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);
287 /* Internal functions.
289 * These functions are useful for code that is doing low-level manipulations of
290 * BIGNUM values. However, be sure that no other function in this file does
291 * what you want before turning to these. */
293 /* bn_correct_top decrements |bn->top| until |bn->d[top-1]| is non-zero or
294 * until |top| is zero. */
295 OPENSSL_EXPORT void bn_correct_top(BIGNUM *bn);
297 /* bn_wexpand ensures that |bn| has at least |words| works of space without
298 * altering its value. It returns one on success or zero on allocation
300 OPENSSL_EXPORT BIGNUM *bn_wexpand(BIGNUM *bn, unsigned words);
305 * Certain BIGNUM operations need to use many temporary variables and
306 * allocating and freeing them can be quite slow. Thus such opertions typically
307 * take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx|
308 * argument to a public function may be NULL, in which case a local |BN_CTX|
309 * will be created just for the lifetime of that call.
311 * A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called
312 * repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made
313 * before calling any other functions that use the |ctx| as an argument.
315 * Finally, |BN_CTX_end| must be called before returning from the function.
316 * When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from
317 * |BN_CTX_get| become invalid. */
319 /* BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure. */
320 OPENSSL_EXPORT BN_CTX *BN_CTX_new(void);
322 /* BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx|
324 OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx);
326 /* BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future
327 * calls to |BN_CTX_get|. */
328 OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx);
330 /* BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once
331 * |BN_CTX_get| has returned NULL, all future calls will also return NULL until
332 * |BN_CTX_end| is called. */
333 OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx);
335 /* BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the
336 * matching |BN_CTX_start| call. */
337 OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx);
340 /* Simple arithmetic */
342 /* BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a|
343 * or |b|. It returns one on success and zero on allocation failure. */
344 OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
346 /* BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may
347 * be the same pointer as either |a| or |b|. It returns one on success and zero
348 * on allocation failure. */
349 OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
351 /* BN_add_word adds |w| to |a|. It returns one on success and zero otherwise. */
352 OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w);
354 /* BN_sub sets |r| = |a| - |b|, where |r| must be a distinct pointer from |a|
355 * and |b|. It returns one on success and zero on allocation failure. */
356 OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
358 /* BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers,
359 * |b| < |a| and |r| must be a distinct pointer from |a| and |b|. It returns
360 * one on success and zero on allocation failure. */
361 OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
363 /* BN_sub_word subtracts |w| from |a|. It returns one on success and zero on
364 * allocation failure. */
365 OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w);
367 /* BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or
368 * |b|. Returns one on success and zero otherwise. */
369 OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
372 /* BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on
373 * allocation failure. */
374 OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w);
376 /* BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as
377 * |a|. Returns one on success and zero otherwise. This is more efficient than
378 * BN_mul(r, a, a, ctx). */
379 OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
381 /* BN_div divides |numerator| by |divisor| and places the result in |quotient|
382 * and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in
383 * which case the respective value is not returned. The result is rounded
384 * towards zero; thus if |numerator| is negative, the remainder will be zero or
385 * negative. It returns one on success or zero on error. */
386 OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem,
387 const BIGNUM *numerator, const BIGNUM *divisor,
390 /* BN_div_word sets |numerator| = |numerator|/|divisor| and returns the
391 * remainder or (BN_ULONG)-1 on error. */
392 OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor);
394 /* BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the
395 * square root of |in|, using |ctx|. It returns one on success or zero on
396 * error. Negative numbers and non-square numbers will result in an error with
397 * appropriate errors on the error queue. */
398 OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx);
401 /* Comparison functions */
403 /* BN_cmp returns a value less than, equal to or greater than zero if |a| is
404 * less than, equal to or greater than |b|, respectively. */
405 OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b);
407 /* BN_ucmp returns a value less than, equal to or greater than zero if the
408 * absolute value of |a| is less than, equal to or greater than the absolute
409 * value of |b|, respectively. */
410 OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
412 /* BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero
414 OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w);
416 /* BN_is_zero returns one if |bn| is zero and zero otherwise. */
417 OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn);
419 /* BN_is_one returns one if |bn| equals one and zero otherwise. */
420 OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn);
422 /* BN_is_word returns one if |bn| is exactly |w| and zero otherwise. */
423 OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w);
425 /* BN_is_odd returns one if |bn| is odd and zero otherwise. */
426 OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn);
429 /* Bitwise operations. */
431 /* BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the
432 * same |BIGNUM|. It returns one on success and zero on allocation failure. */
433 OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
435 /* BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same
436 * pointer. It returns one on success and zero on allocation failure. */
437 OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a);
439 /* BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same
440 * pointer. It returns one on success and zero on allocation failure. */
441 OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
443 /* BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same
444 * pointer. It returns one on success and zero on allocation failure. */
445 OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a);
447 /* BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a|
448 * is 2 then setting bit zero will make it 3. It returns one on success or zero
449 * on allocation failure. */
450 OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n);
452 /* BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if
453 * |a| is 3, clearing bit zero will make it two. It returns one on success or
454 * zero on allocation failure. */
455 OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n);
457 /* BN_is_bit_set returns the value of the |n|th, least-significant bit in |a|,
458 * or zero if the bit doesn't exist. */
459 OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n);
461 /* BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one
462 * on success or zero if |n| is greater than the length of |a| already. */
463 OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n);
466 /* Modulo arithmetic. */
468 /* BN_mod_word returns |a| mod |w|. */
469 OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
471 /* BN_mod is a helper macro that calls |BN_div| and discards the quotient. */
472 #define BN_mod(rem, numerator, divisor, ctx) \
473 BN_div(NULL, (rem), (numerator), (divisor), (ctx))
475 /* BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <=
476 * |rem| < |divisor| is always true. */
477 OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator,
478 const BIGNUM *divisor, BN_CTX *ctx);
480 /* BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero
482 OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
483 const BIGNUM *m, BN_CTX *ctx);
485 /* BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be
486 * non-negative and less than |m|. */
487 OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
490 /* BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero
492 OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
493 const BIGNUM *m, BN_CTX *ctx);
495 /* BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be
496 * non-negative and less than |m|. */
497 OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
500 /* BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero
502 OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
503 const BIGNUM *m, BN_CTX *ctx);
505 /* BN_mod_mul sets |r| = |a|^2 mod |m|. It returns one on success and zero
507 OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
510 /* BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the
511 * same pointer. It returns one on success and zero on error. */
512 OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n,
513 const BIGNUM *m, BN_CTX *ctx);
515 /* BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be
516 * non-negative and less than |m|. */
517 OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n,
520 /* BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the
521 * same pointer. It returns one on success and zero on error. */
522 OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
525 /* BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be
526 * non-negative and less than |m|. */
527 OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a,
530 /* BN_mod_sqrt returns a |BIGNUM|, r, such that r^2 == a (mod p). */
531 OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p,
535 /* Random and prime number generation. */
537 /* BN_rand sets |rnd| to a random number of length |bits|. If |top| is zero,
538 * the most-significant bit will be set. If |top| is one, the two most
539 * significant bits will be set.
541 * If |top| is -1 then no extra action will be taken and |BN_num_bits(rnd)| may
542 * not equal |bits| if the most significant bits randomly ended up as zeros.
544 * If |bottom| is non-zero, the least-significant bit will be set. The function
545 * returns one on success or zero otherwise. */
546 OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
548 /* BN_pseudo_rand is an alias for |BN_rand|. */
549 OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
551 /* BN_rand_range sets |rnd| to a random value [0..range). It returns one on
552 * success and zero otherwise. */
553 OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
555 /* BN_pseudo_rand_range is an alias for BN_rand_range. */
556 OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
558 /* BN_generate_dsa_nonce generates a random number 0 <= out < range. Unlike
559 * BN_rand_range, it also includes the contents of |priv| and |message| in the
560 * generation so that an RNG failure isn't fatal as long as |priv| remains
561 * secret. This is intended for use in DSA and ECDSA where an RNG weakness
562 * leads directly to private key exposure unless this function is used.
563 * It returns one on success and zero on error. */
564 OPENSSL_EXPORT int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
566 const uint8_t *message,
567 size_t message_len, BN_CTX *ctx);
569 /* BN_GENCB holds a callback function that is used by generation functions that
570 * can take a very long time to complete. Use |BN_GENCB_set| to initialise a
571 * |BN_GENCB| structure.
573 * The callback receives the address of that |BN_GENCB| structure as its last
574 * argument and the user is free to put an arbitary pointer in |arg|. The other
575 * arguments are set as follows:
576 * event=BN_GENCB_GENERATED, n=i: after generating the i'th possible prime
578 * event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality
580 * event=BN_GENCB_PRIME_TEST, n=i: when the i'th primality test has finished.
582 * The callback can return zero to abort the generation progress or one to
583 * allow it to continue.
585 * When other code needs to call a BN generation function it will often take a
586 * BN_GENCB argument and may call the function with other argument values. */
587 #define BN_GENCB_GENERATED 0
588 #define BN_GENCB_PRIME_TEST 1
591 void *arg; /* callback-specific data */
592 int (*callback)(int event, int n, struct bn_gencb_st *);
595 /* BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to
597 OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback,
598 int (*f)(int event, int n,
599 struct bn_gencb_st *),
602 /* BN_GENCB_call calls |callback|, if not NULL, and returns the return value of
603 * the callback, or 1 if |callback| is NULL. */
604 OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n);
606 /* BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe
607 * is non-zero then the prime will be such that (ret-1)/2 is also a prime.
608 * (This is needed for Diffie-Hellman groups to ensure that the only subgroups
609 * are of size 2 and (p-1)/2.).
611 * If |add| is not NULL, the prime will fulfill the condition |ret| % |add| ==
612 * |rem| in order to suit a given generator. (If |rem| is NULL then |ret| %
615 * If |cb| is not NULL, it will be called during processing to give an
616 * indication of progress. See the comments for |BN_GENCB|. It returns one on
617 * success and zero otherwise. */
618 OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
619 const BIGNUM *add, const BIGNUM *rem,
622 /* BN_prime_checks is magic value that can be used as the |checks| argument to
623 * the primality testing functions in order to automatically select a number of
624 * Miller-Rabin checks that gives a false positive rate of ~2^{-80}. */
625 #define BN_prime_checks 0
627 /* BN_primality_test sets |*is_probably_prime| to one if |candidate| is
628 * probably a prime number by the Miller-Rabin test or zero if it's certainly
631 * If |do_trial_division| is non-zero then |candidate| will be tested against a
632 * list of small primes before Miller-Rabin tests. The probability of this
633 * function returning a false positive is 2^{2*checks}. If |checks| is
634 * |BN_prime_checks| then a value that results in approximately 2^{-80} false
635 * positive probability is used. If |cb| is not NULL then it is called during
636 * the checking process. See the comment above |BN_GENCB|.
638 * The function returns one on success and zero on error.
640 * (If you are unsure whether you want |do_trial_division|, don't set it.) */
641 OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime,
642 const BIGNUM *candidate, int checks,
643 BN_CTX *ctx, int do_trial_division,
646 /* BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime
647 * number by the Miller-Rabin test, zero if it's certainly not and -1 on error.
649 * If |do_trial_division| is non-zero then |candidate| will be tested against a
650 * list of small primes before Miller-Rabin tests. The probability of this
651 * function returning one when |candidate| is composite is 2^{2*checks}. If
652 * |checks| is |BN_prime_checks| then a value that results in approximately
653 * 2^{-80} false positive probability is used. If |cb| is not NULL then it is
654 * called during the checking process. See the comment above |BN_GENCB|.
656 * WARNING: deprecated. Use |BN_primality_test|. */
657 OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks,
658 BN_CTX *ctx, int do_trial_division,
661 /* BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with
662 * |do_trial_division| set to zero.
664 * WARNING: deprecated: Use |BN_primality_test|. */
665 OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks,
666 BN_CTX *ctx, BN_GENCB *cb);
669 /* Number theory functions */
671 /* BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero
673 OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
676 /* BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If either of |a| or |n|
677 * have |BN_FLG_CONSTTIME| set then the operation is performed in constant
678 * time. If |out| is NULL, a fresh BIGNUM is allocated. It returns the result
679 * or NULL on error. */
680 OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a,
681 const BIGNUM *n, BN_CTX *ctx);
683 /* BN_kronecker returns the Kronecker symbol of |a| and |b| (which is -1, 0 or
684 * 1), or -2 on error. */
685 OPENSSL_EXPORT int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
688 /* Montgomery arithmetic. */
690 /* BN_MONT_CTX contains the precomputed values needed to work in a specific
691 * Montgomery domain. */
693 /* BN_MONT_CTX_new returns a fresh BN_MONT_CTX or NULL on allocation failure. */
694 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void);
696 /* BN_MONT_CTX_init initialises a stack allocated |BN_MONT_CTX|. */
697 OPENSSL_EXPORT void BN_MONT_CTX_init(BN_MONT_CTX *mont);
699 /* BN_MONT_CTX_free frees the contexts of |mont| and, if it was originally
700 * allocated with |BN_MONT_CTX_new|, |mont| itself. */
701 OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont);
703 /* BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or
705 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,
708 /* BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It
709 * returns one on success and zero on error. */
710 OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod,
713 /* BN_MONT_CTX_set_locked takes the lock indicated by |lock| and checks whether
714 * |*pmont| is NULL. If so, it creates a new |BN_MONT_CTX| and sets the modulus
715 * for it to |mod|. It then stores it as |*pmont| and returns it, or NULL on
718 * If |*pmont| is already non-NULL then the existing value is returned. */
719 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont,
720 int lock, const BIGNUM *mod,
723 /* BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. It
724 * returns one on success and zero on error. */
725 OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a,
726 const BN_MONT_CTX *mont, BN_CTX *ctx);
728 /* BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values
729 * out of the Montgomery domain. It returns one on success or zero on error. */
730 OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a,
731 const BN_MONT_CTX *mont, BN_CTX *ctx);
733 /* BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain.
734 * Both |a| and |b| must already be in the Montgomery domain (by
735 * |BN_to_montgomery|). It returns one on success or zero on error. */
736 OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a,
738 const BN_MONT_CTX *mont, BN_CTX *ctx);
741 /* Exponentiation. */
743 /* BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply
744 * algorithm that leaks side-channel information. It returns one on success or
746 OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
749 /* BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best
750 * algorithm for the values provided and can run in constant time if
751 * |BN_FLG_CONSTTIME| is set for |p|. It returns one on success or zero
753 OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
754 const BIGNUM *m, BN_CTX *ctx);
756 OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
757 const BIGNUM *m, BN_CTX *ctx,
760 OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a,
761 const BIGNUM *p, const BIGNUM *m,
762 BN_CTX *ctx, BN_MONT_CTX *in_mont);
764 OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
765 const BIGNUM *m, BN_CTX *ctx,
767 OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1,
768 const BIGNUM *p1, const BIGNUM *a2,
769 const BIGNUM *p2, const BIGNUM *m,
770 BN_CTX *ctx, BN_MONT_CTX *m_ctx);
773 /* Private functions */
776 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks in little-endian
778 int top; /* Index of last used element in |d|, plus one. */
779 int dmax; /* Size of |d|, in words. */
780 int neg; /* one if the number is negative */
781 int flags; /* bitmask of BN_FLG_* values */
784 struct bn_mont_ctx_st {
785 BIGNUM RR; /* used to convert to montgomery form */
786 BIGNUM N; /* The modulus */
787 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
788 * (Ni is only stored for bignum algorithm) */
789 BN_ULONG n0[2]; /* least significant word(s) of Ni;
790 (type changed with 0.9.9, was "BN_ULONG n0;" before) */
792 int ri; /* number of bits in R */
795 OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l);
797 #define BN_FLG_MALLOCED 0x01
798 #define BN_FLG_STATIC_DATA 0x02
799 /* avoid leaking exponent information through timing, BN_mod_exp_mont() will
800 * call BN_mod_exp_mont_consttime, BN_div() will call BN_div_no_branch,
801 * BN_mod_inverse() will call BN_mod_inverse_no_branch. */
802 #define BN_FLG_CONSTTIME 0x04
805 #if defined(__cplusplus)
809 #define BN_F_BN_bn2hex 100
810 #define BN_F_BN_new 101
811 #define BN_F_BN_exp 102
812 #define BN_F_mod_exp_recp 103
813 #define BN_F_BN_mod_sqrt 104
814 #define BN_F_BN_rand 105
815 #define BN_F_BN_rand_range 106
816 #define BN_F_bn_wexpand 107
817 #define BN_F_BN_mod_exp_mont 108
818 #define BN_F_BN_mod_exp2_mont 109
819 #define BN_F_BN_CTX_get 110
820 #define BN_F_BN_mod_inverse 111
821 #define BN_F_BN_bn2dec 112
822 #define BN_F_BN_div 113
823 #define BN_F_BN_div_recp 114
824 #define BN_F_BN_mod_exp_mont_consttime 115
825 #define BN_F_BN_mod_exp_mont_word 116
826 #define BN_F_BN_CTX_start 117
827 #define BN_F_BN_usub 118
828 #define BN_F_BN_mod_lshift_quick 119
829 #define BN_F_BN_CTX_new 120
830 #define BN_F_BN_mod_inverse_no_branch 121
831 #define BN_F_BN_generate_dsa_nonce 122
832 #define BN_F_BN_generate_prime_ex 123
833 #define BN_F_BN_sqrt 124
834 #define BN_R_NOT_A_SQUARE 100
835 #define BN_R_TOO_MANY_ITERATIONS 101
836 #define BN_R_INPUT_NOT_REDUCED 102
837 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 103
838 #define BN_R_NO_INVERSE 104
839 #define BN_R_NOT_INITIALIZED 105
840 #define BN_R_DIV_BY_ZERO 106
841 #define BN_R_CALLED_WITH_EVEN_MODULUS 107
842 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 108
843 #define BN_R_BAD_RECIPROCAL 109
844 #define BN_R_P_IS_NOT_PRIME 110
845 #define BN_R_INVALID_RANGE 111
846 #define BN_R_ARG2_LT_ARG3 112
847 #define BN_R_BIGNUM_TOO_LONG 113
848 #define BN_R_PRIVATE_KEY_TOO_LARGE 114
849 #define BN_R_BITS_TOO_SMALL 115
850 #define BN_R_NEGATIVE_NUMBER 116
852 #endif /* OPENSSL_HEADER_BN_H */