1 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
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.
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).
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.
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
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)"
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
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.]
57 /* ====================================================================
58 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
60 * Redistribution and use in source and binary forms, with or without
61 * modification, are permitted provided that the following conditions
64 * 1. Redistributions of source code must retain the above copyright
65 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
86 * 6. Redistributions of any form whatsoever must retain the following
88 * "This product includes software developed by the OpenSSL Project
89 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
110 /* ====================================================================
111 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
113 * Portions of the attached software ("Contribution") are developed by
114 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
116 * The Contribution is licensed pursuant to the Eric Young open source
117 * license provided above.
119 * The binary polynomial arithmetic software is originally written by
120 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
123 #ifndef OPENSSL_HEADER_BN_H
124 #define OPENSSL_HEADER_BN_H
126 #include <openssl/base.h>
128 #include <stdio.h> /* for FILE* */
130 #if defined(__cplusplus)
135 /* BN provides support for working with arbitary sized integers. For example,
136 * although the largest integer supported by the compiler might be 64 bits, BN
137 * will allow you to work with numbers until you run out of memory. */
140 /* BN_ULONG is the native word size when working with big integers. */
141 #if defined(OPENSSL_64_BIT)
142 #define BN_ULONG uint64_t
144 #elif defined(OPENSSL_32_BIT)
145 #define BN_ULONG uint32_t
148 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
152 /* Allocation and freeing. */
154 /* BN_new creates a new, allocated BIGNUM and initialises it. */
155 OPENSSL_EXPORT BIGNUM *BN_new(void);
157 /* BN_init initialises a stack allocated |BIGNUM|. */
158 OPENSSL_EXPORT void BN_init(BIGNUM *bn);
160 /* BN_free frees the data referenced by |bn| and, if |bn| was originally
161 * allocated on the heap, frees |bn| also. */
162 OPENSSL_EXPORT void BN_free(BIGNUM *bn);
164 /* BN_clear_free erases and frees the data referenced by |bn| and, if |bn| was
165 * originally allocated on the heap, frees |bn| also. */
166 OPENSSL_EXPORT void BN_clear_free(BIGNUM *bn);
168 /* BN_dup allocates a new BIGNUM and sets it equal to |src|. It returns the
169 * allocated BIGNUM on success or NULL otherwise. */
170 OPENSSL_EXPORT BIGNUM *BN_dup(const BIGNUM *src);
172 /* BN_copy sets |dest| equal to |src| and returns |dest|. */
173 OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src);
175 /* BN_clear sets |bn| to zero and erases the old data. */
176 OPENSSL_EXPORT void BN_clear(BIGNUM *bn);
178 /* BN_value_one returns a static BIGNUM with value 1. */
179 OPENSSL_EXPORT const BIGNUM *BN_value_one(void);
181 /* BN_with_flags initialises a stack allocated |BIGNUM| with pointers to the
182 * contents of |in| but with |flags| ORed into the flags field.
184 * Note: the two BIGNUMs share state and so |out| should /not/ be passed to
186 OPENSSL_EXPORT void BN_with_flags(BIGNUM *out, const BIGNUM *in, int flags);
189 /* Basic functions. */
191 /* BN_num_bits returns the minimum number of bits needed to represent the
192 * absolute value of |bn|. */
193 OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn);
195 /* BN_num_bytes returns the minimum number of bytes needed to represent the
196 * absolute value of |bn|. */
197 OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn);
199 /* BN_zero sets |bn| to zero. */
200 OPENSSL_EXPORT void BN_zero(BIGNUM *bn);
202 /* BN_one sets |bn| to one. It returns one on success or zero on allocation
204 OPENSSL_EXPORT int BN_one(BIGNUM *bn);
206 /* BN_set_word sets |bn| to |value|. It returns one on success or zero on
207 * allocation failure. */
208 OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value);
210 /* BN_set_negative sets the sign of |bn|. */
211 OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign);
213 /* BN_is_negative returns one if |bn| is negative and zero otherwise. */
214 OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn);
216 /* BN_get_flags returns |bn->flags| & |flags|. */
217 OPENSSL_EXPORT int BN_get_flags(const BIGNUM *bn, int flags);
219 /* BN_set_flags sets |flags| on |bn|. */
220 OPENSSL_EXPORT void BN_set_flags(BIGNUM *bn, int flags);
223 /* Conversion functions. */
225 /* BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as
226 * a big-endian number, and returns |ret|. If |ret| is NULL then a fresh
227 * |BIGNUM| is allocated and returned. It returns NULL on allocation
229 OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret);
231 /* BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian
232 * integer, which must have |BN_num_bytes| of space available. It returns the
233 * number of bytes written. */
234 OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out);
236 /* BN_bn2bin_padded serialises the absolute value of |in| to |out| as a
237 * big-endian integer. The integer is padded with leading zeros up to size
238 * |len|. If |len| is smaller than |BN_num_bytes|, the function fails and
239 * returns 0. Otherwise, it returns 1. */
240 OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in);
242 /* BN_bn2hex returns an allocated string that contains a NUL-terminated, hex
243 * representation of |bn|. If |bn| is negative, the first char in the resulting
244 * string will be '-'. Returns NULL on allocation failure. */
245 OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn);
247 /* BN_hex2bn parses the leading hex number from |in|, which may be proceeded by
248 * a '-' to indicate a negative number and may contain trailing, non-hex data.
249 * If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and
250 * stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and
251 * updates |*outp|. It returns the number of bytes of |in| processed or zero on
253 OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in);
255 /* BN_bn2dec returns an allocated string that contains a NUL-terminated,
256 * decimal representation of |bn|. If |bn| is negative, the first char in the
257 * resulting string will be '-'. Returns NULL on allocation failure. */
258 OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a);
260 /* BN_dec2bn parses the leading decimal number from |in|, which may be
261 * proceeded by a '-' to indicate a negative number and may contain trailing,
262 * non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the
263 * decimal number and stores it in |*outp|. If |*outp| is NULL then it
264 * allocates a new BIGNUM and updates |*outp|. It returns the number of bytes
265 * of |in| processed or zero on error. */
266 OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in);
268 /* BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in|
269 * begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A
270 * leading '-' is still permitted and comes before the optional 0X/0x. It
271 * returns one on success or zero on error. */
272 OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in);
274 /* BN_print writes a hex encoding of |a| to |bio|. It returns one on success
275 * and zero on error. */
276 OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a);
278 /* BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first. */
279 OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a);
281 /* BN_get_word returns the absolute value of |bn| as a single word. If |bn| is
282 * too large to be represented as a single word, the maximum possible value
283 * will be returned. */
284 OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn);
289 * Certain BIGNUM operations need to use many temporary variables and
290 * allocating and freeing them can be quite slow. Thus such opertions typically
291 * take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx|
292 * argument to a public function may be NULL, in which case a local |BN_CTX|
293 * will be created just for the lifetime of that call.
295 * A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called
296 * repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made
297 * before calling any other functions that use the |ctx| as an argument.
299 * Finally, |BN_CTX_end| must be called before returning from the function.
300 * When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from
301 * |BN_CTX_get| become invalid. */
303 /* BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure. */
304 OPENSSL_EXPORT BN_CTX *BN_CTX_new(void);
306 /* BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx|
308 OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx);
310 /* BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future
311 * calls to |BN_CTX_get|. */
312 OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx);
314 /* BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once
315 * |BN_CTX_get| has returned NULL, all future calls will also return NULL until
316 * |BN_CTX_end| is called. */
317 OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx);
319 /* BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the
320 * matching |BN_CTX_start| call. */
321 OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx);
324 /* Simple arithmetic */
326 /* BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a|
327 * or |b|. It returns one on success and zero on allocation failure. */
328 OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
330 /* BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may
331 * be the same pointer as either |a| or |b|. It returns one on success and zero
332 * on allocation failure. */
333 OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
335 /* BN_add_word adds |w| to |a|. It returns one on success and zero otherwise. */
336 OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w);
338 /* BN_sub sets |r| = |a| + |b|, where |r| must be a distinct pointer from |a|
339 * and |b|. It returns one on success and zero on allocation failure. */
340 OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
342 /* BN_usub sets |r| = |a| + |b|, where |a| and |b| are non-negative integers,
343 * |b| < |a| and |r| must be a distinct pointer from |a| and |b|. It returns
344 * one on success and zero on allocation failure. */
345 OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
347 /* BN_sub_word subtracts |w| from |a|. It returns one on success and zero on
348 * allocation failure. */
349 OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w);
351 /* BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or
352 * |b|. Returns one on success and zero otherwise. */
353 OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
356 /* BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on
357 * allocation failure. */
358 OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w);
360 /* BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as
361 * |a|. Returns one on success and zero otherwise. This is more efficient than
362 * BN_mul(r, a, a, ctx). */
363 OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
365 /* BN_div divides |numerator| by |divisor| and places the result in |quotient|
366 * and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in
367 * which case the respective value is not returned. The result is rounded
368 * towards zero; thus if |numerator| is negative, the remainder will be zero or
369 * negative. It returns one on success or zero on error. */
370 OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem,
371 const BIGNUM *numerator, const BIGNUM *divisor,
374 /* BN_div_word sets |numerator| = |numerator|/|divisor| and returns the
375 * remainder or (BN_ULONG)-1 on error. */
376 OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor);
378 /* BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the
379 * square root of |in|, using |ctx|. It returns one on success or zero on
380 * error. Negative numbers and non-square numbers will result in an error with
381 * appropriate errors on the error queue. */
382 OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx);
385 /* Comparison functions */
387 /* BN_cmp returns a value less than, equal to or greater than zero if |a| is
388 * less than, equal to or greater than |b|, respectively. */
389 OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b);
391 /* BN_ucmp returns a value less than, equal to or greater than zero if the
392 * absolute value of |a| is less than, equal to or greater than the absolute
393 * value of |b|, respectively. */
394 OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
396 /* BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero
398 OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w);
400 /* BN_is_zero returns one if |bn| is zero and zero otherwise. */
401 OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn);
403 /* BN_is_one returns one if |bn| equals one and zero otherwise. */
404 OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn);
406 /* BN_is_word returns one if |bn| is exactly |w| and zero otherwise. */
407 OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w);
409 /* BN_is_odd returns one if |bn| is odd and zero otherwise. */
410 OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn);
413 /* Bitwise operations. */
415 /* BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the
416 * same |BIGNUM|. It returns one on success and zero on allocation failure. */
417 OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
419 /* BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same
420 * pointer. It returns one on success and zero on allocation failure. */
421 OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a);
423 /* BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same
424 * pointer. It returns one on success and zero on allocation failure. */
425 OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
427 /* BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same
428 * pointer. It returns one on success and zero on allocation failure. */
429 OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a);
431 /* BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a|
432 * is 2 then setting bit zero will make it 3. It returns one on success or zero
433 * on allocation failure. */
434 OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n);
436 /* BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if
437 * |a| is 3, clearing bit zero will make it two. It returns one on success or
438 * zero on allocation failure. */
439 OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n);
441 /* BN_is_bit_set returns the value of the |n|th, least-significant bit in |a|,
442 * or zero if the bit doesn't exist. */
443 OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n);
445 /* BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one
446 * on success or zero if |n| is greater than the length of |a| already. */
447 OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n);
450 /* Modulo arithmetic. */
452 /* BN_mod_word returns |a| mod |w|. */
453 OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
455 /* BN_mod is a helper macro that calls |BN_div| and discards the quotient. */
456 #define BN_mod(rem, numerator, divisor, ctx) \
457 BN_div(NULL, (rem), (numerator), (divisor), (ctx))
459 /* BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <=
460 * |rem| < |divisor| is always true. */
461 OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator,
462 const BIGNUM *divisor, BN_CTX *ctx);
464 /* BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero
466 OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
467 const BIGNUM *m, BN_CTX *ctx);
469 /* BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be
470 * non-negative and less than |m|. */
471 OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
474 /* BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero
476 OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
477 const BIGNUM *m, BN_CTX *ctx);
479 /* BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be
480 * non-negative and less than |m|. */
481 OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
484 /* BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero
486 OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
487 const BIGNUM *m, BN_CTX *ctx);
489 /* BN_mod_mul sets |r| = |a|^2 mod |m|. It returns one on success and zero
491 OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
494 /* BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the
495 * same pointer. It returns one on success and zero on error. */
496 OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n,
497 const BIGNUM *m, BN_CTX *ctx);
499 /* BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be
500 * non-negative and less than |m|. */
501 OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n,
504 /* BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the
505 * same pointer. It returns one on success and zero on error. */
506 OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
509 /* BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be
510 * non-negative and less than |m|. */
511 OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a,
514 /* BN_mod_sqrt returns a |BIGNUM|, r, such that r^2 == a (mod p). */
515 OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p,
519 /* Random and prime number generation. */
521 /* BN_rand sets |rnd| to a random number of length |bits|. If |top| is zero,
522 * the most-significant bit will be set. If |top| is one, the two most
523 * significant bits will be set.
525 * If |top| is -1 then no extra action will be taken and |BN_num_bits(rnd)| may
526 * not equal |bits| if the most significant bits randomly ended up as zeros.
528 * If |bottom| is non-zero, the least-significant bit will be set. The function
529 * returns one on success or zero otherwise. */
530 OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
532 /* BN_pseudo_rand is an alias for |BN_rand|. */
533 OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
535 /* BN_rand_range sets |rnd| to a random value [0..range). It returns one on
536 * success and zero otherwise. */
537 OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
539 /* BN_pseudo_rand_range is an alias for BN_rand_range. */
540 OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
542 /* BN_generate_dsa_nonce generates a random number 0 <= out < range. Unlike
543 * BN_rand_range, it also includes the contents of |priv| and |message| in the
544 * generation so that an RNG failure isn't fatal as long as |priv| remains
545 * secret. This is intended for use in DSA and ECDSA where an RNG weakness
546 * leads directly to private key exposure unless this function is used.
547 * It returns one on success and zero on error. */
548 OPENSSL_EXPORT int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
550 const uint8_t *message,
551 size_t message_len, BN_CTX *ctx);
553 /* BN_GENCB holds a callback function that is used by generation functions that
554 * can take a very long time to complete. Use |BN_GENCB_set| to initialise a
555 * |BN_GENCB| structure.
557 * The callback receives the address of that |BN_GENCB| structure as its last
558 * argument and the user is free to put an arbitary pointer in |arg|. The other
559 * arguments are set as follows:
560 * event=BN_GENCB_GENERATED, n=i: after generating the i'th possible prime
562 * event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality
564 * event=BN_GENCB_PRIME_TEST, n=i: when the i'th primality test has finished.
566 * The callback can return zero to abort the generation progress or one to
567 * allow it to continue.
569 * When other code needs to call a BN generation function it will often take a
570 * BN_GENCB argument and may call the function with other argument values. */
571 #define BN_GENCB_GENERATED 0
572 #define BN_GENCB_PRIME_TEST 1
575 void *arg; /* callback-specific data */
576 int (*callback)(int event, int n, struct bn_gencb_st *);
579 /* BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to
581 OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback,
582 int (*f)(int event, int n,
583 struct bn_gencb_st *),
586 /* BN_GENCB_call calls |callback|, if not NULL, and returns the return value of
587 * the callback, or 1 if |callback| is NULL. */
588 OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n);
590 /* BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe
591 * is non-zero then the prime will be such that (ret-1)/2 is also a prime.
592 * (This is needed for Diffie-Hellman groups to ensure that the only subgroups
593 * are of size 2 and (p-1)/2.).
595 * If |add| is not NULL, the prime will fulfill the condition |ret| % |add| ==
596 * |rem| in order to suit a given generator. (If |rem| is NULL then |ret| %
599 * If |cb| is not NULL, it will be called during processing to give an
600 * indication of progress. See the comments for |BN_GENCB|. It returns one on
601 * success and zero otherwise. */
602 OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
603 const BIGNUM *add, const BIGNUM *rem,
606 /* BN_prime_checks is magic value that can be used as the |checks| argument to
607 * the primality testing functions in order to automatically select a number of
608 * Miller-Rabin checks that gives a false positive rate of ~2^{-80}. */
609 #define BN_prime_checks 0
611 /* BN_primality_test sets |*is_probably_prime| to one if |candidate| is
612 * probably a prime number by the Miller-Rabin test or zero if it's certainly
615 * If |do_trial_division| is non-zero then |candidate| will be tested against a
616 * list of small primes before Miller-Rabin tests. The probability of this
617 * function returning a false positive is 2^{2*checks}. If |checks| is
618 * |BN_prime_checks| then a value that results in approximately 2^{-80} false
619 * positive probability is used. If |cb| is not NULL then it is called during
620 * the checking process. See the comment above |BN_GENCB|.
622 * The function returns one on success and zero on error.
624 * (If you are unsure whether you want |do_trial_division|, don't set it.) */
625 OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime,
626 const BIGNUM *candidate, int checks,
627 BN_CTX *ctx, int do_trial_division,
630 /* BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime
631 * number by the Miller-Rabin test, zero if it's certainly not and -1 on error.
633 * If |do_trial_division| is non-zero then |candidate| will be tested against a
634 * list of small primes before Miller-Rabin tests. The probability of this
635 * function returning one when |candidate| is composite is 2^{2*checks}. If
636 * |checks| is |BN_prime_checks| then a value that results in approximately
637 * 2^{-80} false positive probability is used. If |cb| is not NULL then it is
638 * called during the checking process. See the comment above |BN_GENCB|.
640 * WARNING: deprecated. Use |BN_primality_test|. */
641 OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks,
642 BN_CTX *ctx, int do_trial_division,
645 /* BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with
646 * |do_trial_division| set to zero.
648 * WARNING: deprecated: Use |BN_primality_test|. */
649 OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks,
650 BN_CTX *ctx, BN_GENCB *cb);
653 /* Number theory functions */
655 /* BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero
657 OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
660 /* BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If either of |a| or |n|
661 * have |BN_FLG_CONSTTIME| set then the operation is performed in constant
662 * time. If |out| is NULL, a fresh BIGNUM is allocated. It returns the result
663 * or NULL on error. */
664 OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a,
665 const BIGNUM *n, BN_CTX *ctx);
667 /* BN_kronecker returns the Kronecker symbol of |a| and |b| (which is -1, 0 or
668 * 1), or -2 on error. */
669 OPENSSL_EXPORT int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
672 /* Montgomery arithmetic. */
674 /* BN_MONT_CTX contains the precomputed values needed to work in a specific
675 * Montgomery domain. */
677 /* BN_MONT_CTX_new returns a fresh BN_MONT_CTX or NULL on allocation failure. */
678 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void);
680 /* BN_MONT_CTX_init initialises a stack allocated |BN_MONT_CTX|. */
681 OPENSSL_EXPORT void BN_MONT_CTX_init(BN_MONT_CTX *mont);
683 /* BN_MONT_CTX_free frees the contexts of |mont| and, if it was originally
684 * allocated with |BN_MONT_CTX_new|, |mont| itself. */
685 OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont);
687 /* BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or
689 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,
692 /* BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It
693 * returns one on success and zero on error. */
694 OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod,
697 /* BN_MONT_CTX_set_locked takes the lock indicated by |lock| and checks whether
698 * |*pmont| is NULL. If so, it creates a new |BN_MONT_CTX| and sets the modulus
699 * for it to |mod|. It then stores it as |*pmont| and returns it, or NULL on
702 * If |*pmont| is already non-NULL then the existing value is returned. */
703 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont,
704 int lock, const BIGNUM *mod,
707 /* BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. It
708 * returns one on success and zero on error. */
709 OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a,
710 const BN_MONT_CTX *mont, BN_CTX *ctx);
712 /* BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values
713 * out of the Montgomery domain. It returns one on success or zero on error. */
714 OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a,
715 const BN_MONT_CTX *mont, BN_CTX *ctx);
717 /* BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain.
718 * Both |a| and |b| must already be in the Montgomery domain (by
719 * |BN_to_montgomery|). It returns one on success or zero on error. */
720 OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a,
722 const BN_MONT_CTX *mont, BN_CTX *ctx);
725 /* Exponentiation. */
727 /* BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply
728 * algorithm that leaks side-channel information. It returns one on success or
730 OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
733 /* BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best
734 * algorithm for the values provided and can run in constant time if
735 * |BN_FLG_CONSTTIME| is set for |p|. It returns one on success or zero
737 OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
738 const BIGNUM *m, BN_CTX *ctx);
740 OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
741 const BIGNUM *m, BN_CTX *ctx,
744 OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a,
745 const BIGNUM *p, const BIGNUM *m,
746 BN_CTX *ctx, BN_MONT_CTX *in_mont);
748 OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
749 const BIGNUM *m, BN_CTX *ctx,
751 OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1,
752 const BIGNUM *p1, const BIGNUM *a2,
753 const BIGNUM *p2, const BIGNUM *m,
754 BN_CTX *ctx, BN_MONT_CTX *m_ctx);
757 /* Private functions */
760 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks in little-endian
762 int top; /* Index of last used element in |d|, plus one. */
763 int dmax; /* Size of |d|, in words. */
764 int neg; /* one if the number is negative */
765 int flags; /* bitmask of BN_FLG_* values */
768 struct bn_mont_ctx_st {
769 BIGNUM RR; /* used to convert to montgomery form */
770 BIGNUM N; /* The modulus */
771 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
772 * (Ni is only stored for bignum algorithm) */
773 BN_ULONG n0[2]; /* least significant word(s) of Ni;
774 (type changed with 0.9.9, was "BN_ULONG n0;" before) */
776 int ri; /* number of bits in R */
779 unsigned BN_num_bits_word(BN_ULONG l);
781 #define BN_FLG_MALLOCED 0x01
782 #define BN_FLG_STATIC_DATA 0x02
783 /* avoid leaking exponent information through timing, BN_mod_exp_mont() will
784 * call BN_mod_exp_mont_consttime, BN_div() will call BN_div_no_branch,
785 * BN_mod_inverse() will call BN_mod_inverse_no_branch. */
786 #define BN_FLG_CONSTTIME 0x04
789 #if defined(__cplusplus)
793 #define BN_F_BN_bn2hex 100
794 #define BN_F_BN_new 101
795 #define BN_F_BN_exp 102
796 #define BN_F_mod_exp_recp 103
797 #define BN_F_BN_mod_sqrt 104
798 #define BN_F_BN_rand 105
799 #define BN_F_BN_rand_range 106
800 #define BN_F_bn_wexpand 107
801 #define BN_F_BN_mod_exp_mont 108
802 #define BN_F_BN_mod_exp2_mont 109
803 #define BN_F_BN_CTX_get 110
804 #define BN_F_BN_mod_inverse 111
805 #define BN_F_BN_bn2dec 112
806 #define BN_F_BN_div 113
807 #define BN_F_BN_div_recp 114
808 #define BN_F_BN_mod_exp_mont_consttime 115
809 #define BN_F_BN_mod_exp_mont_word 116
810 #define BN_F_BN_CTX_start 117
811 #define BN_F_BN_usub 118
812 #define BN_F_BN_mod_lshift_quick 119
813 #define BN_F_BN_CTX_new 120
814 #define BN_F_BN_mod_inverse_no_branch 121
815 #define BN_F_BN_generate_dsa_nonce 122
816 #define BN_F_BN_generate_prime_ex 123
817 #define BN_F_BN_sqrt 124
818 #define BN_R_NOT_A_SQUARE 100
819 #define BN_R_TOO_MANY_ITERATIONS 101
820 #define BN_R_INPUT_NOT_REDUCED 102
821 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 103
822 #define BN_R_NO_INVERSE 104
823 #define BN_R_NOT_INITIALIZED 105
824 #define BN_R_DIV_BY_ZERO 106
825 #define BN_R_CALLED_WITH_EVEN_MODULUS 107
826 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 108
827 #define BN_R_BAD_RECIPROCAL 109
828 #define BN_R_P_IS_NOT_PRIME 110
829 #define BN_R_INVALID_RANGE 111
830 #define BN_R_ARG2_LT_ARG3 112
831 #define BN_R_BIGNUM_TOO_LONG 113
832 #define BN_R_PRIVATE_KEY_TOO_LARGE 114
833 #define BN_R_BITS_TOO_SMALL 115
834 #define BN_R_NEGATIVE_NUMBER 116
836 #endif /* OPENSSL_HEADER_BN_H */