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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. As this is a public header, bn.h
146  * does not define |__STDC_FORMAT_MACROS| itself. C++ source files which use the
147  * FMT macros must define it externally. */
148 #if defined(OPENSSL_64_BIT)
149 #define BN_ULONG uint64_t
150 #define BN_BITS2 64
151 #define BN_DEC_FMT1 "%" PRIu64
152 #define BN_DEC_FMT2 "%019" PRIu64
153 #define BN_HEX_FMT1 "%" PRIx64
154 #define BN_HEX_FMT2 "%016" PRIx64
155 #elif defined(OPENSSL_32_BIT)
156 #define BN_ULONG uint32_t
157 #define BN_BITS2 32
158 #define BN_DEC_FMT1 "%" PRIu32
159 #define BN_DEC_FMT2 "%09" PRIu32
160 #define BN_HEX_FMT1 "%" PRIx32
161 #define BN_HEX_FMT2 "%08" PRIx64
162 #else
163 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
164 #endif
165 
166 
167 /* Allocation and freeing. */
168 
169 /* BN_new creates a new, allocated BIGNUM and initialises it. */
170 OPENSSL_EXPORT BIGNUM *BN_new(void);
171 
172 /* BN_init initialises a stack allocated |BIGNUM|. */
173 OPENSSL_EXPORT void BN_init(BIGNUM *bn);
174 
175 /* BN_free frees the data referenced by |bn| and, if |bn| was originally
176  * allocated on the heap, frees |bn| also. */
177 OPENSSL_EXPORT void BN_free(BIGNUM *bn);
178 
179 /* BN_clear_free erases and frees the data referenced by |bn| and, if |bn| was
180  * originally allocated on the heap, frees |bn| also. */
181 OPENSSL_EXPORT void BN_clear_free(BIGNUM *bn);
182 
183 /* BN_dup allocates a new BIGNUM and sets it equal to |src|. It returns the
184  * allocated BIGNUM on success or NULL otherwise. */
185 OPENSSL_EXPORT BIGNUM *BN_dup(const BIGNUM *src);
186 
187 /* BN_copy sets |dest| equal to |src| and returns |dest| or NULL on allocation
188  * failure. */
189 OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src);
190 
191 /* BN_clear sets |bn| to zero and erases the old data. */
192 OPENSSL_EXPORT void BN_clear(BIGNUM *bn);
193 
194 /* BN_value_one returns a static BIGNUM with value 1. */
195 OPENSSL_EXPORT const BIGNUM *BN_value_one(void);
196 
197 
198 /* Basic functions. */
199 
200 /* BN_num_bits returns the minimum number of bits needed to represent the
201  * absolute value of |bn|. */
202 OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn);
203 
204 /* BN_num_bytes returns the minimum number of bytes needed to represent the
205  * absolute value of |bn|. */
206 OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn);
207 
208 /* BN_zero sets |bn| to zero. */
209 OPENSSL_EXPORT void BN_zero(BIGNUM *bn);
210 
211 /* BN_one sets |bn| to one. It returns one on success or zero on allocation
212  * failure. */
213 OPENSSL_EXPORT int BN_one(BIGNUM *bn);
214 
215 /* BN_set_word sets |bn| to |value|. It returns one on success or zero on
216  * allocation failure. */
217 OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value);
218 
219 /* BN_set_u64 sets |bn| to |value|. It returns one on success or zero on
220  * allocation failure. */
221 OPENSSL_EXPORT int BN_set_u64(BIGNUM *bn, uint64_t value);
222 
223 /* BN_set_negative sets the sign of |bn|. */
224 OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign);
225 
226 /* BN_is_negative returns one if |bn| is negative and zero otherwise. */
227 OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn);
228 
229 
230 /* Conversion functions. */
231 
232 /* BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as
233  * a big-endian number, and returns |ret|. If |ret| is NULL then a fresh
234  * |BIGNUM| is allocated and returned. It returns NULL on allocation
235  * failure. */
236 OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret);
237 
238 /* BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian
239  * integer, which must have |BN_num_bytes| of space available. It returns the
240  * number of bytes written. */
241 OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out);
242 
243 /* BN_le2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as
244  * a little-endian number, and returns |ret|. If |ret| is NULL then a fresh
245  * |BIGNUM| is allocated and returned. It returns NULL on allocation
246  * failure. */
247 OPENSSL_EXPORT BIGNUM *BN_le2bn(const uint8_t *in, size_t len, BIGNUM *ret);
248 
249 /* BN_bn2le_padded serialises the absolute value of |in| to |out| as a
250  * little-endian integer, which must have |len| of space available, padding
251  * out the remainder of out with zeros. If |len| is smaller than |BN_num_bytes|,
252  * the function fails and returns 0. Otherwise, it returns 1. */
253 OPENSSL_EXPORT int BN_bn2le_padded(uint8_t *out, size_t len, const BIGNUM *in);
254 
255 /* BN_bn2bin_padded serialises the absolute value of |in| to |out| as a
256  * big-endian integer. The integer is padded with leading zeros up to size
257  * |len|. If |len| is smaller than |BN_num_bytes|, the function fails and
258  * returns 0. Otherwise, it returns 1. */
259 OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in);
260 
261 /* BN_bn2cbb_padded behaves like |BN_bn2bin_padded| but writes to a |CBB|. */
262 OPENSSL_EXPORT int BN_bn2cbb_padded(CBB *out, size_t len, const BIGNUM *in);
263 
264 /* BN_bn2hex returns an allocated string that contains a NUL-terminated, hex
265  * representation of |bn|. If |bn| is negative, the first char in the resulting
266  * string will be '-'. Returns NULL on allocation failure. */
267 OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn);
268 
269 /* BN_hex2bn parses the leading hex number from |in|, which may be proceeded by
270  * a '-' to indicate a negative number and may contain trailing, non-hex data.
271  * If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and
272  * stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and
273  * updates |*outp|. It returns the number of bytes of |in| processed or zero on
274  * error. */
275 OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in);
276 
277 /* BN_bn2dec returns an allocated string that contains a NUL-terminated,
278  * decimal representation of |bn|. If |bn| is negative, the first char in the
279  * resulting string will be '-'. Returns NULL on allocation failure. */
280 OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a);
281 
282 /* BN_dec2bn parses the leading decimal number from |in|, which may be
283  * proceeded by a '-' to indicate a negative number and may contain trailing,
284  * non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the
285  * decimal number and stores it in |*outp|. If |*outp| is NULL then it
286  * allocates a new BIGNUM and updates |*outp|. It returns the number of bytes
287  * of |in| processed or zero on error. */
288 OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in);
289 
290 /* BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in|
291  * begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A
292  * leading '-' is still permitted and comes before the optional 0X/0x. It
293  * returns one on success or zero on error. */
294 OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in);
295 
296 /* BN_print writes a hex encoding of |a| to |bio|. It returns one on success
297  * and zero on error. */
298 OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a);
299 
300 /* BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first. */
301 OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a);
302 
303 /* BN_get_word returns the absolute value of |bn| as a single word. If |bn| is
304  * too large to be represented as a single word, the maximum possible value
305  * will be returned. */
306 OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn);
307 
308 /* BN_get_u64 sets |*out| to the absolute value of |bn| as a |uint64_t| and
309  * returns one. If |bn| is too large to be represented as a |uint64_t|, it
310  * returns zero. */
311 OPENSSL_EXPORT int BN_get_u64(const BIGNUM *bn, uint64_t *out);
312 
313 
314 /* ASN.1 functions. */
315 
316 /* BN_parse_asn1_unsigned parses a non-negative DER INTEGER from |cbs| writes
317  * the result to |ret|. It returns one on success and zero on failure. */
318 OPENSSL_EXPORT int BN_parse_asn1_unsigned(CBS *cbs, BIGNUM *ret);
319 
320 /* BN_parse_asn1_unsigned_buggy acts like |BN_parse_asn1_unsigned| but tolerates
321  * some invalid encodings. Do not use this function. */
322 OPENSSL_EXPORT int BN_parse_asn1_unsigned_buggy(CBS *cbs, BIGNUM *ret);
323 
324 /* BN_marshal_asn1 marshals |bn| as a non-negative DER INTEGER and appends the
325  * result to |cbb|. It returns one on success and zero on failure. */
326 OPENSSL_EXPORT int BN_marshal_asn1(CBB *cbb, const BIGNUM *bn);
327 
328 
329 /* BIGNUM pools.
330  *
331  * Certain BIGNUM operations need to use many temporary variables and
332  * allocating and freeing them can be quite slow. Thus such operations typically
333  * take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx|
334  * argument to a public function may be NULL, in which case a local |BN_CTX|
335  * will be created just for the lifetime of that call.
336  *
337  * A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called
338  * repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made
339  * before calling any other functions that use the |ctx| as an argument.
340  *
341  * Finally, |BN_CTX_end| must be called before returning from the function.
342  * When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from
343  * |BN_CTX_get| become invalid. */
344 
345 /* BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure. */
346 OPENSSL_EXPORT BN_CTX *BN_CTX_new(void);
347 
348 /* BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx|
349  * itself. */
350 OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx);
351 
352 /* BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future
353  * calls to |BN_CTX_get|. */
354 OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx);
355 
356 /* BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once
357  * |BN_CTX_get| has returned NULL, all future calls will also return NULL until
358  * |BN_CTX_end| is called. */
359 OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx);
360 
361 /* BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the
362  * matching |BN_CTX_start| call. */
363 OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx);
364 
365 
366 /* Simple arithmetic */
367 
368 /* BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a|
369  * or |b|. It returns one on success and zero on allocation failure. */
370 OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
371 
372 /* BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may
373  * be the same pointer as either |a| or |b|. It returns one on success and zero
374  * on allocation failure. */
375 OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
376 
377 /* BN_add_word adds |w| to |a|. It returns one on success and zero otherwise. */
378 OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w);
379 
380 /* BN_sub sets |r| = |a| - |b|, where |r| may be the same pointer as either |a|
381  * or |b|. It returns one on success and zero on allocation failure. */
382 OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
383 
384 /* BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers,
385  * |b| < |a| and |r| may be the same pointer as either |a| or |b|. It returns
386  * one on success and zero on allocation failure. */
387 OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
388 
389 /* BN_sub_word subtracts |w| from |a|. It returns one on success and zero on
390  * allocation failure. */
391 OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w);
392 
393 /* BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or
394  * |b|. Returns one on success and zero otherwise. */
395 OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
396                           BN_CTX *ctx);
397 
398 /* BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on
399  * allocation failure. */
400 OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w);
401 
402 /* BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as
403  * |a|. Returns one on success and zero otherwise. This is more efficient than
404  * BN_mul(r, a, a, ctx). */
405 OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
406 
407 /* BN_div divides |numerator| by |divisor| and places the result in |quotient|
408  * and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in
409  * which case the respective value is not returned. The result is rounded
410  * towards zero; thus if |numerator| is negative, the remainder will be zero or
411  * negative. It returns one on success or zero on error. */
412 OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem,
413                           const BIGNUM *numerator, const BIGNUM *divisor,
414                           BN_CTX *ctx);
415 
416 /* BN_div_word sets |numerator| = |numerator|/|divisor| and returns the
417  * remainder or (BN_ULONG)-1 on error. */
418 OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor);
419 
420 /* BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the
421  * square root of |in|, using |ctx|. It returns one on success or zero on
422  * error. Negative numbers and non-square numbers will result in an error with
423  * appropriate errors on the error queue. */
424 OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx);
425 
426 
427 /* Comparison functions */
428 
429 /* BN_cmp returns a value less than, equal to or greater than zero if |a| is
430  * less than, equal to or greater than |b|, respectively. */
431 OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b);
432 
433 /* BN_cmp_word is like |BN_cmp| except it takes its second argument as a
434  * |BN_ULONG| instead of a |BIGNUM|. */
435 OPENSSL_EXPORT int BN_cmp_word(const BIGNUM *a, BN_ULONG b);
436 
437 /* BN_ucmp returns a value less than, equal to or greater than zero if the
438  * absolute value of |a| is less than, equal to or greater than the absolute
439  * value of |b|, respectively. */
440 OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
441 
442 /* BN_equal_consttime returns one if |a| is equal to |b|, and zero otherwise.
443  * It takes an amount of time dependent on the sizes of |a| and |b|, but
444  * independent of the contents (including the signs) of |a| and |b|. */
445 OPENSSL_EXPORT int BN_equal_consttime(const BIGNUM *a, const BIGNUM *b);
446 
447 /* BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero
448  * otherwise. */
449 OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w);
450 
451 /* BN_is_zero returns one if |bn| is zero and zero otherwise. */
452 OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn);
453 
454 /* BN_is_one returns one if |bn| equals one and zero otherwise. */
455 OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn);
456 
457 /* BN_is_word returns one if |bn| is exactly |w| and zero otherwise. */
458 OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w);
459 
460 /* BN_is_odd returns one if |bn| is odd and zero otherwise. */
461 OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn);
462 
463 /* BN_is_pow2 returns 1 if |a| is a power of two, and 0 otherwise. */
464 OPENSSL_EXPORT int BN_is_pow2(const BIGNUM *a);
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 the value of the |n|th, least-significant bit in |a|,
495  * or zero if the bit doesn't exist. */
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 greater than the length of |a| already. */
500 OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n);
501 
502 
503 /* Modulo arithmetic. */
504 
505 /* BN_mod_word returns |a| mod |w| or (BN_ULONG)-1 on error. */
506 OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
507 
508 /* BN_mod_pow2 sets |r| = |a| mod 2^|e|. It returns 1 on success and
509  * 0 on error. */
510 OPENSSL_EXPORT int BN_mod_pow2(BIGNUM *r, const BIGNUM *a, size_t e);
511 
512 /* BN_nnmod_pow2 sets |r| = |a| mod 2^|e| where |r| is always positive.
513  * It returns 1 on success and 0 on error. */
514 OPENSSL_EXPORT int BN_nnmod_pow2(BIGNUM *r, const BIGNUM *a, size_t e);
515 
516 /* BN_mod is a helper macro that calls |BN_div| and discards the quotient. */
517 #define BN_mod(rem, numerator, divisor, ctx) \
518   BN_div(NULL, (rem), (numerator), (divisor), (ctx))
519 
520 /* BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <=
521  * |rem| < |divisor| is always true. It returns one on success and zero on
522  * error. */
523 OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator,
524                             const BIGNUM *divisor, BN_CTX *ctx);
525 
526 /* BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero
527  * on error. */
528 OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
529                               const BIGNUM *m, BN_CTX *ctx);
530 
531 /* BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be
532  * non-negative and less than |m|. */
533 OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
534                                     const BIGNUM *m);
535 
536 /* BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero
537  * on error. */
538 OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
539                               const BIGNUM *m, BN_CTX *ctx);
540 
541 /* BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be
542  * non-negative and less than |m|. */
543 OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
544                                     const BIGNUM *m);
545 
546 /* BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero
547  * on error. */
548 OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
549                               const BIGNUM *m, BN_CTX *ctx);
550 
551 /* BN_mod_sqr sets |r| = |a|^2 mod |m|. It returns one on success and zero
552  * on error. */
553 OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
554                               BN_CTX *ctx);
555 
556 /* BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the
557  * same pointer. It returns one on success and zero on error. */
558 OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n,
559                                  const BIGNUM *m, BN_CTX *ctx);
560 
561 /* BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be
562  * non-negative and less than |m|. */
563 OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n,
564                                        const BIGNUM *m);
565 
566 /* BN_mod_lshift1 sets |r| = (|a| << 1) 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_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
569                                   BN_CTX *ctx);
570 
571 /* BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be
572  * non-negative and less than |m|. */
573 OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a,
574                                         const BIGNUM *m);
575 
576 /* BN_mod_sqrt returns a newly-allocated |BIGNUM|, r, such that
577  * r^2 == a (mod p). |p| must be a prime. It returns NULL on error or if |a| is
578  * not a square mod |p|. In the latter case, it will add |BN_R_NOT_A_SQUARE| to
579  * the error queue. */
580 OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p,
581                                    BN_CTX *ctx);
582 
583 
584 /* Random and prime number generation. */
585 
586 /* The following are values for the |top| parameter of |BN_rand|. */
587 #define BN_RAND_TOP_ANY    (-1)
588 #define BN_RAND_TOP_ONE     0
589 #define BN_RAND_TOP_TWO     1
590 
591 /* The following are values for the |bottom| parameter of |BN_rand|. */
592 #define BN_RAND_BOTTOM_ANY  0
593 #define BN_RAND_BOTTOM_ODD  1
594 
595 /* BN_rand sets |rnd| to a random number of length |bits|. It returns one on
596  * success and zero otherwise.
597  *
598  * |top| must be one of the |BN_RAND_TOP_*| values. If |BN_RAND_TOP_ONE|, the
599  * most-significant bit, if any, will be set. If |BN_RAND_TOP_TWO|, the two
600  * most significant bits, if any, will be set. If |BN_RAND_TOP_ANY|, no extra
601  * action will be taken and |BN_num_bits(rnd)| may not equal |bits| if the most
602  * significant bits randomly ended up as zeros.
603  *
604  * |bottom| must be one of the |BN_RAND_BOTTOM_*| values. If
605  * |BN_RAND_BOTTOM_ODD|, the least-significant bit, if any, will be set. If
606  * |BN_RAND_BOTTOM_ANY|, no extra action will be taken. */
607 OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
608 
609 /* BN_pseudo_rand is an alias for |BN_rand|. */
610 OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
611 
612 /* BN_rand_range is equivalent to |BN_rand_range_ex| with |min_inclusive| set
613  * to zero and |max_exclusive| set to |range|. */
614 OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
615 
616 /* BN_rand_range_ex sets |rnd| to a random value in
617  * [min_inclusive..max_exclusive). It returns one on success and zero
618  * otherwise. */
619 OPENSSL_EXPORT int BN_rand_range_ex(BIGNUM *r, BN_ULONG min_inclusive,
620                                     const BIGNUM *max_exclusive);
621 
622 /* BN_pseudo_rand_range is an alias for BN_rand_range. */
623 OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
624 
625 /* BN_generate_dsa_nonce generates a random number 0 <= out < range. Unlike
626  * BN_rand_range, it also includes the contents of |priv| and |message| in the
627  * generation so that an RNG failure isn't fatal as long as |priv| remains
628  * secret. This is intended for use in DSA and ECDSA where an RNG weakness
629  * leads directly to private key exposure unless this function is used.
630  * It returns one on success and zero on error. */
631 OPENSSL_EXPORT int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
632                                          const BIGNUM *priv,
633                                          const uint8_t *message,
634                                          size_t message_len, BN_CTX *ctx);
635 
636 /* BN_GENCB holds a callback function that is used by generation functions that
637  * can take a very long time to complete. Use |BN_GENCB_set| to initialise a
638  * |BN_GENCB| structure.
639  *
640  * The callback receives the address of that |BN_GENCB| structure as its last
641  * argument and the user is free to put an arbitrary pointer in |arg|. The other
642  * arguments are set as follows:
643  *   event=BN_GENCB_GENERATED, n=i:   after generating the i'th possible prime
644  *                                    number.
645  *   event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality
646  *                                    checks.
647  *   event=BN_GENCB_PRIME_TEST, n=i:  when the i'th primality test has finished.
648  *
649  * The callback can return zero to abort the generation progress or one to
650  * allow it to continue.
651  *
652  * When other code needs to call a BN generation function it will often take a
653  * BN_GENCB argument and may call the function with other argument values. */
654 #define BN_GENCB_GENERATED 0
655 #define BN_GENCB_PRIME_TEST 1
656 
657 struct bn_gencb_st {
658   void *arg;        /* callback-specific data */
659   int (*callback)(int event, int n, struct bn_gencb_st *);
660 };
661 
662 /* BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to
663  * |arg|. */
664 OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback,
665                                  int (*f)(int event, int n,
666                                           struct bn_gencb_st *),
667                                  void *arg);
668 
669 /* BN_GENCB_call calls |callback|, if not NULL, and returns the return value of
670  * the callback, or 1 if |callback| is NULL. */
671 OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n);
672 
673 /* BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe
674  * is non-zero then the prime will be such that (ret-1)/2 is also a prime.
675  * (This is needed for Diffie-Hellman groups to ensure that the only subgroups
676  * are of size 2 and (p-1)/2.).
677  *
678  * If |add| is not NULL, the prime will fulfill the condition |ret| % |add| ==
679  * |rem| in order to suit a given generator. (If |rem| is NULL then |ret| %
680  * |add| == 1.)
681  *
682  * If |cb| is not NULL, it will be called during processing to give an
683  * indication of progress. See the comments for |BN_GENCB|. It returns one on
684  * success and zero otherwise. */
685 OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
686                                         const BIGNUM *add, const BIGNUM *rem,
687                                         BN_GENCB *cb);
688 
689 /* BN_prime_checks is magic value that can be used as the |checks| argument to
690  * the primality testing functions in order to automatically select a number of
691  * Miller-Rabin checks that gives a false positive rate of ~2^{-80}. */
692 #define BN_prime_checks 0
693 
694 /* bn_primality_result_t enumerates the outcomes of primality-testing. */
695 enum bn_primality_result_t {
696   bn_probably_prime,
697   bn_composite,
698   bn_non_prime_power_composite,
699 };
700 
701 /* BN_enhanced_miller_rabin_primality_test tests whether |w| is probably a prime
702  * number using the Enhanced Miller-Rabin Test (FIPS 186-4 C.3.2) with
703  * |iterations| iterations and returns the result in |out_result|. Enhanced
704  * Miller-Rabin tests primality for odd integers greater than 3, returning
705  * |bn_probably_prime| if the number is probably prime,
706  * |bn_non_prime_power_composite| if the number is a composite that is not the
707  * power of a single prime, and |bn_composite| otherwise.  If |iterations| is
708  * |BN_prime_checks|, then a value that results in a false positive rate lower
709  * than the number-field sieve security level of |w| is used. It returns one on
710  * success and zero on failure. If |cb| is not NULL, then it is called during
711  * each iteration of the primality test. */
712 int BN_enhanced_miller_rabin_primality_test(
713     enum bn_primality_result_t *out_result, const BIGNUM *w, int iterations,
714     BN_CTX *ctx, BN_GENCB *cb);
715 
716 /* BN_primality_test sets |*is_probably_prime| to one if |candidate| is
717  * probably a prime number by the Miller-Rabin test or zero if it's certainly
718  * not.
719  *
720  * If |do_trial_division| is non-zero then |candidate| will be tested against a
721  * list of small primes before Miller-Rabin tests. The probability of this
722  * function returning a false positive is 2^{2*checks}. If |checks| is
723  * |BN_prime_checks| then a value that results in a false positive rate lower
724  * than the number-field sieve security level of |candidate| is used. If |cb| is
725  * not NULL then it is called during the checking process. See the comment above
726  * |BN_GENCB|.
727  *
728  * The function returns one on success and zero on error.
729  *
730  * (If you are unsure whether you want |do_trial_division|, don't set it.) */
731 OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime,
732                                      const BIGNUM *candidate, int checks,
733                                      BN_CTX *ctx, int do_trial_division,
734                                      BN_GENCB *cb);
735 
736 /* BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime
737  * number by the Miller-Rabin test, zero if it's certainly not and -1 on error.
738  *
739  * If |do_trial_division| is non-zero then |candidate| will be tested against a
740  * list of small primes before Miller-Rabin tests. The probability of this
741  * function returning one when |candidate| is composite is 2^{2*checks}. If
742  * |checks| is |BN_prime_checks| then a value that results in a false positive
743  * rate lower than the number-field sieve security level of |candidate| is used.
744  * If |cb| is not NULL then it is called during the checking process. See the
745  * comment above |BN_GENCB|.
746  *
747  * WARNING: deprecated. Use |BN_primality_test|. */
748 OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks,
749                                            BN_CTX *ctx, int do_trial_division,
750                                            BN_GENCB *cb);
751 
752 /* BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with
753  * |do_trial_division| set to zero.
754  *
755  * WARNING: deprecated: Use |BN_primality_test|. */
756 OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks,
757                                   BN_CTX *ctx, BN_GENCB *cb);
758 
759 
760 /* Number theory functions */
761 
762 /* BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero
763  * otherwise. */
764 OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
765                           BN_CTX *ctx);
766 
767 /* BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If |out| is NULL, a
768  * fresh BIGNUM is allocated. It returns the result or NULL on error.
769  *
770  * If |n| is even then the operation is performed using an algorithm that avoids
771  * some branches but which isn't constant-time. This function shouldn't be used
772  * for secret values; use |BN_mod_inverse_blinded| instead. Or, if |n| is
773  * guaranteed to be prime, use
774  * |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking
775  * advantage of Fermat's Little Theorem. */
776 OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a,
777                                       const BIGNUM *n, BN_CTX *ctx);
778 
779 /* BN_mod_inverse_blinded sets |out| equal to |a|^-1, mod |n|, where |n| is the
780  * Montgomery modulus for |mont|. |a| must be non-negative and must be less
781  * than |n|. |n| must be greater than 1. |a| is blinded (masked by a random
782  * value) to protect it against side-channel attacks. On failure, if the failure
783  * was caused by |a| having no inverse mod |n| then |*out_no_inverse| will be
784  * set to one; otherwise it will be set to zero. */
785 int BN_mod_inverse_blinded(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
786                            const BN_MONT_CTX *mont, BN_CTX *ctx);
787 
788 /* BN_mod_inverse_odd sets |out| equal to |a|^-1, mod |n|. |a| must be
789  * non-negative and must be less than |n|. |n| must be odd. This function
790  * shouldn't be used for secret values; use |BN_mod_inverse_blinded| instead.
791  * Or, if |n| is guaranteed to be prime, use
792  * |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking
793  * advantage of Fermat's Little Theorem. It returns one on success or zero on
794  * failure. On failure, if the failure was caused by |a| having no inverse mod
795  * |n| then |*out_no_inverse| will be set to one; otherwise it will be set to
796  * zero. */
797 int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
798                        const BIGNUM *n, BN_CTX *ctx);
799 
800 
801 /* Montgomery arithmetic. */
802 
803 /* BN_MONT_CTX contains the precomputed values needed to work in a specific
804  * Montgomery domain. */
805 
806 /* BN_MONT_CTX_new returns a fresh BN_MONT_CTX or NULL on allocation failure. */
807 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void);
808 
809 /* BN_MONT_CTX_free frees memory associated with |mont|. */
810 OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont);
811 
812 /* BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or
813  * NULL on error. */
814 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,
815                                              const BN_MONT_CTX *from);
816 
817 /* BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It
818  * returns one on success and zero on error. */
819 OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod,
820                                    BN_CTX *ctx);
821 
822 /* BN_MONT_CTX_set_locked takes |lock| and checks whether |*pmont| is NULL. If
823  * so, it creates a new |BN_MONT_CTX| and sets the modulus for it to |mod|. It
824  * then stores it as |*pmont|. It returns one on success and zero on error.
825  *
826  * If |*pmont| is already non-NULL then it does nothing and returns one. */
827 int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
828                            const BIGNUM *mod, BN_CTX *bn_ctx);
829 
830 /* BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. |a| is
831  * assumed to be in the range [0, n), where |n| is the Montgomery modulus. It
832  * returns one on success or zero on error. */
833 OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a,
834                                     const BN_MONT_CTX *mont, BN_CTX *ctx);
835 
836 /* BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values out
837  * of the Montgomery domain. |a| is assumed to be in the range [0, n), where |n|
838  * is the Montgomery modulus. It returns one on success or zero on error. */
839 OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a,
840                                       const BN_MONT_CTX *mont, BN_CTX *ctx);
841 
842 /* BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain.
843  * Both |a| and |b| must already be in the Montgomery domain (by
844  * |BN_to_montgomery|). In particular, |a| and |b| are assumed to be in the
845  * range [0, n), where |n| is the Montgomery modulus. It returns one on success
846  * or zero on error. */
847 OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a,
848                                          const BIGNUM *b,
849                                          const BN_MONT_CTX *mont, BN_CTX *ctx);
850 
851 
852 /* Exponentiation. */
853 
854 /* BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply
855  * algorithm that leaks side-channel information. It returns one on success or
856  * zero otherwise. */
857 OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
858                           BN_CTX *ctx);
859 
860 /* BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best
861  * algorithm for the values provided. It returns one on success or zero
862  * otherwise. The |BN_mod_exp_mont_consttime| variant must be used if the
863  * exponent is secret. */
864 OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
865                               const BIGNUM *m, BN_CTX *ctx);
866 
867 OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
868                                    const BIGNUM *m, BN_CTX *ctx,
869                                    const BN_MONT_CTX *mont);
870 
871 OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a,
872                                              const BIGNUM *p, const BIGNUM *m,
873                                              BN_CTX *ctx,
874                                              const BN_MONT_CTX *mont);
875 
876 
877 /* Deprecated functions */
878 
879 /* BN_bn2mpi serialises the value of |in| to |out|, using a format that consists
880  * of the number's length in bytes represented as a 4-byte big-endian number,
881  * and the number itself in big-endian format, where the most significant bit
882  * signals a negative number. (The representation of numbers with the MSB set is
883  * prefixed with null byte). |out| must have sufficient space available; to
884  * find the needed amount of space, call the function with |out| set to NULL. */
885 OPENSSL_EXPORT size_t BN_bn2mpi(const BIGNUM *in, uint8_t *out);
886 
887 /* BN_mpi2bn parses |len| bytes from |in| and returns the resulting value. The
888  * bytes at |in| are expected to be in the format emitted by |BN_bn2mpi|.
889  *
890  * If |out| is NULL then a fresh |BIGNUM| is allocated and returned, otherwise
891  * |out| is reused and returned. On error, NULL is returned and the error queue
892  * is updated. */
893 OPENSSL_EXPORT BIGNUM *BN_mpi2bn(const uint8_t *in, size_t len, BIGNUM *out);
894 
895 /* BN_mod_exp_mont_word is like |BN_mod_exp_mont| except that the base |a| is
896  * given as a |BN_ULONG| instead of a |BIGNUM *|. It returns one on success
897  * or zero otherwise. */
898 OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
899                                         const BIGNUM *m, BN_CTX *ctx,
900                                         const BN_MONT_CTX *mont);
901 
902 /* BN_mod_exp2_mont calculates (a1^p1) * (a2^p2) mod m. It returns 1 on success
903  * or zero otherwise. */
904 OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1,
905                                     const BIGNUM *p1, const BIGNUM *a2,
906                                     const BIGNUM *p2, const BIGNUM *m,
907                                     BN_CTX *ctx, const BN_MONT_CTX *mont);
908 
909 
910 /* Private functions */
911 
912 struct bignum_st {
913   BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks in little-endian
914                   order. */
915   int top;   /* Index of last used element in |d|, plus one. */
916   int dmax;  /* Size of |d|, in words. */
917   int neg;   /* one if the number is negative */
918   int flags; /* bitmask of BN_FLG_* values */
919 };
920 
921 struct bn_mont_ctx_st {
922   BIGNUM RR; /* used to convert to montgomery form */
923   BIGNUM N;  /* The modulus */
924   BN_ULONG n0[2]; /* least significant words of (R*Ri-1)/N */
925 };
926 
927 OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l);
928 
929 #define BN_FLG_MALLOCED 0x01
930 #define BN_FLG_STATIC_DATA 0x02
931 /* |BN_FLG_CONSTTIME| has been removed and intentionally omitted so code relying
932  * on it will not compile. Consumers outside BoringSSL should use the
933  * higher-level cryptographic algorithms exposed by other modules. Consumers
934  * within the library should call the appropriate timing-sensitive algorithm
935  * directly. */
936 
937 
938 #if defined(__cplusplus)
939 }  /* extern C */
940 
941 #if (__cplusplus >= 201103L || (__cplusplus < 200000 && __cplusplus > 199711L)) && !defined(OPENSSL_NO_CXX)
942 
943 extern "C++" {
944 
945 namespace bssl {
946 
BORINGSSL_MAKE_DELETER(BIGNUM,BN_free)947 BORINGSSL_MAKE_DELETER(BIGNUM, BN_free)
948 BORINGSSL_MAKE_DELETER(BN_CTX, BN_CTX_free)
949 BORINGSSL_MAKE_DELETER(BN_MONT_CTX, BN_MONT_CTX_free)
950 
951 class BN_CTXScope {
952  public:
953   BN_CTXScope(BN_CTX *ctx) : ctx_(ctx) { BN_CTX_start(ctx_); }
954   ~BN_CTXScope() { BN_CTX_end(ctx_); }
955 
956  private:
957   BN_CTX *ctx_;
958 
959   BN_CTXScope(BN_CTXScope &) = delete;
960   BN_CTXScope &operator=(BN_CTXScope &) = delete;
961 };
962 
963 }  // namespace bssl
964 
965 }  /* extern C++ */
966 #endif
967 
968 #endif
969 
970 #define BN_R_ARG2_LT_ARG3 100
971 #define BN_R_BAD_RECIPROCAL 101
972 #define BN_R_BIGNUM_TOO_LONG 102
973 #define BN_R_BITS_TOO_SMALL 103
974 #define BN_R_CALLED_WITH_EVEN_MODULUS 104
975 #define BN_R_DIV_BY_ZERO 105
976 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 106
977 #define BN_R_INPUT_NOT_REDUCED 107
978 #define BN_R_INVALID_RANGE 108
979 #define BN_R_NEGATIVE_NUMBER 109
980 #define BN_R_NOT_A_SQUARE 110
981 #define BN_R_NOT_INITIALIZED 111
982 #define BN_R_NO_INVERSE 112
983 #define BN_R_PRIVATE_KEY_TOO_LARGE 113
984 #define BN_R_P_IS_NOT_PRIME 114
985 #define BN_R_TOO_MANY_ITERATIONS 115
986 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 116
987 #define BN_R_BAD_ENCODING 117
988 #define BN_R_ENCODE_ERROR 118
989 #define BN_R_INVALID_INPUT 119
990 
991 #endif  /* OPENSSL_HEADER_BN_H */
992