1 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
2 * All rights reserved.
3 *
4 * This package is an SSL implementation written
5 * by Eric Young (eay@cryptsoft.com).
6 * The implementation was written so as to conform with Netscapes SSL.
7 *
8 * This library is free for commercial and non-commercial use as long as
9 * the following conditions are aheared to. The following conditions
10 * apply to all code found in this distribution, be it the RC4, RSA,
11 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
12 * included with this distribution is covered by the same copyright terms
13 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
14 *
15 * Copyright remains Eric Young's, and as such any Copyright notices in
16 * the code are not to be removed.
17 * If this package is used in a product, Eric Young should be given attribution
18 * as the author of the parts of the library used.
19 * This can be in the form of a textual message at program startup or
20 * in documentation (online or textual) provided with the package.
21 *
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
24 * are met:
25 * 1. Redistributions of source code must retain the copyright
26 * notice, this list of conditions and the following disclaimer.
27 * 2. Redistributions in binary form must reproduce the above copyright
28 * notice, this list of conditions and the following disclaimer in the
29 * documentation and/or other materials provided with the distribution.
30 * 3. All advertising materials mentioning features or use of this software
31 * must display the following acknowledgement:
32 * "This product includes cryptographic software written by
33 * Eric Young (eay@cryptsoft.com)"
34 * The word 'cryptographic' can be left out if the rouines from the library
35 * being used are not cryptographic related :-).
36 * 4. If you include any Windows specific code (or a derivative thereof) from
37 * the apps directory (application code) you must include an acknowledgement:
38 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
39 *
40 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
41 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
43 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
44 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
45 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
46 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
48 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
49 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
50 * SUCH DAMAGE.
51 *
52 * The licence and distribution terms for any publically available version or
53 * derivative of this code cannot be changed. i.e. this code cannot simply be
54 * copied and put under another distribution licence
55 * [including the GNU Public Licence.]
56 */
57 /* ====================================================================
58 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
59 *
60 * Redistribution and use in source and binary forms, with or without
61 * modification, are permitted provided that the following conditions
62 * are met:
63 *
64 * 1. Redistributions of source code must retain the above copyright
65 * notice, this list of conditions and the following disclaimer.
66 *
67 * 2. Redistributions in binary form must reproduce the above copyright
68 * notice, this list of conditions and the following disclaimer in
69 * the documentation and/or other materials provided with the
70 * distribution.
71 *
72 * 3. All advertising materials mentioning features or use of this
73 * software must display the following acknowledgment:
74 * "This product includes software developed by the OpenSSL Project
75 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
76 *
77 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
78 * endorse or promote products derived from this software without
79 * prior written permission. For written permission, please contact
80 * openssl-core@openssl.org.
81 *
82 * 5. Products derived from this software may not be called "OpenSSL"
83 * nor may "OpenSSL" appear in their names without prior written
84 * permission of the OpenSSL Project.
85 *
86 * 6. Redistributions of any form whatsoever must retain the following
87 * acknowledgment:
88 * "This product includes software developed by the OpenSSL Project
89 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
90 *
91 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
92 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
93 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
94 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
95 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
96 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
97 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
98 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
99 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
100 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
101 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
102 * OF THE POSSIBILITY OF SUCH DAMAGE.
103 * ====================================================================
104 *
105 * This product includes cryptographic software written by Eric Young
106 * (eay@cryptsoft.com). This product includes software written by Tim
107 * Hudson (tjh@cryptsoft.com).
108 *
109 */
110 /* ====================================================================
111 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
112 *
113 * Portions of the attached software ("Contribution") are developed by
114 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
115 *
116 * The Contribution is licensed pursuant to the Eric Young open source
117 * license provided above.
118 *
119 * The binary polynomial arithmetic software is originally written by
120 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
121 * Laboratories. */
122
123 #ifndef OPENSSL_HEADER_BN_INTERNAL_H
124 #define OPENSSL_HEADER_BN_INTERNAL_H
125
126 #include <openssl/base.h>
127
128 #if defined(OPENSSL_X86_64) && defined(_MSC_VER)
129 OPENSSL_MSVC_PRAGMA(warning(push, 3))
130 #include <intrin.h>
OPENSSL_MSVC_PRAGMA(warning (pop))131 OPENSSL_MSVC_PRAGMA(warning(pop))
132 #pragma intrinsic(__umulh, _umul128)
133 #endif
134
135 #include "../../internal.h"
136
137 #if defined(__cplusplus)
138 extern "C" {
139 #endif
140
141 #if defined(OPENSSL_64_BIT)
142
143 #if defined(BORINGSSL_HAS_UINT128)
144 // MSVC doesn't support two-word integers on 64-bit.
145 #define BN_ULLONG uint128_t
146 #if defined(BORINGSSL_CAN_DIVIDE_UINT128)
147 #define BN_CAN_DIVIDE_ULLONG
148 #endif
149 #endif
150
151 #define BN_BITS2 64
152 #define BN_BYTES 8
153 #define BN_BITS4 32
154 #define BN_MASK2 (0xffffffffffffffffUL)
155 #define BN_MASK2l (0xffffffffUL)
156 #define BN_MASK2h (0xffffffff00000000UL)
157 #define BN_MASK2h1 (0xffffffff80000000UL)
158 #define BN_MONT_CTX_N0_LIMBS 1
159 #define BN_DEC_CONV (10000000000000000000UL)
160 #define BN_DEC_NUM 19
161 #define TOBN(hi, lo) ((BN_ULONG)(hi) << 32 | (lo))
162
163 #elif defined(OPENSSL_32_BIT)
164
165 #define BN_ULLONG uint64_t
166 #define BN_CAN_DIVIDE_ULLONG
167 #define BN_BITS2 32
168 #define BN_BYTES 4
169 #define BN_BITS4 16
170 #define BN_MASK2 (0xffffffffUL)
171 #define BN_MASK2l (0xffffUL)
172 #define BN_MASK2h1 (0xffff8000UL)
173 #define BN_MASK2h (0xffff0000UL)
174 // On some 32-bit platforms, Montgomery multiplication is done using 64-bit
175 // arithmetic with SIMD instructions. On such platforms, |BN_MONT_CTX::n0|
176 // needs to be two words long. Only certain 32-bit platforms actually make use
177 // of n0[1] and shorter R value would suffice for the others. However,
178 // currently only the assembly files know which is which.
179 #define BN_MONT_CTX_N0_LIMBS 2
180 #define BN_DEC_CONV (1000000000UL)
181 #define BN_DEC_NUM 9
182 #define TOBN(hi, lo) (lo), (hi)
183
184 #else
185 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
186 #endif
187
188
189 #define STATIC_BIGNUM(x) \
190 { \
191 (BN_ULONG *)(x), sizeof(x) / sizeof(BN_ULONG), \
192 sizeof(x) / sizeof(BN_ULONG), 0, BN_FLG_STATIC_DATA \
193 }
194
195 #if defined(BN_ULLONG)
196 #define Lw(t) ((BN_ULONG)(t))
197 #define Hw(t) ((BN_ULONG)((t) >> BN_BITS2))
198 #endif
199
200 // bn_minimal_width returns the minimal value of |bn->top| which fits the
201 // value of |bn|.
202 int bn_minimal_width(const BIGNUM *bn);
203
204 // bn_correct_top decrements |bn->top| to |bn_minimal_width|. If |bn| is zero,
205 // |bn->neg| is set to zero.
206 void bn_correct_top(BIGNUM *bn);
207
208 // bn_wexpand ensures that |bn| has at least |words| works of space without
209 // altering its value. It returns one on success or zero on allocation
210 // failure.
211 int bn_wexpand(BIGNUM *bn, size_t words);
212
213 // bn_expand acts the same as |bn_wexpand|, but takes a number of bits rather
214 // than a number of words.
215 int bn_expand(BIGNUM *bn, size_t bits);
216
217 // bn_resize_words adjusts |bn->top| to be |words|. It returns one on success
218 // and zero on allocation error or if |bn|'s value is too large.
219 //
220 // Do not call this function outside of unit tests. Most functions currently
221 // require |BIGNUM|s be minimal. This function breaks that invariant. It is
222 // introduced early so the invariant may be relaxed incrementally.
223 int bn_resize_words(BIGNUM *bn, size_t words);
224
225 // bn_set_words sets |bn| to the value encoded in the |num| words in |words|,
226 // least significant word first.
227 int bn_set_words(BIGNUM *bn, const BN_ULONG *words, size_t num);
228
229 // bn_fits_in_words returns one if |bn| may be represented in |num| words, plus
230 // a sign bit, and zero otherwise.
231 int bn_fits_in_words(const BIGNUM *bn, size_t num);
232
233 // bn_copy_words copies the value of |bn| to |out| and returns one if the value
234 // is representable in |num| words. Otherwise, it returns zero.
235 int bn_copy_words(BN_ULONG *out, size_t num, const BIGNUM *bn);
236
237 // bn_mul_add_words multiples |ap| by |w|, adds the result to |rp|, and places
238 // the result in |rp|. |ap| and |rp| must both be |num| words long. It returns
239 // the carry word of the operation. |ap| and |rp| may be equal but otherwise may
240 // not alias.
241 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num,
242 BN_ULONG w);
243
244 // bn_mul_words multiples |ap| by |w| and places the result in |rp|. |ap| and
245 // |rp| must both be |num| words long. It returns the carry word of the
246 // operation. |ap| and |rp| may be equal but otherwise may not alias.
247 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num, BN_ULONG w);
248
249 // bn_sqr_words sets |rp[2*i]| and |rp[2*i+1]| to |ap[i]|'s square, for all |i|
250 // up to |num|. |ap| is an array of |num| words and |rp| an array of |2*num|
251 // words. |ap| and |rp| may not alias.
252 //
253 // This gives the contribution of the |ap[i]*ap[i]| terms when squaring |ap|.
254 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num);
255
256 // bn_add_words adds |ap| to |bp| and places the result in |rp|, each of which
257 // are |num| words long. It returns the carry bit, which is one if the operation
258 // overflowed and zero otherwise. Any pair of |ap|, |bp|, and |rp| may be equal
259 // to each other but otherwise may not alias.
260 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
261 size_t num);
262
263 // bn_sub_words subtracts |bp| from |ap| and places the result in |rp|. It
264 // returns the borrow bit, which is one if the computation underflowed and zero
265 // otherwise. Any pair of |ap|, |bp|, and |rp| may be equal to each other but
266 // otherwise may not alias.
267 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
268 size_t num);
269
270 // bn_mul_comba4 sets |r| to the product of |a| and |b|.
271 void bn_mul_comba4(BN_ULONG r[8], const BN_ULONG a[4], const BN_ULONG b[4]);
272
273 // bn_mul_comba8 sets |r| to the product of |a| and |b|.
274 void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]);
275
276 // bn_sqr_comba8 sets |r| to |a|^2.
277 void bn_sqr_comba8(BN_ULONG r[16], const BN_ULONG a[4]);
278
279 // bn_sqr_comba4 sets |r| to |a|^2.
280 void bn_sqr_comba4(BN_ULONG r[8], const BN_ULONG a[4]);
281
282 // bn_cmp_words returns a value less than, equal to or greater than zero if
283 // the, length |n|, array |a| is less than, equal to or greater than |b|.
284 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
285
286 // bn_cmp_words returns a value less than, equal to or greater than zero if the
287 // array |a| is less than, equal to or greater than |b|. The arrays can be of
288 // different lengths: |cl| gives the minimum of the two lengths and |dl| gives
289 // the length of |a| minus the length of |b|.
290 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
291
292 // bn_less_than_words returns one if |a| < |b| and zero otherwise, where |a|
293 // and |b| both are |len| words long. It runs in constant time.
294 int bn_less_than_words(const BN_ULONG *a, const BN_ULONG *b, size_t len);
295
296 // bn_in_range_words returns one if |min_inclusive| <= |a| < |max_exclusive|,
297 // where |a| and |max_exclusive| both are |len| words long. This function leaks
298 // which of [0, min_inclusive), [min_inclusive, max_exclusive), and
299 // [max_exclusive, 2^(BN_BITS2*len)) contains |a|, but otherwise the value of
300 // |a| is secret.
301 int bn_in_range_words(const BN_ULONG *a, BN_ULONG min_inclusive,
302 const BN_ULONG *max_exclusive, size_t len);
303
304 // bn_rand_range_words sets |out| to a uniformly distributed random number from
305 // |min_inclusive| to |max_exclusive|. Both |out| and |max_exclusive| are |len|
306 // words long.
307 //
308 // This function runs in time independent of the result, but |min_inclusive| and
309 // |max_exclusive| are public data. (Information about the range is unavoidably
310 // leaked by how many iterations it took to select a number.)
311 int bn_rand_range_words(BN_ULONG *out, BN_ULONG min_inclusive,
312 const BN_ULONG *max_exclusive, size_t len,
313 const uint8_t additional_data[32]);
314
315 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
316 const BN_ULONG *np, const BN_ULONG *n0, int num);
317
318 uint64_t bn_mont_n0(const BIGNUM *n);
319 int bn_mod_exp_base_2_vartime(BIGNUM *r, unsigned p, const BIGNUM *n);
320
321 #if defined(OPENSSL_X86_64) && defined(_MSC_VER)
322 #define BN_UMULT_LOHI(low, high, a, b) ((low) = _umul128((a), (b), &(high)))
323 #endif
324
325 #if !defined(BN_ULLONG) && !defined(BN_UMULT_LOHI)
326 #error "Either BN_ULLONG or BN_UMULT_LOHI must be defined on every platform."
327 #endif
328
329 // bn_mod_inverse_prime sets |out| to the modular inverse of |a| modulo |p|,
330 // computed with Fermat's Little Theorem. It returns one on success and zero on
331 // error. If |mont_p| is NULL, one will be computed temporarily.
332 int bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
333 BN_CTX *ctx, const BN_MONT_CTX *mont_p);
334
335 // bn_mod_inverse_secret_prime behaves like |bn_mod_inverse_prime| but uses
336 // |BN_mod_exp_mont_consttime| instead of |BN_mod_exp_mont| in hopes of
337 // protecting the exponent.
338 int bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
339 BN_CTX *ctx, const BN_MONT_CTX *mont_p);
340
341 // bn_jacobi returns the Jacobi symbol of |a| and |b| (which is -1, 0 or 1), or
342 // -2 on error.
343 int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
344
345 // bn_is_bit_set_words returns one if bit |bit| is set in |a| and zero
346 // otherwise.
347 int bn_is_bit_set_words(const BN_ULONG *a, size_t num, unsigned bit);
348
349 // bn_one_to_montgomery sets |r| to one in Montgomery form. It returns one on
350 // success and zero on error. This function treats the bit width of the modulus
351 // as public.
352 int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx);
353
354 // bn_less_than_montgomery_R returns one if |bn| is less than the Montgomery R
355 // value for |mont| and zero otherwise.
356 int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont);
357
358
359 // Low-level operations for small numbers.
360 //
361 // The following functions implement algorithms suitable for use with scalars
362 // and field elements in elliptic curves. They rely on the number being small
363 // both to stack-allocate various temporaries and because they do not implement
364 // optimizations useful for the larger values used in RSA.
365
366 // BN_SMALL_MAX_WORDS is the largest size input these functions handle. This
367 // limit allows temporaries to be more easily stack-allocated. This limit is set
368 // to accommodate P-521.
369 #if defined(OPENSSL_32_BIT)
370 #define BN_SMALL_MAX_WORDS 17
371 #else
372 #define BN_SMALL_MAX_WORDS 9
373 #endif
374
375 // bn_mul_small sets |r| to |a|*|b|. |num_r| must be |num_a| + |num_b|. |r| may
376 // not alias with |a| or |b|. This function returns one on success and zero if
377 // lengths are inconsistent.
378 int bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a,
379 const BN_ULONG *b, size_t num_b);
380
381 // bn_sqr_small sets |r| to |a|^2. |num_a| must be at most |BN_SMALL_MAX_WORDS|.
382 // |num_r| must be |num_a|*2. |r| and |a| may not alias. This function returns
383 // one on success and zero on programmer error.
384 int bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a);
385
386 // In the following functions, the modulus must be at most |BN_SMALL_MAX_WORDS|
387 // words long.
388
389 // bn_to_montgomery_small sets |r| to |a| translated to the Montgomery domain.
390 // |num_a| and |num_r| must be the length of the modulus, which is
391 // |mont->N.top|. |a| must be fully reduced. This function returns one on
392 // success and zero if lengths are inconsistent. |r| and |a| may alias.
393 int bn_to_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
394 size_t num_a, const BN_MONT_CTX *mont);
395
396 // bn_from_montgomery_small sets |r| to |a| translated out of the Montgomery
397 // domain. |num_r| must be the length of the modulus, which is |mont->N.top|.
398 // |a| must be at most |mont->N.top| * R and |num_a| must be at most 2 *
399 // |mont->N.top|. This function returns one on success and zero if lengths are
400 // inconsistent. |r| and |a| may alias.
401 int bn_from_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
402 size_t num_a, const BN_MONT_CTX *mont);
403
404 // bn_one_to_montgomery_small sets |r| to one in Montgomery form. It returns one
405 // on success and zero on error. |num_r| must be the length of the modulus,
406 // which is |mont->N.top|. This function treats the bit width of the modulus as
407 // public.
408 int bn_one_to_montgomery_small(BN_ULONG *r, size_t num_r,
409 const BN_MONT_CTX *mont);
410
411 // bn_mod_mul_montgomery_small sets |r| to |a| * |b| mod |mont->N|. Both inputs
412 // and outputs are in the Montgomery domain. |num_r| must be the length of the
413 // modulus, which is |mont->N.top|. This function returns one on success and
414 // zero on internal error or inconsistent lengths. Any two of |r|, |a|, and |b|
415 // may alias.
416 //
417 // This function requires |a| * |b| < N * R, where N is the modulus and R is the
418 // Montgomery divisor, 2^(N.top * BN_BITS2). This should generally be satisfied
419 // by ensuring |a| and |b| are fully reduced, however ECDSA has one computation
420 // which requires the more general bound.
421 int bn_mod_mul_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
422 size_t num_a, const BN_ULONG *b, size_t num_b,
423 const BN_MONT_CTX *mont);
424
425 // bn_mod_exp_mont_small sets |r| to |a|^|p| mod |mont->N|. It returns one on
426 // success and zero on programmer or internal error. Both inputs and outputs are
427 // in the Montgomery domain. |num_r| and |num_a| must be |mont->N.top|, which
428 // must be at most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced. This
429 // function runs in time independent of |a|, but |p| and |mont->N| are public
430 // values.
431 //
432 // Note this function differs from |BN_mod_exp_mont| which uses Montgomery
433 // reduction but takes input and output outside the Montgomery domain. Combine
434 // this function with |bn_from_montgomery_small| and |bn_to_montgomery_small|
435 // if necessary.
436 int bn_mod_exp_mont_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
437 size_t num_a, const BN_ULONG *p, size_t num_p,
438 const BN_MONT_CTX *mont);
439
440 // bn_mod_inverse_prime_mont_small sets |r| to |a|^-1 mod |mont->N|. |mont->N|
441 // must be a prime. |num_r| and |num_a| must be |mont->N.top|, which must be at
442 // most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced. This function runs in
443 // time independent of |a|, but |mont->N| is a public value.
444 int bn_mod_inverse_prime_mont_small(BN_ULONG *r, size_t num_r,
445 const BN_ULONG *a, size_t num_a,
446 const BN_MONT_CTX *mont);
447
448
449 #if defined(__cplusplus)
450 } // extern C
451 #endif
452
453 #endif // OPENSSL_HEADER_BN_INTERNAL_H
454