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 (c) 1998-2018 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
111 /* ====================================================================
112 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
114 * Portions of the attached software ("Contribution") are developed by
115 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
117 * The Contribution is licensed pursuant to the Eric Young open source
118 * license provided above.
120 * The binary polynomial arithmetic software is originally written by
121 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
129 # include <openssl/e_os2.h>
130 # ifndef OPENSSL_NO_FP_API
131 # include <stdio.h> /* FILE */
133 # include <openssl/ossl_typ.h>
134 # include <openssl/crypto.h>
141 * These preprocessor symbols control various aspects of the bignum headers
142 * and library code. They're not defined by any "normal" configuration, as
143 * they are intended for development and testing purposes. NB: defining all
144 * three can be useful for debugging application code as well as openssl
145 * itself. BN_DEBUG - turn on various debugging alterations to the bignum
146 * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
147 * mismanagement of bignum internals. You must also define BN_DEBUG.
149 /* #define BN_DEBUG */
150 /* #define BN_DEBUG_RAND */
152 # ifndef OPENSSL_SMALL_FOOTPRINT
153 # define BN_MUL_COMBA
154 # define BN_SQR_COMBA
155 # define BN_RECURSION
159 * This next option uses the C libraries (2 word)/(1 word) function. If it is
160 * not defined, I use my C version (which is slower). The reason for this
161 * flag is that when the particular C compiler library routine is used, and
162 * the library is linked with a different compiler, the library is missing.
163 * This mostly happens when the library is built with gcc and then linked
164 * using normal cc. This would be a common occurrence because gcc normally
165 * produces code that is 2 times faster than system compilers for the big
166 * number stuff. For machines with only one compiler (or shared libraries),
167 * this should be on. Again this in only really a problem on machines using
168 * "long long's", are 32bit, and are not using my assembler code.
170 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
171 defined(OPENSSL_SYS_WIN32) || defined(linux)
178 * assuming long is 64bit - this is the DEC Alpha unsigned long long is only
179 * 64 bits :-(, don't define BN_LLONG for the DEC Alpha
181 # ifdef SIXTY_FOUR_BIT_LONG
182 # define BN_ULLONG unsigned long long
183 # define BN_ULONG unsigned long
184 # define BN_LONG long
189 # define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
190 # define BN_MASK2 (0xffffffffffffffffL)
191 # define BN_MASK2l (0xffffffffL)
192 # define BN_MASK2h (0xffffffff00000000L)
193 # define BN_MASK2h1 (0xffffffff80000000L)
194 # define BN_TBIT (0x8000000000000000L)
195 # define BN_DEC_CONV (10000000000000000000UL)
196 # define BN_DEC_FMT1 "%lu"
197 # define BN_DEC_FMT2 "%019lu"
198 # define BN_DEC_NUM 19
199 # define BN_HEX_FMT1 "%lX"
200 # define BN_HEX_FMT2 "%016lX"
204 * This is where the long long data type is 64 bits, but long is 32. For
205 * machines where there are 64bit registers, this is the mode to use. IRIX,
206 * on R4000 and above should use this mode, along with the relevant assembler
207 * code :-). Do NOT define BN_LLONG.
209 # ifdef SIXTY_FOUR_BIT
212 # define BN_ULONG unsigned long long
213 # define BN_LONG long long
218 # define BN_MASK2 (0xffffffffffffffffLL)
219 # define BN_MASK2l (0xffffffffL)
220 # define BN_MASK2h (0xffffffff00000000LL)
221 # define BN_MASK2h1 (0xffffffff80000000LL)
222 # define BN_TBIT (0x8000000000000000LL)
223 # define BN_DEC_CONV (10000000000000000000ULL)
224 # define BN_DEC_FMT1 "%llu"
225 # define BN_DEC_FMT2 "%019llu"
226 # define BN_DEC_NUM 19
227 # define BN_HEX_FMT1 "%llX"
228 # define BN_HEX_FMT2 "%016llX"
231 # ifdef THIRTY_TWO_BIT
233 # if defined(_WIN32) && !defined(__GNUC__)
234 # define BN_ULLONG unsigned __int64
235 # define BN_MASK (0xffffffffffffffffI64)
237 # define BN_ULLONG unsigned long long
238 # define BN_MASK (0xffffffffffffffffLL)
241 # define BN_ULONG unsigned int
247 # define BN_MASK2 (0xffffffffL)
248 # define BN_MASK2l (0xffff)
249 # define BN_MASK2h1 (0xffff8000L)
250 # define BN_MASK2h (0xffff0000L)
251 # define BN_TBIT (0x80000000L)
252 # define BN_DEC_CONV (1000000000L)
253 # define BN_DEC_FMT1 "%u"
254 # define BN_DEC_FMT2 "%09u"
255 # define BN_DEC_NUM 9
256 # define BN_HEX_FMT1 "%X"
257 # define BN_HEX_FMT2 "%08X"
260 # define BN_DEFAULT_BITS 1280
262 # define BN_FLG_MALLOCED 0x01
263 # define BN_FLG_STATIC_DATA 0x02
266 * avoid leaking exponent information through timing,
267 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
268 * BN_div() will call BN_div_no_branch,
269 * BN_mod_inverse() will call BN_mod_inverse_no_branch.
271 # define BN_FLG_CONSTTIME 0x04
273 # ifdef OPENSSL_NO_DEPRECATED
274 /* deprecated name for the flag */
275 # define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
277 * avoid leaking exponent information through timings
278 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime)
282 # ifndef OPENSSL_NO_DEPRECATED
283 # define BN_FLG_FREE 0x8000
284 /* used for debuging */
286 # define BN_set_flags(b,n) ((b)->flags|=(n))
287 # define BN_get_flags(b,n) ((b)->flags&(n))
290 * get a clone of a BIGNUM with changed flags, for *temporary* use only (the
291 * two BIGNUMs cannot not be used in parallel!)
293 # define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
294 (dest)->top=(b)->top, \
295 (dest)->dmax=(b)->dmax, \
296 (dest)->neg=(b)->neg, \
297 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
298 | ((b)->flags & ~BN_FLG_MALLOCED) \
299 | BN_FLG_STATIC_DATA \
302 /* Already declared in ossl_typ.h */
304 typedef struct bignum_st BIGNUM;
305 /* Used for temp variables (declaration hidden in bn_lcl.h) */
306 typedef struct bignum_ctx BN_CTX;
307 typedef struct bn_blinding_st BN_BLINDING;
308 typedef struct bn_mont_ctx_st BN_MONT_CTX;
309 typedef struct bn_recp_ctx_st BN_RECP_CTX;
310 typedef struct bn_gencb_st BN_GENCB;
314 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit
316 int top; /* Index of last used d +1. */
317 /* The next are internal book keeping for bn_expand. */
318 int dmax; /* Size of the d array. */
319 int neg; /* one if the number is negative */
323 /* Used for montgomery multiplication */
324 struct bn_mont_ctx_st {
325 int ri; /* number of bits in R */
326 BIGNUM RR; /* used to convert to montgomery form */
327 BIGNUM N; /* The modulus */
328 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only
329 * stored for bignum algorithm) */
330 BN_ULONG n0[2]; /* least significant word(s) of Ni; (type
331 * changed with 0.9.9, was "BN_ULONG n0;"
337 * Used for reciprocal division/mod functions It cannot be shared between
340 struct bn_recp_ctx_st {
341 BIGNUM N; /* the divisor */
342 BIGNUM Nr; /* the reciprocal */
348 /* Used for slow "generation" functions. */
350 unsigned int ver; /* To handle binary (in)compatibility */
351 void *arg; /* callback-specific data */
353 /* if(ver==1) - handles old style callbacks */
354 void (*cb_1) (int, int, void *);
355 /* if(ver==2) - new callback style */
356 int (*cb_2) (int, int, BN_GENCB *);
359 /* Wrapper function to make using BN_GENCB easier, */
360 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
361 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
362 # define BN_GENCB_set_old(gencb, callback, cb_arg) { \
363 BN_GENCB *tmp_gencb = (gencb); \
364 tmp_gencb->ver = 1; \
365 tmp_gencb->arg = (cb_arg); \
366 tmp_gencb->cb.cb_1 = (callback); }
367 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
368 # define BN_GENCB_set(gencb, callback, cb_arg) { \
369 BN_GENCB *tmp_gencb = (gencb); \
370 tmp_gencb->ver = 2; \
371 tmp_gencb->arg = (cb_arg); \
372 tmp_gencb->cb.cb_2 = (callback); }
374 # define BN_prime_checks 0 /* default: select number of iterations based
375 * on the size of the number */
378 * BN_prime_checks_for_size() returns the number of Miller-Rabin iterations
379 * that will be done for checking that a random number is probably prime. The
380 * error rate for accepting a composite number as prime depends on the size of
381 * the prime |b|. The error rates used are for calculating an RSA key with 2 primes,
382 * and so the level is what you would expect for a key of double the size of the
385 * This table is generated using the algorithm of FIPS PUB 186-4
386 * Digital Signature Standard (DSS), section F.1, page 117.
387 * (https://dx.doi.org/10.6028/NIST.FIPS.186-4)
389 * The following magma script was used to generate the output:
393 * for M:=3 to Floor(2*Sqrt(k-1)-1) do
400 * s+:=(RealField(32)!2)^-(j+(k-1)/j);
402 * S+:=2^(m-(m-1)*t)*s;
405 * B:=8*(Pi(RealField(32))^2-6)/3*2^(k-2)*S;
406 * pkt:=2.00743*Log(2)*k*2^-k*(A+B);
407 * seclevel:=Floor(-Log(2,pkt));
408 * if seclevel ge securitybits then
409 * printf "k: %5o, security: %o bits (t: %o, M: %o)\n",k,seclevel,t,M;
413 * if seclevel ge securitybits then break; end if;
416 * It can be run online at:
417 * http://magma.maths.usyd.edu.au/calc
420 * k: 1024, security: 129 bits (t: 6, M: 23)
422 * k is the number of bits of the prime, securitybits is the level we want to
425 * prime length | RSA key size | # MR tests | security level
426 * -------------+--------------|------------+---------------
427 * (b) >= 6394 | >= 12788 | 3 | 256 bit
428 * (b) >= 3747 | >= 7494 | 3 | 192 bit
429 * (b) >= 1345 | >= 2690 | 4 | 128 bit
430 * (b) >= 1080 | >= 2160 | 5 | 128 bit
431 * (b) >= 852 | >= 1704 | 5 | 112 bit
432 * (b) >= 476 | >= 952 | 5 | 80 bit
433 * (b) >= 400 | >= 800 | 6 | 80 bit
434 * (b) >= 347 | >= 694 | 7 | 80 bit
435 * (b) >= 308 | >= 616 | 8 | 80 bit
436 * (b) >= 55 | >= 110 | 27 | 64 bit
437 * (b) >= 6 | >= 12 | 34 | 64 bit
440 # define BN_prime_checks_for_size(b) ((b) >= 3747 ? 3 : \
449 # define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
451 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
452 # define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
453 (((w) == 0) && ((a)->top == 0)))
454 # define BN_is_zero(a) ((a)->top == 0)
455 # define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
456 # define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
457 # define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
459 # define BN_one(a) (BN_set_word((a),1))
460 # define BN_zero_ex(a) \
462 BIGNUM *_tmp_bn = (a); \
466 # ifdef OPENSSL_NO_DEPRECATED
467 # define BN_zero(a) BN_zero_ex(a)
469 # define BN_zero(a) (BN_set_word((a),0))
472 const BIGNUM *BN_value_one(void);
473 char *BN_options(void);
474 BN_CTX *BN_CTX_new(void);
475 # ifndef OPENSSL_NO_DEPRECATED
476 void BN_CTX_init(BN_CTX *c);
478 void BN_CTX_free(BN_CTX *c);
479 void BN_CTX_start(BN_CTX *ctx);
480 BIGNUM *BN_CTX_get(BN_CTX *ctx);
481 void BN_CTX_end(BN_CTX *ctx);
482 int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
483 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
484 int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
485 int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
486 int BN_num_bits(const BIGNUM *a);
487 int BN_num_bits_word(BN_ULONG);
488 BIGNUM *BN_new(void);
489 void BN_init(BIGNUM *);
490 void BN_clear_free(BIGNUM *a);
491 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
492 void BN_swap(BIGNUM *a, BIGNUM *b);
493 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
494 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
495 BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
496 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
497 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
498 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
499 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
500 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
501 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
502 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
503 /** BN_set_negative sets sign of a BIGNUM
504 * \param b pointer to the BIGNUM object
505 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
507 void BN_set_negative(BIGNUM *b, int n);
508 /** BN_is_negative returns 1 if the BIGNUM is negative
509 * \param a pointer to the BIGNUM object
510 * \return 1 if a < 0 and 0 otherwise
512 # define BN_is_negative(a) ((a)->neg != 0)
514 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
516 # define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
517 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
518 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
520 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
522 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
524 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
526 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
528 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
529 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
530 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
531 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
533 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
535 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
536 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
537 int BN_mul_word(BIGNUM *a, BN_ULONG w);
538 int BN_add_word(BIGNUM *a, BN_ULONG w);
539 int BN_sub_word(BIGNUM *a, BN_ULONG w);
540 int BN_set_word(BIGNUM *a, BN_ULONG w);
541 BN_ULONG BN_get_word(const BIGNUM *a);
543 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
544 void BN_free(BIGNUM *a);
545 int BN_is_bit_set(const BIGNUM *a, int n);
546 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
547 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
548 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
550 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
551 const BIGNUM *m, BN_CTX *ctx);
552 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
553 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
554 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
555 const BIGNUM *m, BN_CTX *ctx,
556 BN_MONT_CTX *in_mont);
557 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
558 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
559 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
560 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
561 BN_CTX *ctx, BN_MONT_CTX *m_ctx);
562 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
563 const BIGNUM *m, BN_CTX *ctx);
565 int BN_mask_bits(BIGNUM *a, int n);
566 # ifndef OPENSSL_NO_FP_API
567 int BN_print_fp(FILE *fp, const BIGNUM *a);
570 int BN_print(BIO *fp, const BIGNUM *a);
572 int BN_print(void *fp, const BIGNUM *a);
574 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
575 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
576 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
577 void BN_clear(BIGNUM *a);
578 BIGNUM *BN_dup(const BIGNUM *a);
579 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
580 int BN_set_bit(BIGNUM *a, int n);
581 int BN_clear_bit(BIGNUM *a, int n);
582 char *BN_bn2hex(const BIGNUM *a);
583 char *BN_bn2dec(const BIGNUM *a);
584 int BN_hex2bn(BIGNUM **a, const char *str);
585 int BN_dec2bn(BIGNUM **a, const char *str);
586 int BN_asc2bn(BIGNUM **a, const char *str);
587 int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
588 int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
591 BIGNUM *BN_mod_inverse(BIGNUM *ret,
592 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
593 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
594 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
596 void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
598 /* Deprecated versions */
599 # ifndef OPENSSL_NO_DEPRECATED
600 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
601 const BIGNUM *add, const BIGNUM *rem,
602 void (*callback) (int, int, void *), void *cb_arg);
603 int BN_is_prime(const BIGNUM *p, int nchecks,
604 void (*callback) (int, int, void *),
605 BN_CTX *ctx, void *cb_arg);
606 int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
607 void (*callback) (int, int, void *), BN_CTX *ctx,
608 void *cb_arg, int do_trial_division);
609 # endif /* !defined(OPENSSL_NO_DEPRECATED) */
612 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
613 const BIGNUM *rem, BN_GENCB *cb);
614 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
615 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
616 int do_trial_division, BN_GENCB *cb);
618 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
620 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
621 const BIGNUM *Xp, const BIGNUM *Xp1,
622 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
624 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1,
625 BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e,
626 BN_CTX *ctx, BN_GENCB *cb);
628 BN_MONT_CTX *BN_MONT_CTX_new(void);
629 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
630 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
631 BN_MONT_CTX *mont, BN_CTX *ctx);
632 # define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
633 (r),(a),&((mont)->RR),(mont),(ctx))
634 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a,
635 BN_MONT_CTX *mont, BN_CTX *ctx);
636 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
637 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
638 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
639 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
640 const BIGNUM *mod, BN_CTX *ctx);
642 /* BN_BLINDING flags */
643 # define BN_BLINDING_NO_UPDATE 0x00000001
644 # define BN_BLINDING_NO_RECREATE 0x00000002
646 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
647 void BN_BLINDING_free(BN_BLINDING *b);
648 int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
649 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
650 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
651 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
652 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
654 # ifndef OPENSSL_NO_DEPRECATED
655 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
656 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
658 CRYPTO_THREADID *BN_BLINDING_thread_id(BN_BLINDING *);
659 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
660 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
661 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
662 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
663 int (*bn_mod_exp) (BIGNUM *r,
671 # ifndef OPENSSL_NO_DEPRECATED
672 void BN_set_params(int mul, int high, int low, int mont);
673 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
676 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
677 BN_RECP_CTX *BN_RECP_CTX_new(void);
678 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
679 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
680 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
681 BN_RECP_CTX *recp, BN_CTX *ctx);
682 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
683 const BIGNUM *m, BN_CTX *ctx);
684 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
685 BN_RECP_CTX *recp, BN_CTX *ctx);
687 # ifndef OPENSSL_NO_EC2M
690 * Functions for arithmetic over binary polynomials represented by BIGNUMs.
691 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
692 * ignored. Note that input arguments are not const so that their bit arrays
693 * can be expanded to the appropriate size if needed.
699 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
700 # define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
704 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
705 /* r = (a * b) mod p */
706 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
707 const BIGNUM *p, BN_CTX *ctx);
708 /* r = (a * a) mod p */
709 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
710 /* r = (1 / b) mod p */
711 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
712 /* r = (a / b) mod p */
713 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
714 const BIGNUM *p, BN_CTX *ctx);
715 /* r = (a ^ b) mod p */
716 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
717 const BIGNUM *p, BN_CTX *ctx);
718 /* r = sqrt(a) mod p */
719 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
721 /* r^2 + r = a mod p */
722 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
724 # define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
726 * Some functions allow for representation of the irreducible polynomials
727 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
728 * t^p[0] + t^p[1] + ... + t^p[k]
729 * where m = p[0] > p[1] > ... > p[k] = 0.
732 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
733 /* r = (a * b) mod p */
734 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
735 const int p[], BN_CTX *ctx);
736 /* r = (a * a) mod p */
737 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
739 /* r = (1 / b) mod p */
740 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
742 /* r = (a / b) mod p */
743 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
744 const int p[], BN_CTX *ctx);
745 /* r = (a ^ b) mod p */
746 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
747 const int p[], BN_CTX *ctx);
748 /* r = sqrt(a) mod p */
749 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
750 const int p[], BN_CTX *ctx);
751 /* r^2 + r = a mod p */
752 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
753 const int p[], BN_CTX *ctx);
754 int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
755 int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
760 * faster mod functions for the 'NIST primes' 0 <= a < p^2
762 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
763 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
764 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
765 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
766 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
768 const BIGNUM *BN_get0_nist_prime_192(void);
769 const BIGNUM *BN_get0_nist_prime_224(void);
770 const BIGNUM *BN_get0_nist_prime_256(void);
771 const BIGNUM *BN_get0_nist_prime_384(void);
772 const BIGNUM *BN_get0_nist_prime_521(void);
774 /* library internal functions */
776 # define bn_expand(a,bits) \
778 bits > (INT_MAX - BN_BITS2 + 1) ? \
781 (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax) ? \
784 bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2) \
787 # define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
788 BIGNUM *bn_expand2(BIGNUM *a, int words);
789 # ifndef OPENSSL_NO_DEPRECATED
790 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
794 * Bignum consistency macros
795 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
796 * bignum data after direct manipulations on the data. There is also an
797 * "internal" macro, bn_check_top(), for verifying that there are no leading
798 * zeroes. Unfortunately, some auditing is required due to the fact that
799 * bn_fix_top() has become an overabused duct-tape because bignum data is
800 * occasionally passed around in an inconsistent state. So the following
801 * changes have been made to sort this out;
802 * - bn_fix_top()s implementation has been moved to bn_correct_top()
803 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
804 * bn_check_top() is as before.
805 * - if BN_DEBUG *is* defined;
806 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
807 * consistent. (ed: only if BN_DEBUG_RAND is defined)
808 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
809 * The idea is to have debug builds flag up inconsistent bignums when they
810 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
811 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
812 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
813 * was not appropriate, we convert it permanently to bn_check_top() and track
814 * down the cause of the bug. Eventually, no internal code should be using the
815 * bn_fix_top() macro. External applications and libraries should try this with
816 * their own code too, both in terms of building against the openssl headers
817 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
818 * defined. This not only improves external code, it provides more test
819 * coverage for openssl's own code.
824 /* We only need assert() when debugging */
828 * The new BN_FLG_FIXED_TOP flag marks vectors that were not treated with
829 * bn_correct_top, in other words such vectors are permitted to have zeros
830 * in most significant limbs. Such vectors are used internally to achieve
831 * execution time invariance for critical operations with private keys.
832 * It's BN_DEBUG-only flag, because user application is not supposed to
833 * observe it anyway. Moreover, optimizing compiler would actually remove
834 * all operations manipulating the bit in question in non-BN_DEBUG build.
836 # define BN_FLG_FIXED_TOP 0x10000
837 # ifdef BN_DEBUG_RAND
838 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
839 # ifndef RAND_pseudo_bytes
840 int RAND_pseudo_bytes(unsigned char *buf, int num);
841 # define BN_DEBUG_TRIX
843 # define bn_pollute(a) \
845 const BIGNUM *_bnum1 = (a); \
846 if(_bnum1->top < _bnum1->dmax) { \
847 unsigned char _tmp_char; \
848 /* We cast away const without the compiler knowing, any \
849 * *genuinely* constant variables that aren't mutable \
850 * wouldn't be constructed with top!=dmax. */ \
851 BN_ULONG *_not_const; \
852 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
853 /* Debug only - safe to ignore error return */ \
854 RAND_pseudo_bytes(&_tmp_char, 1); \
855 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
856 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
859 # ifdef BN_DEBUG_TRIX
860 # undef RAND_pseudo_bytes
863 # define bn_pollute(a)
865 # define bn_check_top(a) \
867 const BIGNUM *_bnum2 = (a); \
868 if (_bnum2 != NULL) { \
869 int _top = _bnum2->top; \
870 assert((_top == 0) || \
871 (_bnum2->flags & BN_FLG_FIXED_TOP) || \
872 (_bnum2->d[_top - 1] != 0)); \
873 bn_pollute(_bnum2); \
877 # define bn_fix_top(a) bn_check_top(a)
879 # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
880 # define bn_wcheck_size(bn, words) \
882 const BIGNUM *_bnum2 = (bn); \
883 assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \
884 /* avoid unused variable warning with NDEBUG */ \
888 # else /* !BN_DEBUG */
890 # define BN_FLG_FIXED_TOP 0
891 # define bn_pollute(a)
892 # define bn_check_top(a)
893 # define bn_fix_top(a) bn_correct_top(a)
894 # define bn_check_size(bn, bits)
895 # define bn_wcheck_size(bn, words)
899 # define bn_correct_top(a) \
902 int tmp_top = (a)->top; \
905 for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \
906 if (*(ftl--)) break; \
907 (a)->top = tmp_top; \
914 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
916 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
917 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
918 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
919 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
921 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
924 /* Primes from RFC 2409 */
925 BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
926 BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
928 /* Primes from RFC 3526 */
929 BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
930 BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
931 BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
932 BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
933 BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
934 BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
936 int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
938 /* BEGIN ERROR CODES */
940 * The following lines are auto generated by the script mkerr.pl. Any changes
941 * made after this point may be overwritten when the script is next run.
943 void ERR_load_BN_strings(void);
945 /* Error codes for the BN functions. */
947 /* Function codes. */
948 # define BN_F_BNRAND 127
949 # define BN_F_BN_BLINDING_CONVERT_EX 100
950 # define BN_F_BN_BLINDING_CREATE_PARAM 128
951 # define BN_F_BN_BLINDING_INVERT_EX 101
952 # define BN_F_BN_BLINDING_NEW 102
953 # define BN_F_BN_BLINDING_UPDATE 103
954 # define BN_F_BN_BN2DEC 104
955 # define BN_F_BN_BN2HEX 105
956 # define BN_F_BN_CTX_GET 116
957 # define BN_F_BN_CTX_NEW 106
958 # define BN_F_BN_CTX_START 129
959 # define BN_F_BN_DIV 107
960 # define BN_F_BN_DIV_NO_BRANCH 138
961 # define BN_F_BN_DIV_RECP 130
962 # define BN_F_BN_EXP 123
963 # define BN_F_BN_EXPAND2 108
964 # define BN_F_BN_EXPAND_INTERNAL 120
965 # define BN_F_BN_GF2M_MOD 131
966 # define BN_F_BN_GF2M_MOD_EXP 132
967 # define BN_F_BN_GF2M_MOD_MUL 133
968 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
969 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
970 # define BN_F_BN_GF2M_MOD_SQR 136
971 # define BN_F_BN_GF2M_MOD_SQRT 137
972 # define BN_F_BN_LSHIFT 145
973 # define BN_F_BN_MOD_EXP2_MONT 118
974 # define BN_F_BN_MOD_EXP_MONT 109
975 # define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
976 # define BN_F_BN_MOD_EXP_MONT_WORD 117
977 # define BN_F_BN_MOD_EXP_RECP 125
978 # define BN_F_BN_MOD_EXP_SIMPLE 126
979 # define BN_F_BN_MOD_INVERSE 110
980 # define BN_F_BN_MOD_INVERSE_NO_BRANCH 139
981 # define BN_F_BN_MOD_LSHIFT_QUICK 119
982 # define BN_F_BN_MOD_MUL_RECIPROCAL 111
983 # define BN_F_BN_MOD_SQRT 121
984 # define BN_F_BN_MPI2BN 112
985 # define BN_F_BN_NEW 113
986 # define BN_F_BN_RAND 114
987 # define BN_F_BN_RAND_RANGE 122
988 # define BN_F_BN_RSHIFT 146
989 # define BN_F_BN_USUB 115
992 # define BN_R_ARG2_LT_ARG3 100
993 # define BN_R_BAD_RECIPROCAL 101
994 # define BN_R_BIGNUM_TOO_LONG 114
995 # define BN_R_BITS_TOO_SMALL 118
996 # define BN_R_CALLED_WITH_EVEN_MODULUS 102
997 # define BN_R_DIV_BY_ZERO 103
998 # define BN_R_ENCODING_ERROR 104
999 # define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
1000 # define BN_R_INPUT_NOT_REDUCED 110
1001 # define BN_R_INVALID_LENGTH 106
1002 # define BN_R_INVALID_RANGE 115
1003 # define BN_R_INVALID_SHIFT 119
1004 # define BN_R_NOT_A_SQUARE 111
1005 # define BN_R_NOT_INITIALIZED 107
1006 # define BN_R_NO_INVERSE 108
1007 # define BN_R_NO_SOLUTION 116
1008 # define BN_R_P_IS_NOT_PRIME 112
1009 # define BN_R_TOO_MANY_ITERATIONS 113
1010 # define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109