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 */
101 /* This next option uses the C libraries (2 word)/(1 word) function.
102 * If it is not defined, I use my C version (which is slower).
103 * The reason for this flag is that when the particular C compiler
104 * library routine is used, and the library is linked with a different
105 * compiler, the library is missing. This mostly happens when the
106 * library is built with gcc and then linked using normal cc. This would
107 * be a common occurrence because gcc normally produces code that is
108 * 2 times faster than system compilers for the big number stuff.
109 * For machines with only one compiler (or shared libraries), this should
110 * be on. Again this in only really a problem on machines
111 * using "long long's", are 32bit, and are not using my assembler code. */
112 #if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
113 defined(OPENSSL_SYS_WIN32) || defined(linux)
119 /* assuming long is 64bit - this is the DEC Alpha
120 * unsigned long long is only 64 bits :-(, don't define
121 * BN_LLONG for the DEC Alpha */
122 #ifdef SIXTY_FOUR_BIT_LONG
123 #define BN_ULLONG unsigned long long
124 #define BN_ULONG unsigned long
130 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
131 #define BN_MASK2 (0xffffffffffffffffL)
132 #define BN_MASK2l (0xffffffffL)
133 #define BN_MASK2h (0xffffffff00000000L)
134 #define BN_MASK2h1 (0xffffffff80000000L)
135 #define BN_TBIT (0x8000000000000000L)
136 #define BN_DEC_CONV (10000000000000000000UL)
137 #define BN_DEC_FMT1 "%lu"
138 #define BN_DEC_FMT2 "%019lu"
139 #define BN_DEC_NUM 19
142 /* This is where the long long data type is 64 bits, but long is 32.
143 * For machines where there are 64bit registers, this is the mode to use.
144 * IRIX, on R4000 and above should use this mode, along with the relevant
145 * assembler code :-). Do NOT define BN_LLONG.
147 #ifdef SIXTY_FOUR_BIT
150 #define BN_ULONG unsigned long long
151 #define BN_LONG long long
156 #define BN_MASK2 (0xffffffffffffffffLL)
157 #define BN_MASK2l (0xffffffffL)
158 #define BN_MASK2h (0xffffffff00000000LL)
159 #define BN_MASK2h1 (0xffffffff80000000LL)
160 #define BN_TBIT (0x8000000000000000LL)
161 #define BN_DEC_CONV (10000000000000000000ULL)
162 #define BN_DEC_FMT1 "%llu"
163 #define BN_DEC_FMT2 "%019llu"
164 #define BN_DEC_NUM 19
167 #ifdef THIRTY_TWO_BIT
169 # if defined(OPENSSL_SYS_WIN32) && !defined(__GNUC__)
170 # define BN_ULLONG unsigned __int64
172 # define BN_ULLONG unsigned long long
175 #define BN_ULONG unsigned long
181 #ifdef OPENSSL_SYS_WIN32
182 /* VC++ doesn't like the LL suffix */
183 #define BN_MASK (0xffffffffffffffffL)
185 #define BN_MASK (0xffffffffffffffffLL)
187 #define BN_MASK2 (0xffffffffL)
188 #define BN_MASK2l (0xffff)
189 #define BN_MASK2h1 (0xffff8000L)
190 #define BN_MASK2h (0xffff0000L)
191 #define BN_TBIT (0x80000000L)
192 #define BN_DEC_CONV (1000000000L)
193 #define BN_DEC_FMT1 "%lu"
194 #define BN_DEC_FMT2 "%09lu"
202 #define BN_ULLONG unsigned long
203 #define BN_ULONG unsigned short
204 #define BN_LONG short
209 #define BN_MASK (0xffffffff)
210 #define BN_MASK2 (0xffff)
211 #define BN_MASK2l (0xff)
212 #define BN_MASK2h1 (0xff80)
213 #define BN_MASK2h (0xff00)
214 #define BN_TBIT (0x8000)
215 #define BN_DEC_CONV (100000)
216 #define BN_DEC_FMT1 "%u"
217 #define BN_DEC_FMT2 "%05u"
225 #define BN_ULLONG unsigned short
226 #define BN_ULONG unsigned char
232 #define BN_MASK (0xffff)
233 #define BN_MASK2 (0xff)
234 #define BN_MASK2l (0xf)
235 #define BN_MASK2h1 (0xf8)
236 #define BN_MASK2h (0xf0)
237 #define BN_TBIT (0x80)
238 #define BN_DEC_CONV (100)
239 #define BN_DEC_FMT1 "%u"
240 #define BN_DEC_FMT2 "%02u"
244 #define BN_DEFAULT_BITS 1280
246 #define BN_FLG_MALLOCED 0x01
247 #define BN_FLG_STATIC_DATA 0x02
250 * avoid leaking exponent information through timing,
251 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
252 * BN_div() will call BN_div_no_branch,
253 * BN_mod_inverse() will call BN_mod_inverse_no_branch.
255 #define BN_FLG_CONSTTIME 0x04
257 #ifdef OPENSSL_NO_DEPRECATED
258 /* deprecated name for the flag */
259 #define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
261 * avoid leaking exponent information through timings
262 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime)
266 #ifndef OPENSSL_NO_DEPRECATED
267 #define BN_FLG_FREE 0x8000 /* used for debuging */
269 #define BN_set_flags(b,n) ((b)->flags|=(n))
270 #define BN_get_flags(b,n) ((b)->flags&(n))
272 /* get a clone of a BIGNUM with changed flags, for *temporary* use only
273 * (the two BIGNUMs cannot not be used in parallel!) */
274 #define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
275 (dest)->top=(b)->top, \
276 (dest)->dmax=(b)->dmax, \
277 (dest)->neg=(b)->neg, \
278 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
279 | ((b)->flags & ~BN_FLG_MALLOCED) \
280 | BN_FLG_STATIC_DATA \
283 /* Already declared in ossl_typ.h */
285 typedef struct bignum_st BIGNUM;
286 /* Used for temp variables (declaration hidden in bn_lcl.h) */
287 typedef struct bignum_ctx BN_CTX;
288 typedef struct bn_blinding_st BN_BLINDING;
289 typedef struct bn_mont_ctx_st BN_MONT_CTX;
290 typedef struct bn_recp_ctx_st BN_RECP_CTX;
291 typedef struct bn_gencb_st BN_GENCB;
296 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
297 int top; /* Index of last used d +1. */
298 /* The next are internal book keeping for bn_expand. */
299 int dmax; /* Size of the d array. */
300 int neg; /* one if the number is negative */
304 /* Used for montgomery multiplication */
305 struct bn_mont_ctx_st
307 int ri; /* number of bits in R */
308 BIGNUM RR; /* used to convert to montgomery form */
309 BIGNUM N; /* The modulus */
310 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
311 * (Ni is only stored for bignum algorithm) */
313 /* OpenSSL 0.9.9 preview: */
314 BN_ULONG n0[2];/* least significant word(s) of Ni */
316 BN_ULONG n0; /* least significant word of Ni */
321 /* Used for reciprocal division/mod functions
322 * It cannot be shared between threads
324 struct bn_recp_ctx_st
326 BIGNUM N; /* the divisor */
327 BIGNUM Nr; /* the reciprocal */
333 /* Used for slow "generation" functions. */
336 unsigned int ver; /* To handle binary (in)compatibility */
337 void *arg; /* callback-specific data */
340 /* if(ver==1) - handles old style callbacks */
341 void (*cb_1)(int, int, void *);
342 /* if(ver==2) - new callback style */
343 int (*cb_2)(int, int, BN_GENCB *);
346 /* Wrapper function to make using BN_GENCB easier, */
347 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
348 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
349 #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
350 BN_GENCB *tmp_gencb = (gencb); \
351 tmp_gencb->ver = 1; \
352 tmp_gencb->arg = (cb_arg); \
353 tmp_gencb->cb.cb_1 = (callback); }
354 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
355 #define BN_GENCB_set(gencb, callback, cb_arg) { \
356 BN_GENCB *tmp_gencb = (gencb); \
357 tmp_gencb->ver = 2; \
358 tmp_gencb->arg = (cb_arg); \
359 tmp_gencb->cb.cb_2 = (callback); }
361 #define BN_prime_checks 0 /* default: select number of iterations
362 based on the size of the number */
364 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
365 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
366 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
367 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
368 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
369 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
382 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
384 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
385 #define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
386 (((w) == 0) && ((a)->top == 0)))
387 #define BN_is_zero(a) ((a)->top == 0)
388 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
389 #define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
390 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
392 #define BN_one(a) (BN_set_word((a),1))
393 #define BN_zero_ex(a) \
395 BIGNUM *_tmp_bn = (a); \
399 #ifdef OPENSSL_NO_DEPRECATED
400 #define BN_zero(a) BN_zero_ex(a)
402 #define BN_zero(a) (BN_set_word((a),0))
405 const BIGNUM *BN_value_one(void);
406 char * BN_options(void);
407 BN_CTX *BN_CTX_new(void);
408 #ifndef OPENSSL_NO_DEPRECATED
409 void BN_CTX_init(BN_CTX *c);
411 void BN_CTX_free(BN_CTX *c);
412 void BN_CTX_start(BN_CTX *ctx);
413 BIGNUM *BN_CTX_get(BN_CTX *ctx);
414 void BN_CTX_end(BN_CTX *ctx);
415 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
416 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
417 int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
418 int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
419 int BN_num_bits(const BIGNUM *a);
420 int BN_num_bits_word(BN_ULONG);
421 BIGNUM *BN_new(void);
422 void BN_init(BIGNUM *);
423 void BN_clear_free(BIGNUM *a);
424 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
425 void BN_swap(BIGNUM *a, BIGNUM *b);
426 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
427 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
428 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
429 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
430 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
431 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
432 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
433 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
434 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
435 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
436 /** BN_set_negative sets sign of a BIGNUM
437 * \param b pointer to the BIGNUM object
438 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
440 void BN_set_negative(BIGNUM *b, int n);
441 /** BN_is_negative returns 1 if the BIGNUM is negative
442 * \param a pointer to the BIGNUM object
443 * \return 1 if a < 0 and 0 otherwise
445 #define BN_is_negative(a) ((a)->neg != 0)
447 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
449 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
450 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
451 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
452 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
453 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
454 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
455 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
456 const BIGNUM *m, BN_CTX *ctx);
457 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
458 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
459 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
460 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
461 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
463 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
464 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
465 int BN_mul_word(BIGNUM *a, BN_ULONG w);
466 int BN_add_word(BIGNUM *a, BN_ULONG w);
467 int BN_sub_word(BIGNUM *a, BN_ULONG w);
468 int BN_set_word(BIGNUM *a, BN_ULONG w);
469 BN_ULONG BN_get_word(const BIGNUM *a);
471 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
472 void BN_free(BIGNUM *a);
473 int BN_is_bit_set(const BIGNUM *a, int n);
474 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
475 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
476 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
478 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
479 const BIGNUM *m,BN_CTX *ctx);
480 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
481 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
482 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
483 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont);
484 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
485 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
486 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
487 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
488 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
489 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
490 const BIGNUM *m,BN_CTX *ctx);
492 int BN_mask_bits(BIGNUM *a,int n);
493 #ifndef OPENSSL_NO_FP_API
494 int BN_print_fp(FILE *fp, const BIGNUM *a);
497 int BN_print(BIO *fp, const BIGNUM *a);
499 int BN_print(void *fp, const BIGNUM *a);
501 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
502 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
503 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
504 void BN_clear(BIGNUM *a);
505 BIGNUM *BN_dup(const BIGNUM *a);
506 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
507 int BN_set_bit(BIGNUM *a, int n);
508 int BN_clear_bit(BIGNUM *a, int n);
509 char * BN_bn2hex(const BIGNUM *a);
510 char * BN_bn2dec(const BIGNUM *a);
511 int BN_hex2bn(BIGNUM **a, const char *str);
512 int BN_dec2bn(BIGNUM **a, const char *str);
513 int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
514 int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
515 BIGNUM *BN_mod_inverse(BIGNUM *ret,
516 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
517 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
518 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
520 void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
522 /* Deprecated versions */
523 #ifndef OPENSSL_NO_DEPRECATED
524 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
525 const BIGNUM *add, const BIGNUM *rem,
526 void (*callback)(int,int,void *),void *cb_arg);
527 int BN_is_prime(const BIGNUM *p,int nchecks,
528 void (*callback)(int,int,void *),
529 BN_CTX *ctx,void *cb_arg);
530 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
531 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
532 int do_trial_division);
533 #endif /* !defined(OPENSSL_NO_DEPRECATED) */
536 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
537 const BIGNUM *rem, BN_GENCB *cb);
538 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
539 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
540 int do_trial_division, BN_GENCB *cb);
542 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
544 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
545 const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2,
546 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb);
547 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
548 BIGNUM *Xp1, BIGNUM *Xp2,
550 const BIGNUM *e, BN_CTX *ctx,
553 BN_MONT_CTX *BN_MONT_CTX_new(void );
554 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
555 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
556 BN_MONT_CTX *mont, BN_CTX *ctx);
557 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
558 (r),(a),&((mont)->RR),(mont),(ctx))
559 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
560 BN_MONT_CTX *mont, BN_CTX *ctx);
561 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
562 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
563 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
564 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
565 const BIGNUM *mod, BN_CTX *ctx);
567 /* BN_BLINDING flags */
568 #define BN_BLINDING_NO_UPDATE 0x00000001
569 #define BN_BLINDING_NO_RECREATE 0x00000002
571 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, /* const */ BIGNUM *mod);
572 void BN_BLINDING_free(BN_BLINDING *b);
573 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
574 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
575 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
576 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
577 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b, BN_CTX *);
578 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
579 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
580 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
581 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
582 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
583 const BIGNUM *e, /* const */ BIGNUM *m, BN_CTX *ctx,
584 int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
585 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
588 #ifndef OPENSSL_NO_DEPRECATED
589 void BN_set_params(int mul,int high,int low,int mont);
590 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
593 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
594 BN_RECP_CTX *BN_RECP_CTX_new(void);
595 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
596 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
597 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
598 BN_RECP_CTX *recp,BN_CTX *ctx);
599 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
600 const BIGNUM *m, BN_CTX *ctx);
601 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
602 BN_RECP_CTX *recp, BN_CTX *ctx);
604 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
606 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
609 * Note that input arguments are not const so that their bit arrays can
610 * be expanded to the appropriate size if needed.
614 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
615 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
617 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
618 /* r = (a * b) mod p */
619 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
620 const BIGNUM *p, BN_CTX *ctx);
621 /* r = (a * a) mod p */
622 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
624 /* r = (1 / b) mod p */
625 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
627 /* r = (a / b) mod p */
628 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
629 const BIGNUM *p, BN_CTX *ctx);
630 /* r = (a ^ b) mod p */
631 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
632 const BIGNUM *p, BN_CTX *ctx);
633 /* r = sqrt(a) mod p */
634 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
636 /* r^2 + r = a mod p */
637 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
639 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
641 * Some functions allow for representation of the irreducible polynomials
642 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
643 * t^p[0] + t^p[1] + ... + t^p[k]
644 * where m = p[0] > p[1] > ... > p[k] = 0.
647 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]);
648 /* r = (a * b) mod p */
649 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
650 const unsigned int p[], BN_CTX *ctx);
651 /* r = (a * a) mod p */
652 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[],
654 /* r = (1 / b) mod p */
655 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[],
657 /* r = (a / b) mod p */
658 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
659 const unsigned int p[], BN_CTX *ctx);
660 /* r = (a ^ b) mod p */
661 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
662 const unsigned int p[], BN_CTX *ctx);
663 /* r = sqrt(a) mod p */
664 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
665 const unsigned int p[], BN_CTX *ctx);
666 /* r^2 + r = a mod p */
667 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
668 const unsigned int p[], BN_CTX *ctx);
669 int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
670 int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
672 /* faster mod functions for the 'NIST primes'
674 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
675 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
676 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
677 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
678 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
680 const BIGNUM *BN_get0_nist_prime_192(void);
681 const BIGNUM *BN_get0_nist_prime_224(void);
682 const BIGNUM *BN_get0_nist_prime_256(void);
683 const BIGNUM *BN_get0_nist_prime_384(void);
684 const BIGNUM *BN_get0_nist_prime_521(void);
686 /* library internal functions */
688 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
689 (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
690 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
691 BIGNUM *bn_expand2(BIGNUM *a, int words);
692 #ifndef OPENSSL_NO_DEPRECATED
693 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
697 * Bignum consistency macros
698 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
699 * bignum data after direct manipulations on the data. There is also an
700 * "internal" macro, bn_check_top(), for verifying that there are no leading
701 * zeroes. Unfortunately, some auditing is required due to the fact that
702 * bn_fix_top() has become an overabused duct-tape because bignum data is
703 * occasionally passed around in an inconsistent state. So the following
704 * changes have been made to sort this out;
705 * - bn_fix_top()s implementation has been moved to bn_correct_top()
706 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
707 * bn_check_top() is as before.
708 * - if BN_DEBUG *is* defined;
709 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
710 * consistent. (ed: only if BN_DEBUG_RAND is defined)
711 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
712 * The idea is to have debug builds flag up inconsistent bignums when they
713 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
714 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
715 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
716 * was not appropriate, we convert it permanently to bn_check_top() and track
717 * down the cause of the bug. Eventually, no internal code should be using the
718 * bn_fix_top() macro. External applications and libraries should try this with
719 * their own code too, both in terms of building against the openssl headers
720 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
721 * defined. This not only improves external code, it provides more test
722 * coverage for openssl's own code.
727 /* We only need assert() when debugging */
731 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
732 #ifndef RAND_pseudo_bytes
733 int RAND_pseudo_bytes(unsigned char *buf,int num);
734 #define BN_DEBUG_TRIX
736 #define bn_pollute(a) \
738 const BIGNUM *_bnum1 = (a); \
739 if(_bnum1->top < _bnum1->dmax) { \
740 unsigned char _tmp_char; \
741 /* We cast away const without the compiler knowing, any \
742 * *genuinely* constant variables that aren't mutable \
743 * wouldn't be constructed with top!=dmax. */ \
744 BN_ULONG *_not_const; \
745 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
746 RAND_pseudo_bytes(&_tmp_char, 1); \
747 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
748 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
752 #undef RAND_pseudo_bytes
755 #define bn_pollute(a)
757 #define bn_check_top(a) \
759 const BIGNUM *_bnum2 = (a); \
760 if (_bnum2 != NULL) { \
761 assert((_bnum2->top == 0) || \
762 (_bnum2->d[_bnum2->top - 1] != 0)); \
763 bn_pollute(_bnum2); \
767 #define bn_fix_top(a) bn_check_top(a)
769 #define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
770 #define bn_wcheck_size(bn, words) \
772 const BIGNUM *_bnum2 = (bn); \
773 assert(words <= (_bnum2)->dmax && words >= (_bnum2)->top); \
776 #else /* !BN_DEBUG */
778 #define bn_pollute(a)
779 #define bn_check_top(a)
780 #define bn_fix_top(a) bn_correct_top(a)
781 #define bn_check_size(bn, bits)
782 #define bn_wcheck_size(bn, words)
786 #define bn_correct_top(a) \
791 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
792 if (*(ftl--)) break; \
797 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
798 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
799 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
800 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
801 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
802 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
804 /* Primes from RFC 2409 */
805 BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
806 BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
808 /* Primes from RFC 3526 */
809 BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
810 BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
811 BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
812 BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
813 BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
814 BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
816 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
818 /* BEGIN ERROR CODES */
819 /* The following lines are auto generated by the script mkerr.pl. Any changes
820 * made after this point may be overwritten when the script is next run.
822 void ERR_load_BN_strings(void);
824 /* Error codes for the BN functions. */
826 /* Function codes. */
827 #define BN_F_BNRAND 127
828 #define BN_F_BN_BLINDING_CONVERT_EX 100
829 #define BN_F_BN_BLINDING_CREATE_PARAM 128
830 #define BN_F_BN_BLINDING_INVERT_EX 101
831 #define BN_F_BN_BLINDING_NEW 102
832 #define BN_F_BN_BLINDING_UPDATE 103
833 #define BN_F_BN_BN2DEC 104
834 #define BN_F_BN_BN2HEX 105
835 #define BN_F_BN_CTX_GET 116
836 #define BN_F_BN_CTX_NEW 106
837 #define BN_F_BN_CTX_START 129
838 #define BN_F_BN_DIV 107
839 #define BN_F_BN_DIV_NO_BRANCH 138
840 #define BN_F_BN_DIV_RECP 130
841 #define BN_F_BN_EXP 123
842 #define BN_F_BN_EXPAND2 108
843 #define BN_F_BN_EXPAND_INTERNAL 120
844 #define BN_F_BN_GF2M_MOD 131
845 #define BN_F_BN_GF2M_MOD_EXP 132
846 #define BN_F_BN_GF2M_MOD_MUL 133
847 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
848 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
849 #define BN_F_BN_GF2M_MOD_SQR 136
850 #define BN_F_BN_GF2M_MOD_SQRT 137
851 #define BN_F_BN_MOD_EXP2_MONT 118
852 #define BN_F_BN_MOD_EXP_MONT 109
853 #define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
854 #define BN_F_BN_MOD_EXP_MONT_WORD 117
855 #define BN_F_BN_MOD_EXP_RECP 125
856 #define BN_F_BN_MOD_EXP_SIMPLE 126
857 #define BN_F_BN_MOD_INVERSE 110
858 #define BN_F_BN_MOD_INVERSE_NO_BRANCH 139
859 #define BN_F_BN_MOD_LSHIFT_QUICK 119
860 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
861 #define BN_F_BN_MOD_SQRT 121
862 #define BN_F_BN_MPI2BN 112
863 #define BN_F_BN_NEW 113
864 #define BN_F_BN_RAND 114
865 #define BN_F_BN_RAND_RANGE 122
866 #define BN_F_BN_USUB 115
869 #define BN_R_ARG2_LT_ARG3 100
870 #define BN_R_BAD_RECIPROCAL 101
871 #define BN_R_BIGNUM_TOO_LONG 114
872 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
873 #define BN_R_DIV_BY_ZERO 103
874 #define BN_R_ENCODING_ERROR 104
875 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
876 #define BN_R_INPUT_NOT_REDUCED 110
877 #define BN_R_INVALID_LENGTH 106
878 #define BN_R_INVALID_RANGE 115
879 #define BN_R_NOT_A_SQUARE 111
880 #define BN_R_NOT_INITIALIZED 107
881 #define BN_R_NO_INVERSE 108
882 #define BN_R_NO_SOLUTION 116
883 #define BN_R_P_IS_NOT_PRIME 112
884 #define BN_R_TOO_MANY_ITERATIONS 113
885 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109