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 */
266 /* Used for montgomery multiplication */
267 typedef struct bn_mont_ctx_st
269 int ri; /* number of bits in R */
270 BIGNUM RR; /* used to convert to montgomery form */
271 BIGNUM N; /* The modulus */
272 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
273 * (Ni is only stored for bignum algorithm) */
274 BN_ULONG n0; /* least significant word of Ni */
278 /* Used for reciprocal division/mod functions
279 * It cannot be shared between threads
281 typedef struct bn_recp_ctx_st
283 BIGNUM N; /* the divisor */
284 BIGNUM Nr; /* the reciprocal */
290 #define BN_prime_checks 0 /* default: select number of iterations
291 based on the size of the number */
293 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
294 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
295 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
296 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
297 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
298 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
311 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
313 /* Note that BN_abs_is_word does not work reliably for w == 0 */
314 #define BN_abs_is_word(a,w) (((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w)))
315 #define BN_is_zero(a) (((a)->top == 0) || BN_abs_is_word(a,0))
316 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
317 #define BN_is_word(a,w) ((w) ? BN_abs_is_word((a),(w)) && !(a)->neg : \
319 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
321 #define BN_one(a) (BN_set_word((a),1))
322 #define BN_zero(a) (BN_set_word((a),0))
324 /*#define BN_ascii2bn(a) BN_hex2bn(a) */
325 /*#define BN_bn2ascii(a) BN_bn2hex(a) */
327 const BIGNUM *BN_value_one(void);
328 char * BN_options(void);
329 BN_CTX *BN_CTX_new(void);
330 void BN_CTX_init(BN_CTX *c);
331 void BN_CTX_free(BN_CTX *c);
332 void BN_CTX_start(BN_CTX *ctx);
333 BIGNUM *BN_CTX_get(BN_CTX *ctx);
334 void BN_CTX_end(BN_CTX *ctx);
335 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
336 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
337 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
338 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
339 int BN_num_bits(const BIGNUM *a);
340 int BN_num_bits_word(BN_ULONG);
341 BIGNUM *BN_new(void);
342 void BN_init(BIGNUM *);
343 void BN_clear_free(BIGNUM *a);
344 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
345 /* BN_ncopy(): like BN_copy() but copies at most the first n BN_ULONGs */
346 BIGNUM *BN_ncopy(BIGNUM *a, const BIGNUM *b, size_t n);
347 void BN_swap(BIGNUM *a, BIGNUM *b);
348 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
349 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
350 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
351 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
352 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
353 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
354 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
355 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
356 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
357 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
359 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
361 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
362 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
363 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
364 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
365 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
366 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
367 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
368 const BIGNUM *m, BN_CTX *ctx);
369 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
370 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
371 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
372 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
373 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
375 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
376 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
377 int BN_mul_word(BIGNUM *a, BN_ULONG w);
378 int BN_add_word(BIGNUM *a, BN_ULONG w);
379 int BN_sub_word(BIGNUM *a, BN_ULONG w);
380 int BN_set_word(BIGNUM *a, BN_ULONG w);
381 BN_ULONG BN_get_word(const BIGNUM *a);
383 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
384 void BN_free(BIGNUM *a);
385 int BN_is_bit_set(const BIGNUM *a, int n);
386 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
387 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
388 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
390 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
391 const BIGNUM *m,BN_CTX *ctx);
392 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
393 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
394 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
395 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
396 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
397 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
398 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
399 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
400 const BIGNUM *m,BN_CTX *ctx);
402 int BN_mask_bits(BIGNUM *a,int n);
403 #ifndef OPENSSL_NO_FP_API
404 int BN_print_fp(FILE *fp, const BIGNUM *a);
407 int BN_print(BIO *fp, const BIGNUM *a);
409 int BN_print(void *fp, const BIGNUM *a);
411 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
412 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
413 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
414 void BN_clear(BIGNUM *a);
415 BIGNUM *BN_dup(const BIGNUM *a);
416 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
417 int BN_set_bit(BIGNUM *a, int n);
418 int BN_clear_bit(BIGNUM *a, int n);
419 char * BN_bn2hex(const BIGNUM *a);
420 char * BN_bn2dec(const BIGNUM *a);
421 int BN_hex2bn(BIGNUM **a, const char *str);
422 int BN_dec2bn(BIGNUM **a, const char *str);
423 int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
424 int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
425 BIGNUM *BN_mod_inverse(BIGNUM *ret,
426 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
427 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
428 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
429 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
430 const BIGNUM *add, const BIGNUM *rem,
431 void (*callback)(int,int,void *),void *cb_arg);
432 int BN_is_prime(const BIGNUM *p,int nchecks,
433 void (*callback)(int,int,void *),
434 BN_CTX *ctx,void *cb_arg);
435 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
436 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
437 int do_trial_division);
439 BN_MONT_CTX *BN_MONT_CTX_new(void );
440 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
441 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
442 BN_MONT_CTX *mont, BN_CTX *ctx);
443 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
444 (r),(a),&((mont)->RR),(mont),(ctx))
445 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
446 BN_MONT_CTX *mont, BN_CTX *ctx);
447 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
448 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
449 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
451 BN_BLINDING *BN_BLINDING_new(BIGNUM *A,BIGNUM *Ai,BIGNUM *mod);
452 void BN_BLINDING_free(BN_BLINDING *b);
453 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
454 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *r, BN_CTX *ctx);
455 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
457 void BN_set_params(int mul,int high,int low,int mont);
458 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
460 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
461 BN_RECP_CTX *BN_RECP_CTX_new(void);
462 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
463 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
464 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
465 BN_RECP_CTX *recp,BN_CTX *ctx);
466 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
467 const BIGNUM *m, BN_CTX *ctx);
468 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
469 BN_RECP_CTX *recp, BN_CTX *ctx);
471 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
473 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is ignored.
475 * Note that input arguments are not const so that their bit arrays can
476 * be expanded to the appropriate size if needed.
478 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /* r = a + b */
479 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
480 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /* r = a mod p */
481 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
482 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = (a * a) mod p */
483 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (1 / b) mod p */
484 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
485 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
486 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = sqrt(a) mod p */
487 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r^2 + r = a mod p */
488 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
489 /* Some functions allow for representation of the irreducible polynomials
490 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
491 * t^p[0] + t^p[1] + ... + t^p[k]
492 * where m = p[0] > p[1] > ... > p[k] = 0.
494 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]); /* r = a mod p */
495 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a * b) mod p */
496 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = (a * a) mod p */
497 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (1 / b) mod p */
498 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a / b) mod p */
499 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
500 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
501 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
502 int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
503 int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
505 /* faster mod functions for the 'NIST primes'
507 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
508 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
509 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
510 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
511 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
513 const BIGNUM *BN_get0_nist_prime_192(void);
514 const BIGNUM *BN_get0_nist_prime_224(void);
515 const BIGNUM *BN_get0_nist_prime_256(void);
516 const BIGNUM *BN_get0_nist_prime_384(void);
517 const BIGNUM *BN_get0_nist_prime_521(void);
519 /* library internal functions */
521 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
522 (a):bn_expand2((a),(bits)/BN_BITS2+1))
523 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
524 BIGNUM *bn_expand2(BIGNUM *a, int words);
525 BIGNUM *bn_dup_expand(const BIGNUM *a, int words);
527 #define bn_fix_top(a) \
532 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
533 if (*(ftl--)) break; \
537 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
538 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
539 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
540 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
541 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
542 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
545 void bn_dump1(FILE *o, const char *a, const BN_ULONG *b,int n);
546 # define bn_print(a) {fprintf(stderr, #a "="); BN_print_fp(stderr,a); \
547 fprintf(stderr,"\n");}
548 # define bn_dump(a,n) bn_dump1(stderr,#a,a,n);
551 # define bn_dump(a,b)
554 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
556 /* BEGIN ERROR CODES */
557 /* The following lines are auto generated by the script mkerr.pl. Any changes
558 * made after this point may be overwritten when the script is next run.
560 void ERR_load_BN_strings(void);
562 /* Error codes for the BN functions. */
564 /* Function codes. */
565 #define BN_F_BN_BLINDING_CONVERT 100
566 #define BN_F_BN_BLINDING_INVERT 101
567 #define BN_F_BN_BLINDING_NEW 102
568 #define BN_F_BN_BLINDING_UPDATE 103
569 #define BN_F_BN_BN2DEC 104
570 #define BN_F_BN_BN2HEX 105
571 #define BN_F_BN_CTX_GET 116
572 #define BN_F_BN_CTX_NEW 106
573 #define BN_F_BN_DIV 107
574 #define BN_F_BN_EXPAND2 108
575 #define BN_F_BN_EXPAND_INTERNAL 120
576 #define BN_F_BN_GF2M_MOD 126
577 #define BN_F_BN_GF2M_MOD_DIV 123
578 #define BN_F_BN_GF2M_MOD_EXP 127
579 #define BN_F_BN_GF2M_MOD_MUL 124
580 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 128
581 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 129
582 #define BN_F_BN_GF2M_MOD_SQR 125
583 #define BN_F_BN_MOD_EXP2_MONT 118
584 #define BN_F_BN_MOD_EXP_MONT 109
585 #define BN_F_BN_MOD_EXP_MONT_WORD 117
586 #define BN_F_BN_MOD_INVERSE 110
587 #define BN_F_BN_MOD_LSHIFT_QUICK 119
588 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
589 #define BN_F_BN_MOD_SQRT 121
590 #define BN_F_BN_MPI2BN 112
591 #define BN_F_BN_NEW 113
592 #define BN_F_BN_RAND 114
593 #define BN_F_BN_RAND_RANGE 122
594 #define BN_F_BN_USUB 115
597 #define BN_R_ARG2_LT_ARG3 100
598 #define BN_R_BAD_RECIPROCAL 101
599 #define BN_R_BIGNUM_TOO_LONG 114
600 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
601 #define BN_R_DIV_BY_ZERO 103
602 #define BN_R_ENCODING_ERROR 104
603 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
604 #define BN_R_INPUT_NOT_REDUCED 110
605 #define BN_R_INVALID_LENGTH 106
606 #define BN_R_INVALID_RANGE 115
607 #define BN_R_NOT_A_SQUARE 111
608 #define BN_R_NOT_IMPLEMENTED 116
609 #define BN_R_NOT_INITIALIZED 107
610 #define BN_R_NO_INVERSE 108
611 #define BN_R_P_IS_NOT_PRIME 112
612 #define BN_R_TOO_MANY_ITERATIONS 113
613 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109