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.
93 * BN_STRICT - disables anything (not already caught by BN_DEBUG) that uses the
94 * old ambiguity over zero representation. At some point, this behaviour should
97 /* #define BN_DEBUG */
98 /* #define BN_DEBUG_RAND */
99 /* #define BN_STRICT */
101 #ifdef OPENSSL_SYS_VMS
102 #undef BN_LLONG /* experimental, so far... */
109 /* This next option uses the C libraries (2 word)/(1 word) function.
110 * If it is not defined, I use my C version (which is slower).
111 * The reason for this flag is that when the particular C compiler
112 * library routine is used, and the library is linked with a different
113 * compiler, the library is missing. This mostly happens when the
114 * library is built with gcc and then linked using normal cc. This would
115 * be a common occurrence because gcc normally produces code that is
116 * 2 times faster than system compilers for the big number stuff.
117 * For machines with only one compiler (or shared libraries), this should
118 * be on. Again this in only really a problem on machines
119 * using "long long's", are 32bit, and are not using my assembler code. */
120 #if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
121 defined(OPENSSL_SYS_WIN32) || defined(linux)
127 /* assuming long is 64bit - this is the DEC Alpha
128 * unsigned long long is only 64 bits :-(, don't define
129 * BN_LLONG for the DEC Alpha */
130 #ifdef SIXTY_FOUR_BIT_LONG
131 #define BN_ULLONG unsigned long long
132 #define BN_ULONG unsigned long
138 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
139 #define BN_MASK2 (0xffffffffffffffffL)
140 #define BN_MASK2l (0xffffffffL)
141 #define BN_MASK2h (0xffffffff00000000L)
142 #define BN_MASK2h1 (0xffffffff80000000L)
143 #define BN_TBIT (0x8000000000000000L)
144 #define BN_DEC_CONV (10000000000000000000UL)
145 #define BN_DEC_FMT1 "%lu"
146 #define BN_DEC_FMT2 "%019lu"
147 #define BN_DEC_NUM 19
150 /* This is where the long long data type is 64 bits, but long is 32.
151 * For machines where there are 64bit registers, this is the mode to use.
152 * IRIX, on R4000 and above should use this mode, along with the relevant
153 * assembler code :-). Do NOT define BN_LLONG.
155 #ifdef SIXTY_FOUR_BIT
158 #define BN_ULONG unsigned long long
159 #define BN_LONG long long
164 #define BN_MASK2 (0xffffffffffffffffLL)
165 #define BN_MASK2l (0xffffffffL)
166 #define BN_MASK2h (0xffffffff00000000LL)
167 #define BN_MASK2h1 (0xffffffff80000000LL)
168 #define BN_TBIT (0x8000000000000000LL)
169 #define BN_DEC_CONV (10000000000000000000ULL)
170 #define BN_DEC_FMT1 "%llu"
171 #define BN_DEC_FMT2 "%019llu"
172 #define BN_DEC_NUM 19
175 #ifdef THIRTY_TWO_BIT
176 #if defined(OPENSSL_SYS_WIN32) && !defined(__GNUC__)
177 #define BN_ULLONG unsigned _int64
179 #define BN_ULLONG unsigned long long
181 #define BN_ULONG unsigned long
187 #ifdef OPENSSL_SYS_WIN32
188 /* VC++ doesn't like the LL suffix */
189 #define BN_MASK (0xffffffffffffffffL)
191 #define BN_MASK (0xffffffffffffffffLL)
193 #define BN_MASK2 (0xffffffffL)
194 #define BN_MASK2l (0xffff)
195 #define BN_MASK2h1 (0xffff8000L)
196 #define BN_MASK2h (0xffff0000L)
197 #define BN_TBIT (0x80000000L)
198 #define BN_DEC_CONV (1000000000L)
199 #define BN_DEC_FMT1 "%lu"
200 #define BN_DEC_FMT2 "%09lu"
208 #define BN_ULLONG unsigned long
209 #define BN_ULONG unsigned short
210 #define BN_LONG short
215 #define BN_MASK (0xffffffff)
216 #define BN_MASK2 (0xffff)
217 #define BN_MASK2l (0xff)
218 #define BN_MASK2h1 (0xff80)
219 #define BN_MASK2h (0xff00)
220 #define BN_TBIT (0x8000)
221 #define BN_DEC_CONV (100000)
222 #define BN_DEC_FMT1 "%u"
223 #define BN_DEC_FMT2 "%05u"
231 #define BN_ULLONG unsigned short
232 #define BN_ULONG unsigned char
238 #define BN_MASK (0xffff)
239 #define BN_MASK2 (0xff)
240 #define BN_MASK2l (0xf)
241 #define BN_MASK2h1 (0xf8)
242 #define BN_MASK2h (0xf0)
243 #define BN_TBIT (0x80)
244 #define BN_DEC_CONV (100)
245 #define BN_DEC_FMT1 "%u"
246 #define BN_DEC_FMT2 "%02u"
250 #define BN_DEFAULT_BITS 1280
252 #define BN_FLG_MALLOCED 0x01
253 #define BN_FLG_STATIC_DATA 0x02
254 #ifndef OPENSSL_NO_DEPRECATED
255 #define BN_FLG_FREE 0x8000 /* used for debuging */
257 #define BN_set_flags(b,n) ((b)->flags|=(n))
258 #define BN_get_flags(b,n) ((b)->flags&(n))
260 /* Already declared in ossl_typ.h */
262 typedef struct bignum_st BIGNUM;
263 /* Used for temp variables (declaration hidden in bn_lcl.h) */
264 typedef struct bignum_ctx BN_CTX;
265 typedef struct bn_blinding_st BN_BLINDING;
266 typedef struct bn_mont_ctx_st BN_MONT_CTX;
267 typedef struct bn_recp_ctx_st BN_RECP_CTX;
268 typedef struct bn_gencb_st BN_GENCB;
273 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
274 int top; /* Index of last used d +1. */
275 /* The next are internal book keeping for bn_expand. */
276 int dmax; /* Size of the d array. */
277 int neg; /* one if the number is negative */
281 struct bn_blinding_st
286 BIGNUM *mod; /* just a reference */
287 unsigned long thread_id; /* added in OpenSSL 0.9.6j and 0.9.7b;
288 * used only by crypto/rsa/rsa_eay.c, rsa_lib.c */
291 /* Used for montgomery multiplication */
292 struct bn_mont_ctx_st
294 int ri; /* number of bits in R */
295 BIGNUM RR; /* used to convert to montgomery form */
296 BIGNUM N; /* The modulus */
297 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
298 * (Ni is only stored for bignum algorithm) */
299 BN_ULONG n0; /* least significant word of Ni */
303 /* Used for reciprocal division/mod functions
304 * It cannot be shared between threads
306 struct bn_recp_ctx_st
308 BIGNUM N; /* the divisor */
309 BIGNUM Nr; /* the reciprocal */
315 /* Used for slow "generation" functions. */
318 unsigned int ver; /* To handle binary (in)compatibility */
319 void *arg; /* callback-specific data */
322 /* if(ver==1) - handles old style callbacks */
323 void (*cb_1)(int, int, void *);
324 /* if(ver==2) - new callback style */
325 int (*cb_2)(int, int, BN_GENCB *);
328 /* Wrapper function to make using BN_GENCB easier, */
329 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
330 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
331 #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
332 BN_GENCB *tmp_gencb = (gencb); \
333 tmp_gencb->ver = 1; \
334 tmp_gencb->arg = (cb_arg); \
335 tmp_gencb->cb.cb_1 = (callback); }
336 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
337 #define BN_GENCB_set(gencb, callback, cb_arg) { \
338 BN_GENCB *tmp_gencb = (gencb); \
339 tmp_gencb->ver = 2; \
340 tmp_gencb->arg = (cb_arg); \
341 tmp_gencb->cb.cb_2 = (callback); }
343 #define BN_prime_checks 0 /* default: select number of iterations
344 based on the size of the number */
346 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
347 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
348 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
349 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
350 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
351 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
364 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
366 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
367 #define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
368 (((w) == 0) && ((a)->top == 0)))
370 #define BN_is_zero(a) ((a)->top == 0)
372 #define BN_is_zero(a) BN_abs_is_word(a,0)
374 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
375 #define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
376 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
378 #define BN_one(a) (BN_set_word((a),1))
379 #define BN_zero_ex(a) \
381 BIGNUM *_tmp_bn = (a); \
385 #ifdef OPENSSL_NO_DEPRECATED
386 #define BN_zero(a) BN_zero_ex(a)
388 #define BN_zero(a) (BN_set_word((a),0))
390 /* BN_set_sign(BIGNUM *, int) sets the sign of a BIGNUM
391 * (0 for a non-negative value, 1 for negative) */
392 #define BN_set_sign(a,b) ((a)->neg = (b))
393 /* BN_get_sign(BIGNUM *) returns the sign of the BIGNUM */
394 #define BN_get_sign(a) ((a)->neg)
396 /*#define BN_ascii2bn(a) BN_hex2bn(a) */
397 /*#define BN_bn2ascii(a) BN_bn2hex(a) */
399 const BIGNUM *BN_value_one(void);
400 char * BN_options(void);
401 BN_CTX *BN_CTX_new(void);
402 #ifndef OPENSSL_NO_DEPRECATED
403 void BN_CTX_init(BN_CTX *c);
405 void BN_CTX_free(BN_CTX *c);
406 void BN_CTX_start(BN_CTX *ctx);
407 BIGNUM *BN_CTX_get(BN_CTX *ctx);
408 void BN_CTX_end(BN_CTX *ctx);
409 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
410 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
411 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
412 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
413 int BN_num_bits(const BIGNUM *a);
414 int BN_num_bits_word(BN_ULONG);
415 BIGNUM *BN_new(void);
416 void BN_init(BIGNUM *);
417 void BN_clear_free(BIGNUM *a);
418 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
419 /* BN_ncopy(): like BN_copy() but copies at most the first n BN_ULONGs */
420 BIGNUM *BN_ncopy(BIGNUM *a, const BIGNUM *b, size_t n);
421 void BN_swap(BIGNUM *a, BIGNUM *b);
422 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
423 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
424 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
425 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
426 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
427 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
428 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
429 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
430 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
431 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
433 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
435 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
436 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
437 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
438 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
439 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
440 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
441 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
442 const BIGNUM *m, BN_CTX *ctx);
443 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
444 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
445 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
446 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
447 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
449 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
450 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
451 int BN_mul_word(BIGNUM *a, BN_ULONG w);
452 int BN_add_word(BIGNUM *a, BN_ULONG w);
453 int BN_sub_word(BIGNUM *a, BN_ULONG w);
454 int BN_set_word(BIGNUM *a, BN_ULONG w);
455 BN_ULONG BN_get_word(const BIGNUM *a);
457 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
458 void BN_free(BIGNUM *a);
459 int BN_is_bit_set(const BIGNUM *a, int n);
460 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
461 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
462 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
464 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
465 const BIGNUM *m,BN_CTX *ctx);
466 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
467 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
468 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
469 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
470 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
471 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
472 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
473 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
474 const BIGNUM *m,BN_CTX *ctx);
476 int BN_mask_bits(BIGNUM *a,int n);
477 #ifndef OPENSSL_NO_FP_API
478 int BN_print_fp(FILE *fp, const BIGNUM *a);
481 int BN_print(BIO *fp, const BIGNUM *a);
483 int BN_print(void *fp, const BIGNUM *a);
485 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
486 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
487 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
488 void BN_clear(BIGNUM *a);
489 BIGNUM *BN_dup(const BIGNUM *a);
490 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
491 int BN_set_bit(BIGNUM *a, int n);
492 int BN_clear_bit(BIGNUM *a, int n);
493 char * BN_bn2hex(const BIGNUM *a);
494 char * BN_bn2dec(const BIGNUM *a);
495 int BN_hex2bn(BIGNUM **a, const char *str);
496 int BN_dec2bn(BIGNUM **a, const char *str);
497 int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
498 int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
499 BIGNUM *BN_mod_inverse(BIGNUM *ret,
500 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
501 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
502 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
504 /* Deprecated versions */
505 #ifndef OPENSSL_NO_DEPRECATED
506 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
507 const BIGNUM *add, const BIGNUM *rem,
508 void (*callback)(int,int,void *),void *cb_arg);
509 int BN_is_prime(const BIGNUM *p,int nchecks,
510 void (*callback)(int,int,void *),
511 BN_CTX *ctx,void *cb_arg);
512 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
513 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
514 int do_trial_division);
515 #endif /* !defined(OPENSSL_NO_DEPRECATED) */
518 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
519 const BIGNUM *rem, BN_GENCB *cb);
520 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
521 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
522 int do_trial_division, BN_GENCB *cb);
524 BN_MONT_CTX *BN_MONT_CTX_new(void );
525 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
526 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
527 BN_MONT_CTX *mont, BN_CTX *ctx);
528 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
529 (r),(a),&((mont)->RR),(mont),(ctx))
530 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
531 BN_MONT_CTX *mont, BN_CTX *ctx);
532 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
533 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
534 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
536 BN_BLINDING *BN_BLINDING_new(BIGNUM *A,BIGNUM *Ai,BIGNUM *mod);
537 void BN_BLINDING_free(BN_BLINDING *b);
538 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
539 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *r, BN_CTX *ctx);
540 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
542 #ifndef OPENSSL_NO_DEPRECATED
543 void BN_set_params(int mul,int high,int low,int mont);
544 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
547 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
548 BN_RECP_CTX *BN_RECP_CTX_new(void);
549 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
550 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
551 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
552 BN_RECP_CTX *recp,BN_CTX *ctx);
553 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
554 const BIGNUM *m, BN_CTX *ctx);
555 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
556 BN_RECP_CTX *recp, BN_CTX *ctx);
558 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
560 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
563 * Note that input arguments are not const so that their bit arrays can
564 * be expanded to the appropriate size if needed.
567 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
568 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
569 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
570 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
571 const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
572 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
573 BN_CTX *ctx); /* r = (a * a) mod p */
574 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
575 BN_CTX *ctx); /* r = (1 / b) mod p */
576 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
577 const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
578 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
579 const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
580 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
581 BN_CTX *ctx); /* r = sqrt(a) mod p */
582 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
583 BN_CTX *ctx); /* r^2 + r = a mod p */
584 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
585 /* Some functions allow for representation of the irreducible polynomials
586 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
587 * t^p[0] + t^p[1] + ... + t^p[k]
588 * where m = p[0] > p[1] > ... > p[k] = 0.
590 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]);
592 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
593 const unsigned int p[], BN_CTX *ctx); /* r = (a * b) mod p */
594 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[],
595 BN_CTX *ctx); /* r = (a * a) mod p */
596 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[],
597 BN_CTX *ctx); /* r = (1 / b) mod p */
598 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
599 const unsigned int p[], BN_CTX *ctx); /* r = (a / b) mod p */
600 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
601 const unsigned int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
602 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
603 const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
604 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
605 const unsigned int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
606 int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
607 int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
609 /* faster mod functions for the 'NIST primes'
611 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
612 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
613 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
614 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
615 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
617 const BIGNUM *BN_get0_nist_prime_192(void);
618 const BIGNUM *BN_get0_nist_prime_224(void);
619 const BIGNUM *BN_get0_nist_prime_256(void);
620 const BIGNUM *BN_get0_nist_prime_384(void);
621 const BIGNUM *BN_get0_nist_prime_521(void);
623 /* library internal functions */
625 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
626 (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
627 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
628 BIGNUM *bn_expand2(BIGNUM *a, int words);
629 #ifndef OPENSSL_NO_DEPRECATED
630 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
633 /* Bignum consistency macros
634 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
635 * bignum data after direct manipulations on the data. There is also an
636 * "internal" macro, bn_check_top(), for verifying that there are no leading
637 * zeroes. Unfortunately, some auditing is required due to the fact that
638 * bn_fix_top() has become an overabused duct-tape because bignum data is
639 * occasionally passed around in an inconsistent state. So the following
640 * changes have been made to sort this out;
641 * - bn_fix_top()s implementation has been moved to bn_correct_top()
642 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
643 * bn_check_top() is as before.
644 * - if BN_DEBUG *is* defined;
645 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
646 * consistent. (ed: only if BN_DEBUG_RAND is defined)
647 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
648 * The idea is to have debug builds flag up inconsistent bignums when they
649 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
650 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
651 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
652 * was not appropriate, we convert it permanently to bn_check_top() and track
653 * down the cause of the bug. Eventually, no internal code should be using the
654 * bn_fix_top() macro. External applications and libraries should try this with
655 * their own code too, both in terms of building against the openssl headers
656 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
657 * defined. This not only improves external code, it provides more test
658 * coverage for openssl's own code.
663 /* We only need assert() when debugging */
667 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
668 #ifndef RAND_pseudo_bytes
669 int RAND_pseudo_bytes(unsigned char *buf,int num);
670 #define BN_DEBUG_TRIX
672 #define bn_pollute(a) \
674 const BIGNUM *_bnum1 = (a); \
675 if(_bnum1->top < _bnum1->dmax) { \
676 unsigned char _tmp_char; \
677 /* We cast away const without the compiler knowing, any \
678 * *genuinely* constant variables that aren't mutable \
679 * wouldn't be constructed with top!=dmax. */ \
680 BN_ULONG *_not_const; \
681 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
682 RAND_pseudo_bytes(&_tmp_char, 1); \
683 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
684 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
688 #undef RAND_pseudo_bytes
691 #define bn_pollute(a)
693 #define bn_check_top(a) \
695 const BIGNUM *_bnum2 = (a); \
696 assert((_bnum2->top == 0) || \
697 (_bnum2->d[_bnum2->top - 1] != 0)); \
698 bn_pollute(_bnum2); \
701 #define bn_fix_top(a) bn_check_top(a)
703 #else /* !BN_DEBUG */
705 #define bn_pollute(a)
706 #define bn_check_top(a)
707 #define bn_fix_top(a) bn_correct_top(a)
711 #define bn_correct_top(a) \
716 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
717 if (*(ftl--)) break; \
722 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
723 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
724 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
725 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
726 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
727 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
729 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
731 /* BEGIN ERROR CODES */
732 /* The following lines are auto generated by the script mkerr.pl. Any changes
733 * made after this point may be overwritten when the script is next run.
735 void ERR_load_BN_strings(void);
737 /* Error codes for the BN functions. */
739 /* Function codes. */
740 #define BN_F_BN_BLINDING_CONVERT 100
741 #define BN_F_BN_BLINDING_INVERT 101
742 #define BN_F_BN_BLINDING_NEW 102
743 #define BN_F_BN_BLINDING_UPDATE 103
744 #define BN_F_BN_BN2DEC 104
745 #define BN_F_BN_BN2HEX 105
746 #define BN_F_BN_CTX_GET 116
747 #define BN_F_BN_CTX_NEW 106
748 #define BN_F_BN_DIV 107
749 #define BN_F_BN_EXPAND2 108
750 #define BN_F_BN_EXPAND_INTERNAL 120
751 #define BN_F_BN_GF2M_MOD 126
752 #define BN_F_BN_GF2M_MOD_DIV 123
753 #define BN_F_BN_GF2M_MOD_EXP 127
754 #define BN_F_BN_GF2M_MOD_MUL 124
755 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 128
756 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 129
757 #define BN_F_BN_GF2M_MOD_SQR 125
758 #define BN_F_BN_MOD_EXP2_MONT 118
759 #define BN_F_BN_MOD_EXP_MONT 109
760 #define BN_F_BN_MOD_EXP_MONT_WORD 117
761 #define BN_F_BN_MOD_INVERSE 110
762 #define BN_F_BN_MOD_LSHIFT_QUICK 119
763 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
764 #define BN_F_BN_MOD_SQRT 121
765 #define BN_F_BN_MPI2BN 112
766 #define BN_F_BN_NEW 113
767 #define BN_F_BN_RAND 114
768 #define BN_F_BN_RAND_RANGE 122
769 #define BN_F_BN_USUB 115
772 #define BN_R_ARG2_LT_ARG3 100
773 #define BN_R_BAD_RECIPROCAL 101
774 #define BN_R_BIGNUM_TOO_LONG 114
775 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
776 #define BN_R_DIV_BY_ZERO 103
777 #define BN_R_ENCODING_ERROR 104
778 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
779 #define BN_R_INPUT_NOT_REDUCED 110
780 #define BN_R_INVALID_LENGTH 106
781 #define BN_R_INVALID_RANGE 115
782 #define BN_R_NOT_A_SQUARE 111
783 #define BN_R_NOT_IMPLEMENTED 116
784 #define BN_R_NOT_INITIALIZED 107
785 #define BN_R_NO_INVERSE 108
786 #define BN_R_NO_SOLUTION 117
787 #define BN_R_P_IS_NOT_PRIME 112
788 #define BN_R_TOO_MANY_ITERATIONS 113
789 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109