876 // assumed to be in the range [0, n), where |n| is the Montgomery modulus. It
877 // returns one on success or zero on error.
878 OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a,
879                                     const BN_MONT_CTX *mont, BN_CTX *ctx);
880 
881 // BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values out
882 // of the Montgomery domain. |a| is assumed to be in the range [0, n*R), where
883 // |n| is the Montgomery modulus. Note n < R, so inputs in the range [0, n*n)
884 // are valid. This function returns one on success or zero on error.
885 OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a,
886                                       const BN_MONT_CTX *mont, BN_CTX *ctx);
887 
888 // BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain.
889 // Both |a| and |b| must already be in the Montgomery domain (by
890 // |BN_to_montgomery|). In particular, |a| and |b| are assumed to be in the
891 // range [0, n), where |n| is the Montgomery modulus. It returns one on success
892 // or zero on error.
893 OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a,
894                                          const BIGNUM *b,
895                                          const BN_MONT_CTX *mont, BN_CTX *ctx);
896 
897 
898 // Exponentiation.
899 
900 // BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply
901 // algorithm that leaks side-channel information. It returns one on success or
902 // zero otherwise.
903 OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
904                           BN_CTX *ctx);
905 
906 // BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best
907 // algorithm for the values provided. It returns one on success or zero
908 // otherwise. The |BN_mod_exp_mont_consttime| variant must be used if the
909 // exponent is secret.
910 OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
911                               const BIGNUM *m, BN_CTX *ctx);
912 
913 // BN_mod_exp_mont behaves like |BN_mod_exp| but treats |a| as secret and
914 // requires 0 <= |a| < |m|.
915 OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
916                                    const BIGNUM *m, BN_CTX *ctx,
917                                    const BN_MONT_CTX *mont);
918 
919 // BN_mod_exp_mont_consttime behaves like |BN_mod_exp| but treats |a|, |p|, and
920 // |m| as secret and requires 0 <= |a| < |m|.
921 OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a,
922                                              const BIGNUM *p, const BIGNUM *m,
923                                              BN_CTX *ctx,
924                                              const BN_MONT_CTX *mont);
925 
926 
927 // Deprecated functions
928 
929 // BN_bn2mpi serialises the value of |in| to |out|, using a format that consists
930 // of the number's length in bytes represented as a 4-byte big-endian number,
931 // and the number itself in big-endian format, where the most significant bit
932 // signals a negative number. (The representation of numbers with the MSB set is
933 // prefixed with null byte). |out| must have sufficient space available; to
934 // find the needed amount of space, call the function with |out| set to NULL.
935 OPENSSL_EXPORT size_t BN_bn2mpi(const BIGNUM *in, uint8_t *out);
936 
937 // BN_mpi2bn parses |len| bytes from |in| and returns the resulting value. The
938 // bytes at |in| are expected to be in the format emitted by |BN_bn2mpi|.
939 //
940 // If |out| is NULL then a fresh |BIGNUM| is allocated and returned, otherwise
941 // |out| is reused and returned. On error, NULL is returned and the error queue
942 // is updated.
943 OPENSSL_EXPORT BIGNUM *BN_mpi2bn(const uint8_t *in, size_t len, BIGNUM *out);
944 
945 // BN_mod_exp_mont_word is like |BN_mod_exp_mont| except that the base |a| is
946 // given as a |BN_ULONG| instead of a |BIGNUM *|. It returns one on success
947 // or zero otherwise.
948 OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
949                                         const BIGNUM *m, BN_CTX *ctx,
950                                         const BN_MONT_CTX *mont);
951 
952 // BN_mod_exp2_mont calculates (a1^p1) * (a2^p2) mod m. It returns 1 on success
953 // or zero otherwise.
954 OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1,
955                                     const BIGNUM *p1, const BIGNUM *a2,
956                                     const BIGNUM *p2, const BIGNUM *m,
957                                     BN_CTX *ctx, const BN_MONT_CTX *mont);
958 
959 // BN_MONT_CTX_new returns a fresh |BN_MONT_CTX| or NULL on allocation failure.
960 // Use |BN_MONT_CTX_new_for_modulus| instead.
961 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void);
962 
963 // BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It
964 // returns one on success and zero on error. Use |BN_MONT_CTX_new_for_modulus|
965 // instead.
966 OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod,
967                                    BN_CTX *ctx);
968 
969 // BN_bn2binpad behaves like |BN_bn2bin_padded|, but it returns |len| on success
970 // and -1 on error.
971 //
972 // Use |BN_bn2bin_padded| instead. It is |size_t|-clean.
973 OPENSSL_EXPORT int BN_bn2binpad(const BIGNUM *in, uint8_t *out, int len);
974 
975 // BN_bn2lebinpad behaves like |BN_bn2le_padded|, but it returns |len| on
976 // success and -1 on error.
977 //
978 // Use |BN_bn2le_padded| instead. It is |size_t|-clean.
979 OPENSSL_EXPORT int BN_bn2lebinpad(const BIGNUM *in, uint8_t *out, int len);
980 
981 // BN_prime_checks is a deprecated alias for |BN_prime_checks_for_validation|.
982 // Use |BN_prime_checks_for_generation| or |BN_prime_checks_for_validation|
983 // instead. (This defaults to the |_for_validation| value in order to be
984 // conservative.)
985 #define BN_prime_checks BN_prime_checks_for_validation
986 
987 // BN_secure_new calls |BN_new|.
988 OPENSSL_EXPORT BIGNUM *BN_secure_new(void);
989 
990 // BN_le2bn calls |BN_lebin2bn|.
991 OPENSSL_EXPORT BIGNUM *BN_le2bn(const uint8_t *in, size_t len, BIGNUM *ret);
992 
993 
994 // Private functions
995 
996 struct bignum_st {
997   // d is a pointer to an array of |width| |BN_BITS2|-bit chunks in
998   // little-endian order. This stores the absolute value of the number.
999   BN_ULONG *d;
1000   // width is the number of elements of |d| which are valid. This value is not
1001   // necessarily minimal; the most-significant words of |d| may be zero.
1002   // |width| determines a potentially loose upper-bound on the absolute value
1003   // of the |BIGNUM|.
1004   //
1005   // Functions taking |BIGNUM| inputs must compute the same answer for all
1006   // possible widths. |bn_minimal_width|, |bn_set_minimal_width|, and other
1007   // helpers may be used to recover the minimal width, provided it is not
1008   // secret. If it is secret, use a different algorithm. Functions may output
1009   // minimal or non-minimal |BIGNUM|s depending on secrecy requirements, but
1010   // those which cause widths to unboundedly grow beyond the minimal value
1011   // should be documented such.
1012   //
1013   // Note this is different from historical |BIGNUM| semantics.
1014   int width;
1015   // dmax is number of elements of |d| which are allocated.
1016   int dmax;
1017   // neg is one if the number if negative and zero otherwise.
1018   int neg;
1019   // flags is a bitmask of |BN_FLG_*| values
1020   int flags;
1021 };
1022 
1023 struct bn_mont_ctx_st {
1024   // RR is R^2, reduced modulo |N|. It is used to convert to Montgomery form. It
1025   // is guaranteed to have the same width as |N|.
1026   BIGNUM RR;
1027   // N is the modulus. It is always stored in minimal form, so |N.width|
1028   // determines R.
1029   BIGNUM N;
1030   BN_ULONG n0[2];  // least significant words of (R*Ri-1)/N
1031 };
1032 
1033 OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l);
1034 
1035 #define BN_FLG_MALLOCED 0x01
1036 #define BN_FLG_STATIC_DATA 0x02
1037 // |BN_FLG_CONSTTIME| has been removed and intentionally omitted so code relying
1038 // on it will not compile. Consumers outside BoringSSL should use the
1039 // higher-level cryptographic algorithms exposed by other modules. Consumers
1040 // within the library should call the appropriate timing-sensitive algorithm
1041 // directly.
1042 
1043 
1044 #if defined(__cplusplus)
1045 }  // extern C
1046 
1047 #if !defined(BORINGSSL_NO_CXX)
1048 extern "C++" {
1049 
1050 BSSL_NAMESPACE_BEGIN
1051 
BORINGSSL_MAKE_DELETER(BIGNUM,BN_free)1052 BORINGSSL_MAKE_DELETER(BIGNUM, BN_free)
1053 BORINGSSL_MAKE_DELETER(BN_CTX, BN_CTX_free)
1054 BORINGSSL_MAKE_DELETER(BN_MONT_CTX, BN_MONT_CTX_free)
1055 
1056 class BN_CTXScope {
1057  public:
1058   BN_CTXScope(BN_CTX *ctx) : ctx_(ctx) { BN_CTX_start(ctx_); }
1059   ~BN_CTXScope() { BN_CTX_end(ctx_); }
1060 
1061  private:
1062   BN_CTX *ctx_;
1063 
1064   BN_CTXScope(BN_CTXScope &) = delete;
1065   BN_CTXScope &operator=(BN_CTXScope &) = delete;
1066 };
1067 
1068 BSSL_NAMESPACE_END
1069 
1070 }  // extern C++
1071 #endif
1072 
1073 #endif
1074 
1075 #define BN_R_ARG2_LT_ARG3 100
1076 #define BN_R_BAD_RECIPROCAL 101
1077 #define BN_R_BIGNUM_TOO_LONG 102
1078 #define BN_R_BITS_TOO_SMALL 103
1079 #define BN_R_CALLED_WITH_EVEN_MODULUS 104
1080 #define BN_R_DIV_BY_ZERO 105
1081 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 106
1082 #define BN_R_INPUT_NOT_REDUCED 107
1083 #define BN_R_INVALID_RANGE 108
1084 #define BN_R_NEGATIVE_NUMBER 109
1085 #define BN_R_NOT_A_SQUARE 110
1086 #define BN_R_NOT_INITIALIZED 111
1087 #define BN_R_NO_INVERSE 112
1088 #define BN_R_PRIVATE_KEY_TOO_LARGE 113
1089 #define BN_R_P_IS_NOT_PRIME 114
1090 #define BN_R_TOO_MANY_ITERATIONS 115
1091 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 116
1092 #define BN_R_BAD_ENCODING 117
1093 #define BN_R_ENCODE_ERROR 118
1094 #define BN_R_INVALID_INPUT 119
1095 
1096 #endif  // OPENSSL_HEADER_BN_H
1097