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1 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
2  * All rights reserved.
3  *
4  * This package is an SSL implementation written
5  * by Eric Young (eay@cryptsoft.com).
6  * The implementation was written so as to conform with Netscapes SSL.
7  *
8  * This library is free for commercial and non-commercial use as long as
9  * the following conditions are aheared to.  The following conditions
10  * apply to all code found in this distribution, be it the RC4, RSA,
11  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
12  * included with this distribution is covered by the same copyright terms
13  * except that the holder is Tim Hudson (tjh@cryptsoft.com).
14  *
15  * Copyright remains Eric Young's, and as such any Copyright notices in
16  * the code are not to be removed.
17  * If this package is used in a product, Eric Young should be given attribution
18  * as the author of the parts of the library used.
19  * This can be in the form of a textual message at program startup or
20  * in documentation (online or textual) provided with the package.
21  *
22  * Redistribution and use in source and binary forms, with or without
23  * modification, are permitted provided that the following conditions
24  * are met:
25  * 1. Redistributions of source code must retain the copyright
26  *    notice, this list of conditions and the following disclaimer.
27  * 2. Redistributions in binary form must reproduce the above copyright
28  *    notice, this list of conditions and the following disclaimer in the
29  *    documentation and/or other materials provided with the distribution.
30  * 3. All advertising materials mentioning features or use of this software
31  *    must display the following acknowledgement:
32  *    "This product includes cryptographic software written by
33  *     Eric Young (eay@cryptsoft.com)"
34  *    The word 'cryptographic' can be left out if the rouines from the library
35  *    being used are not cryptographic related :-).
36  * 4. If you include any Windows specific code (or a derivative thereof) from
37  *    the apps directory (application code) you must include an acknowledgement:
38  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
39  *
40  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
41  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
43  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
44  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
45  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
46  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
48  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
49  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
50  * SUCH DAMAGE.
51  *
52  * The licence and distribution terms for any publically available version or
53  * derivative of this code cannot be changed.  i.e. this code cannot simply be
54  * copied and put under another distribution licence
55  * [including the GNU Public Licence.]
56  */
57 /* ====================================================================
58  * Copyright (c) 1998-2006 The OpenSSL Project.  All rights reserved.
59  *
60  * Redistribution and use in source and binary forms, with or without
61  * modification, are permitted provided that the following conditions
62  * are met:
63  *
64  * 1. Redistributions of source code must retain the above copyright
65  *    notice, this list of conditions and the following disclaimer.
66  *
67  * 2. Redistributions in binary form must reproduce the above copyright
68  *    notice, this list of conditions and the following disclaimer in
69  *    the documentation and/or other materials provided with the
70  *    distribution.
71  *
72  * 3. All advertising materials mentioning features or use of this
73  *    software must display the following acknowledgment:
74  *    "This product includes software developed by the OpenSSL Project
75  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
76  *
77  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
78  *    endorse or promote products derived from this software without
79  *    prior written permission. For written permission, please contact
80  *    openssl-core@openssl.org.
81  *
82  * 5. Products derived from this software may not be called "OpenSSL"
83  *    nor may "OpenSSL" appear in their names without prior written
84  *    permission of the OpenSSL Project.
85  *
86  * 6. Redistributions of any form whatsoever must retain the following
87  *    acknowledgment:
88  *    "This product includes software developed by the OpenSSL Project
89  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
90  *
91  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
92  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
93  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
94  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
95  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
96  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
97  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
98  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
99  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
100  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
101  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
102  * OF THE POSSIBILITY OF SUCH DAMAGE.
103  * ====================================================================
104  *
105  * This product includes cryptographic software written by Eric Young
106  * (eay@cryptsoft.com).  This product includes software written by Tim
107  * Hudson (tjh@cryptsoft.com).
108  *
109  */
110 /* ====================================================================
111  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
112  *
113  * Portions of the attached software ("Contribution") are developed by
114  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
115  *
116  * The Contribution is licensed pursuant to the Eric Young open source
117  * license provided above.
118  *
119  * The binary polynomial arithmetic software is originally written by
120  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
121  * Laboratories. */
122 
123 #ifndef OPENSSL_HEADER_BN_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 numbers until you run out of memory.
140 
141 
142 // BN_ULONG is the native word size when working with big integers.
143 //
144 // Note: on some platforms, inttypes.h does not define print format macros in
145 // C++ unless |__STDC_FORMAT_MACROS| defined. This is due to text in C99 which
146 // was never adopted in any C++ standard and explicitly overruled in C++11. As
147 // this is a public header, bn.h does not define |__STDC_FORMAT_MACROS| itself.
148 // Projects which use |BN_*_FMT*| with outdated C headers may need to define it
149 // externally.
150 #if defined(OPENSSL_64_BIT)
151 #define BN_ULONG uint64_t
152 #define BN_BITS2 64
153 #define BN_DEC_FMT1 "%" PRIu64
154 #define BN_DEC_FMT2 "%019" PRIu64
155 #define BN_HEX_FMT1 "%" PRIx64
156 #define BN_HEX_FMT2 "%016" PRIx64
157 #elif defined(OPENSSL_32_BIT)
158 #define BN_ULONG uint32_t
159 #define BN_BITS2 32
160 #define BN_DEC_FMT1 "%" PRIu32
161 #define BN_DEC_FMT2 "%09" PRIu32
162 #define BN_HEX_FMT1 "%" PRIx32
163 #define BN_HEX_FMT2 "%08" PRIx32
164 #else
165 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
166 #endif
167 
168 
169 // Allocation and freeing.
170 
171 // BN_new creates a new, allocated BIGNUM and initialises it.
172 OPENSSL_EXPORT BIGNUM *BN_new(void);
173 
174 // BN_init initialises a stack allocated |BIGNUM|.
175 OPENSSL_EXPORT void BN_init(BIGNUM *bn);
176 
177 // BN_free frees the data referenced by |bn| and, if |bn| was originally
178 // allocated on the heap, frees |bn| also.
179 OPENSSL_EXPORT void BN_free(BIGNUM *bn);
180 
181 // BN_clear_free erases and frees the data referenced by |bn| and, if |bn| was
182 // originally allocated on the heap, frees |bn| also.
183 OPENSSL_EXPORT void BN_clear_free(BIGNUM *bn);
184 
185 // BN_dup allocates a new BIGNUM and sets it equal to |src|. It returns the
186 // allocated BIGNUM on success or NULL otherwise.
187 OPENSSL_EXPORT BIGNUM *BN_dup(const BIGNUM *src);
188 
189 // BN_copy sets |dest| equal to |src| and returns |dest| or NULL on allocation
190 // failure.
191 OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src);
192 
193 // BN_clear sets |bn| to zero and erases the old data.
194 OPENSSL_EXPORT void BN_clear(BIGNUM *bn);
195 
196 // BN_value_one returns a static BIGNUM with value 1.
197 OPENSSL_EXPORT const BIGNUM *BN_value_one(void);
198 
199 
200 // Basic functions.
201 
202 // BN_num_bits returns the minimum number of bits needed to represent the
203 // absolute value of |bn|.
204 OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn);
205 
206 // BN_num_bytes returns the minimum number of bytes needed to represent the
207 // absolute value of |bn|.
208 OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn);
209 
210 // BN_zero sets |bn| to zero.
211 OPENSSL_EXPORT void BN_zero(BIGNUM *bn);
212 
213 // BN_one sets |bn| to one. It returns one on success or zero on allocation
214 // failure.
215 OPENSSL_EXPORT int BN_one(BIGNUM *bn);
216 
217 // BN_set_word sets |bn| to |value|. It returns one on success or zero on
218 // allocation failure.
219 OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value);
220 
221 // BN_set_u64 sets |bn| to |value|. It returns one on success or zero on
222 // allocation failure.
223 OPENSSL_EXPORT int BN_set_u64(BIGNUM *bn, uint64_t value);
224 
225 // BN_set_negative sets the sign of |bn|.
226 OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign);
227 
228 // BN_is_negative returns one if |bn| is negative and zero otherwise.
229 OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn);
230 
231 
232 // Conversion functions.
233 
234 // BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as
235 // a big-endian number, and returns |ret|. If |ret| is NULL then a fresh
236 // |BIGNUM| is allocated and returned. It returns NULL on allocation
237 // failure.
238 OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret);
239 
240 // BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian
241 // integer, which must have |BN_num_bytes| of space available. It returns the
242 // number of bytes written. Note this function leaks the magnitude of |in|. If
243 // |in| is secret, use |BN_bn2bin_padded| instead.
244 OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out);
245 
246 // BN_le2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as
247 // a little-endian number, and returns |ret|. If |ret| is NULL then a fresh
248 // |BIGNUM| is allocated and returned. It returns NULL on allocation
249 // failure.
250 OPENSSL_EXPORT BIGNUM *BN_le2bn(const uint8_t *in, size_t len, BIGNUM *ret);
251 
252 // BN_bn2le_padded serialises the absolute value of |in| to |out| as a
253 // little-endian integer, which must have |len| of space available, padding
254 // out the remainder of out with zeros. If |len| is smaller than |BN_num_bytes|,
255 // the function fails and returns 0. Otherwise, it returns 1.
256 OPENSSL_EXPORT int BN_bn2le_padded(uint8_t *out, size_t len, const BIGNUM *in);
257 
258 // BN_bn2bin_padded serialises the absolute value of |in| to |out| as a
259 // big-endian integer. The integer is padded with leading zeros up to size
260 // |len|. If |len| is smaller than |BN_num_bytes|, the function fails and
261 // returns 0. Otherwise, it returns 1.
262 OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in);
263 
264 // BN_bn2cbb_padded behaves like |BN_bn2bin_padded| but writes to a |CBB|.
265 OPENSSL_EXPORT int BN_bn2cbb_padded(CBB *out, size_t len, const BIGNUM *in);
266 
267 // BN_bn2hex returns an allocated string that contains a NUL-terminated, hex
268 // representation of |bn|. If |bn| is negative, the first char in the resulting
269 // string will be '-'. Returns NULL on allocation failure.
270 OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn);
271 
272 // BN_hex2bn parses the leading hex number from |in|, which may be proceeded by
273 // a '-' to indicate a negative number and may contain trailing, non-hex data.
274 // If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and
275 // stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and
276 // updates |*outp|. It returns the number of bytes of |in| processed or zero on
277 // error.
278 OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in);
279 
280 // BN_bn2dec returns an allocated string that contains a NUL-terminated,
281 // decimal representation of |bn|. If |bn| is negative, the first char in the
282 // resulting string will be '-'. Returns NULL on allocation failure.
283 OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a);
284 
285 // BN_dec2bn parses the leading decimal number from |in|, which may be
286 // proceeded by a '-' to indicate a negative number and may contain trailing,
287 // non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the
288 // decimal number and stores it in |*outp|. If |*outp| is NULL then it
289 // allocates a new BIGNUM and updates |*outp|. It returns the number of bytes
290 // of |in| processed or zero on error.
291 OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in);
292 
293 // BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in|
294 // begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A
295 // leading '-' is still permitted and comes before the optional 0X/0x. It
296 // returns one on success or zero on error.
297 OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in);
298 
299 // BN_print writes a hex encoding of |a| to |bio|. It returns one on success
300 // and zero on error.
301 OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a);
302 
303 // BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first.
304 OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a);
305 
306 // BN_get_word returns the absolute value of |bn| as a single word. If |bn| is
307 // too large to be represented as a single word, the maximum possible value
308 // will be returned.
309 OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn);
310 
311 // BN_get_u64 sets |*out| to the absolute value of |bn| as a |uint64_t| and
312 // returns one. If |bn| is too large to be represented as a |uint64_t|, it
313 // returns zero.
314 OPENSSL_EXPORT int BN_get_u64(const BIGNUM *bn, uint64_t *out);
315 
316 
317 // ASN.1 functions.
318 
319 // BN_parse_asn1_unsigned parses a non-negative DER INTEGER from |cbs| writes
320 // the result to |ret|. It returns one on success and zero on failure.
321 OPENSSL_EXPORT int BN_parse_asn1_unsigned(CBS *cbs, BIGNUM *ret);
322 
323 // BN_marshal_asn1 marshals |bn| as a non-negative DER INTEGER and appends the
324 // result to |cbb|. It returns one on success and zero on failure.
325 OPENSSL_EXPORT int BN_marshal_asn1(CBB *cbb, const BIGNUM *bn);
326 
327 
328 // BIGNUM pools.
329 //
330 // Certain BIGNUM operations need to use many temporary variables and
331 // allocating and freeing them can be quite slow. Thus such operations typically
332 // take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx|
333 // argument to a public function may be NULL, in which case a local |BN_CTX|
334 // will be created just for the lifetime of that call.
335 //
336 // A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called
337 // repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made
338 // before calling any other functions that use the |ctx| as an argument.
339 //
340 // Finally, |BN_CTX_end| must be called before returning from the function.
341 // When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from
342 // |BN_CTX_get| become invalid.
343 
344 // BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure.
345 OPENSSL_EXPORT BN_CTX *BN_CTX_new(void);
346 
347 // BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx|
348 // itself.
349 OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx);
350 
351 // BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future
352 // calls to |BN_CTX_get|.
353 OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx);
354 
355 // BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once
356 // |BN_CTX_get| has returned NULL, all future calls will also return NULL until
357 // |BN_CTX_end| is called.
358 OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx);
359 
360 // BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the
361 // matching |BN_CTX_start| call.
362 OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx);
363 
364 
365 // Simple arithmetic
366 
367 // BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a|
368 // or |b|. It returns one on success and zero on allocation failure.
369 OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
370 
371 // BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may
372 // be the same pointer as either |a| or |b|. It returns one on success and zero
373 // on allocation failure.
374 OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
375 
376 // BN_add_word adds |w| to |a|. It returns one on success and zero otherwise.
377 OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w);
378 
379 // BN_sub sets |r| = |a| - |b|, where |r| may be the same pointer as either |a|
380 // or |b|. It returns one on success and zero on allocation failure.
381 OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
382 
383 // BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers,
384 // |b| < |a| and |r| may be the same pointer as either |a| or |b|. It returns
385 // one on success and zero on allocation failure.
386 OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
387 
388 // BN_sub_word subtracts |w| from |a|. It returns one on success and zero on
389 // allocation failure.
390 OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w);
391 
392 // BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or
393 // |b|. Returns one on success and zero otherwise.
394 OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
395                           BN_CTX *ctx);
396 
397 // BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on
398 // allocation failure.
399 OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w);
400 
401 // BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as
402 // |a|. Returns one on success and zero otherwise. This is more efficient than
403 // BN_mul(r, a, a, ctx).
404 OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
405 
406 // BN_div divides |numerator| by |divisor| and places the result in |quotient|
407 // and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in
408 // which case the respective value is not returned. The result is rounded
409 // towards zero; thus if |numerator| is negative, the remainder will be zero or
410 // negative. It returns one on success or zero on error.
411 OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem,
412                           const BIGNUM *numerator, const BIGNUM *divisor,
413                           BN_CTX *ctx);
414 
415 // BN_div_word sets |numerator| = |numerator|/|divisor| and returns the
416 // remainder or (BN_ULONG)-1 on error.
417 OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor);
418 
419 // BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the
420 // square root of |in|, using |ctx|. It returns one on success or zero on
421 // error. Negative numbers and non-square numbers will result in an error with
422 // appropriate errors on the error queue.
423 OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx);
424 
425 
426 // Comparison functions
427 
428 // BN_cmp returns a value less than, equal to or greater than zero if |a| is
429 // less than, equal to or greater than |b|, respectively.
430 OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b);
431 
432 // BN_cmp_word is like |BN_cmp| except it takes its second argument as a
433 // |BN_ULONG| instead of a |BIGNUM|.
434 OPENSSL_EXPORT int BN_cmp_word(const BIGNUM *a, BN_ULONG b);
435 
436 // BN_ucmp returns a value less than, equal to or greater than zero if the
437 // absolute value of |a| is less than, equal to or greater than the absolute
438 // value of |b|, respectively.
439 OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
440 
441 // BN_equal_consttime returns one if |a| is equal to |b|, and zero otherwise.
442 // It takes an amount of time dependent on the sizes of |a| and |b|, but
443 // independent of the contents (including the signs) of |a| and |b|.
444 OPENSSL_EXPORT int BN_equal_consttime(const BIGNUM *a, const BIGNUM *b);
445 
446 // BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero
447 // otherwise.
448 OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w);
449 
450 // BN_is_zero returns one if |bn| is zero and zero otherwise.
451 OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn);
452 
453 // BN_is_one returns one if |bn| equals one and zero otherwise.
454 OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn);
455 
456 // BN_is_word returns one if |bn| is exactly |w| and zero otherwise.
457 OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w);
458 
459 // BN_is_odd returns one if |bn| is odd and zero otherwise.
460 OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn);
461 
462 // BN_is_pow2 returns 1 if |a| is a power of two, and 0 otherwise.
463 OPENSSL_EXPORT int BN_is_pow2(const BIGNUM *a);
464 
465 
466 // Bitwise operations.
467 
468 // BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the
469 // same |BIGNUM|. It returns one on success and zero on allocation failure.
470 OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
471 
472 // BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same
473 // pointer. It returns one on success and zero on allocation failure.
474 OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a);
475 
476 // BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same
477 // pointer. It returns one on success and zero on allocation failure.
478 OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
479 
480 // BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same
481 // pointer. It returns one on success and zero on allocation failure.
482 OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a);
483 
484 // BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a|
485 // is 2 then setting bit zero will make it 3. It returns one on success or zero
486 // on allocation failure.
487 OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n);
488 
489 // BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if
490 // |a| is 3, clearing bit zero will make it two. It returns one on success or
491 // zero on allocation failure.
492 OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n);
493 
494 // BN_is_bit_set returns one if the |n|th least-significant bit in |a| exists
495 // and is set. Otherwise, it returns zero.
496 OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n);
497 
498 // BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one
499 // on success or zero if |n| is negative.
500 //
501 // This differs from OpenSSL which additionally returns zero if |a|'s word
502 // length is less than or equal to |n|, rounded down to a number of words. Note
503 // word size is platform-dependent, so this behavior is also difficult to rely
504 // on in OpenSSL and not very useful.
505 OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n);
506 
507 // BN_count_low_zero_bits returns the number of low-order zero bits in |bn|, or
508 // the number of factors of two which divide it. It returns zero if |bn| is
509 // zero.
510 OPENSSL_EXPORT int BN_count_low_zero_bits(const BIGNUM *bn);
511 
512 
513 // Modulo arithmetic.
514 
515 // BN_mod_word returns |a| mod |w| or (BN_ULONG)-1 on error.
516 OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
517 
518 // BN_mod_pow2 sets |r| = |a| mod 2^|e|. It returns 1 on success and
519 // 0 on error.
520 OPENSSL_EXPORT int BN_mod_pow2(BIGNUM *r, const BIGNUM *a, size_t e);
521 
522 // BN_nnmod_pow2 sets |r| = |a| mod 2^|e| where |r| is always positive.
523 // It returns 1 on success and 0 on error.
524 OPENSSL_EXPORT int BN_nnmod_pow2(BIGNUM *r, const BIGNUM *a, size_t e);
525 
526 // BN_mod is a helper macro that calls |BN_div| and discards the quotient.
527 #define BN_mod(rem, numerator, divisor, ctx) \
528   BN_div(NULL, (rem), (numerator), (divisor), (ctx))
529 
530 // BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <=
531 // |rem| < |divisor| is always true. It returns one on success and zero on
532 // error.
533 OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator,
534                             const BIGNUM *divisor, BN_CTX *ctx);
535 
536 // BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero
537 // on error.
538 OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
539                               const BIGNUM *m, BN_CTX *ctx);
540 
541 // BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be
542 // non-negative and less than |m|.
543 OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
544                                     const BIGNUM *m);
545 
546 // BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero
547 // on error.
548 OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
549                               const BIGNUM *m, BN_CTX *ctx);
550 
551 // BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be
552 // non-negative and less than |m|.
553 OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
554                                     const BIGNUM *m);
555 
556 // BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero
557 // on error.
558 OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
559                               const BIGNUM *m, BN_CTX *ctx);
560 
561 // BN_mod_sqr sets |r| = |a|^2 mod |m|. It returns one on success and zero
562 // on error.
563 OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
564                               BN_CTX *ctx);
565 
566 // BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the
567 // same pointer. It returns one on success and zero on error.
568 OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n,
569                                  const BIGNUM *m, BN_CTX *ctx);
570 
571 // BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be
572 // non-negative and less than |m|.
573 OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n,
574                                        const BIGNUM *m);
575 
576 // BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the
577 // same pointer. It returns one on success and zero on error.
578 OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
579                                   BN_CTX *ctx);
580 
581 // BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be
582 // non-negative and less than |m|.
583 OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a,
584                                         const BIGNUM *m);
585 
586 // BN_mod_sqrt returns a newly-allocated |BIGNUM|, r, such that
587 // r^2 == a (mod p). |p| must be a prime. It returns NULL on error or if |a| is
588 // not a square mod |p|. In the latter case, it will add |BN_R_NOT_A_SQUARE| to
589 // the error queue.
590 OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p,
591                                    BN_CTX *ctx);
592 
593 
594 // Random and prime number generation.
595 
596 // The following are values for the |top| parameter of |BN_rand|.
597 #define BN_RAND_TOP_ANY    (-1)
598 #define BN_RAND_TOP_ONE     0
599 #define BN_RAND_TOP_TWO     1
600 
601 // The following are values for the |bottom| parameter of |BN_rand|.
602 #define BN_RAND_BOTTOM_ANY  0
603 #define BN_RAND_BOTTOM_ODD  1
604 
605 // BN_rand sets |rnd| to a random number of length |bits|. It returns one on
606 // success and zero otherwise.
607 //
608 // |top| must be one of the |BN_RAND_TOP_*| values. If |BN_RAND_TOP_ONE|, the
609 // most-significant bit, if any, will be set. If |BN_RAND_TOP_TWO|, the two
610 // most significant bits, if any, will be set. If |BN_RAND_TOP_ANY|, no extra
611 // action will be taken and |BN_num_bits(rnd)| may not equal |bits| if the most
612 // significant bits randomly ended up as zeros.
613 //
614 // |bottom| must be one of the |BN_RAND_BOTTOM_*| values. If
615 // |BN_RAND_BOTTOM_ODD|, the least-significant bit, if any, will be set. If
616 // |BN_RAND_BOTTOM_ANY|, no extra action will be taken.
617 OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
618 
619 // BN_pseudo_rand is an alias for |BN_rand|.
620 OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
621 
622 // BN_rand_range is equivalent to |BN_rand_range_ex| with |min_inclusive| set
623 // to zero and |max_exclusive| set to |range|.
624 OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
625 
626 // BN_rand_range_ex sets |rnd| to a random value in
627 // [min_inclusive..max_exclusive). It returns one on success and zero
628 // otherwise.
629 OPENSSL_EXPORT int BN_rand_range_ex(BIGNUM *r, BN_ULONG min_inclusive,
630                                     const BIGNUM *max_exclusive);
631 
632 // BN_pseudo_rand_range is an alias for BN_rand_range.
633 OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
634 
635 #define BN_GENCB_GENERATED 0
636 #define BN_GENCB_PRIME_TEST 1
637 
638 // bn_gencb_st, or |BN_GENCB|, holds a callback function that is used by
639 // generation functions that can take a very long time to complete. Use
640 // |BN_GENCB_set| to initialise a |BN_GENCB| structure.
641 //
642 // The callback receives the address of that |BN_GENCB| structure as its last
643 // argument and the user is free to put an arbitrary pointer in |arg|. The other
644 // arguments are set as follows:
645 //   event=BN_GENCB_GENERATED, n=i:   after generating the i'th possible prime
646 //                                    number.
647 //   event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality
648 //                                    checks.
649 //   event=BN_GENCB_PRIME_TEST, n=i:  when the i'th primality test has finished.
650 //
651 // The callback can return zero to abort the generation progress or one to
652 // allow it to continue.
653 //
654 // When other code needs to call a BN generation function it will often take a
655 // BN_GENCB argument and may call the function with other argument values.
656 struct bn_gencb_st {
657   void *arg;        // callback-specific data
658   int (*callback)(int event, int n, struct bn_gencb_st *);
659 };
660 
661 // BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to
662 // |arg|.
663 OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback,
664                                  int (*f)(int event, int n, BN_GENCB *),
665                                  void *arg);
666 
667 // BN_GENCB_call calls |callback|, if not NULL, and returns the return value of
668 // the callback, or 1 if |callback| is NULL.
669 OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n);
670 
671 // BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe
672 // is non-zero then the prime will be such that (ret-1)/2 is also a prime.
673 // (This is needed for Diffie-Hellman groups to ensure that the only subgroups
674 // are of size 2 and (p-1)/2.).
675 //
676 // If |add| is not NULL, the prime will fulfill the condition |ret| % |add| ==
677 // |rem| in order to suit a given generator. (If |rem| is NULL then |ret| %
678 // |add| == 1.)
679 //
680 // If |cb| is not NULL, it will be called during processing to give an
681 // indication of progress. See the comments for |BN_GENCB|. It returns one on
682 // success and zero otherwise.
683 OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
684                                         const BIGNUM *add, const BIGNUM *rem,
685                                         BN_GENCB *cb);
686 
687 // BN_prime_checks is magic value that can be used as the |checks| argument to
688 // the primality testing functions in order to automatically select a number of
689 // Miller-Rabin checks that gives a false positive rate of ~2^{-80}.
690 #define BN_prime_checks 0
691 
692 // bn_primality_result_t enumerates the outcomes of primality-testing.
693 enum bn_primality_result_t {
694   bn_probably_prime,
695   bn_composite,
696   bn_non_prime_power_composite,
697 };
698 
699 // BN_enhanced_miller_rabin_primality_test tests whether |w| is probably a prime
700 // number using the Enhanced Miller-Rabin Test (FIPS 186-4 C.3.2) with
701 // |iterations| iterations and returns the result in |out_result|. Enhanced
702 // Miller-Rabin tests primality for odd integers greater than 3, returning
703 // |bn_probably_prime| if the number is probably prime,
704 // |bn_non_prime_power_composite| if the number is a composite that is not the
705 // power of a single prime, and |bn_composite| otherwise. It returns one on
706 // success and zero on failure. If |cb| is not NULL, then it is called during
707 // each iteration of the primality test.
708 //
709 // If |iterations| is |BN_prime_checks|, then a value that results in a false
710 // positive rate lower than the number-field sieve security level of |w| is
711 // used, provided |w| was generated randomly. |BN_prime_checks| is not suitable
712 // for inputs potentially crafted by an adversary.
713 OPENSSL_EXPORT int BN_enhanced_miller_rabin_primality_test(
714     enum bn_primality_result_t *out_result, const BIGNUM *w, int iterations,
715     BN_CTX *ctx, BN_GENCB *cb);
716 
717 // BN_primality_test sets |*is_probably_prime| to one if |candidate| is
718 // probably a prime number by the Miller-Rabin test or zero if it's certainly
719 // not.
720 //
721 // If |do_trial_division| is non-zero then |candidate| will be tested against a
722 // list of small primes before Miller-Rabin tests. The probability of this
723 // function returning a false positive is 2^{2*checks}. If |checks| is
724 // |BN_prime_checks| then a value that results in a false positive rate lower
725 // than the number-field sieve security level of |candidate| is used, provided
726 // |candidate| was generated randomly. |BN_prime_checks| is not suitable for
727 // inputs potentially crafted by an adversary.
728 //
729 // If |cb| is not NULL then it is called during the checking process. See the
730 // comment above |BN_GENCB|.
731 //
732 // The function returns one on success and zero on error.
733 OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime,
734                                      const BIGNUM *candidate, int checks,
735                                      BN_CTX *ctx, int do_trial_division,
736                                      BN_GENCB *cb);
737 
738 // BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime
739 // number by the Miller-Rabin test, zero if it's certainly not and -1 on error.
740 //
741 // If |do_trial_division| is non-zero then |candidate| will be tested against a
742 // list of small primes before Miller-Rabin tests. The probability of this
743 // function returning one when |candidate| is composite is 2^{2*checks}. If
744 // |checks| is |BN_prime_checks| then a value that results in a false positive
745 // rate lower than the number-field sieve security level of |candidate| is used,
746 // provided |candidate| was generated randomly. |BN_prime_checks| is not
747 // suitable for inputs potentially crafted by an adversary.
748 //
749 // If |cb| is not NULL then it is called during the checking process. See the
750 // comment above |BN_GENCB|.
751 //
752 // WARNING: deprecated. Use |BN_primality_test|.
753 OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks,
754                                            BN_CTX *ctx, int do_trial_division,
755                                            BN_GENCB *cb);
756 
757 // BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with
758 // |do_trial_division| set to zero.
759 //
760 // WARNING: deprecated: Use |BN_primality_test|.
761 OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks,
762                                   BN_CTX *ctx, BN_GENCB *cb);
763 
764 
765 // Number theory functions
766 
767 // BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero
768 // otherwise.
769 OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
770                           BN_CTX *ctx);
771 
772 // BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If |out| is NULL, a
773 // fresh BIGNUM is allocated. It returns the result or NULL on error.
774 //
775 // If |n| is even then the operation is performed using an algorithm that avoids
776 // some branches but which isn't constant-time. This function shouldn't be used
777 // for secret values; use |BN_mod_inverse_blinded| instead. Or, if |n| is
778 // guaranteed to be prime, use
779 // |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking
780 // advantage of Fermat's Little Theorem.
781 OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a,
782                                       const BIGNUM *n, BN_CTX *ctx);
783 
784 // BN_mod_inverse_blinded sets |out| equal to |a|^-1, mod |n|, where |n| is the
785 // Montgomery modulus for |mont|. |a| must be non-negative and must be less
786 // than |n|. |n| must be greater than 1. |a| is blinded (masked by a random
787 // value) to protect it against side-channel attacks. On failure, if the failure
788 // was caused by |a| having no inverse mod |n| then |*out_no_inverse| will be
789 // set to one; otherwise it will be set to zero.
790 //
791 // Note this function may incorrectly report |a| has no inverse if the random
792 // blinding value has no inverse. It should only be used when |n| has few
793 // non-invertible elements, such as an RSA modulus.
794 int BN_mod_inverse_blinded(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
795                            const BN_MONT_CTX *mont, BN_CTX *ctx);
796 
797 // BN_mod_inverse_odd sets |out| equal to |a|^-1, mod |n|. |a| must be
798 // non-negative and must be less than |n|. |n| must be odd. This function
799 // shouldn't be used for secret values; use |BN_mod_inverse_blinded| instead.
800 // Or, if |n| is guaranteed to be prime, use
801 // |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking
802 // advantage of Fermat's Little Theorem. It returns one on success or zero on
803 // failure. On failure, if the failure was caused by |a| having no inverse mod
804 // |n| then |*out_no_inverse| will be set to one; otherwise it will be set to
805 // zero.
806 int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
807                        const BIGNUM *n, BN_CTX *ctx);
808 
809 
810 // Montgomery arithmetic.
811 
812 // BN_MONT_CTX contains the precomputed values needed to work in a specific
813 // Montgomery domain.
814 
815 // BN_MONT_CTX_new_for_modulus returns a fresh |BN_MONT_CTX| given the modulus,
816 // |mod| or NULL on error. Note this function assumes |mod| is public.
817 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod,
818                                                         BN_CTX *ctx);
819 
820 // BN_MONT_CTX_new_consttime behaves like |BN_MONT_CTX_new_for_modulus| but
821 // treats |mod| as secret.
822 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new_consttime(const BIGNUM *mod,
823                                                       BN_CTX *ctx);
824 
825 // BN_MONT_CTX_free frees memory associated with |mont|.
826 OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont);
827 
828 // BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or
829 // NULL on error.
830 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,
831                                              const BN_MONT_CTX *from);
832 
833 // BN_MONT_CTX_set_locked takes |lock| and checks whether |*pmont| is NULL. If
834 // so, it creates a new |BN_MONT_CTX| and sets the modulus for it to |mod|. It
835 // then stores it as |*pmont|. It returns one on success and zero on error. Note
836 // this function assumes |mod| is public.
837 //
838 // If |*pmont| is already non-NULL then it does nothing and returns one.
839 int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
840                            const BIGNUM *mod, BN_CTX *bn_ctx);
841 
842 // BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. |a| is
843 // assumed to be in the range [0, n), where |n| is the Montgomery modulus. It
844 // returns one on success or zero on error.
845 OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a,
846                                     const BN_MONT_CTX *mont, BN_CTX *ctx);
847 
848 // BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values out
849 // of the Montgomery domain. |a| is assumed to be in the range [0, n), where |n|
850 // is the Montgomery modulus. It returns one on success or zero on error.
851 OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a,
852                                       const BN_MONT_CTX *mont, BN_CTX *ctx);
853 
854 // BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain.
855 // Both |a| and |b| must already be in the Montgomery domain (by
856 // |BN_to_montgomery|). In particular, |a| and |b| are assumed to be in the
857 // range [0, n), where |n| is the Montgomery modulus. It returns one on success
858 // or zero on error.
859 OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a,
860                                          const BIGNUM *b,
861                                          const BN_MONT_CTX *mont, BN_CTX *ctx);
862 
863 
864 // Exponentiation.
865 
866 // BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply
867 // algorithm that leaks side-channel information. It returns one on success or
868 // zero otherwise.
869 OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
870                           BN_CTX *ctx);
871 
872 // BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best
873 // algorithm for the values provided. It returns one on success or zero
874 // otherwise. The |BN_mod_exp_mont_consttime| variant must be used if the
875 // exponent is secret.
876 OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
877                               const BIGNUM *m, BN_CTX *ctx);
878 
879 // BN_mod_exp_mont behaves like |BN_mod_exp| but treats |a| as secret and
880 // requires 0 <= |a| < |m|.
881 OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
882                                    const BIGNUM *m, BN_CTX *ctx,
883                                    const BN_MONT_CTX *mont);
884 
885 // BN_mod_exp_mont_consttime behaves like |BN_mod_exp| but treats |a|, |p|, and
886 // |m| as secret and requires 0 <= |a| < |m|.
887 OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a,
888                                              const BIGNUM *p, const BIGNUM *m,
889                                              BN_CTX *ctx,
890                                              const BN_MONT_CTX *mont);
891 
892 
893 // Deprecated functions
894 
895 // BN_bn2mpi serialises the value of |in| to |out|, using a format that consists
896 // of the number's length in bytes represented as a 4-byte big-endian number,
897 // and the number itself in big-endian format, where the most significant bit
898 // signals a negative number. (The representation of numbers with the MSB set is
899 // prefixed with null byte). |out| must have sufficient space available; to
900 // find the needed amount of space, call the function with |out| set to NULL.
901 OPENSSL_EXPORT size_t BN_bn2mpi(const BIGNUM *in, uint8_t *out);
902 
903 // BN_mpi2bn parses |len| bytes from |in| and returns the resulting value. The
904 // bytes at |in| are expected to be in the format emitted by |BN_bn2mpi|.
905 //
906 // If |out| is NULL then a fresh |BIGNUM| is allocated and returned, otherwise
907 // |out| is reused and returned. On error, NULL is returned and the error queue
908 // is updated.
909 OPENSSL_EXPORT BIGNUM *BN_mpi2bn(const uint8_t *in, size_t len, BIGNUM *out);
910 
911 // BN_mod_exp_mont_word is like |BN_mod_exp_mont| except that the base |a| is
912 // given as a |BN_ULONG| instead of a |BIGNUM *|. It returns one on success
913 // or zero otherwise.
914 OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
915                                         const BIGNUM *m, BN_CTX *ctx,
916                                         const BN_MONT_CTX *mont);
917 
918 // BN_mod_exp2_mont calculates (a1^p1) * (a2^p2) mod m. It returns 1 on success
919 // or zero otherwise.
920 OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1,
921                                     const BIGNUM *p1, const BIGNUM *a2,
922                                     const BIGNUM *p2, const BIGNUM *m,
923                                     BN_CTX *ctx, const BN_MONT_CTX *mont);
924 
925 // BN_MONT_CTX_new returns a fresh |BN_MONT_CTX| or NULL on allocation failure.
926 // Use |BN_MONT_CTX_new_for_modulus| instead.
927 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void);
928 
929 // BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It
930 // returns one on success and zero on error. Use |BN_MONT_CTX_new_for_modulus|
931 // instead.
932 OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod,
933                                    BN_CTX *ctx);
934 
935 // BN_bn2binpad behaves like |BN_bn2bin_padded|, but it returns |len| on success
936 // and -1 on error.
937 //
938 // Use |BN_bn2bin_padded| instead. It is |size_t|-clean.
939 OPENSSL_EXPORT int BN_bn2binpad(const BIGNUM *in, uint8_t *out, int len);
940 
941 
942 // Private functions
943 
944 struct bignum_st {
945   // d is a pointer to an array of |width| |BN_BITS2|-bit chunks in
946   // little-endian order. This stores the absolute value of the number.
947   BN_ULONG *d;
948   // width is the number of elements of |d| which are valid. This value is not
949   // necessarily minimal; the most-significant words of |d| may be zero.
950   // |width| determines a potentially loose upper-bound on the absolute value
951   // of the |BIGNUM|.
952   //
953   // Functions taking |BIGNUM| inputs must compute the same answer for all
954   // possible widths. |bn_minimal_width|, |bn_set_minimal_width|, and other
955   // helpers may be used to recover the minimal width, provided it is not
956   // secret. If it is secret, use a different algorithm. Functions may output
957   // minimal or non-minimal |BIGNUM|s depending on secrecy requirements, but
958   // those which cause widths to unboundedly grow beyond the minimal value
959   // should be documented such.
960   //
961   // Note this is different from historical |BIGNUM| semantics.
962   int width;
963   // dmax is number of elements of |d| which are allocated.
964   int dmax;
965   // neg is one if the number if negative and zero otherwise.
966   int neg;
967   // flags is a bitmask of |BN_FLG_*| values
968   int flags;
969 };
970 
971 struct bn_mont_ctx_st {
972   // RR is R^2, reduced modulo |N|. It is used to convert to Montgomery form. It
973   // is guaranteed to have the same width as |N|.
974   BIGNUM RR;
975   // N is the modulus. It is always stored in minimal form, so |N.width|
976   // determines R.
977   BIGNUM N;
978   BN_ULONG n0[2];  // least significant words of (R*Ri-1)/N
979 };
980 
981 OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l);
982 
983 #define BN_FLG_MALLOCED 0x01
984 #define BN_FLG_STATIC_DATA 0x02
985 // |BN_FLG_CONSTTIME| has been removed and intentionally omitted so code relying
986 // on it will not compile. Consumers outside BoringSSL should use the
987 // higher-level cryptographic algorithms exposed by other modules. Consumers
988 // within the library should call the appropriate timing-sensitive algorithm
989 // directly.
990 
991 
992 #if defined(__cplusplus)
993 }  // extern C
994 
995 #if !defined(BORINGSSL_NO_CXX)
996 extern "C++" {
997 
998 BSSL_NAMESPACE_BEGIN
999 
BORINGSSL_MAKE_DELETER(BIGNUM,BN_free)1000 BORINGSSL_MAKE_DELETER(BIGNUM, BN_free)
1001 BORINGSSL_MAKE_DELETER(BN_CTX, BN_CTX_free)
1002 BORINGSSL_MAKE_DELETER(BN_MONT_CTX, BN_MONT_CTX_free)
1003 
1004 class BN_CTXScope {
1005  public:
1006   BN_CTXScope(BN_CTX *ctx) : ctx_(ctx) { BN_CTX_start(ctx_); }
1007   ~BN_CTXScope() { BN_CTX_end(ctx_); }
1008 
1009  private:
1010   BN_CTX *ctx_;
1011 
1012   BN_CTXScope(BN_CTXScope &) = delete;
1013   BN_CTXScope &operator=(BN_CTXScope &) = delete;
1014 };
1015 
1016 BSSL_NAMESPACE_END
1017 
1018 }  // extern C++
1019 #endif
1020 
1021 #endif
1022 
1023 #define BN_R_ARG2_LT_ARG3 100
1024 #define BN_R_BAD_RECIPROCAL 101
1025 #define BN_R_BIGNUM_TOO_LONG 102
1026 #define BN_R_BITS_TOO_SMALL 103
1027 #define BN_R_CALLED_WITH_EVEN_MODULUS 104
1028 #define BN_R_DIV_BY_ZERO 105
1029 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 106
1030 #define BN_R_INPUT_NOT_REDUCED 107
1031 #define BN_R_INVALID_RANGE 108
1032 #define BN_R_NEGATIVE_NUMBER 109
1033 #define BN_R_NOT_A_SQUARE 110
1034 #define BN_R_NOT_INITIALIZED 111
1035 #define BN_R_NO_INVERSE 112
1036 #define BN_R_PRIVATE_KEY_TOO_LARGE 113
1037 #define BN_R_P_IS_NOT_PRIME 114
1038 #define BN_R_TOO_MANY_ITERATIONS 115
1039 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 116
1040 #define BN_R_BAD_ENCODING 117
1041 #define BN_R_ENCODE_ERROR 118
1042 #define BN_R_INVALID_INPUT 119
1043 
1044 #endif  // OPENSSL_HEADER_BN_H
1045