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.
75 #include <openssl/e_os2.h>
76 #ifndef OPENSSL_NO_FP_API
77 #include <stdio.h> /* FILE */
79 #include <openssl/ossl_typ.h>
85 /* These preprocessor symbols control various aspects of the bignum headers and
86 * library code. They're not defined by any "normal" configuration, as they are
87 * intended for development and testing purposes. NB: defining all three can be
88 * useful for debugging application code as well as openssl itself.
90 * BN_DEBUG - turn on various debugging alterations to the bignum code
91 * BN_DEBUG_RAND - uses random poisoning of unused words to trip up
92 * mismanagement of bignum internals. You must also define BN_DEBUG.
94 /* #define BN_DEBUG */
95 /* #define BN_DEBUG_RAND */
97 #ifndef OPENSSL_SMALL_FOOTPRINT
103 /* This next option uses the C libraries (2 word)/(1 word) function.
104 * If it is not defined, I use my C version (which is slower).
105 * The reason for this flag is that when the particular C compiler
106 * library routine is used, and the library is linked with a different
107 * compiler, the library is missing. This mostly happens when the
108 * library is built with gcc and then linked using normal cc. This would
109 * be a common occurrence because gcc normally produces code that is
110 * 2 times faster than system compilers for the big number stuff.
111 * For machines with only one compiler (or shared libraries), this should
112 * be on. Again this in only really a problem on machines
113 * using "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)
121 /* assuming long is 64bit - this is the DEC Alpha
122 * unsigned long long is only 64 bits :-(, don't define
123 * BN_LLONG for the DEC Alpha */
124 #ifdef SIXTY_FOUR_BIT_LONG
125 #define BN_ULLONG unsigned long long
126 #define BN_ULONG unsigned long
132 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
133 #define BN_MASK2 (0xffffffffffffffffL)
134 #define BN_MASK2l (0xffffffffL)
135 #define BN_MASK2h (0xffffffff00000000L)
136 #define BN_MASK2h1 (0xffffffff80000000L)
137 #define BN_TBIT (0x8000000000000000L)
138 #define BN_DEC_CONV (10000000000000000000UL)
139 #define BN_DEC_FMT1 "%lu"
140 #define BN_DEC_FMT2 "%019lu"
141 #define BN_DEC_NUM 19
142 #define BN_HEX_FMT1 "%lX"
143 #define BN_HEX_FMT2 "%016lX"
146 /* This is where the long long data type is 64 bits, but long is 32.
147 * For machines where there are 64bit registers, this is the mode to use.
148 * IRIX, on R4000 and above should use this mode, along with the relevant
149 * assembler 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
169 #define BN_HEX_FMT1 "%llX"
170 #define BN_HEX_FMT2 "%016llX"
173 #ifdef THIRTY_TWO_BIT
175 # if defined(_WIN32) && !defined(__GNUC__)
176 # define BN_ULLONG unsigned __int64
177 # define BN_MASK (0xffffffffffffffffI64)
179 # define BN_ULLONG unsigned long long
180 # define BN_MASK (0xffffffffffffffffLL)
183 #define BN_ULONG unsigned int
189 #define BN_MASK2 (0xffffffffL)
190 #define BN_MASK2l (0xffff)
191 #define BN_MASK2h1 (0xffff8000L)
192 #define BN_MASK2h (0xffff0000L)
193 #define BN_TBIT (0x80000000L)
194 #define BN_DEC_CONV (1000000000L)
195 #define BN_DEC_FMT1 "%u"
196 #define BN_DEC_FMT2 "%09u"
198 #define BN_HEX_FMT1 "%X"
199 #define BN_HEX_FMT2 "%08X"
202 #define BN_DEFAULT_BITS 1280
204 #define BN_FLG_MALLOCED 0x01
205 #define BN_FLG_STATIC_DATA 0x02
206 #define BN_FLG_EXP_CONSTTIME 0x04 /* avoid leaking exponent information through timings
207 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime) */
208 #ifndef OPENSSL_NO_DEPRECATED
209 #define BN_FLG_FREE 0x8000 /* used for debuging */
211 #define BN_set_flags(b,n) ((b)->flags|=(n))
212 #define BN_get_flags(b,n) ((b)->flags&(n))
214 /* get a clone of a BIGNUM with changed flags, for *temporary* use only
215 * (the two BIGNUMs cannot not be used in parallel!) */
216 #define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
217 (dest)->top=(b)->top, \
218 (dest)->dmax=(b)->dmax, \
219 (dest)->neg=(b)->neg, \
220 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
221 | ((b)->flags & ~BN_FLG_MALLOCED) \
222 | BN_FLG_STATIC_DATA \
225 /* Already declared in ossl_typ.h */
227 typedef struct bignum_st BIGNUM;
228 /* Used for temp variables (declaration hidden in bn_lcl.h) */
229 typedef struct bignum_ctx BN_CTX;
230 typedef struct bn_blinding_st BN_BLINDING;
231 typedef struct bn_mont_ctx_st BN_MONT_CTX;
232 typedef struct bn_recp_ctx_st BN_RECP_CTX;
233 typedef struct bn_gencb_st BN_GENCB;
238 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
239 int top; /* Index of last used d +1. */
240 /* The next are internal book keeping for bn_expand. */
241 int dmax; /* Size of the d array. */
242 int neg; /* one if the number is negative */
246 /* Used for montgomery multiplication */
247 struct bn_mont_ctx_st
249 int ri; /* number of bits in R */
250 BIGNUM RR; /* used to convert to montgomery form */
251 BIGNUM N; /* The modulus */
252 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
253 * (Ni is only stored for bignum algorithm) */
254 BN_ULONG n0[2];/* least significant word(s) of Ni */
258 /* Used for reciprocal division/mod functions
259 * It cannot be shared between threads
261 struct bn_recp_ctx_st
263 BIGNUM N; /* the divisor */
264 BIGNUM Nr; /* the reciprocal */
270 /* Used for slow "generation" functions. */
273 unsigned int ver; /* To handle binary (in)compatibility */
274 void *arg; /* callback-specific data */
277 /* if(ver==1) - handles old style callbacks */
278 void (*cb_1)(int, int, void *);
279 /* if(ver==2) - new callback style */
280 int (*cb_2)(int, int, BN_GENCB *);
283 /* Wrapper function to make using BN_GENCB easier, */
284 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
285 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
286 #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
287 BN_GENCB *tmp_gencb = (gencb); \
288 tmp_gencb->ver = 1; \
289 tmp_gencb->arg = (cb_arg); \
290 tmp_gencb->cb.cb_1 = (callback); }
291 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
292 #define BN_GENCB_set(gencb, callback, cb_arg) { \
293 BN_GENCB *tmp_gencb = (gencb); \
294 tmp_gencb->ver = 2; \
295 tmp_gencb->arg = (cb_arg); \
296 tmp_gencb->cb.cb_2 = (callback); }
298 #define BN_prime_checks 0 /* default: select number of iterations
299 based on the size of the number */
301 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
302 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
303 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
304 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
305 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
306 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
319 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
321 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
322 #define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
323 (((w) == 0) && ((a)->top == 0)))
324 #define BN_is_zero(a) ((a)->top == 0)
325 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
326 #define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
327 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
329 #define BN_one(a) (BN_set_word((a),1))
330 #define BN_zero_ex(a) \
332 BIGNUM *_tmp_bn = (a); \
336 #ifdef OPENSSL_NO_DEPRECATED
337 #define BN_zero(a) BN_zero_ex(a)
339 #define BN_zero(a) (BN_set_word((a),0))
342 const BIGNUM *BN_value_one(void);
343 char * BN_options(void);
344 BN_CTX *BN_CTX_new(void);
345 #ifndef OPENSSL_NO_DEPRECATED
346 void BN_CTX_init(BN_CTX *c);
348 void BN_CTX_free(BN_CTX *c);
349 void BN_CTX_start(BN_CTX *ctx);
350 BIGNUM *BN_CTX_get(BN_CTX *ctx);
351 void BN_CTX_end(BN_CTX *ctx);
352 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
353 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
354 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
355 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
356 int BN_num_bits(const BIGNUM *a);
357 int BN_num_bits_word(BN_ULONG);
358 BIGNUM *BN_new(void);
359 void BN_init(BIGNUM *);
360 void BN_clear_free(BIGNUM *a);
361 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
362 void BN_swap(BIGNUM *a, BIGNUM *b);
363 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
364 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
365 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
366 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
367 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
368 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
369 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
370 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
371 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
372 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
373 /** BN_set_negative sets sign of a BIGNUM
374 * \param b pointer to the BIGNUM object
375 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
377 void BN_set_negative(BIGNUM *b, int n);
378 /** BN_is_negative returns 1 if the BIGNUM is negative
379 * \param a pointer to the BIGNUM object
380 * \return 1 if a < 0 and 0 otherwise
382 #define BN_is_negative(a) ((a)->neg != 0)
384 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
386 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
387 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
388 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
389 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
390 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
391 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
392 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
393 const BIGNUM *m, BN_CTX *ctx);
394 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
395 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
396 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
397 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
398 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
400 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
401 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
402 int BN_mul_word(BIGNUM *a, BN_ULONG w);
403 int BN_add_word(BIGNUM *a, BN_ULONG w);
404 int BN_sub_word(BIGNUM *a, BN_ULONG w);
405 int BN_set_word(BIGNUM *a, BN_ULONG w);
406 BN_ULONG BN_get_word(const BIGNUM *a);
408 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
409 void BN_free(BIGNUM *a);
410 int BN_is_bit_set(const BIGNUM *a, int n);
411 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
412 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
413 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
415 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
416 const BIGNUM *m,BN_CTX *ctx);
417 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
418 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
419 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
420 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont);
421 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
422 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
423 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
424 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
425 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
426 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
427 const BIGNUM *m,BN_CTX *ctx);
429 int BN_mask_bits(BIGNUM *a,int n);
430 #ifndef OPENSSL_NO_FP_API
431 int BN_print_fp(FILE *fp, const BIGNUM *a);
434 int BN_print(BIO *fp, const BIGNUM *a);
436 int BN_print(void *fp, const BIGNUM *a);
438 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
439 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
440 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
441 void BN_clear(BIGNUM *a);
442 BIGNUM *BN_dup(const BIGNUM *a);
443 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
444 int BN_set_bit(BIGNUM *a, int n);
445 int BN_clear_bit(BIGNUM *a, int n);
446 char * BN_bn2hex(const BIGNUM *a);
447 char * BN_bn2dec(const BIGNUM *a);
448 int BN_hex2bn(BIGNUM **a, const char *str);
449 int BN_dec2bn(BIGNUM **a, const char *str);
450 int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
451 int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
452 BIGNUM *BN_mod_inverse(BIGNUM *ret,
453 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
454 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
455 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
457 /* Deprecated versions */
458 #ifndef OPENSSL_NO_DEPRECATED
459 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
460 const BIGNUM *add, const BIGNUM *rem,
461 void (*callback)(int,int,void *),void *cb_arg);
462 int BN_is_prime(const BIGNUM *p,int nchecks,
463 void (*callback)(int,int,void *),
464 BN_CTX *ctx,void *cb_arg);
465 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
466 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
467 int do_trial_division);
468 #endif /* !defined(OPENSSL_NO_DEPRECATED) */
471 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
472 const BIGNUM *rem, BN_GENCB *cb);
473 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
474 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
475 int do_trial_division, BN_GENCB *cb);
477 BN_MONT_CTX *BN_MONT_CTX_new(void );
478 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
479 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
480 BN_MONT_CTX *mont, BN_CTX *ctx);
481 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
482 (r),(a),&((mont)->RR),(mont),(ctx))
483 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
484 BN_MONT_CTX *mont, BN_CTX *ctx);
485 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
486 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
487 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
488 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
489 const BIGNUM *mod, BN_CTX *ctx);
491 /* BN_BLINDING flags */
492 #define BN_BLINDING_NO_UPDATE 0x00000001
493 #define BN_BLINDING_NO_RECREATE 0x00000002
495 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
496 void BN_BLINDING_free(BN_BLINDING *b);
497 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
498 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
499 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
500 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
501 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b, BN_CTX *);
502 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
503 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
504 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
505 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
506 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
507 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
508 int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
509 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
512 #ifndef OPENSSL_NO_DEPRECATED
513 void BN_set_params(int mul,int high,int low,int mont);
514 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
517 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
518 BN_RECP_CTX *BN_RECP_CTX_new(void);
519 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
520 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
521 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
522 BN_RECP_CTX *recp,BN_CTX *ctx);
523 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
524 const BIGNUM *m, BN_CTX *ctx);
525 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
526 BN_RECP_CTX *recp, BN_CTX *ctx);
528 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
530 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
533 * Note that input arguments are not const so that their bit arrays can
534 * be expanded to the appropriate size if needed.
537 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
538 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
539 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
540 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
541 const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
542 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
543 BN_CTX *ctx); /* r = (a * a) mod p */
544 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
545 BN_CTX *ctx); /* r = (1 / b) mod p */
546 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
547 const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
548 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
549 const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
550 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
551 BN_CTX *ctx); /* r = sqrt(a) mod p */
552 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
553 BN_CTX *ctx); /* r^2 + r = a mod p */
554 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
555 /* Some functions allow for representation of the irreducible polynomials
556 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
557 * t^p[0] + t^p[1] + ... + t^p[k]
558 * where m = p[0] > p[1] > ... > p[k] = 0.
560 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]);
562 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
563 const unsigned int p[], BN_CTX *ctx); /* r = (a * b) mod p */
564 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[],
565 BN_CTX *ctx); /* r = (a * a) mod p */
566 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[],
567 BN_CTX *ctx); /* r = (1 / b) mod p */
568 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
569 const unsigned int p[], BN_CTX *ctx); /* r = (a / b) mod p */
570 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
571 const unsigned int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
572 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
573 const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
574 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
575 const unsigned int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
576 int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
577 int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
579 /* faster mod functions for the 'NIST primes'
581 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
582 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
583 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
584 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
585 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
587 const BIGNUM *BN_get0_nist_prime_192(void);
588 const BIGNUM *BN_get0_nist_prime_224(void);
589 const BIGNUM *BN_get0_nist_prime_256(void);
590 const BIGNUM *BN_get0_nist_prime_384(void);
591 const BIGNUM *BN_get0_nist_prime_521(void);
593 /* library internal functions */
595 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
596 (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
597 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
598 BIGNUM *bn_expand2(BIGNUM *a, int words);
599 #ifndef OPENSSL_NO_DEPRECATED
600 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
603 /* Bignum consistency macros
604 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
605 * bignum data after direct manipulations on the data. There is also an
606 * "internal" macro, bn_check_top(), for verifying that there are no leading
607 * zeroes. Unfortunately, some auditing is required due to the fact that
608 * bn_fix_top() has become an overabused duct-tape because bignum data is
609 * occasionally passed around in an inconsistent state. So the following
610 * changes have been made to sort this out;
611 * - bn_fix_top()s implementation has been moved to bn_correct_top()
612 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
613 * bn_check_top() is as before.
614 * - if BN_DEBUG *is* defined;
615 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
616 * consistent. (ed: only if BN_DEBUG_RAND is defined)
617 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
618 * The idea is to have debug builds flag up inconsistent bignums when they
619 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
620 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
621 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
622 * was not appropriate, we convert it permanently to bn_check_top() and track
623 * down the cause of the bug. Eventually, no internal code should be using the
624 * bn_fix_top() macro. External applications and libraries should try this with
625 * their own code too, both in terms of building against the openssl headers
626 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
627 * defined. This not only improves external code, it provides more test
628 * coverage for openssl's own code.
633 /* We only need assert() when debugging */
637 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
638 #ifndef RAND_pseudo_bytes
639 int RAND_pseudo_bytes(unsigned char *buf,int num);
640 #define BN_DEBUG_TRIX
642 #define bn_pollute(a) \
644 const BIGNUM *_bnum1 = (a); \
645 if(_bnum1->top < _bnum1->dmax) { \
646 unsigned char _tmp_char; \
647 /* We cast away const without the compiler knowing, any \
648 * *genuinely* constant variables that aren't mutable \
649 * wouldn't be constructed with top!=dmax. */ \
650 BN_ULONG *_not_const; \
651 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
652 RAND_pseudo_bytes(&_tmp_char, 1); \
653 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
654 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
658 #undef RAND_pseudo_bytes
661 #define bn_pollute(a)
663 #define bn_check_top(a) \
665 const BIGNUM *_bnum2 = (a); \
666 if (_bnum2 != NULL) { \
667 assert((_bnum2->top == 0) || \
668 (_bnum2->d[_bnum2->top - 1] != 0)); \
669 bn_pollute(_bnum2); \
673 #define bn_fix_top(a) bn_check_top(a)
675 #else /* !BN_DEBUG */
677 #define bn_pollute(a)
678 #define bn_check_top(a)
679 #define bn_fix_top(a) bn_correct_top(a)
683 #define bn_correct_top(a) \
688 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
689 if (*(ftl--)) break; \
694 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
695 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
696 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
697 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
698 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
699 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
701 /* Primes from RFC 2409 */
702 BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
703 BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
705 /* Primes from RFC 3526 */
706 BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
707 BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
708 BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
709 BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
710 BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
711 BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
713 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
715 /* BEGIN ERROR CODES */
716 /* The following lines are auto generated by the script mkerr.pl. Any changes
717 * made after this point may be overwritten when the script is next run.
719 void ERR_load_BN_strings(void);
721 /* Error codes for the BN functions. */
723 /* Function codes. */
724 #define BN_F_BNRAND 127
725 #define BN_F_BN_BLINDING_CONVERT_EX 100
726 #define BN_F_BN_BLINDING_CREATE_PARAM 128
727 #define BN_F_BN_BLINDING_INVERT_EX 101
728 #define BN_F_BN_BLINDING_NEW 102
729 #define BN_F_BN_BLINDING_UPDATE 103
730 #define BN_F_BN_BN2DEC 104
731 #define BN_F_BN_BN2HEX 105
732 #define BN_F_BN_CTX_GET 116
733 #define BN_F_BN_CTX_NEW 106
734 #define BN_F_BN_CTX_START 129
735 #define BN_F_BN_DIV 107
736 #define BN_F_BN_DIV_RECP 130
737 #define BN_F_BN_EXP 123
738 #define BN_F_BN_EXPAND2 108
739 #define BN_F_BN_EXPAND_INTERNAL 120
740 #define BN_F_BN_GF2M_MOD 131
741 #define BN_F_BN_GF2M_MOD_EXP 132
742 #define BN_F_BN_GF2M_MOD_MUL 133
743 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
744 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
745 #define BN_F_BN_GF2M_MOD_SQR 136
746 #define BN_F_BN_GF2M_MOD_SQRT 137
747 #define BN_F_BN_MOD_EXP2_MONT 118
748 #define BN_F_BN_MOD_EXP_MONT 109
749 #define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
750 #define BN_F_BN_MOD_EXP_MONT_WORD 117
751 #define BN_F_BN_MOD_EXP_RECP 125
752 #define BN_F_BN_MOD_EXP_SIMPLE 126
753 #define BN_F_BN_MOD_INVERSE 110
754 #define BN_F_BN_MOD_LSHIFT_QUICK 119
755 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
756 #define BN_F_BN_MOD_SQRT 121
757 #define BN_F_BN_MPI2BN 112
758 #define BN_F_BN_NEW 113
759 #define BN_F_BN_RAND 114
760 #define BN_F_BN_RAND_RANGE 122
761 #define BN_F_BN_USUB 115
764 #define BN_R_ARG2_LT_ARG3 100
765 #define BN_R_BAD_RECIPROCAL 101
766 #define BN_R_BIGNUM_TOO_LONG 114
767 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
768 #define BN_R_DIV_BY_ZERO 103
769 #define BN_R_ENCODING_ERROR 104
770 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
771 #define BN_R_INPUT_NOT_REDUCED 110
772 #define BN_R_INVALID_LENGTH 106
773 #define BN_R_INVALID_RANGE 115
774 #define BN_R_NOT_A_SQUARE 111
775 #define BN_R_NOT_INITIALIZED 107
776 #define BN_R_NO_INVERSE 108
777 #define BN_R_NO_SOLUTION 116
778 #define BN_R_P_IS_NOT_PRIME 112
779 #define BN_R_TOO_MANY_ITERATIONS 113
780 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109