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 #ifdef OPENSSL_SYS_VMS
85 #undef BN_LLONG /* experimental, so far... */
92 /* This next option uses the C libraries (2 word)/(1 word) function.
93 * If it is not defined, I use my C version (which is slower).
94 * The reason for this flag is that when the particular C compiler
95 * library routine is used, and the library is linked with a different
96 * compiler, the library is missing. This mostly happens when the
97 * library is built with gcc and then linked using normal cc. This would
98 * be a common occurrence because gcc normally produces code that is
99 * 2 times faster than system compilers for the big number stuff.
100 * For machines with only one compiler (or shared libraries), this should
101 * be on. Again this in only really a problem on machines
102 * using "long long's", are 32bit, and are not using my assembler code. */
103 #if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
104 defined(OPENSSL_SYS_WIN32) || defined(linux)
110 /* assuming long is 64bit - this is the DEC Alpha
111 * unsigned long long is only 64 bits :-(, don't define
112 * BN_LLONG for the DEC Alpha */
113 #ifdef SIXTY_FOUR_BIT_LONG
114 #define BN_ULLONG unsigned long long
115 #define BN_ULONG unsigned long
121 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
122 #define BN_MASK2 (0xffffffffffffffffL)
123 #define BN_MASK2l (0xffffffffL)
124 #define BN_MASK2h (0xffffffff00000000L)
125 #define BN_MASK2h1 (0xffffffff80000000L)
126 #define BN_TBIT (0x8000000000000000L)
127 #define BN_DEC_CONV (10000000000000000000UL)
128 #define BN_DEC_FMT1 "%lu"
129 #define BN_DEC_FMT2 "%019lu"
130 #define BN_DEC_NUM 19
133 /* This is where the long long data type is 64 bits, but long is 32.
134 * For machines where there are 64bit registers, this is the mode to use.
135 * IRIX, on R4000 and above should use this mode, along with the relevant
136 * assembler code :-). Do NOT define BN_LLONG.
138 #ifdef SIXTY_FOUR_BIT
141 #define BN_ULONG unsigned long long
142 #define BN_LONG long long
147 #define BN_MASK2 (0xffffffffffffffffLL)
148 #define BN_MASK2l (0xffffffffL)
149 #define BN_MASK2h (0xffffffff00000000LL)
150 #define BN_MASK2h1 (0xffffffff80000000LL)
151 #define BN_TBIT (0x8000000000000000LL)
152 #define BN_DEC_CONV (10000000000000000000ULL)
153 #define BN_DEC_FMT1 "%llu"
154 #define BN_DEC_FMT2 "%019llu"
155 #define BN_DEC_NUM 19
158 #ifdef THIRTY_TWO_BIT
159 #if defined(OPENSSL_SYS_WIN32) && !defined(__GNUC__)
160 #define BN_ULLONG unsigned _int64
162 #define BN_ULLONG unsigned long long
164 #define BN_ULONG unsigned long
170 #ifdef OPENSSL_SYS_WIN32
171 /* VC++ doesn't like the LL suffix */
172 #define BN_MASK (0xffffffffffffffffL)
174 #define BN_MASK (0xffffffffffffffffLL)
176 #define BN_MASK2 (0xffffffffL)
177 #define BN_MASK2l (0xffff)
178 #define BN_MASK2h1 (0xffff8000L)
179 #define BN_MASK2h (0xffff0000L)
180 #define BN_TBIT (0x80000000L)
181 #define BN_DEC_CONV (1000000000L)
182 #define BN_DEC_FMT1 "%lu"
183 #define BN_DEC_FMT2 "%09lu"
191 #define BN_ULLONG unsigned long
192 #define BN_ULONG unsigned short
193 #define BN_LONG short
198 #define BN_MASK (0xffffffff)
199 #define BN_MASK2 (0xffff)
200 #define BN_MASK2l (0xff)
201 #define BN_MASK2h1 (0xff80)
202 #define BN_MASK2h (0xff00)
203 #define BN_TBIT (0x8000)
204 #define BN_DEC_CONV (100000)
205 #define BN_DEC_FMT1 "%u"
206 #define BN_DEC_FMT2 "%05u"
214 #define BN_ULLONG unsigned short
215 #define BN_ULONG unsigned char
221 #define BN_MASK (0xffff)
222 #define BN_MASK2 (0xff)
223 #define BN_MASK2l (0xf)
224 #define BN_MASK2h1 (0xf8)
225 #define BN_MASK2h (0xf0)
226 #define BN_TBIT (0x80)
227 #define BN_DEC_CONV (100)
228 #define BN_DEC_FMT1 "%u"
229 #define BN_DEC_FMT2 "%02u"
233 #define BN_DEFAULT_BITS 1280
239 #define BN_FLG_MALLOCED 0x01
240 #define BN_FLG_STATIC_DATA 0x02
241 #define BN_FLG_FREE 0x8000 /* used for debuging */
242 #define BN_set_flags(b,n) ((b)->flags|=(n))
243 #define BN_get_flags(b,n) ((b)->flags&(n))
245 typedef struct bignum_st
247 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
248 int top; /* Index of last used d +1. */
249 /* The next are internal book keeping for bn_expand. */
250 int dmax; /* Size of the d array. */
251 int neg; /* one if the number is negative */
255 /* Used for temp variables (declaration hidden in bn_lcl.h) */
256 typedef struct bignum_ctx BN_CTX;
258 typedef struct bn_blinding_st
263 BIGNUM *mod; /* just a reference */
264 unsigned long thread_id; /* added in OpenSSL 0.9.6j and 0.9.7b;
265 * used only by crypto/rsa/rsa_eay.c, rsa_lib.c */
268 /* Used for montgomery multiplication */
269 typedef struct bn_mont_ctx_st
271 int ri; /* number of bits in R */
272 BIGNUM RR; /* used to convert to montgomery form */
273 BIGNUM N; /* The modulus */
274 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
275 * (Ni is only stored for bignum algorithm) */
276 BN_ULONG n0; /* least significant word of Ni */
280 /* Used for reciprocal division/mod functions
281 * It cannot be shared between threads
283 typedef struct bn_recp_ctx_st
285 BIGNUM N; /* the divisor */
286 BIGNUM Nr; /* the reciprocal */
292 /* Used for slow "generation" functions. */
293 typedef struct bn_gencb_st BN_GENCB;
296 unsigned int ver; /* To handle binary (in)compatibility */
297 void *arg; /* callback-specific data */
300 /* if(ver==1) - handles old style callbacks */
301 void (*cb_1)(int, int, void *);
302 /* if(ver==2) - new callback style */
303 int (*cb_2)(int, int, BN_GENCB *);
306 /* Wrapper function to make using BN_GENCB easier, */
307 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
308 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
309 #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
310 BN_GENCB *tmp_gencb = (gencb); \
311 tmp_gencb->ver = 1; \
312 tmp_gencb->arg = (cb_arg); \
313 tmp_gencb->cb.cb_1 = (callback); }
314 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
315 #define BN_GENCB_set(gencb, callback, cb_arg) { \
316 BN_GENCB *tmp_gencb = (gencb); \
317 tmp_gencb->ver = 2; \
318 tmp_gencb->arg = (cb_arg); \
319 tmp_gencb->cb.cb_2 = (callback); }
321 #define BN_prime_checks 0 /* default: select number of iterations
322 based on the size of the number */
324 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
325 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
326 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
327 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
328 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
329 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
342 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
344 /* Note that BN_abs_is_word does not work reliably for w == 0 */
345 #define BN_abs_is_word(a,w) (((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w)))
346 #define BN_is_zero(a) (((a)->top == 0) || BN_abs_is_word(a,0))
347 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
348 #define BN_is_word(a,w) ((w) ? BN_abs_is_word((a),(w)) && !(a)->neg : \
350 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
352 #define BN_one(a) (BN_set_word((a),1))
353 #define BN_zero(a) (BN_set_word((a),0))
354 /* BN_set_sign(BIGNUM *, int) sets the sign of a BIGNUM
355 * (0 for a non-negative value, 1 for negative) */
356 #define BN_set_sign(a,b) ((a)->neg = (b))
357 /* BN_get_sign(BIGNUM *) returns the sign of the BIGNUM */
358 #define BN_get_sign(a) ((a)->neg)
360 /*#define BN_ascii2bn(a) BN_hex2bn(a) */
361 /*#define BN_bn2ascii(a) BN_bn2hex(a) */
363 const BIGNUM *BN_value_one(void);
364 char * BN_options(void);
365 BN_CTX *BN_CTX_new(void);
366 #ifndef OPENSSL_NO_DEPRECATED
367 void BN_CTX_init(BN_CTX *c);
369 void BN_CTX_free(BN_CTX *c);
370 void BN_CTX_start(BN_CTX *ctx);
371 BIGNUM *BN_CTX_get(BN_CTX *ctx);
372 void BN_CTX_end(BN_CTX *ctx);
373 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
374 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
375 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
376 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
377 int BN_num_bits(const BIGNUM *a);
378 int BN_num_bits_word(BN_ULONG);
379 BIGNUM *BN_new(void);
380 void BN_init(BIGNUM *);
381 void BN_clear_free(BIGNUM *a);
382 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
383 /* BN_ncopy(): like BN_copy() but copies at most the first n BN_ULONGs */
384 BIGNUM *BN_ncopy(BIGNUM *a, const BIGNUM *b, size_t n);
385 void BN_swap(BIGNUM *a, BIGNUM *b);
386 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
387 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
388 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
389 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
390 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
391 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
392 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
393 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
394 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
395 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
397 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
399 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
400 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
401 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
402 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
403 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
404 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
405 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
406 const BIGNUM *m, BN_CTX *ctx);
407 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
408 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
409 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
410 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
411 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
413 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
414 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
415 int BN_mul_word(BIGNUM *a, BN_ULONG w);
416 int BN_add_word(BIGNUM *a, BN_ULONG w);
417 int BN_sub_word(BIGNUM *a, BN_ULONG w);
418 int BN_set_word(BIGNUM *a, BN_ULONG w);
419 BN_ULONG BN_get_word(const BIGNUM *a);
421 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
422 void BN_free(BIGNUM *a);
423 int BN_is_bit_set(const BIGNUM *a, int n);
424 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
425 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
426 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
428 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
429 const BIGNUM *m,BN_CTX *ctx);
430 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
431 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
432 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
433 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
434 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
435 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
436 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
437 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
438 const BIGNUM *m,BN_CTX *ctx);
440 int BN_mask_bits(BIGNUM *a,int n);
441 #ifndef OPENSSL_NO_FP_API
442 int BN_print_fp(FILE *fp, const BIGNUM *a);
445 int BN_print(BIO *fp, const BIGNUM *a);
447 int BN_print(void *fp, const BIGNUM *a);
449 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
450 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
451 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
452 void BN_clear(BIGNUM *a);
453 BIGNUM *BN_dup(const BIGNUM *a);
454 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
455 int BN_set_bit(BIGNUM *a, int n);
456 int BN_clear_bit(BIGNUM *a, int n);
457 char * BN_bn2hex(const BIGNUM *a);
458 char * BN_bn2dec(const BIGNUM *a);
459 int BN_hex2bn(BIGNUM **a, const char *str);
460 int BN_dec2bn(BIGNUM **a, const char *str);
461 int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
462 int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
463 BIGNUM *BN_mod_inverse(BIGNUM *ret,
464 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
465 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
466 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
468 /* Deprecated versions */
469 #ifndef OPENSSL_NO_DEPRECATED
470 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
471 const BIGNUM *add, const BIGNUM *rem,
472 void (*callback)(int,int,void *),void *cb_arg);
473 int BN_is_prime(const BIGNUM *p,int nchecks,
474 void (*callback)(int,int,void *),
475 BN_CTX *ctx,void *cb_arg);
476 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
477 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
478 int do_trial_division);
479 #endif /* !defined(OPENSSL_NO_DEPRECATED) */
482 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
483 const BIGNUM *rem, BN_GENCB *cb);
484 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
485 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
486 int do_trial_division, BN_GENCB *cb);
488 BN_MONT_CTX *BN_MONT_CTX_new(void );
489 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
490 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
491 BN_MONT_CTX *mont, BN_CTX *ctx);
492 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
493 (r),(a),&((mont)->RR),(mont),(ctx))
494 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
495 BN_MONT_CTX *mont, BN_CTX *ctx);
496 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
497 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
498 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
500 BN_BLINDING *BN_BLINDING_new(BIGNUM *A,BIGNUM *Ai,BIGNUM *mod);
501 void BN_BLINDING_free(BN_BLINDING *b);
502 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
503 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *r, BN_CTX *ctx);
504 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
506 void BN_set_params(int mul,int high,int low,int mont);
507 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
509 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
510 BN_RECP_CTX *BN_RECP_CTX_new(void);
511 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
512 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
513 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
514 BN_RECP_CTX *recp,BN_CTX *ctx);
515 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
516 const BIGNUM *m, BN_CTX *ctx);
517 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
518 BN_RECP_CTX *recp, BN_CTX *ctx);
520 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
522 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
525 * Note that input arguments are not const so that their bit arrays can
526 * be expanded to the appropriate size if needed.
529 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
530 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
531 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
532 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
533 const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
534 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
535 BN_CTX *ctx); /* r = (a * a) mod p */
536 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
537 BN_CTX *ctx); /* r = (1 / b) mod p */
538 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
539 const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
540 int BN_GF2m_mod_exp(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_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
543 BN_CTX *ctx); /* r = sqrt(a) mod p */
544 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
545 BN_CTX *ctx); /* r^2 + r = a mod p */
546 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
547 /* Some functions allow for representation of the irreducible polynomials
548 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
549 * t^p[0] + t^p[1] + ... + t^p[k]
550 * where m = p[0] > p[1] > ... > p[k] = 0.
552 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]);
554 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
555 const unsigned int p[], BN_CTX *ctx); /* r = (a * b) mod p */
556 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[],
557 BN_CTX *ctx); /* r = (a * a) mod p */
558 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[],
559 BN_CTX *ctx); /* r = (1 / b) mod p */
560 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
561 const unsigned int p[], BN_CTX *ctx); /* r = (a / b) mod p */
562 int BN_GF2m_mod_exp_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_sqrt_arr(BIGNUM *r, const BIGNUM *a,
565 const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
566 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
567 const unsigned int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
568 int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
569 int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
571 /* faster mod functions for the 'NIST primes'
573 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
574 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
575 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
576 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
577 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
579 const BIGNUM *BN_get0_nist_prime_192(void);
580 const BIGNUM *BN_get0_nist_prime_224(void);
581 const BIGNUM *BN_get0_nist_prime_256(void);
582 const BIGNUM *BN_get0_nist_prime_384(void);
583 const BIGNUM *BN_get0_nist_prime_521(void);
585 /* library internal functions */
587 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
588 (a):bn_expand2((a),(bits)/BN_BITS2+1))
589 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
590 BIGNUM *bn_expand2(BIGNUM *a, int words);
591 BIGNUM *bn_dup_expand(const BIGNUM *a, int words);
593 /* Bignum consistency macros
594 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
595 * bignum data after direct manipulations on the data. There is also an
596 * "internal" macro, bn_check_top(), for verifying that there are no leading
597 * zeroes. Unfortunately, some auditing is required due to the fact that
598 * bn_fix_top() has become an overabused duct-tape because bignum data is
599 * occasionally passed around in an inconsistent state. So the following
600 * changes have been made to sort this out;
601 * - bn_fix_top()s implementation has been moved to bn_correct_top()
602 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
603 * bn_check_top() is as before.
604 * - if BN_DEBUG *is* defined;
605 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
606 * consistent. (ed: only if BN_DEBUG_RAND is defined)
607 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
608 * The idea is to have debug builds flag up inconsistent bignums when they
609 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
610 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
611 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
612 * was not appropriate, we convert it permanently to bn_check_top() and track
613 * down the cause of the bug. Eventually, no internal code should be using the
614 * bn_fix_top() macro. External applications and libraries should try this with
615 * their own code too, both in terms of building against the openssl headers
616 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
617 * defined. This not only improves external code, it provides more test
618 * coverage for openssl's own code.
620 #define bn_correct_top(a) \
625 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
626 if (*(ftl--)) break; \
630 /* #define BN_DEBUG_RAND */
634 /* We only need assert() when debugging */
638 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
639 #ifndef RAND_pseudo_bytes
640 int RAND_pseudo_bytes(unsigned char *buf,int num);
641 #define BN_DEBUG_TRIX
643 #define bn_check_top(a) \
645 const BIGNUM *_tbignum = (a); \
646 assert((_tbignum->top == 0) || \
647 (_tbignum->d[_tbignum->top - 1] != 0)); \
648 if(_tbignum->top < _tbignum->dmax) { \
649 /* We cast away const without the compiler knowing, any \
650 * *genuinely* constant variables that aren't mutable \
651 * wouldn't be constructed with top!=dmax. */ \
652 BN_ULONG *_not_const; \
653 memcpy(&_not_const, &_tbignum->d, sizeof(BN_ULONG*)); \
654 RAND_pseudo_bytes((unsigned char *)(_not_const + _tbignum->top), \
655 (_tbignum->dmax - _tbignum->top) * sizeof(BN_ULONG)); \
659 #undef RAND_pseudo_bytes
661 #else /* !BN_DEBUG_RAND */
662 #define bn_check_top(a) \
664 const BIGNUM *_tbignum = (a); \
665 assert((_tbignum->top == 0) || \
666 (_tbignum->d[_tbignum->top - 1] != 0)); \
670 #define bn_fix_top(a) bn_check_top(a)
672 #else /* !BN_DEBUG */
674 #define bn_check_top(a)
675 #define bn_fix_top(a) bn_correct_top(a)
679 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
680 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
681 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
682 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
683 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
684 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
687 void bn_dump1(FILE *o, const char *a, const BN_ULONG *b,int n);
688 # define bn_print(a) {fprintf(stderr, #a "="); BN_print_fp(stderr,a); \
689 fprintf(stderr,"\n");}
690 # define bn_dump(a,n) bn_dump1(stderr,#a,a,n);
693 # define bn_dump(a,b)
696 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
698 /* BEGIN ERROR CODES */
699 /* The following lines are auto generated by the script mkerr.pl. Any changes
700 * made after this point may be overwritten when the script is next run.
702 void ERR_load_BN_strings(void);
704 /* Error codes for the BN functions. */
706 /* Function codes. */
707 #define BN_F_BN_BLINDING_CONVERT 100
708 #define BN_F_BN_BLINDING_INVERT 101
709 #define BN_F_BN_BLINDING_NEW 102
710 #define BN_F_BN_BLINDING_UPDATE 103
711 #define BN_F_BN_BN2DEC 104
712 #define BN_F_BN_BN2HEX 105
713 #define BN_F_BN_CTX_GET 116
714 #define BN_F_BN_CTX_NEW 106
715 #define BN_F_BN_DIV 107
716 #define BN_F_BN_EXPAND2 108
717 #define BN_F_BN_EXPAND_INTERNAL 120
718 #define BN_F_BN_GF2M_MOD 126
719 #define BN_F_BN_GF2M_MOD_DIV 123
720 #define BN_F_BN_GF2M_MOD_EXP 127
721 #define BN_F_BN_GF2M_MOD_MUL 124
722 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 128
723 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 129
724 #define BN_F_BN_GF2M_MOD_SQR 125
725 #define BN_F_BN_MOD_EXP2_MONT 118
726 #define BN_F_BN_MOD_EXP_MONT 109
727 #define BN_F_BN_MOD_EXP_MONT_WORD 117
728 #define BN_F_BN_MOD_INVERSE 110
729 #define BN_F_BN_MOD_LSHIFT_QUICK 119
730 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
731 #define BN_F_BN_MOD_SQRT 121
732 #define BN_F_BN_MPI2BN 112
733 #define BN_F_BN_NEW 113
734 #define BN_F_BN_RAND 114
735 #define BN_F_BN_RAND_RANGE 122
736 #define BN_F_BN_USUB 115
739 #define BN_R_ARG2_LT_ARG3 100
740 #define BN_R_BAD_RECIPROCAL 101
741 #define BN_R_BIGNUM_TOO_LONG 114
742 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
743 #define BN_R_DIV_BY_ZERO 103
744 #define BN_R_ENCODING_ERROR 104
745 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
746 #define BN_R_INPUT_NOT_REDUCED 110
747 #define BN_R_INVALID_LENGTH 106
748 #define BN_R_INVALID_RANGE 115
749 #define BN_R_NOT_A_SQUARE 111
750 #define BN_R_NOT_IMPLEMENTED 116
751 #define BN_R_NOT_INITIALIZED 107
752 #define BN_R_NO_INVERSE 108
753 #define BN_R_P_IS_NOT_PRIME 112
754 #define BN_R_TOO_MANY_ITERATIONS 113
755 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109