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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 arbitary 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 #elif defined(OPENSSL_32_BIT)
155 #define BN_ULONG uint32_t
156 #define BN_BITS2 32
157 #define BN_DEC_FMT1	"%" PRIu32
158 #define BN_DEC_FMT2	"%09" PRIu32
159 #define BN_HEX_FMT1	"%" PRIx32
160 #else
161 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
162 #endif
163 
164 
165 /* Allocation and freeing. */
166 
167 /* BN_new creates a new, allocated BIGNUM and initialises it. */
168 OPENSSL_EXPORT BIGNUM *BN_new(void);
169 
170 /* BN_init initialises a stack allocated |BIGNUM|. */
171 OPENSSL_EXPORT void BN_init(BIGNUM *bn);
172 
173 /* BN_free frees the data referenced by |bn| and, if |bn| was originally
174  * allocated on the heap, frees |bn| also. */
175 OPENSSL_EXPORT void BN_free(BIGNUM *bn);
176 
177 /* BN_clear_free erases and frees the data referenced by |bn| and, if |bn| was
178  * originally allocated on the heap, frees |bn| also. */
179 OPENSSL_EXPORT void BN_clear_free(BIGNUM *bn);
180 
181 /* BN_dup allocates a new BIGNUM and sets it equal to |src|. It returns the
182  * allocated BIGNUM on success or NULL otherwise. */
183 OPENSSL_EXPORT BIGNUM *BN_dup(const BIGNUM *src);
184 
185 /* BN_copy sets |dest| equal to |src| and returns |dest| or NULL on allocation
186  * failure. */
187 OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src);
188 
189 /* BN_clear sets |bn| to zero and erases the old data. */
190 OPENSSL_EXPORT void BN_clear(BIGNUM *bn);
191 
192 /* BN_value_one returns a static BIGNUM with value 1. */
193 OPENSSL_EXPORT const BIGNUM *BN_value_one(void);
194 
195 /* BN_with_flags initialises a stack allocated |BIGNUM| with pointers to the
196  * contents of |in| but with |flags| ORed into the flags field.
197  *
198  * Note: the two BIGNUMs share state and so |out| should /not/ be passed to
199  * |BN_free|. */
200 OPENSSL_EXPORT void BN_with_flags(BIGNUM *out, const BIGNUM *in, int flags);
201 
202 
203 /* Basic functions. */
204 
205 /* BN_num_bits returns the minimum number of bits needed to represent the
206  * absolute value of |bn|. */
207 OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn);
208 
209 /* BN_num_bytes returns the minimum number of bytes needed to represent the
210  * absolute value of |bn|. */
211 OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn);
212 
213 /* BN_zero sets |bn| to zero. */
214 OPENSSL_EXPORT void BN_zero(BIGNUM *bn);
215 
216 /* BN_one sets |bn| to one. It returns one on success or zero on allocation
217  * failure. */
218 OPENSSL_EXPORT int BN_one(BIGNUM *bn);
219 
220 /* BN_set_word sets |bn| to |value|. It returns one on success or zero on
221  * allocation failure. */
222 OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value);
223 
224 /* BN_set_negative sets the sign of |bn|. */
225 OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign);
226 
227 /* BN_is_negative returns one if |bn| is negative and zero otherwise. */
228 OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn);
229 
230 /* BN_get_flags returns |bn->flags| & |flags|. */
231 OPENSSL_EXPORT int BN_get_flags(const BIGNUM *bn, int flags);
232 
233 /* BN_set_flags sets |flags| on |bn|. */
234 OPENSSL_EXPORT void BN_set_flags(BIGNUM *bn, int flags);
235 
236 
237 /* Conversion functions. */
238 
239 /* BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as
240  * a big-endian number, and returns |ret|. If |ret| is NULL then a fresh
241  * |BIGNUM| is allocated and returned. It returns NULL on allocation
242  * failure. */
243 OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret);
244 
245 /* BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian
246  * integer, which must have |BN_num_bytes| of space available. It returns the
247  * number of bytes written. */
248 OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out);
249 
250 /* BN_bn2bin_padded serialises the absolute value of |in| to |out| as a
251  * big-endian integer. The integer is padded with leading zeros up to size
252  * |len|. If |len| is smaller than |BN_num_bytes|, the function fails and
253  * returns 0. Otherwise, it returns 1. */
254 OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in);
255 
256 /* BN_bn2cbb_padded behaves like |BN_bn2bin_padded| but writes to a |CBB|. */
257 OPENSSL_EXPORT int BN_bn2cbb_padded(CBB *out, size_t len, const BIGNUM *in);
258 
259 /* BN_bn2hex returns an allocated string that contains a NUL-terminated, hex
260  * representation of |bn|. If |bn| is negative, the first char in the resulting
261  * string will be '-'. Returns NULL on allocation failure. */
262 OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn);
263 
264 /* BN_hex2bn parses the leading hex number from |in|, which may be proceeded by
265  * a '-' to indicate a negative number and may contain trailing, non-hex data.
266  * If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and
267  * stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and
268  * updates |*outp|. It returns the number of bytes of |in| processed or zero on
269  * error. */
270 OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in);
271 
272 /* BN_bn2dec returns an allocated string that contains a NUL-terminated,
273  * decimal representation of |bn|. If |bn| is negative, the first char in the
274  * resulting string will be '-'. Returns NULL on allocation failure. */
275 OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a);
276 
277 /* BN_dec2bn parses the leading decimal number from |in|, which may be
278  * proceeded by a '-' to indicate a negative number and may contain trailing,
279  * non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the
280  * decimal number and stores it in |*outp|. If |*outp| is NULL then it
281  * allocates a new BIGNUM and updates |*outp|. It returns the number of bytes
282  * of |in| processed or zero on error. */
283 OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in);
284 
285 /* BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in|
286  * begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A
287  * leading '-' is still permitted and comes before the optional 0X/0x. It
288  * returns one on success or zero on error. */
289 OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in);
290 
291 /* BN_print writes a hex encoding of |a| to |bio|. It returns one on success
292  * and zero on error. */
293 OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a);
294 
295 /* BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first. */
296 OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a);
297 
298 /* BN_get_word returns the absolute value of |bn| as a single word. If |bn| is
299  * too large to be represented as a single word, the maximum possible value
300  * will be returned. */
301 OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn);
302 
303 
304 /* ASN.1 functions. */
305 
306 /* BN_cbs2unsigned parses a non-negative DER INTEGER from |cbs| writes the
307  * result to |ret|. It returns one on success and zero on failure. */
308 OPENSSL_EXPORT int BN_cbs2unsigned(CBS *cbs, BIGNUM *ret);
309 
310 /* BN_cbs2unsigned_buggy acts like |BN_cbs2unsigned| but tolerates some invalid
311  * encodings. Do not use this function. */
312 OPENSSL_EXPORT int BN_cbs2unsigned_buggy(CBS *cbs, BIGNUM *ret);
313 
314 /* BN_bn2cbb marshals |bn| as a non-negative DER INTEGER and appends the result
315  * to |cbb|. It returns one on success and zero on failure. */
316 OPENSSL_EXPORT int BN_bn2cbb(CBB *cbb, const BIGNUM *bn);
317 
318 
319 /* Internal functions.
320  *
321  * These functions are useful for code that is doing low-level manipulations of
322  * BIGNUM values. However, be sure that no other function in this file does
323  * what you want before turning to these. */
324 
325 /* bn_correct_top decrements |bn->top| until |bn->d[top-1]| is non-zero or
326  * until |top| is zero. */
327 OPENSSL_EXPORT void bn_correct_top(BIGNUM *bn);
328 
329 /* bn_wexpand ensures that |bn| has at least |words| works of space without
330  * altering its value. It returns one on success or zero on allocation
331  * failure. */
332 OPENSSL_EXPORT BIGNUM *bn_wexpand(BIGNUM *bn, size_t words);
333 
334 
335 /* BIGNUM pools.
336  *
337  * Certain BIGNUM operations need to use many temporary variables and
338  * allocating and freeing them can be quite slow. Thus such opertions typically
339  * take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx|
340  * argument to a public function may be NULL, in which case a local |BN_CTX|
341  * will be created just for the lifetime of that call.
342  *
343  * A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called
344  * repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made
345  * before calling any other functions that use the |ctx| as an argument.
346  *
347  * Finally, |BN_CTX_end| must be called before returning from the function.
348  * When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from
349  * |BN_CTX_get| become invalid. */
350 
351 /* BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure. */
352 OPENSSL_EXPORT BN_CTX *BN_CTX_new(void);
353 
354 /* BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx|
355  * itself. */
356 OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx);
357 
358 /* BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future
359  * calls to |BN_CTX_get|. */
360 OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx);
361 
362 /* BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once
363  * |BN_CTX_get| has returned NULL, all future calls will also return NULL until
364  * |BN_CTX_end| is called. */
365 OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx);
366 
367 /* BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the
368  * matching |BN_CTX_start| call. */
369 OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx);
370 
371 
372 /* Simple arithmetic */
373 
374 /* BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a|
375  * or |b|. It returns one on success and zero on allocation failure. */
376 OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
377 
378 /* BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may
379  * be the same pointer as either |a| or |b|. It returns one on success and zero
380  * on allocation failure. */
381 OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
382 
383 /* BN_add_word adds |w| to |a|. It returns one on success and zero otherwise. */
384 OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w);
385 
386 /* BN_sub sets |r| = |a| - |b|, where |r| must be a distinct pointer from |a|
387  * and |b|. It returns one on success and zero on allocation failure. */
388 OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
389 
390 /* BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers,
391  * |b| < |a| and |r| must be a distinct pointer from |a| and |b|. It returns
392  * one on success and zero on allocation failure. */
393 OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
394 
395 /* BN_sub_word subtracts |w| from |a|. It returns one on success and zero on
396  * allocation failure. */
397 OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w);
398 
399 /* BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or
400  * |b|. Returns one on success and zero otherwise. */
401 OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
402                           BN_CTX *ctx);
403 
404 /* BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on
405  * allocation failure. */
406 OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w);
407 
408 /* BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as
409  * |a|. Returns one on success and zero otherwise. This is more efficient than
410  * BN_mul(r, a, a, ctx). */
411 OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
412 
413 /* BN_div divides |numerator| by |divisor| and places the result in |quotient|
414  * and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in
415  * which case the respective value is not returned. The result is rounded
416  * towards zero; thus if |numerator| is negative, the remainder will be zero or
417  * negative. It returns one on success or zero on error. */
418 OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem,
419                           const BIGNUM *numerator, const BIGNUM *divisor,
420                           BN_CTX *ctx);
421 
422 /* BN_div_word sets |numerator| = |numerator|/|divisor| and returns the
423  * remainder or (BN_ULONG)-1 on error. */
424 OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor);
425 
426 /* BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the
427  * square root of |in|, using |ctx|. It returns one on success or zero on
428  * error. Negative numbers and non-square numbers will result in an error with
429  * appropriate errors on the error queue. */
430 OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx);
431 
432 
433 /* Comparison functions */
434 
435 /* BN_cmp returns a value less than, equal to or greater than zero if |a| is
436  * less than, equal to or greater than |b|, respectively. */
437 OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b);
438 
439 /* BN_ucmp returns a value less than, equal to or greater than zero if the
440  * absolute value of |a| is less than, equal to or greater than the absolute
441  * value of |b|, respectively. */
442 OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
443 
444 /* BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero
445  * otherwise. */
446 OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w);
447 
448 /* BN_is_zero returns one if |bn| is zero and zero otherwise. */
449 OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn);
450 
451 /* BN_is_one returns one if |bn| equals one and zero otherwise. */
452 OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn);
453 
454 /* BN_is_word returns one if |bn| is exactly |w| and zero otherwise. */
455 OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w);
456 
457 /* BN_is_odd returns one if |bn| is odd and zero otherwise. */
458 OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn);
459 
460 
461 /* Bitwise operations. */
462 
463 /* BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the
464  * same |BIGNUM|. It returns one on success and zero on allocation failure. */
465 OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
466 
467 /* BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same
468  * pointer. It returns one on success and zero on allocation failure. */
469 OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a);
470 
471 /* BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same
472  * pointer. It returns one on success and zero on allocation failure. */
473 OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
474 
475 /* BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same
476  * pointer. It returns one on success and zero on allocation failure. */
477 OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a);
478 
479 /* BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a|
480  * is 2 then setting bit zero will make it 3. It returns one on success or zero
481  * on allocation failure. */
482 OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n);
483 
484 /* BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if
485  * |a| is 3, clearing bit zero will make it two. It returns one on success or
486  * zero on allocation failure. */
487 OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n);
488 
489 /* BN_is_bit_set returns the value of the |n|th, least-significant bit in |a|,
490  * or zero if the bit doesn't exist. */
491 OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n);
492 
493 /* BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one
494  * on success or zero if |n| is greater than the length of |a| already. */
495 OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n);
496 
497 
498 /* Modulo arithmetic. */
499 
500 /* BN_mod_word returns |a| mod |w|. */
501 OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
502 
503 /* BN_mod is a helper macro that calls |BN_div| and discards the quotient. */
504 #define BN_mod(rem, numerator, divisor, ctx) \
505   BN_div(NULL, (rem), (numerator), (divisor), (ctx))
506 
507 /* BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <=
508  * |rem| < |divisor| is always true. It returns one on success and zero on
509  * error. */
510 OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator,
511                             const BIGNUM *divisor, BN_CTX *ctx);
512 
513 /* BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero
514  * on error. */
515 OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
516                               const BIGNUM *m, BN_CTX *ctx);
517 
518 /* BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be
519  * non-negative and less than |m|. */
520 OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
521                                     const BIGNUM *m);
522 
523 /* BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero
524  * on error. */
525 OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
526                               const BIGNUM *m, BN_CTX *ctx);
527 
528 /* BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be
529  * non-negative and less than |m|. */
530 OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
531                                     const BIGNUM *m);
532 
533 /* BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero
534  * on error. */
535 OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
536                               const BIGNUM *m, BN_CTX *ctx);
537 
538 /* BN_mod_sqr sets |r| = |a|^2 mod |m|. It returns one on success and zero
539  * on error. */
540 OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
541                               BN_CTX *ctx);
542 
543 /* BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the
544  * same pointer. It returns one on success and zero on error. */
545 OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n,
546                                  const BIGNUM *m, BN_CTX *ctx);
547 
548 /* BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be
549  * non-negative and less than |m|. */
550 OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n,
551                                        const BIGNUM *m);
552 
553 /* BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the
554  * same pointer. It returns one on success and zero on error. */
555 OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
556                                   BN_CTX *ctx);
557 
558 /* BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be
559  * non-negative and less than |m|. */
560 OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a,
561                                         const BIGNUM *m);
562 
563 /* BN_mod_sqrt returns a |BIGNUM|, r, such that r^2 == a (mod p). */
564 OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p,
565                                    BN_CTX *ctx);
566 
567 
568 /* Random and prime number generation. */
569 
570 /* BN_rand sets |rnd| to a random number of length |bits|. If |top| is zero, the
571  * most-significant bit, if any, will be set. If |top| is one, the two most
572  * significant bits, if any, will be set.
573  *
574  * If |top| is -1 then no extra action will be taken and |BN_num_bits(rnd)| may
575  * not equal |bits| if the most significant bits randomly ended up as zeros.
576  *
577  * If |bottom| is non-zero, the least-significant bit, if any, will be set. The
578  * function returns one on success or zero otherwise. */
579 OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
580 
581 /* BN_pseudo_rand is an alias for |BN_rand|. */
582 OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
583 
584 /* BN_rand_range sets |rnd| to a random value [0..range). It returns one on
585  * success and zero otherwise. */
586 OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
587 
588 /* BN_pseudo_rand_range is an alias for BN_rand_range. */
589 OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
590 
591 /* BN_generate_dsa_nonce generates a random number 0 <= out < range. Unlike
592  * BN_rand_range, it also includes the contents of |priv| and |message| in the
593  * generation so that an RNG failure isn't fatal as long as |priv| remains
594  * secret. This is intended for use in DSA and ECDSA where an RNG weakness
595  * leads directly to private key exposure unless this function is used.
596  * It returns one on success and zero on error. */
597 OPENSSL_EXPORT int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
598                                          const BIGNUM *priv,
599                                          const uint8_t *message,
600                                          size_t message_len, BN_CTX *ctx);
601 
602 /* BN_GENCB holds a callback function that is used by generation functions that
603  * can take a very long time to complete. Use |BN_GENCB_set| to initialise a
604  * |BN_GENCB| structure.
605  *
606  * The callback receives the address of that |BN_GENCB| structure as its last
607  * argument and the user is free to put an arbitary pointer in |arg|. The other
608  * arguments are set as follows:
609  *   event=BN_GENCB_GENERATED, n=i:   after generating the i'th possible prime
610  *                                    number.
611  *   event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality
612  *                                    checks.
613  *   event=BN_GENCB_PRIME_TEST, n=i:  when the i'th primality test has finished.
614  *
615  * The callback can return zero to abort the generation progress or one to
616  * allow it to continue.
617  *
618  * When other code needs to call a BN generation function it will often take a
619  * BN_GENCB argument and may call the function with other argument values. */
620 #define BN_GENCB_GENERATED 0
621 #define BN_GENCB_PRIME_TEST 1
622 
623 struct bn_gencb_st {
624   void *arg;        /* callback-specific data */
625   int (*callback)(int event, int n, struct bn_gencb_st *);
626 };
627 
628 /* BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to
629  * |arg|. */
630 OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback,
631                                  int (*f)(int event, int n,
632                                           struct bn_gencb_st *),
633                                  void *arg);
634 
635 /* BN_GENCB_call calls |callback|, if not NULL, and returns the return value of
636  * the callback, or 1 if |callback| is NULL. */
637 OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n);
638 
639 /* BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe
640  * is non-zero then the prime will be such that (ret-1)/2 is also a prime.
641  * (This is needed for Diffie-Hellman groups to ensure that the only subgroups
642  * are of size 2 and (p-1)/2.).
643  *
644  * If |add| is not NULL, the prime will fulfill the condition |ret| % |add| ==
645  * |rem| in order to suit a given generator. (If |rem| is NULL then |ret| %
646  * |add| == 1.)
647  *
648  * If |cb| is not NULL, it will be called during processing to give an
649  * indication of progress. See the comments for |BN_GENCB|. It returns one on
650  * success and zero otherwise. */
651 OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
652                                         const BIGNUM *add, const BIGNUM *rem,
653                                         BN_GENCB *cb);
654 
655 /* BN_prime_checks is magic value that can be used as the |checks| argument to
656  * the primality testing functions in order to automatically select a number of
657  * Miller-Rabin checks that gives a false positive rate of ~2^{-80}. */
658 #define BN_prime_checks 0
659 
660 /* BN_primality_test sets |*is_probably_prime| to one if |candidate| is
661  * probably a prime number by the Miller-Rabin test or zero if it's certainly
662  * not.
663  *
664  * If |do_trial_division| is non-zero then |candidate| will be tested against a
665  * list of small primes before Miller-Rabin tests. The probability of this
666  * function returning a false positive is 2^{2*checks}. If |checks| is
667  * |BN_prime_checks| then a value that results in approximately 2^{-80} false
668  * positive probability is used. If |cb| is not NULL then it is called during
669  * the checking process. See the comment above |BN_GENCB|.
670  *
671  * The function returns one on success and zero on error.
672  *
673  * (If you are unsure whether you want |do_trial_division|, don't set it.) */
674 OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime,
675                                      const BIGNUM *candidate, int checks,
676                                      BN_CTX *ctx, int do_trial_division,
677                                      BN_GENCB *cb);
678 
679 /* BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime
680  * number by the Miller-Rabin test, zero if it's certainly not and -1 on error.
681  *
682  * If |do_trial_division| is non-zero then |candidate| will be tested against a
683  * list of small primes before Miller-Rabin tests. The probability of this
684  * function returning one when |candidate| is composite is 2^{2*checks}. If
685  * |checks| is |BN_prime_checks| then a value that results in approximately
686  * 2^{-80} false positive probability is used. If |cb| is not NULL then it is
687  * called during the checking process. See the comment above |BN_GENCB|.
688  *
689  * WARNING: deprecated. Use |BN_primality_test|. */
690 OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks,
691                                            BN_CTX *ctx, int do_trial_division,
692                                            BN_GENCB *cb);
693 
694 /* BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with
695  * |do_trial_division| set to zero.
696  *
697  * WARNING: deprecated: Use |BN_primality_test|. */
698 OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks,
699                                   BN_CTX *ctx, BN_GENCB *cb);
700 
701 
702 /* Number theory functions */
703 
704 /* BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero
705  * otherwise. */
706 OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
707                           BN_CTX *ctx);
708 
709 /* BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If either of |a| or |n|
710  * have |BN_FLG_CONSTTIME| set then the operation is performed in constant
711  * time. If |out| is NULL, a fresh BIGNUM is allocated. It returns the result
712  * or NULL on error. */
713 OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a,
714                                       const BIGNUM *n, BN_CTX *ctx);
715 
716 /* BN_mod_inverse_ex acts like |BN_mod_inverse| except that, when it returns
717  * zero, it will set |*out_no_inverse| to one if the failure was caused because
718  * |a| has no inverse mod |n|. Otherwise it will set |*out_no_inverse| to
719  * zero. */
720 OPENSSL_EXPORT BIGNUM *BN_mod_inverse_ex(BIGNUM *out, int *out_no_inverse,
721                                          const BIGNUM *a, const BIGNUM *n,
722                                          BN_CTX *ctx);
723 
724 /* BN_kronecker returns the Kronecker symbol of |a| and |b| (which is -1, 0 or
725  * 1), or -2 on error. */
726 OPENSSL_EXPORT int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
727 
728 
729 /* Montgomery arithmetic. */
730 
731 /* BN_MONT_CTX contains the precomputed values needed to work in a specific
732  * Montgomery domain. */
733 
734 /* BN_MONT_CTX_new returns a fresh BN_MONT_CTX or NULL on allocation failure. */
735 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void);
736 
737 /* BN_MONT_CTX_free frees memory associated with |mont|. */
738 OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont);
739 
740 /* BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or
741  * NULL on error. */
742 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,
743                                              const BN_MONT_CTX *from);
744 
745 /* BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It
746  * returns one on success and zero on error. */
747 OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod,
748                                    BN_CTX *ctx);
749 
750 /* BN_MONT_CTX_set_locked takes |lock| and checks whether |*pmont| is NULL. If
751  * so, it creates a new |BN_MONT_CTX| and sets the modulus for it to |mod|. It
752  * then stores it as |*pmont| and returns it, or NULL on error.
753  *
754  * If |*pmont| is already non-NULL then the existing value is returned. */
755 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
756                                     const BIGNUM *mod, BN_CTX *bn_ctx);
757 
758 /* BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. It
759  * returns one on success and zero on error. */
760 OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a,
761                                     const BN_MONT_CTX *mont, BN_CTX *ctx);
762 
763 /* BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values
764  * out of the Montgomery domain. It returns one on success or zero on error. */
765 OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a,
766                                       const BN_MONT_CTX *mont, BN_CTX *ctx);
767 
768 /* BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain.
769  * Both |a| and |b| must already be in the Montgomery domain (by
770  * |BN_to_montgomery|). It returns one on success or zero on error. */
771 OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a,
772                                          const BIGNUM *b,
773                                          const BN_MONT_CTX *mont, BN_CTX *ctx);
774 
775 
776 /* Exponentiation. */
777 
778 /* BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply
779  * algorithm that leaks side-channel information. It returns one on success or
780  * zero otherwise. */
781 OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
782                           BN_CTX *ctx);
783 
784 /* BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best
785  * algorithm for the values provided and can run in constant time if
786  * |BN_FLG_CONSTTIME| is set for |p|. It returns one on success or zero
787  * otherwise. */
788 OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
789                               const BIGNUM *m, BN_CTX *ctx);
790 
791 OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
792                                    const BIGNUM *m, BN_CTX *ctx,
793                                    const BN_MONT_CTX *mont);
794 
795 OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a,
796                                              const BIGNUM *p, const BIGNUM *m,
797                                              BN_CTX *ctx,
798                                              const BN_MONT_CTX *mont);
799 
800 OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
801                                         const BIGNUM *m, BN_CTX *ctx,
802                                         const BN_MONT_CTX *mont);
803 OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1,
804                                     const BIGNUM *p1, const BIGNUM *a2,
805                                     const BIGNUM *p2, const BIGNUM *m,
806                                     BN_CTX *ctx, const BN_MONT_CTX *mont);
807 
808 
809 /* Deprecated functions */
810 
811 /* BN_bn2mpi serialises the value of |in| to |out|, using a format that consists
812  * of the number's length in bytes represented as a 4-byte big-endian number,
813  * and the number itself in big-endian format, where the most significant bit
814  * signals a negative number. (The representation of numbers with the MSB set is
815  * prefixed with null byte). |out| must have sufficient space available; to
816  * find the needed amount of space, call the function with |out| set to NULL. */
817 OPENSSL_EXPORT size_t BN_bn2mpi(const BIGNUM *in, uint8_t *out);
818 
819 /* BN_mpi2bn parses |len| bytes from |in| and returns the resulting value. The
820  * bytes at |in| are expected to be in the format emitted by |BN_bn2mpi|.
821  *
822  * If |out| is NULL then a fresh |BIGNUM| is allocated and returned, otherwise
823  * |out| is reused and returned. On error, NULL is returned and the error queue
824  * is updated. */
825 OPENSSL_EXPORT BIGNUM *BN_mpi2bn(const uint8_t *in, size_t len, BIGNUM *out);
826 
827 
828 /* Private functions */
829 
830 struct bignum_st {
831   BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks in little-endian
832                   order. */
833   int top;   /* Index of last used element in |d|, plus one. */
834   int dmax;  /* Size of |d|, in words. */
835   int neg;   /* one if the number is negative */
836   int flags; /* bitmask of BN_FLG_* values */
837 };
838 
839 struct bn_mont_ctx_st {
840   BIGNUM RR; /* used to convert to montgomery form */
841   BIGNUM N;  /* The modulus */
842   BN_ULONG n0[2]; /* least significant words of (R*Ri-1)/N */
843 };
844 
845 OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l);
846 
847 #define BN_FLG_MALLOCED 0x01
848 #define BN_FLG_STATIC_DATA 0x02
849 /* avoid leaking exponent information through timing, BN_mod_exp_mont() will
850  * call BN_mod_exp_mont_consttime, BN_div() will call BN_div_no_branch,
851  * BN_mod_inverse() will call BN_mod_inverse_no_branch. */
852 #define BN_FLG_CONSTTIME 0x04
853 
854 
855 /* Android compatibility section.
856  *
857  * These functions are declared, temporarily, for Android because
858  * wpa_supplicant will take a little time to sync with upstream. Outside of
859  * Android they'll have no definition. */
860 
861 OPENSSL_EXPORT BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
862 
863 
864 #if defined(__cplusplus)
865 }  /* extern C */
866 #endif
867 
868 #define BN_R_ARG2_LT_ARG3 100
869 #define BN_R_BAD_RECIPROCAL 101
870 #define BN_R_BIGNUM_TOO_LONG 102
871 #define BN_R_BITS_TOO_SMALL 103
872 #define BN_R_CALLED_WITH_EVEN_MODULUS 104
873 #define BN_R_DIV_BY_ZERO 105
874 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 106
875 #define BN_R_INPUT_NOT_REDUCED 107
876 #define BN_R_INVALID_RANGE 108
877 #define BN_R_NEGATIVE_NUMBER 109
878 #define BN_R_NOT_A_SQUARE 110
879 #define BN_R_NOT_INITIALIZED 111
880 #define BN_R_NO_INVERSE 112
881 #define BN_R_PRIVATE_KEY_TOO_LARGE 113
882 #define BN_R_P_IS_NOT_PRIME 114
883 #define BN_R_TOO_MANY_ITERATIONS 115
884 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 116
885 #define BN_R_BAD_ENCODING 117
886 #define BN_R_ENCODE_ERROR 118
887 
888 #endif  /* OPENSSL_HEADER_BN_H */
889