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 */
84 /* These preprocessor symbols control various aspects of the bignum headers and
85 * library code. They're not defined by any "normal" configuration, as they are
86 * intended for development and testing purposes. NB: defining all three can be
87 * useful for debugging application code as well as openssl itself.
89 * BN_DEBUG - turn on various debugging alterations to the bignum code
90 * BN_DEBUG_RAND - uses random poisoning of unused words to trip up
91 * mismanagement of bignum internals. You must also define BN_DEBUG.
92 * BN_STRICT - disables anything (not already caught by BN_DEBUG) that uses the
93 * old ambiguity over zero representation. At some point, this behaviour should
96 /* #define BN_DEBUG */
97 /* #define BN_DEBUG_RAND */
98 /* #define BN_STRICT */
100 #ifdef OPENSSL_SYS_VMS
101 #undef BN_LLONG /* experimental, so far... */
108 /* This next option uses the C libraries (2 word)/(1 word) function.
109 * If it is not defined, I use my C version (which is slower).
110 * The reason for this flag is that when the particular C compiler
111 * library routine is used, and the library is linked with a different
112 * compiler, the library is missing. This mostly happens when the
113 * library is built with gcc and then linked using normal cc. This would
114 * be a common occurrence because gcc normally produces code that is
115 * 2 times faster than system compilers for the big number stuff.
116 * For machines with only one compiler (or shared libraries), this should
117 * be on. Again this in only really a problem on machines
118 * using "long long's", are 32bit, and are not using my assembler code. */
119 #if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
120 defined(OPENSSL_SYS_WIN32) || defined(linux)
126 /* assuming long is 64bit - this is the DEC Alpha
127 * unsigned long long is only 64 bits :-(, don't define
128 * BN_LLONG for the DEC Alpha */
129 #ifdef SIXTY_FOUR_BIT_LONG
130 #define BN_ULLONG unsigned long long
131 #define BN_ULONG unsigned long
137 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
138 #define BN_MASK2 (0xffffffffffffffffL)
139 #define BN_MASK2l (0xffffffffL)
140 #define BN_MASK2h (0xffffffff00000000L)
141 #define BN_MASK2h1 (0xffffffff80000000L)
142 #define BN_TBIT (0x8000000000000000L)
143 #define BN_DEC_CONV (10000000000000000000UL)
144 #define BN_DEC_FMT1 "%lu"
145 #define BN_DEC_FMT2 "%019lu"
146 #define BN_DEC_NUM 19
149 /* This is where the long long data type is 64 bits, but long is 32.
150 * For machines where there are 64bit registers, this is the mode to use.
151 * IRIX, on R4000 and above should use this mode, along with the relevant
152 * assembler code :-). Do NOT define BN_LLONG.
154 #ifdef SIXTY_FOUR_BIT
157 #define BN_ULONG unsigned long long
158 #define BN_LONG long long
163 #define BN_MASK2 (0xffffffffffffffffLL)
164 #define BN_MASK2l (0xffffffffL)
165 #define BN_MASK2h (0xffffffff00000000LL)
166 #define BN_MASK2h1 (0xffffffff80000000LL)
167 #define BN_TBIT (0x8000000000000000LL)
168 #define BN_DEC_CONV (10000000000000000000ULL)
169 #define BN_DEC_FMT1 "%llu"
170 #define BN_DEC_FMT2 "%019llu"
171 #define BN_DEC_NUM 19
174 #ifdef THIRTY_TWO_BIT
175 #if defined(OPENSSL_SYS_WIN32) && !defined(__GNUC__)
176 #define BN_ULLONG unsigned _int64
178 #define BN_ULLONG unsigned long long
180 #define BN_ULONG unsigned long
186 #ifdef OPENSSL_SYS_WIN32
187 /* VC++ doesn't like the LL suffix */
188 #define BN_MASK (0xffffffffffffffffL)
190 #define BN_MASK (0xffffffffffffffffLL)
192 #define BN_MASK2 (0xffffffffL)
193 #define BN_MASK2l (0xffff)
194 #define BN_MASK2h1 (0xffff8000L)
195 #define BN_MASK2h (0xffff0000L)
196 #define BN_TBIT (0x80000000L)
197 #define BN_DEC_CONV (1000000000L)
198 #define BN_DEC_FMT1 "%lu"
199 #define BN_DEC_FMT2 "%09lu"
207 #define BN_ULLONG unsigned long
208 #define BN_ULONG unsigned short
209 #define BN_LONG short
214 #define BN_MASK (0xffffffff)
215 #define BN_MASK2 (0xffff)
216 #define BN_MASK2l (0xff)
217 #define BN_MASK2h1 (0xff80)
218 #define BN_MASK2h (0xff00)
219 #define BN_TBIT (0x8000)
220 #define BN_DEC_CONV (100000)
221 #define BN_DEC_FMT1 "%u"
222 #define BN_DEC_FMT2 "%05u"
230 #define BN_ULLONG unsigned short
231 #define BN_ULONG unsigned char
237 #define BN_MASK (0xffff)
238 #define BN_MASK2 (0xff)
239 #define BN_MASK2l (0xf)
240 #define BN_MASK2h1 (0xf8)
241 #define BN_MASK2h (0xf0)
242 #define BN_TBIT (0x80)
243 #define BN_DEC_CONV (100)
244 #define BN_DEC_FMT1 "%u"
245 #define BN_DEC_FMT2 "%02u"
249 #define BN_DEFAULT_BITS 1280
255 #define BN_FLG_MALLOCED 0x01
256 #define BN_FLG_STATIC_DATA 0x02
257 #ifndef OPENSSL_NO_DEPRECATED
258 #define BN_FLG_FREE 0x8000 /* used for debuging */
260 #define BN_set_flags(b,n) ((b)->flags|=(n))
261 #define BN_get_flags(b,n) ((b)->flags&(n))
263 typedef struct bignum_st
265 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
266 int top; /* Index of last used d +1. */
267 /* The next are internal book keeping for bn_expand. */
268 int dmax; /* Size of the d array. */
269 int neg; /* one if the number is negative */
273 /* Used for temp variables (declaration hidden in bn_lcl.h) */
274 typedef struct bignum_ctx BN_CTX;
276 typedef struct bn_blinding_st
281 BIGNUM *mod; /* just a reference */
282 unsigned long thread_id; /* added in OpenSSL 0.9.6j and 0.9.7b;
283 * used only by crypto/rsa/rsa_eay.c, rsa_lib.c */
286 /* Used for montgomery multiplication */
287 typedef struct bn_mont_ctx_st
289 int ri; /* number of bits in R */
290 BIGNUM RR; /* used to convert to montgomery form */
291 BIGNUM N; /* The modulus */
292 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
293 * (Ni is only stored for bignum algorithm) */
294 BN_ULONG n0; /* least significant word of Ni */
298 /* Used for reciprocal division/mod functions
299 * It cannot be shared between threads
301 typedef struct bn_recp_ctx_st
303 BIGNUM N; /* the divisor */
304 BIGNUM Nr; /* the reciprocal */
310 /* Used for slow "generation" functions. */
311 typedef struct bn_gencb_st BN_GENCB;
314 unsigned int ver; /* To handle binary (in)compatibility */
315 void *arg; /* callback-specific data */
318 /* if(ver==1) - handles old style callbacks */
319 void (*cb_1)(int, int, void *);
320 /* if(ver==2) - new callback style */
321 int (*cb_2)(int, int, BN_GENCB *);
324 /* Wrapper function to make using BN_GENCB easier, */
325 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
326 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
327 #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
328 BN_GENCB *tmp_gencb = (gencb); \
329 tmp_gencb->ver = 1; \
330 tmp_gencb->arg = (cb_arg); \
331 tmp_gencb->cb.cb_1 = (callback); }
332 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
333 #define BN_GENCB_set(gencb, callback, cb_arg) { \
334 BN_GENCB *tmp_gencb = (gencb); \
335 tmp_gencb->ver = 2; \
336 tmp_gencb->arg = (cb_arg); \
337 tmp_gencb->cb.cb_2 = (callback); }
339 #define BN_prime_checks 0 /* default: select number of iterations
340 based on the size of the number */
342 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
343 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
344 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
345 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
346 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
347 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
360 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
362 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
363 #define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
364 (((w) == 0) && ((a)->top == 0)))
366 #define BN_is_zero(a) ((a)->top == 0)
368 #define BN_is_zero(a) BN_abs_is_word(a,0)
370 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
371 #define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
372 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
374 #define BN_one(a) (BN_set_word((a),1))
375 #define BN_zero(a) (BN_set_word((a),0))
376 /* BN_set_sign(BIGNUM *, int) sets the sign of a BIGNUM
377 * (0 for a non-negative value, 1 for negative) */
378 #define BN_set_sign(a,b) ((a)->neg = (b))
379 /* BN_get_sign(BIGNUM *) returns the sign of the BIGNUM */
380 #define BN_get_sign(a) ((a)->neg)
382 /*#define BN_ascii2bn(a) BN_hex2bn(a) */
383 /*#define BN_bn2ascii(a) BN_bn2hex(a) */
385 const BIGNUM *BN_value_one(void);
386 char * BN_options(void);
387 BN_CTX *BN_CTX_new(void);
388 #ifndef OPENSSL_NO_DEPRECATED
389 void BN_CTX_init(BN_CTX *c);
391 void BN_CTX_free(BN_CTX *c);
392 void BN_CTX_start(BN_CTX *ctx);
393 BIGNUM *BN_CTX_get(BN_CTX *ctx);
394 void BN_CTX_end(BN_CTX *ctx);
395 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
396 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
397 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
398 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
399 int BN_num_bits(const BIGNUM *a);
400 int BN_num_bits_word(BN_ULONG);
401 BIGNUM *BN_new(void);
402 void BN_init(BIGNUM *);
403 void BN_clear_free(BIGNUM *a);
404 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
405 /* BN_ncopy(): like BN_copy() but copies at most the first n BN_ULONGs */
406 BIGNUM *BN_ncopy(BIGNUM *a, const BIGNUM *b, size_t n);
407 void BN_swap(BIGNUM *a, BIGNUM *b);
408 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
409 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
410 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
411 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
412 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
413 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
414 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
415 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
416 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
417 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
419 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
421 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
422 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
423 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
424 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
425 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
426 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
427 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
428 const BIGNUM *m, BN_CTX *ctx);
429 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
430 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
431 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
432 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
433 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
435 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
436 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
437 int BN_mul_word(BIGNUM *a, BN_ULONG w);
438 int BN_add_word(BIGNUM *a, BN_ULONG w);
439 int BN_sub_word(BIGNUM *a, BN_ULONG w);
440 int BN_set_word(BIGNUM *a, BN_ULONG w);
441 BN_ULONG BN_get_word(const BIGNUM *a);
443 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
444 void BN_free(BIGNUM *a);
445 int BN_is_bit_set(const BIGNUM *a, int n);
446 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
447 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
448 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
450 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
451 const BIGNUM *m,BN_CTX *ctx);
452 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
453 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
454 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
455 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
456 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
457 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
458 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
459 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
460 const BIGNUM *m,BN_CTX *ctx);
462 int BN_mask_bits(BIGNUM *a,int n);
463 #ifndef OPENSSL_NO_FP_API
464 int BN_print_fp(FILE *fp, const BIGNUM *a);
467 int BN_print(BIO *fp, const BIGNUM *a);
469 int BN_print(void *fp, const BIGNUM *a);
471 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
472 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
473 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
474 void BN_clear(BIGNUM *a);
475 BIGNUM *BN_dup(const BIGNUM *a);
476 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
477 int BN_set_bit(BIGNUM *a, int n);
478 int BN_clear_bit(BIGNUM *a, int n);
479 char * BN_bn2hex(const BIGNUM *a);
480 char * BN_bn2dec(const BIGNUM *a);
481 int BN_hex2bn(BIGNUM **a, const char *str);
482 int BN_dec2bn(BIGNUM **a, const char *str);
483 int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
484 int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
485 BIGNUM *BN_mod_inverse(BIGNUM *ret,
486 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
487 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
488 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
490 /* Deprecated versions */
491 #ifndef OPENSSL_NO_DEPRECATED
492 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
493 const BIGNUM *add, const BIGNUM *rem,
494 void (*callback)(int,int,void *),void *cb_arg);
495 int BN_is_prime(const BIGNUM *p,int nchecks,
496 void (*callback)(int,int,void *),
497 BN_CTX *ctx,void *cb_arg);
498 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
499 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
500 int do_trial_division);
501 #endif /* !defined(OPENSSL_NO_DEPRECATED) */
504 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
505 const BIGNUM *rem, BN_GENCB *cb);
506 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
507 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
508 int do_trial_division, BN_GENCB *cb);
510 BN_MONT_CTX *BN_MONT_CTX_new(void );
511 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
512 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
513 BN_MONT_CTX *mont, BN_CTX *ctx);
514 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
515 (r),(a),&((mont)->RR),(mont),(ctx))
516 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
517 BN_MONT_CTX *mont, BN_CTX *ctx);
518 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
519 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
520 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
522 BN_BLINDING *BN_BLINDING_new(BIGNUM *A,BIGNUM *Ai,BIGNUM *mod);
523 void BN_BLINDING_free(BN_BLINDING *b);
524 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
525 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *r, BN_CTX *ctx);
526 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
528 void BN_set_params(int mul,int high,int low,int mont);
529 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
531 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
532 BN_RECP_CTX *BN_RECP_CTX_new(void);
533 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
534 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
535 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
536 BN_RECP_CTX *recp,BN_CTX *ctx);
537 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
538 const BIGNUM *m, BN_CTX *ctx);
539 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
540 BN_RECP_CTX *recp, BN_CTX *ctx);
542 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
544 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
547 * Note that input arguments are not const so that their bit arrays can
548 * be expanded to the appropriate size if needed.
551 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
552 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
553 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
554 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
555 const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
556 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
557 BN_CTX *ctx); /* r = (a * a) mod p */
558 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
559 BN_CTX *ctx); /* r = (1 / b) mod p */
560 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
561 const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
562 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
563 const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
564 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
565 BN_CTX *ctx); /* r = sqrt(a) mod p */
566 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
567 BN_CTX *ctx); /* r^2 + r = a mod p */
568 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
569 /* Some functions allow for representation of the irreducible polynomials
570 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
571 * t^p[0] + t^p[1] + ... + t^p[k]
572 * where m = p[0] > p[1] > ... > p[k] = 0.
574 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]);
576 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
577 const unsigned int p[], BN_CTX *ctx); /* r = (a * b) mod p */
578 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[],
579 BN_CTX *ctx); /* r = (a * a) mod p */
580 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[],
581 BN_CTX *ctx); /* r = (1 / b) mod p */
582 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
583 const unsigned int p[], BN_CTX *ctx); /* r = (a / b) mod p */
584 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
585 const unsigned int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
586 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
587 const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
588 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
589 const unsigned int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
590 int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
591 int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
593 /* faster mod functions for the 'NIST primes'
595 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
596 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
597 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
598 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
599 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
601 const BIGNUM *BN_get0_nist_prime_192(void);
602 const BIGNUM *BN_get0_nist_prime_224(void);
603 const BIGNUM *BN_get0_nist_prime_256(void);
604 const BIGNUM *BN_get0_nist_prime_384(void);
605 const BIGNUM *BN_get0_nist_prime_521(void);
607 /* library internal functions */
609 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
610 (a):bn_expand2((a),(bits)/BN_BITS2+1))
611 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
612 BIGNUM *bn_expand2(BIGNUM *a, int words);
613 BIGNUM *bn_dup_expand(const BIGNUM *a, int words);
615 /* Bignum consistency macros
616 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
617 * bignum data after direct manipulations on the data. There is also an
618 * "internal" macro, bn_check_top(), for verifying that there are no leading
619 * zeroes. Unfortunately, some auditing is required due to the fact that
620 * bn_fix_top() has become an overabused duct-tape because bignum data is
621 * occasionally passed around in an inconsistent state. So the following
622 * changes have been made to sort this out;
623 * - bn_fix_top()s implementation has been moved to bn_correct_top()
624 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
625 * bn_check_top() is as before.
626 * - if BN_DEBUG *is* defined;
627 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
628 * consistent. (ed: only if BN_DEBUG_RAND is defined)
629 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
630 * The idea is to have debug builds flag up inconsistent bignums when they
631 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
632 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
633 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
634 * was not appropriate, we convert it permanently to bn_check_top() and track
635 * down the cause of the bug. Eventually, no internal code should be using the
636 * bn_fix_top() macro. External applications and libraries should try this with
637 * their own code too, both in terms of building against the openssl headers
638 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
639 * defined. This not only improves external code, it provides more test
640 * coverage for openssl's own code.
645 /* We only need assert() when debugging */
649 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
650 #ifndef RAND_pseudo_bytes
651 int RAND_pseudo_bytes(unsigned char *buf,int num);
652 #define BN_DEBUG_TRIX
654 #define bn_pollute(a) \
656 const BIGNUM *_bnum1 = (a); \
657 if(_bnum1->top < _bnum1->dmax) { \
658 unsigned char _tmp_char; \
659 /* We cast away const without the compiler knowing, any \
660 * *genuinely* constant variables that aren't mutable \
661 * wouldn't be constructed with top!=dmax. */ \
662 BN_ULONG *_not_const; \
663 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
664 RAND_pseudo_bytes(&_tmp_char, 1); \
665 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
666 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
670 #undef RAND_pseudo_bytes
673 #define bn_pollute(a)
675 #define bn_check_top(a) \
677 const BIGNUM *_bnum2 = (a); \
678 assert((_bnum2->top == 0) || \
679 (_bnum2->d[_bnum2->top - 1] != 0)); \
680 bn_pollute(_bnum2); \
683 #define bn_fix_top(a) bn_check_top(a)
685 #else /* !BN_DEBUG */
687 #define bn_pollute(a)
688 #define bn_check_top(a)
689 #define bn_fix_top(a) bn_correct_top(a)
693 #define bn_correct_top(a) \
698 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
699 if (*(ftl--)) break; \
704 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
705 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
706 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
707 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
708 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
709 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
712 void bn_dump1(FILE *o, const char *a, const BN_ULONG *b,int n);
713 # define bn_print(a) {fprintf(stderr, #a "="); BN_print_fp(stderr,a); \
714 fprintf(stderr,"\n");}
715 # define bn_dump(a,n) bn_dump1(stderr,#a,a,n);
718 # define bn_dump(a,b)
721 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
723 /* BEGIN ERROR CODES */
724 /* The following lines are auto generated by the script mkerr.pl. Any changes
725 * made after this point may be overwritten when the script is next run.
727 void ERR_load_BN_strings(void);
729 /* Error codes for the BN functions. */
731 /* Function codes. */
732 #define BN_F_BN_BLINDING_CONVERT 100
733 #define BN_F_BN_BLINDING_INVERT 101
734 #define BN_F_BN_BLINDING_NEW 102
735 #define BN_F_BN_BLINDING_UPDATE 103
736 #define BN_F_BN_BN2DEC 104
737 #define BN_F_BN_BN2HEX 105
738 #define BN_F_BN_CTX_GET 116
739 #define BN_F_BN_CTX_NEW 106
740 #define BN_F_BN_DIV 107
741 #define BN_F_BN_EXPAND2 108
742 #define BN_F_BN_EXPAND_INTERNAL 120
743 #define BN_F_BN_GF2M_MOD 126
744 #define BN_F_BN_GF2M_MOD_DIV 123
745 #define BN_F_BN_GF2M_MOD_EXP 127
746 #define BN_F_BN_GF2M_MOD_MUL 124
747 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 128
748 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 129
749 #define BN_F_BN_GF2M_MOD_SQR 125
750 #define BN_F_BN_MOD_EXP2_MONT 118
751 #define BN_F_BN_MOD_EXP_MONT 109
752 #define BN_F_BN_MOD_EXP_MONT_WORD 117
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_IMPLEMENTED 116
776 #define BN_R_NOT_INITIALIZED 107
777 #define BN_R_NO_INVERSE 108
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