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 * In addition, Sun covenants to all licensees who provide a reciprocal
68 * covenant with respect to their own patents if any, not to sue under
69 * current and future patent claims necessarily infringed by the making,
70 * using, practicing, selling, offering for sale and/or otherwise
71 * disposing of the Contribution as delivered hereunder
72 * (or portions thereof), provided that such covenant shall not apply:
73 * 1) for code that a licensee deletes from the Contribution;
74 * 2) separates from the Contribution; or
75 * 3) for infringements caused by:
76 * i) the modification of the Contribution or
77 * ii) the combination of the Contribution with other software or
78 * devices where such combination causes the infringement.
80 * The binary polynomial arithmetic software is originally written by
81 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
88 #include <openssl/e_os2.h>
89 #ifndef OPENSSL_NO_FP_API
90 #include <stdio.h> /* FILE */
97 #ifdef OPENSSL_SYS_VMS
98 #undef BN_LLONG /* experimental, so far... */
105 /* This next option uses the C libraries (2 word)/(1 word) function.
106 * If it is not defined, I use my C version (which is slower).
107 * The reason for this flag is that when the particular C compiler
108 * library routine is used, and the library is linked with a different
109 * compiler, the library is missing. This mostly happens when the
110 * library is built with gcc and then linked using normal cc. This would
111 * be a common occurrence because gcc normally produces code that is
112 * 2 times faster than system compilers for the big number stuff.
113 * For machines with only one compiler (or shared libraries), this should
114 * be on. Again this in only really a problem on machines
115 * using "long long's", are 32bit, and are not using my assembler code. */
116 #if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
117 defined(OPENSSL_SYS_WIN32) || defined(linux)
123 /* assuming long is 64bit - this is the DEC Alpha
124 * unsigned long long is only 64 bits :-(, don't define
125 * BN_LLONG for the DEC Alpha */
126 #ifdef SIXTY_FOUR_BIT_LONG
127 #define BN_ULLONG unsigned long long
128 #define BN_ULONG unsigned long
134 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
135 #define BN_MASK2 (0xffffffffffffffffL)
136 #define BN_MASK2l (0xffffffffL)
137 #define BN_MASK2h (0xffffffff00000000L)
138 #define BN_MASK2h1 (0xffffffff80000000L)
139 #define BN_TBIT (0x8000000000000000L)
140 #define BN_DEC_CONV (10000000000000000000UL)
141 #define BN_DEC_FMT1 "%lu"
142 #define BN_DEC_FMT2 "%019lu"
143 #define BN_DEC_NUM 19
146 /* This is where the long long data type is 64 bits, but long is 32.
147 * For machines where there are 64bit registers, this is the mode to use.
148 * IRIX, on R4000 and above should use this mode, along with the relevant
149 * assembler code :-). Do NOT define BN_LLONG.
151 #ifdef SIXTY_FOUR_BIT
154 #define BN_ULONG unsigned long long
155 #define BN_LONG long long
160 #define BN_MASK2 (0xffffffffffffffffLL)
161 #define BN_MASK2l (0xffffffffL)
162 #define BN_MASK2h (0xffffffff00000000LL)
163 #define BN_MASK2h1 (0xffffffff80000000LL)
164 #define BN_TBIT (0x8000000000000000LL)
165 #define BN_DEC_CONV (10000000000000000000ULL)
166 #define BN_DEC_FMT1 "%llu"
167 #define BN_DEC_FMT2 "%019llu"
168 #define BN_DEC_NUM 19
171 #ifdef THIRTY_TWO_BIT
172 #if defined(OPENSSL_SYS_WIN32) && !defined(__GNUC__)
173 #define BN_ULLONG unsigned _int64
175 #define BN_ULLONG unsigned long long
177 #define BN_ULONG unsigned long
183 #ifdef OPENSSL_SYS_WIN32
184 /* VC++ doesn't like the LL suffix */
185 #define BN_MASK (0xffffffffffffffffL)
187 #define BN_MASK (0xffffffffffffffffLL)
189 #define BN_MASK2 (0xffffffffL)
190 #define BN_MASK2l (0xffff)
191 #define BN_MASK2h1 (0xffff8000L)
192 #define BN_MASK2h (0xffff0000L)
193 #define BN_TBIT (0x80000000L)
194 #define BN_DEC_CONV (1000000000L)
195 #define BN_DEC_FMT1 "%lu"
196 #define BN_DEC_FMT2 "%09lu"
204 #define BN_ULLONG unsigned long
205 #define BN_ULONG unsigned short
206 #define BN_LONG short
211 #define BN_MASK (0xffffffff)
212 #define BN_MASK2 (0xffff)
213 #define BN_MASK2l (0xff)
214 #define BN_MASK2h1 (0xff80)
215 #define BN_MASK2h (0xff00)
216 #define BN_TBIT (0x8000)
217 #define BN_DEC_CONV (100000)
218 #define BN_DEC_FMT1 "%u"
219 #define BN_DEC_FMT2 "%05u"
227 #define BN_ULLONG unsigned short
228 #define BN_ULONG unsigned char
234 #define BN_MASK (0xffff)
235 #define BN_MASK2 (0xff)
236 #define BN_MASK2l (0xf)
237 #define BN_MASK2h1 (0xf8)
238 #define BN_MASK2h (0xf0)
239 #define BN_TBIT (0x80)
240 #define BN_DEC_CONV (100)
241 #define BN_DEC_FMT1 "%u"
242 #define BN_DEC_FMT2 "%02u"
246 #define BN_DEFAULT_BITS 1280
252 #define BN_FLG_MALLOCED 0x01
253 #define BN_FLG_STATIC_DATA 0x02
254 #define BN_FLG_FREE 0x8000 /* used for debuging */
255 #define BN_set_flags(b,n) ((b)->flags|=(n))
256 #define BN_get_flags(b,n) ((b)->flags&(n))
258 typedef struct bignum_st
260 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
261 int top; /* Index of last used d +1. */
262 /* The next are internal book keeping for bn_expand. */
263 int dmax; /* Size of the d array. */
264 int neg; /* one if the number is negative */
268 /* Used for temp variables (declaration hidden in bn_lcl.h) */
269 typedef struct bignum_ctx BN_CTX;
271 typedef struct bn_blinding_st
276 BIGNUM *mod; /* just a reference */
279 /* Used for montgomery multiplication */
280 typedef struct bn_mont_ctx_st
282 int ri; /* number of bits in R */
283 BIGNUM RR; /* used to convert to montgomery form */
284 BIGNUM N; /* The modulus */
285 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
286 * (Ni is only stored for bignum algorithm) */
287 BN_ULONG n0; /* least significant word of Ni */
291 /* Used for reciprocal division/mod functions
292 * It cannot be shared between threads
294 typedef struct bn_recp_ctx_st
296 BIGNUM N; /* the divisor */
297 BIGNUM Nr; /* the reciprocal */
303 #define BN_prime_checks 0 /* default: select number of iterations
304 based on the size of the number */
306 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
307 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
308 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
309 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
310 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
311 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
324 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
326 /* Note that BN_abs_is_word does not work reliably for w == 0 */
327 #define BN_abs_is_word(a,w) (((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w)))
328 #define BN_is_zero(a) (((a)->top == 0) || BN_abs_is_word(a,0))
329 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
330 #define BN_is_word(a,w) ((w) ? BN_abs_is_word((a),(w)) && !(a)->neg : \
332 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
334 #define BN_one(a) (BN_set_word((a),1))
335 #define BN_zero(a) (BN_set_word((a),0))
337 /*#define BN_ascii2bn(a) BN_hex2bn(a) */
338 /*#define BN_bn2ascii(a) BN_bn2hex(a) */
340 const BIGNUM *BN_value_one(void);
341 char * BN_options(void);
342 BN_CTX *BN_CTX_new(void);
343 void BN_CTX_init(BN_CTX *c);
344 void BN_CTX_free(BN_CTX *c);
345 void BN_CTX_start(BN_CTX *ctx);
346 BIGNUM *BN_CTX_get(BN_CTX *ctx);
347 void BN_CTX_end(BN_CTX *ctx);
348 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
349 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
350 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
351 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
352 int BN_num_bits(const BIGNUM *a);
353 int BN_num_bits_word(BN_ULONG);
354 BIGNUM *BN_new(void);
355 void BN_init(BIGNUM *);
356 void BN_clear_free(BIGNUM *a);
357 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
358 /* BN_ncopy(): like BN_copy() but copies at most the first n BN_ULONGs */
359 BIGNUM *BN_ncopy(BIGNUM *a, const BIGNUM *b, size_t n);
360 void BN_swap(BIGNUM *a, BIGNUM *b);
361 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
362 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
363 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
364 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
365 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
366 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
367 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
368 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
369 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
370 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
372 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
374 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
375 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
376 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
377 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
378 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
379 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
380 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
381 const BIGNUM *m, BN_CTX *ctx);
382 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
383 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
384 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
385 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
386 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
388 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
389 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
390 int BN_mul_word(BIGNUM *a, BN_ULONG w);
391 int BN_add_word(BIGNUM *a, BN_ULONG w);
392 int BN_sub_word(BIGNUM *a, BN_ULONG w);
393 int BN_set_word(BIGNUM *a, BN_ULONG w);
394 BN_ULONG BN_get_word(const BIGNUM *a);
396 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
397 void BN_free(BIGNUM *a);
398 int BN_is_bit_set(const BIGNUM *a, int n);
399 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
400 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
401 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
403 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
404 const BIGNUM *m,BN_CTX *ctx);
405 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
406 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
407 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
408 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
409 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
410 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
411 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
412 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
413 const BIGNUM *m,BN_CTX *ctx);
415 int BN_mask_bits(BIGNUM *a,int n);
416 #ifndef OPENSSL_NO_FP_API
417 int BN_print_fp(FILE *fp, const BIGNUM *a);
420 int BN_print(BIO *fp, const BIGNUM *a);
422 int BN_print(void *fp, const BIGNUM *a);
424 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
425 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
426 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
427 void BN_clear(BIGNUM *a);
428 BIGNUM *BN_dup(const BIGNUM *a);
429 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
430 int BN_set_bit(BIGNUM *a, int n);
431 int BN_clear_bit(BIGNUM *a, int n);
432 char * BN_bn2hex(const BIGNUM *a);
433 char * BN_bn2dec(const BIGNUM *a);
434 int BN_hex2bn(BIGNUM **a, const char *str);
435 int BN_dec2bn(BIGNUM **a, const char *str);
436 int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
437 int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
438 BIGNUM *BN_mod_inverse(BIGNUM *ret,
439 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
440 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
441 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
442 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
443 const BIGNUM *add, const BIGNUM *rem,
444 void (*callback)(int,int,void *),void *cb_arg);
445 int BN_is_prime(const BIGNUM *p,int nchecks,
446 void (*callback)(int,int,void *),
447 BN_CTX *ctx,void *cb_arg);
448 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
449 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
450 int do_trial_division);
452 BN_MONT_CTX *BN_MONT_CTX_new(void );
453 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
454 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
455 BN_MONT_CTX *mont, BN_CTX *ctx);
456 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
457 (r),(a),&((mont)->RR),(mont),(ctx))
458 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
459 BN_MONT_CTX *mont, BN_CTX *ctx);
460 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
461 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
462 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
464 BN_BLINDING *BN_BLINDING_new(BIGNUM *A,BIGNUM *Ai,BIGNUM *mod);
465 void BN_BLINDING_free(BN_BLINDING *b);
466 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
467 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *r, BN_CTX *ctx);
468 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
470 void BN_set_params(int mul,int high,int low,int mont);
471 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
473 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
474 BN_RECP_CTX *BN_RECP_CTX_new(void);
475 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
476 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
477 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
478 BN_RECP_CTX *recp,BN_CTX *ctx);
479 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
480 const BIGNUM *m, BN_CTX *ctx);
481 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
482 BN_RECP_CTX *recp, BN_CTX *ctx);
484 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
486 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is ignored.
488 * Note that input arguments are not const so that their bit arrays can
489 * be expanded to the appropriate size if needed.
491 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /* r = a + b */
492 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
493 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /* r = a mod p */
494 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
495 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = (a * a) mod p */
496 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (1 / b) mod p */
497 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
498 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
499 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = sqrt(a) mod p */
500 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r^2 + r = a mod p */
501 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
502 /* Some functions allow for representation of the irreducible polynomials
503 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
504 * t^p[0] + t^p[1] + ... + t^p[k]
505 * where m = p[0] > p[1] > ... > p[k] = 0.
507 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]); /* r = a mod p */
508 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 */
509 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = (a * a) mod p */
510 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (1 / b) mod p */
511 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 */
512 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 */
513 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
514 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 */
515 int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
516 int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
518 /* faster mod functions for the 'NIST primes'
520 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
521 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
522 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
523 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
524 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
526 const BIGNUM *BN_get0_nist_prime_192(void);
527 const BIGNUM *BN_get0_nist_prime_224(void);
528 const BIGNUM *BN_get0_nist_prime_256(void);
529 const BIGNUM *BN_get0_nist_prime_384(void);
530 const BIGNUM *BN_get0_nist_prime_521(void);
532 /* library internal functions */
534 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
535 (a):bn_expand2((a),(bits)/BN_BITS2+1))
536 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
537 BIGNUM *bn_expand2(BIGNUM *a, int words);
538 BIGNUM *bn_dup_expand(const BIGNUM *a, int words);
540 #define bn_fix_top(a) \
545 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
546 if (*(ftl--)) break; \
550 #define bn_clear_top2max(a) \
552 int index = (a)->dmax - (a)->top; \
553 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
554 for (; index != 0; index--) \
558 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
559 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
560 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
561 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
562 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
563 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
566 void bn_dump1(FILE *o, const char *a, const BN_ULONG *b,int n);
567 # define bn_print(a) {fprintf(stderr, #a "="); BN_print_fp(stderr,a); \
568 fprintf(stderr,"\n");}
569 # define bn_dump(a,n) bn_dump1(stderr,#a,a,n);
572 # define bn_dump(a,b)
575 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
577 /* BEGIN ERROR CODES */
578 /* The following lines are auto generated by the script mkerr.pl. Any changes
579 * made after this point may be overwritten when the script is next run.
581 void ERR_load_BN_strings(void);
583 /* Error codes for the BN functions. */
585 /* Function codes. */
586 #define BN_F_BN_BLINDING_CONVERT 100
587 #define BN_F_BN_BLINDING_INVERT 101
588 #define BN_F_BN_BLINDING_NEW 102
589 #define BN_F_BN_BLINDING_UPDATE 103
590 #define BN_F_BN_BN2DEC 104
591 #define BN_F_BN_BN2HEX 105
592 #define BN_F_BN_CTX_GET 116
593 #define BN_F_BN_CTX_NEW 106
594 #define BN_F_BN_DIV 107
595 #define BN_F_BN_EXPAND2 108
596 #define BN_F_BN_EXPAND_INTERNAL 120
597 #define BN_F_BN_GF2M_MOD 126
598 #define BN_F_BN_GF2M_MOD_DIV 123
599 #define BN_F_BN_GF2M_MOD_EXP 127
600 #define BN_F_BN_GF2M_MOD_MUL 124
601 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 128
602 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 129
603 #define BN_F_BN_GF2M_MOD_SQR 125
604 #define BN_F_BN_MOD_EXP2_MONT 118
605 #define BN_F_BN_MOD_EXP_MONT 109
606 #define BN_F_BN_MOD_EXP_MONT_WORD 117
607 #define BN_F_BN_MOD_INVERSE 110
608 #define BN_F_BN_MOD_LSHIFT_QUICK 119
609 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
610 #define BN_F_BN_MOD_SQRT 121
611 #define BN_F_BN_MPI2BN 112
612 #define BN_F_BN_NEW 113
613 #define BN_F_BN_RAND 114
614 #define BN_F_BN_RAND_RANGE 122
615 #define BN_F_BN_USUB 115
618 #define BN_R_ARG2_LT_ARG3 100
619 #define BN_R_BAD_RECIPROCAL 101
620 #define BN_R_BIGNUM_TOO_LONG 114
621 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
622 #define BN_R_DIV_BY_ZERO 103
623 #define BN_R_ENCODING_ERROR 104
624 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
625 #define BN_R_INPUT_NOT_REDUCED 110
626 #define BN_R_INVALID_LENGTH 106
627 #define BN_R_INVALID_RANGE 115
628 #define BN_R_NOT_A_SQUARE 111
629 #define BN_R_NOT_IMPLEMENTED 116
630 #define BN_R_NOT_INITIALIZED 107
631 #define BN_R_NO_INVERSE 108
632 #define BN_R_P_IS_NOT_PRIME 112
633 #define BN_R_TOO_MANY_ITERATIONS 113
634 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109