2 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
58 /* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
64 * The Contribution is licensed pursuant to the Eric Young open source
65 * license provided above.
67 * The binary polynomial arithmetic software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
73 # define HEADER_BN_H
\r
75 # include <limits.h>
\r
76 # include <openssl/e_os2.h>
\r
77 # ifndef OPENSSL_NO_FP_API
\r
78 # include <stdio.h> /* FILE */
\r
80 # include <openssl/ossl_typ.h>
87 * These preprocessor symbols control various aspects of the bignum headers
88 * and library code. They're not defined by any "normal" configuration, as
89 * they are intended for development and testing purposes. NB: defining all
90 * three can be useful for debugging application code as well as openssl
91 * itself. BN_DEBUG - turn on various debugging alterations to the bignum
92 * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
93 * mismanagement of bignum internals. You must also define BN_DEBUG.
95 /* #define BN_DEBUG */
96 /* #define BN_DEBUG_RAND */
100 # define BN_RECURSION
103 * This next option uses the C libraries (2 word)/(1 word) function. If it is
104 * not defined, I use my C version (which is slower). The reason for this
105 * flag is that when the particular C compiler library routine is used, and
106 * the library is linked with a different compiler, the library is missing.
107 * This mostly happens when the library is built with gcc and then linked
108 * using normal cc. This would be a common occurrence because gcc normally
109 * produces code that is 2 times faster than system compilers for the big
110 * number stuff. For machines with only one compiler (or shared libraries),
111 * this should be on. Again this in only really a problem on machines using
112 * "long long's", are 32bit, and are not using my assembler code.
114 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
115 defined(OPENSSL_SYS_WIN32) || defined(linux)
122 * assuming long is 64bit - this is the DEC Alpha unsigned long long is only
123 * 64 bits :-(, don't define BN_LLONG for the DEC Alpha
125 # ifdef SIXTY_FOUR_BIT_LONG
126 # define BN_ULLONG unsigned long long
127 # define BN_ULONG unsigned long
128 # define BN_LONG long
133 # define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
134 # define BN_MASK2 (0xffffffffffffffffL)
135 # define BN_MASK2l (0xffffffffL)
136 # define BN_MASK2h (0xffffffff00000000L)
137 # define BN_MASK2h1 (0xffffffff80000000L)
138 # define BN_TBIT (0x8000000000000000L)
139 # define BN_DEC_CONV (10000000000000000000UL)
140 # define BN_DEC_FMT1 "%lu"
141 # define BN_DEC_FMT2 "%019lu"
142 # define BN_DEC_NUM 19
146 * This is where the long long data type is 64 bits, but long is 32. For
147 * machines where there are 64bit registers, this is the mode to use. IRIX,
148 * on R4000 and above should use this mode, along with the relevant assembler
149 * code :-). Do NOT define BN_LLONG.
151 # ifdef SIXTY_FOUR_BIT
154 # define BN_ULONG unsigned long long
155 # define BN_LONG long long
160 # define BN_MASK2 (0xffffffffffffffffLL)
161 # define BN_MASK2l (0xffffffffL)
162 # define BN_MASK2h (0xffffffff00000000LL)
163 # define BN_MASK2h1 (0xffffffff80000000LL)
164 # define BN_TBIT (0x8000000000000000LL)
165 # define BN_DEC_CONV (10000000000000000000ULL)
166 # define BN_DEC_FMT1 "%llu"
167 # define BN_DEC_FMT2 "%019llu"
168 # define BN_DEC_NUM 19
171 # ifdef THIRTY_TWO_BIT
173 # if defined(OPENSSL_SYS_WIN32) && !defined(__GNUC__)
174 # define BN_ULLONG unsigned __int64
176 # define BN_ULLONG unsigned long long
179 # define BN_ULONG unsigned long
180 # define BN_LONG long
185 # ifdef OPENSSL_SYS_WIN32
186 /* VC++ doesn't like the LL suffix */
187 # define BN_MASK (0xffffffffffffffffL)
189 # define BN_MASK (0xffffffffffffffffLL)
191 # define BN_MASK2 (0xffffffffL)
192 # define BN_MASK2l (0xffff)
193 # define BN_MASK2h1 (0xffff8000L)
194 # define BN_MASK2h (0xffff0000L)
195 # define BN_TBIT (0x80000000L)
196 # define BN_DEC_CONV (1000000000L)
197 # define BN_DEC_FMT1 "%lu"
198 # define BN_DEC_FMT2 "%09lu"
199 # define BN_DEC_NUM 9
206 # define BN_ULLONG unsigned long
207 # define BN_ULONG unsigned short
208 # define BN_LONG short
213 # define BN_MASK (0xffffffff)
214 # define BN_MASK2 (0xffff)
215 # define BN_MASK2l (0xff)
216 # define BN_MASK2h1 (0xff80)
217 # define BN_MASK2h (0xff00)
218 # define BN_TBIT (0x8000)
219 # define BN_DEC_CONV (100000)
220 # define BN_DEC_FMT1 "%u"
221 # define BN_DEC_FMT2 "%05u"
222 # define BN_DEC_NUM 5
229 # define BN_ULLONG unsigned short
230 # define BN_ULONG unsigned char
231 # define BN_LONG char
236 # define BN_MASK (0xffff)
237 # define BN_MASK2 (0xff)
238 # define BN_MASK2l (0xf)
239 # define BN_MASK2h1 (0xf8)
240 # define BN_MASK2h (0xf0)
241 # define BN_TBIT (0x80)
242 # define BN_DEC_CONV (100)
243 # define BN_DEC_FMT1 "%u"
244 # define BN_DEC_FMT2 "%02u"
245 # define BN_DEC_NUM 2
248 # define BN_DEFAULT_BITS 1280
250 # define BN_FLG_MALLOCED 0x01
251 # define BN_FLG_STATIC_DATA 0x02
254 * avoid leaking exponent information through timing,
255 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
256 * BN_div() will call BN_div_no_branch,
257 * BN_mod_inverse() will call BN_mod_inverse_no_branch.
259 # define BN_FLG_CONSTTIME 0x04
261 # ifdef OPENSSL_NO_DEPRECATED
262 /* deprecated name for the flag */
263 # define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
265 * avoid leaking exponent information through timings
266 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime)
270 # ifndef OPENSSL_NO_DEPRECATED
271 # define BN_FLG_FREE 0x8000
272 /* used for debuging */
274 # define BN_set_flags(b,n) ((b)->flags|=(n))
275 # define BN_get_flags(b,n) ((b)->flags&(n))
278 * get a clone of a BIGNUM with changed flags, for *temporary* use only (the
279 * two BIGNUMs cannot not be used in parallel!)
281 # define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
282 (dest)->top=(b)->top, \
283 (dest)->dmax=(b)->dmax, \
284 (dest)->neg=(b)->neg, \
285 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
286 | ((b)->flags & ~BN_FLG_MALLOCED) \
287 | BN_FLG_STATIC_DATA \
290 /* Already declared in ossl_typ.h */
292 typedef struct bignum_st BIGNUM;
293 /* Used for temp variables (declaration hidden in bn_lcl.h) */
294 typedef struct bignum_ctx BN_CTX;
295 typedef struct bn_blinding_st BN_BLINDING;
296 typedef struct bn_mont_ctx_st BN_MONT_CTX;
297 typedef struct bn_recp_ctx_st BN_RECP_CTX;
298 typedef struct bn_gencb_st BN_GENCB;
302 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit
304 int top; /* Index of last used d +1. */
305 /* The next are internal book keeping for bn_expand. */
306 int dmax; /* Size of the d array. */
307 int neg; /* one if the number is negative */
311 /* Used for montgomery multiplication */
312 struct bn_mont_ctx_st {
313 int ri; /* number of bits in R */
314 BIGNUM RR; /* used to convert to montgomery form */
315 BIGNUM N; /* The modulus */
316 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only
317 * stored for bignum algorithm) */
319 /* OpenSSL 0.9.9 preview: */
320 BN_ULONG n0[2]; /* least significant word(s) of Ni */
322 BN_ULONG n0; /* least significant word of Ni */
328 * Used for reciprocal division/mod functions It cannot be shared between
331 struct bn_recp_ctx_st {
332 BIGNUM N; /* the divisor */
333 BIGNUM Nr; /* the reciprocal */
339 /* Used for slow "generation" functions. */
341 unsigned int ver; /* To handle binary (in)compatibility */
342 void *arg; /* callback-specific data */
344 /* if(ver==1) - handles old style callbacks */
345 void (*cb_1) (int, int, void *);
346 /* if(ver==2) - new callback style */
347 int (*cb_2) (int, int, BN_GENCB *);
350 /* Wrapper function to make using BN_GENCB easier, */
351 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
352 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
353 # define BN_GENCB_set_old(gencb, callback, cb_arg) { \
354 BN_GENCB *tmp_gencb = (gencb); \
355 tmp_gencb->ver = 1; \
356 tmp_gencb->arg = (cb_arg); \
357 tmp_gencb->cb.cb_1 = (callback); }
358 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
359 # define BN_GENCB_set(gencb, callback, cb_arg) { \
360 BN_GENCB *tmp_gencb = (gencb); \
361 tmp_gencb->ver = 2; \
362 tmp_gencb->arg = (cb_arg); \
363 tmp_gencb->cb.cb_2 = (callback); }
365 # define BN_prime_checks 0 /* default: select number of iterations based
366 * on the size of the number */
369 * number of Miller-Rabin iterations for an error rate of less than 2^-80 for
370 * random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook of
371 * Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
372 * original paper: Damgaard, Landrock, Pomerance: Average case error
373 * estimates for the strong probable prime test. -- Math. Comp. 61 (1993)
376 # define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
389 # define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
391 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
392 # define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
393 (((w) == 0) && ((a)->top == 0)))
394 # define BN_is_zero(a) ((a)->top == 0)
395 # define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
396 # define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
397 # define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
399 # define BN_one(a) (BN_set_word((a),1))
400 # define BN_zero_ex(a) \
402 BIGNUM *_tmp_bn = (a); \
406 # ifdef OPENSSL_NO_DEPRECATED
407 # define BN_zero(a) BN_zero_ex(a)
409 # define BN_zero(a) (BN_set_word((a),0))
412 const BIGNUM *BN_value_one(void);
413 char *BN_options(void);
414 BN_CTX *BN_CTX_new(void);
415 # ifndef OPENSSL_NO_DEPRECATED
416 void BN_CTX_init(BN_CTX *c);
418 void BN_CTX_free(BN_CTX *c);
419 void BN_CTX_start(BN_CTX *ctx);
420 BIGNUM *BN_CTX_get(BN_CTX *ctx);
421 void BN_CTX_end(BN_CTX *ctx);
422 int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
423 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
424 int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
425 int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
426 int BN_num_bits(const BIGNUM *a);
427 int BN_num_bits_word(BN_ULONG);
428 BIGNUM *BN_new(void);
429 void BN_init(BIGNUM *);
430 void BN_clear_free(BIGNUM *a);
431 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
432 void BN_swap(BIGNUM *a, BIGNUM *b);
433 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
434 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
435 BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
436 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
437 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
438 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
439 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
440 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
441 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
442 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
443 /** BN_set_negative sets sign of a BIGNUM
444 * \param b pointer to the BIGNUM object
445 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
447 void BN_set_negative(BIGNUM *b, int n);
448 /** BN_is_negative returns 1 if the BIGNUM is negative
449 * \param a pointer to the BIGNUM object
450 * \return 1 if a < 0 and 0 otherwise
452 # define BN_is_negative(a) ((a)->neg != 0)
454 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
456 # define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
457 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
458 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
460 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
462 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
464 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
466 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
468 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
469 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
470 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
471 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
473 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
475 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
476 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
477 int BN_mul_word(BIGNUM *a, BN_ULONG w);
478 int BN_add_word(BIGNUM *a, BN_ULONG w);
479 int BN_sub_word(BIGNUM *a, BN_ULONG w);
480 int BN_set_word(BIGNUM *a, BN_ULONG w);
481 BN_ULONG BN_get_word(const BIGNUM *a);
483 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
484 void BN_free(BIGNUM *a);
485 int BN_is_bit_set(const BIGNUM *a, int n);
486 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
487 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
488 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
490 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
491 const BIGNUM *m, BN_CTX *ctx);
492 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
493 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
494 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
495 const BIGNUM *m, BN_CTX *ctx,
496 BN_MONT_CTX *in_mont);
497 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
498 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
499 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
500 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
501 BN_CTX *ctx, BN_MONT_CTX *m_ctx);
502 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
503 const BIGNUM *m, BN_CTX *ctx);
505 int BN_mask_bits(BIGNUM *a, int n);
506 # ifndef OPENSSL_NO_FP_API
507 int BN_print_fp(FILE *fp, const BIGNUM *a);
510 int BN_print(BIO *fp, const BIGNUM *a);
512 int BN_print(void *fp, const BIGNUM *a);
514 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
515 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
516 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
517 void BN_clear(BIGNUM *a);
518 BIGNUM *BN_dup(const BIGNUM *a);
519 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
520 int BN_set_bit(BIGNUM *a, int n);
521 int BN_clear_bit(BIGNUM *a, int n);
522 char *BN_bn2hex(const BIGNUM *a);
523 char *BN_bn2dec(const BIGNUM *a);
524 int BN_hex2bn(BIGNUM **a, const char *str);
525 int BN_dec2bn(BIGNUM **a, const char *str);
526 int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
527 int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
530 BIGNUM *BN_mod_inverse(BIGNUM *ret,
531 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
532 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
533 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
535 void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
537 /* Deprecated versions */
538 # ifndef OPENSSL_NO_DEPRECATED
539 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
540 const BIGNUM *add, const BIGNUM *rem,
541 void (*callback) (int, int, void *), void *cb_arg);
542 int BN_is_prime(const BIGNUM *p, int nchecks,
543 void (*callback) (int, int, void *),
544 BN_CTX *ctx, void *cb_arg);
545 int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
546 void (*callback) (int, int, void *), BN_CTX *ctx,
547 void *cb_arg, int do_trial_division);
548 # endif /* !defined(OPENSSL_NO_DEPRECATED) */
551 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
552 const BIGNUM *rem, BN_GENCB *cb);
553 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
554 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
555 int do_trial_division, BN_GENCB *cb);
557 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
559 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
560 const BIGNUM *Xp, const BIGNUM *Xp1,
561 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
563 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1,
564 BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e,
565 BN_CTX *ctx, BN_GENCB *cb);
567 BN_MONT_CTX *BN_MONT_CTX_new(void);
568 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
569 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
570 BN_MONT_CTX *mont, BN_CTX *ctx);
571 # define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
572 (r),(a),&((mont)->RR),(mont),(ctx))
573 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a,
574 BN_MONT_CTX *mont, BN_CTX *ctx);
575 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
576 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
577 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
578 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
579 const BIGNUM *mod, BN_CTX *ctx);
581 /* BN_BLINDING flags */
582 # define BN_BLINDING_NO_UPDATE 0x00000001
583 # define BN_BLINDING_NO_RECREATE 0x00000002
585 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
586 void BN_BLINDING_free(BN_BLINDING *b);
587 int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
588 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
589 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
590 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
591 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
593 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
594 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
595 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
596 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
597 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
598 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
599 int (*bn_mod_exp) (BIGNUM *r,
607 # ifndef OPENSSL_NO_DEPRECATED
608 void BN_set_params(int mul, int high, int low, int mont);
609 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
612 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
613 BN_RECP_CTX *BN_RECP_CTX_new(void);
614 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
615 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
616 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
617 BN_RECP_CTX *recp, BN_CTX *ctx);
618 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
619 const BIGNUM *m, BN_CTX *ctx);
620 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
621 BN_RECP_CTX *recp, BN_CTX *ctx);
624 * Functions for arithmetic over binary polynomials represented by BIGNUMs.
625 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
626 * ignored. Note that input arguments are not const so that their bit arrays
627 * can be expanded to the appropriate size if needed.
633 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
634 # define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
638 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
639 /* r = (a * b) mod p */
640 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
641 const BIGNUM *p, BN_CTX *ctx);
642 /* r = (a * a) mod p */
643 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
644 /* r = (1 / b) mod p */
645 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
646 /* r = (a / b) mod p */
647 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
648 const BIGNUM *p, BN_CTX *ctx);
649 /* r = (a ^ b) mod p */
650 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
651 const BIGNUM *p, BN_CTX *ctx);
652 /* r = sqrt(a) mod p */
653 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
655 /* r^2 + r = a mod p */
656 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
658 # define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
660 * Some functions allow for representation of the irreducible polynomials
661 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
662 * t^p[0] + t^p[1] + ... + t^p[k]
663 * where m = p[0] > p[1] > ... > p[k] = 0.
666 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]);
667 /* r = (a * b) mod p */
668 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
669 const unsigned int p[], BN_CTX *ctx);
670 /* r = (a * a) mod p */
671 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[],
673 /* r = (1 / b) mod p */
674 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[],
676 /* r = (a / b) mod p */
677 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
678 const unsigned int p[], BN_CTX *ctx);
679 /* r = (a ^ b) mod p */
680 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
681 const unsigned int p[], BN_CTX *ctx);
682 /* r = sqrt(a) mod p */
683 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
684 const unsigned int p[], BN_CTX *ctx);
685 /* r^2 + r = a mod p */
686 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
687 const unsigned int p[], BN_CTX *ctx);
688 int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
689 int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
692 * faster mod functions for the 'NIST primes' 0 <= a < p^2
694 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
695 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
696 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
697 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
698 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
700 const BIGNUM *BN_get0_nist_prime_192(void);
701 const BIGNUM *BN_get0_nist_prime_224(void);
702 const BIGNUM *BN_get0_nist_prime_256(void);
703 const BIGNUM *BN_get0_nist_prime_384(void);
704 const BIGNUM *BN_get0_nist_prime_521(void);
706 /* library internal functions */
\r
708 # define bn_expand(a,bits) \
\r
710 bits > (INT_MAX - BN_BITS2 + 1) ? \
\r
713 (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax) ? \
\r
716 bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2) \
\r
719 # define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
\r
720 BIGNUM *bn_expand2(BIGNUM *a, int words);
\r
721 # ifndef OPENSSL_NO_DEPRECATED
\r
722 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
726 * Bignum consistency macros
727 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
728 * bignum data after direct manipulations on the data. There is also an
729 * "internal" macro, bn_check_top(), for verifying that there are no leading
730 * zeroes. Unfortunately, some auditing is required due to the fact that
731 * bn_fix_top() has become an overabused duct-tape because bignum data is
732 * occasionally passed around in an inconsistent state. So the following
733 * changes have been made to sort this out;
734 * - bn_fix_top()s implementation has been moved to bn_correct_top()
735 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
736 * bn_check_top() is as before.
737 * - if BN_DEBUG *is* defined;
738 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
739 * consistent. (ed: only if BN_DEBUG_RAND is defined)
740 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
741 * The idea is to have debug builds flag up inconsistent bignums when they
742 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
743 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
744 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
745 * was not appropriate, we convert it permanently to bn_check_top() and track
746 * down the cause of the bug. Eventually, no internal code should be using the
747 * bn_fix_top() macro. External applications and libraries should try this with
748 * their own code too, both in terms of building against the openssl headers
749 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
750 * defined. This not only improves external code, it provides more test
751 * coverage for openssl's own code.
756 /* We only need assert() when debugging */
759 # ifdef BN_DEBUG_RAND
760 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
761 # ifndef RAND_pseudo_bytes
762 int RAND_pseudo_bytes(unsigned char *buf, int num);
763 # define BN_DEBUG_TRIX
765 # define bn_pollute(a) \
767 const BIGNUM *_bnum1 = (a); \
768 if(_bnum1->top < _bnum1->dmax) { \
769 unsigned char _tmp_char; \
770 /* We cast away const without the compiler knowing, any \
771 * *genuinely* constant variables that aren't mutable \
772 * wouldn't be constructed with top!=dmax. */ \
773 BN_ULONG *_not_const; \
774 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
775 RAND_pseudo_bytes(&_tmp_char, 1); \
776 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
777 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
780 # ifdef BN_DEBUG_TRIX
781 # undef RAND_pseudo_bytes
784 # define bn_pollute(a)
786 # define bn_check_top(a) \
788 const BIGNUM *_bnum2 = (a); \
789 if (_bnum2 != NULL) { \
790 assert((_bnum2->top == 0) || \
791 (_bnum2->d[_bnum2->top - 1] != 0)); \
792 bn_pollute(_bnum2); \
796 # define bn_fix_top(a) bn_check_top(a)
798 # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
799 # define bn_wcheck_size(bn, words) \
801 const BIGNUM *_bnum2 = (bn); \
802 assert(words <= (_bnum2)->dmax && words >= (_bnum2)->top); \
805 # else /* !BN_DEBUG */
807 # define bn_pollute(a)
808 # define bn_check_top(a)
809 # define bn_fix_top(a) bn_correct_top(a)
810 # define bn_check_size(bn, bits)
811 # define bn_wcheck_size(bn, words)
815 # define bn_correct_top(a) \
820 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
821 if (*(ftl--)) break; \
826 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
828 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
829 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
830 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
831 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
833 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
836 /* Primes from RFC 2409 */
837 BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
838 BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
840 /* Primes from RFC 3526 */
841 BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
842 BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
843 BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
844 BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
845 BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
846 BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
848 int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
850 /* BEGIN ERROR CODES */
852 * The following lines are auto generated by the script mkerr.pl. Any changes
853 * made after this point may be overwritten when the script is next run.
855 void ERR_load_BN_strings(void);
857 /* Error codes for the BN functions. */
859 /* Function codes. */
860 # define BN_F_BNRAND 127
861 # define BN_F_BN_BLINDING_CONVERT_EX 100
862 # define BN_F_BN_BLINDING_CREATE_PARAM 128
863 # define BN_F_BN_BLINDING_INVERT_EX 101
864 # define BN_F_BN_BLINDING_NEW 102
865 # define BN_F_BN_BLINDING_UPDATE 103
866 # define BN_F_BN_BN2DEC 104
867 # define BN_F_BN_BN2HEX 105
868 # define BN_F_BN_CTX_GET 116
869 # define BN_F_BN_CTX_NEW 106
870 # define BN_F_BN_CTX_START 129
871 # define BN_F_BN_DIV 107
872 # define BN_F_BN_DIV_NO_BRANCH 138
873 # define BN_F_BN_DIV_RECP 130
874 # define BN_F_BN_EXP 123
875 # define BN_F_BN_EXPAND2 108
876 # define BN_F_BN_EXPAND_INTERNAL 120
877 # define BN_F_BN_GF2M_MOD 131
878 # define BN_F_BN_GF2M_MOD_EXP 132
879 # define BN_F_BN_GF2M_MOD_MUL 133
880 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
881 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
882 # define BN_F_BN_GF2M_MOD_SQR 136
883 # define BN_F_BN_GF2M_MOD_SQRT 137
884 # define BN_F_BN_LSHIFT 145
885 # define BN_F_BN_MOD_EXP2_MONT 118
886 # define BN_F_BN_MOD_EXP_MONT 109
887 # define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
888 # define BN_F_BN_MOD_EXP_MONT_WORD 117
889 # define BN_F_BN_MOD_EXP_RECP 125
890 # define BN_F_BN_MOD_EXP_SIMPLE 126
891 # define BN_F_BN_MOD_INVERSE 110
892 # define BN_F_BN_MOD_INVERSE_NO_BRANCH 139
893 # define BN_F_BN_MOD_LSHIFT_QUICK 119
894 # define BN_F_BN_MOD_MUL_RECIPROCAL 111
895 # define BN_F_BN_MOD_SQRT 121
896 # define BN_F_BN_MPI2BN 112
897 # define BN_F_BN_NEW 113
898 # define BN_F_BN_RAND 114
899 # define BN_F_BN_RAND_RANGE 122
900 # define BN_F_BN_RSHIFT 146
901 # define BN_F_BN_USUB 115
904 # define BN_R_ARG2_LT_ARG3 100
905 # define BN_R_BAD_RECIPROCAL 101
906 # define BN_R_BIGNUM_TOO_LONG 114
907 # define BN_R_BITS_TOO_SMALL 118
908 # define BN_R_CALLED_WITH_EVEN_MODULUS 102
909 # define BN_R_DIV_BY_ZERO 103
910 # define BN_R_ENCODING_ERROR 104
911 # define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
912 # define BN_R_INPUT_NOT_REDUCED 110
913 # define BN_R_INVALID_LENGTH 106
914 # define BN_R_INVALID_RANGE 115
915 # define BN_R_INVALID_SHIFT 119
916 # define BN_R_NOT_A_SQUARE 111
917 # define BN_R_NOT_INITIALIZED 107
918 # define BN_R_NO_INVERSE 108
919 # define BN_R_NO_SOLUTION 116
920 # define BN_R_P_IS_NOT_PRIME 112
921 # define BN_R_TOO_MANY_ITERATIONS 113
922 # define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109