1 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
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.
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).
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.
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
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)"
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
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.]
57 /* ====================================================================
58 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
60 * Redistribution and use in source and binary forms, with or without
61 * modification, are permitted provided that the following conditions
64 * 1. Redistributions of source code must retain the above copyright
65 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
86 * 6. Redistributions of any form whatsoever must retain the following
88 * "This product includes software developed by the OpenSSL Project
89 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
110 /* ====================================================================
111 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
113 * Portions of the attached software ("Contribution") are developed by
114 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
116 * The Contribution is licensed pursuant to the Eric Young open source
117 * license provided above.
119 * The binary polynomial arithmetic software is originally written by
120 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
123 #ifndef OPENSSL_HEADER_BN_INTERNAL_H
124 #define OPENSSL_HEADER_BN_INTERNAL_H
126 #include <openssl/base.h>
128 #if defined(OPENSSL_X86_64) && defined(_MSC_VER)
129 OPENSSL_MSVC_PRAGMA(warning(push, 3))
131 OPENSSL_MSVC_PRAGMA(warning(pop))
132 #pragma intrinsic(__umulh, _umul128)
135 #include "../../internal.h"
137 #if defined(__cplusplus)
141 #if defined(OPENSSL_64_BIT)
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
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))
163 #elif defined(OPENSSL_32_BIT)
165 #define BN_ULLONG uint64_t
166 #define BN_CAN_DIVIDE_ULLONG
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)
182 #define TOBN(hi, lo) (lo), (hi)
185 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
189 #define STATIC_BIGNUM(x) \
191 (BN_ULONG *)(x), sizeof(x) / sizeof(BN_ULONG), \
192 sizeof(x) / sizeof(BN_ULONG), 0, BN_FLG_STATIC_DATA \
195 #if defined(BN_ULLONG)
196 #define Lw(t) ((BN_ULONG)(t))
197 #define Hw(t) ((BN_ULONG)((t) >> BN_BITS2))
200 // bn_minimal_width returns the minimal value of |bn->top| which fits the
202 int bn_minimal_width(const BIGNUM *bn);
204 // bn_set_minimal_width sets |bn->width| to |bn_minimal_width(bn)|. If |bn| is
205 // zero, |bn->neg| is set to zero.
206 void bn_set_minimal_width(BIGNUM *bn);
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
211 int bn_wexpand(BIGNUM *bn, size_t words);
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);
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 OPENSSL_EXPORT int bn_resize_words(BIGNUM *bn, size_t words);
221 // bn_select_words sets |r| to |a| if |mask| is all ones or |b| if |mask| is
223 void bn_select_words(BN_ULONG *r, BN_ULONG mask, const BN_ULONG *a,
224 const BN_ULONG *b, size_t num);
226 // bn_set_words sets |bn| to the value encoded in the |num| words in |words|,
227 // least significant word first.
228 int bn_set_words(BIGNUM *bn, const BN_ULONG *words, size_t num);
230 // bn_fits_in_words returns one if |bn| may be represented in |num| words, plus
231 // a sign bit, and zero otherwise.
232 int bn_fits_in_words(const BIGNUM *bn, size_t num);
234 // bn_copy_words copies the value of |bn| to |out| and returns one if the value
235 // is representable in |num| words. Otherwise, it returns zero.
236 int bn_copy_words(BN_ULONG *out, size_t num, const BIGNUM *bn);
238 // bn_mul_add_words multiples |ap| by |w|, adds the result to |rp|, and places
239 // the result in |rp|. |ap| and |rp| must both be |num| words long. It returns
240 // the carry word of the operation. |ap| and |rp| may be equal but otherwise may
242 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num,
245 // bn_mul_words multiples |ap| by |w| and places the result in |rp|. |ap| and
246 // |rp| must both be |num| words long. It returns the carry word of the
247 // operation. |ap| and |rp| may be equal but otherwise may not alias.
248 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num, BN_ULONG w);
250 // bn_sqr_words sets |rp[2*i]| and |rp[2*i+1]| to |ap[i]|'s square, for all |i|
251 // up to |num|. |ap| is an array of |num| words and |rp| an array of |2*num|
252 // words. |ap| and |rp| may not alias.
254 // This gives the contribution of the |ap[i]*ap[i]| terms when squaring |ap|.
255 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num);
257 // bn_add_words adds |ap| to |bp| and places the result in |rp|, each of which
258 // are |num| words long. It returns the carry bit, which is one if the operation
259 // overflowed and zero otherwise. Any pair of |ap|, |bp|, and |rp| may be equal
260 // to each other but otherwise may not alias.
261 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
264 // bn_sub_words subtracts |bp| from |ap| and places the result in |rp|. It
265 // returns the borrow bit, which is one if the computation underflowed and zero
266 // otherwise. Any pair of |ap|, |bp|, and |rp| may be equal to each other but
267 // otherwise may not alias.
268 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
271 // bn_mul_comba4 sets |r| to the product of |a| and |b|.
272 void bn_mul_comba4(BN_ULONG r[8], const BN_ULONG a[4], const BN_ULONG b[4]);
274 // bn_mul_comba8 sets |r| to the product of |a| and |b|.
275 void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]);
277 // bn_sqr_comba8 sets |r| to |a|^2.
278 void bn_sqr_comba8(BN_ULONG r[16], const BN_ULONG a[4]);
280 // bn_sqr_comba4 sets |r| to |a|^2.
281 void bn_sqr_comba4(BN_ULONG r[8], const BN_ULONG a[4]);
283 // bn_less_than_words returns one if |a| < |b| and zero otherwise, where |a|
284 // and |b| both are |len| words long. It runs in constant time.
285 int bn_less_than_words(const BN_ULONG *a, const BN_ULONG *b, size_t len);
287 // bn_in_range_words returns one if |min_inclusive| <= |a| < |max_exclusive|,
288 // where |a| and |max_exclusive| both are |len| words long. |a| and
289 // |max_exclusive| are treated as secret.
290 int bn_in_range_words(const BN_ULONG *a, BN_ULONG min_inclusive,
291 const BN_ULONG *max_exclusive, size_t len);
293 // bn_rand_range_words sets |out| to a uniformly distributed random number from
294 // |min_inclusive| to |max_exclusive|. Both |out| and |max_exclusive| are |len|
297 // This function runs in time independent of the result, but |min_inclusive| and
298 // |max_exclusive| are public data. (Information about the range is unavoidably
299 // leaked by how many iterations it took to select a number.)
300 int bn_rand_range_words(BN_ULONG *out, BN_ULONG min_inclusive,
301 const BN_ULONG *max_exclusive, size_t len,
302 const uint8_t additional_data[32]);
304 // bn_range_secret_range behaves like |BN_rand_range_ex|, but treats
305 // |max_exclusive| as secret. Because of this constraint, the distribution of
306 // values returned is more complex.
308 // Rather than repeatedly generating values until one is in range, which would
309 // leak information, it generates one value. If the value is in range, it sets
310 // |*out_is_uniform| to one. Otherwise, it sets |*out_is_uniform| to zero,
311 // fixing up the value to force it in range.
313 // The subset of calls to |bn_rand_secret_range| which set |*out_is_uniform| to
314 // one are uniformly distributed in the target range. Calls overall are not.
315 // This function is intended for use in situations where the extra values are
316 // still usable and where the number of iterations needed to reach the target
317 // number of uniform outputs may be blinded for negligible probabilities of
320 // Although this function treats |max_exclusive| as secret, it treats the number
321 // of bits in |max_exclusive| as public.
322 int bn_rand_secret_range(BIGNUM *r, int *out_is_uniform, BN_ULONG min_inclusive,
323 const BIGNUM *max_exclusive);
325 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
326 const BN_ULONG *np, const BN_ULONG *n0, int num);
328 uint64_t bn_mont_n0(const BIGNUM *n);
330 // bn_mod_exp_base_2_consttime calculates r = 2**p (mod n). |p| must be larger
331 // than log_2(n); i.e. 2**p must be larger than |n|. |n| must be positive and
332 // odd. |p| and the bit width of |n| are assumed public, but |n| is otherwise
333 // treated as secret.
334 int bn_mod_exp_base_2_consttime(BIGNUM *r, unsigned p, const BIGNUM *n,
337 #if defined(OPENSSL_X86_64) && defined(_MSC_VER)
338 #define BN_UMULT_LOHI(low, high, a, b) ((low) = _umul128((a), (b), &(high)))
341 #if !defined(BN_ULLONG) && !defined(BN_UMULT_LOHI)
342 #error "Either BN_ULLONG or BN_UMULT_LOHI must be defined on every platform."
345 // bn_jacobi returns the Jacobi symbol of |a| and |b| (which is -1, 0 or 1), or
347 int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
349 // bn_is_bit_set_words returns one if bit |bit| is set in |a| and zero
351 int bn_is_bit_set_words(const BN_ULONG *a, size_t num, unsigned bit);
353 // bn_one_to_montgomery sets |r| to one in Montgomery form. It returns one on
354 // success and zero on error. This function treats the bit width of the modulus
356 int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx);
358 // bn_less_than_montgomery_R returns one if |bn| is less than the Montgomery R
359 // value for |mont| and zero otherwise.
360 int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont);
362 // bn_mod_u16_consttime returns |bn| mod |d|, ignoring |bn|'s sign bit. It runs
363 // in time independent of the value of |bn|, but it treats |d| as public.
364 OPENSSL_EXPORT uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d);
366 // bn_odd_number_is_obviously_composite returns one if |bn| is divisible by one
367 // of the first several odd primes and zero otherwise.
368 int bn_odd_number_is_obviously_composite(const BIGNUM *bn);
370 // bn_rshift1_words sets |r| to |a| >> 1, where both arrays are |num| bits wide.
371 void bn_rshift1_words(BN_ULONG *r, const BN_ULONG *a, size_t num);
373 // bn_rshift_secret_shift behaves like |BN_rshift| but runs in time independent
374 // of both |a| and |n|.
375 OPENSSL_EXPORT int bn_rshift_secret_shift(BIGNUM *r, const BIGNUM *a,
376 unsigned n, BN_CTX *ctx);
379 // Constant-time non-modular arithmetic.
381 // The following functions implement non-modular arithmetic in constant-time
382 // and pessimally set |r->width| to the largest possible word size.
384 // Note this means that, e.g., repeatedly multiplying by one will cause widths
385 // to increase without bound. The corresponding public API functions minimize
386 // their outputs to avoid regressing calculator consumers.
388 // bn_uadd_consttime behaves like |BN_uadd|, but it pessimally sets
389 // |r->width| = |a->width| + |b->width| + 1.
390 int bn_uadd_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
392 // bn_usub_consttime behaves like |BN_usub|, but it pessimally sets
393 // |r->width| = |a->width|.
394 int bn_usub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
396 // bn_abs_sub_consttime sets |r| to the absolute value of |a| - |b|, treating
397 // both inputs as secret. It returns one on success and zero on error.
398 OPENSSL_EXPORT int bn_abs_sub_consttime(BIGNUM *r, const BIGNUM *a,
399 const BIGNUM *b, BN_CTX *ctx);
401 // bn_mul_consttime behaves like |BN_mul|, but it rejects negative inputs and
402 // pessimally sets |r->width| to |a->width| + |b->width|, to avoid leaking
403 // information about |a| and |b|.
404 int bn_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
406 // bn_sqrt_consttime behaves like |BN_sqrt|, but it pessimally sets |r->width|
407 // to 2*|a->width|, to avoid leaking information about |a| and |b|.
408 int bn_sqr_consttime(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
410 // bn_div_consttime behaves like |BN_div|, but it rejects negative inputs and
411 // treats both inputs, including their magnitudes, as secret. It is, as a
412 // result, much slower than |BN_div| and should only be used for rare operations
413 // where Montgomery reduction is not available.
415 // Note that |quotient->width| will be set pessimally to |numerator->width|.
416 OPENSSL_EXPORT int bn_div_consttime(BIGNUM *quotient, BIGNUM *remainder,
417 const BIGNUM *numerator,
418 const BIGNUM *divisor, BN_CTX *ctx);
420 // bn_is_relatively_prime checks whether GCD(|x|, |y|) is one. On success, it
421 // returns one and sets |*out_relatively_prime| to one if the GCD was one and
422 // zero otherwise. On error, it returns zero.
423 OPENSSL_EXPORT int bn_is_relatively_prime(int *out_relatively_prime,
424 const BIGNUM *x, const BIGNUM *y,
427 // bn_lcm_consttime sets |r| to LCM(|a|, |b|). It returns one and success and
428 // zero on error. |a| and |b| are both treated as secret.
429 OPENSSL_EXPORT int bn_lcm_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
433 // Constant-time modular arithmetic.
435 // The following functions implement basic constant-time modular arithmetic.
437 // bn_mod_add_consttime acts like |BN_mod_add_quick| but takes a |BN_CTX|.
438 int bn_mod_add_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
439 const BIGNUM *m, BN_CTX *ctx);
441 // bn_mod_sub_consttime acts like |BN_mod_sub_quick| but takes a |BN_CTX|.
442 int bn_mod_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
443 const BIGNUM *m, BN_CTX *ctx);
445 // bn_mod_lshift1_consttime acts like |BN_mod_lshift1_quick| but takes a
447 int bn_mod_lshift1_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
450 // bn_mod_lshift_consttime acts like |BN_mod_lshift_quick| but takes a |BN_CTX|.
451 int bn_mod_lshift_consttime(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
454 // bn_mod_inverse_consttime sets |r| to |a|^-1, mod |n|. |a| must be non-
455 // negative and less than |n|. It returns one on success and zero on error. On
456 // failure, if the failure was caused by |a| having no inverse mod |n| then
457 // |*out_no_inverse| will be set to one; otherwise it will be set to zero.
459 // This function treats both |a| and |n| as secret, provided they are both non-
460 // zero and the inverse exists. It should only be used for even moduli where
461 // none of the less general implementations are applicable.
462 OPENSSL_EXPORT int bn_mod_inverse_consttime(BIGNUM *r, int *out_no_inverse,
463 const BIGNUM *a, const BIGNUM *n,
466 // bn_mod_inverse_prime sets |out| to the modular inverse of |a| modulo |p|,
467 // computed with Fermat's Little Theorem. It returns one on success and zero on
468 // error. If |mont_p| is NULL, one will be computed temporarily.
469 int bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
470 BN_CTX *ctx, const BN_MONT_CTX *mont_p);
472 // bn_mod_inverse_secret_prime behaves like |bn_mod_inverse_prime| but uses
473 // |BN_mod_exp_mont_consttime| instead of |BN_mod_exp_mont| in hopes of
474 // protecting the exponent.
475 int bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
476 BN_CTX *ctx, const BN_MONT_CTX *mont_p);
479 // Low-level operations for small numbers.
481 // The following functions implement algorithms suitable for use with scalars
482 // and field elements in elliptic curves. They rely on the number being small
483 // both to stack-allocate various temporaries and because they do not implement
484 // optimizations useful for the larger values used in RSA.
486 // BN_SMALL_MAX_WORDS is the largest size input these functions handle. This
487 // limit allows temporaries to be more easily stack-allocated. This limit is set
488 // to accommodate P-521.
489 #if defined(OPENSSL_32_BIT)
490 #define BN_SMALL_MAX_WORDS 17
492 #define BN_SMALL_MAX_WORDS 9
495 // bn_mul_small sets |r| to |a|*|b|. |num_r| must be |num_a| + |num_b|. |r| may
496 // not alias with |a| or |b|. This function returns one on success and zero if
497 // lengths are inconsistent.
498 int bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a,
499 const BN_ULONG *b, size_t num_b);
501 // bn_sqr_small sets |r| to |a|^2. |num_a| must be at most |BN_SMALL_MAX_WORDS|.
502 // |num_r| must be |num_a|*2. |r| and |a| may not alias. This function returns
503 // one on success and zero on programmer error.
504 int bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a);
506 // In the following functions, the modulus must be at most |BN_SMALL_MAX_WORDS|
509 // bn_to_montgomery_small sets |r| to |a| translated to the Montgomery domain.
510 // |num_a| and |num_r| must be the length of the modulus, which is
511 // |mont->N.top|. |a| must be fully reduced. This function returns one on
512 // success and zero if lengths are inconsistent. |r| and |a| may alias.
513 int bn_to_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
514 size_t num_a, const BN_MONT_CTX *mont);
516 // bn_from_montgomery_small sets |r| to |a| translated out of the Montgomery
517 // domain. |num_r| must be the length of the modulus, which is |mont->N.top|.
518 // |a| must be at most |mont->N.top| * R and |num_a| must be at most 2 *
519 // |mont->N.top|. This function returns one on success and zero if lengths are
520 // inconsistent. |r| and |a| may alias.
521 int bn_from_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
522 size_t num_a, const BN_MONT_CTX *mont);
524 // bn_one_to_montgomery_small sets |r| to one in Montgomery form. It returns one
525 // on success and zero on error. |num_r| must be the length of the modulus,
526 // which is |mont->N.top|. This function treats the bit width of the modulus as
528 int bn_one_to_montgomery_small(BN_ULONG *r, size_t num_r,
529 const BN_MONT_CTX *mont);
531 // bn_mod_mul_montgomery_small sets |r| to |a| * |b| mod |mont->N|. Both inputs
532 // and outputs are in the Montgomery domain. |num_r| must be the length of the
533 // modulus, which is |mont->N.top|. This function returns one on success and
534 // zero on internal error or inconsistent lengths. Any two of |r|, |a|, and |b|
537 // This function requires |a| * |b| < N * R, where N is the modulus and R is the
538 // Montgomery divisor, 2^(N.top * BN_BITS2). This should generally be satisfied
539 // by ensuring |a| and |b| are fully reduced, however ECDSA has one computation
540 // which requires the more general bound.
541 int bn_mod_mul_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
542 size_t num_a, const BN_ULONG *b, size_t num_b,
543 const BN_MONT_CTX *mont);
545 // bn_mod_exp_mont_small sets |r| to |a|^|p| mod |mont->N|. It returns one on
546 // success and zero on programmer or internal error. Both inputs and outputs are
547 // in the Montgomery domain. |num_r| and |num_a| must be |mont->N.top|, which
548 // must be at most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced. This
549 // function runs in time independent of |a|, but |p| and |mont->N| are public
552 // Note this function differs from |BN_mod_exp_mont| which uses Montgomery
553 // reduction but takes input and output outside the Montgomery domain. Combine
554 // this function with |bn_from_montgomery_small| and |bn_to_montgomery_small|
556 int bn_mod_exp_mont_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
557 size_t num_a, const BN_ULONG *p, size_t num_p,
558 const BN_MONT_CTX *mont);
560 // bn_mod_inverse_prime_mont_small sets |r| to |a|^-1 mod |mont->N|. |mont->N|
561 // must be a prime. |num_r| and |num_a| must be |mont->N.top|, which must be at
562 // most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced. This function runs in
563 // time independent of |a|, but |mont->N| is a public value.
564 int bn_mod_inverse_prime_mont_small(BN_ULONG *r, size_t num_r,
565 const BN_ULONG *a, size_t num_a,
566 const BN_MONT_CTX *mont);
569 #if defined(__cplusplus)
573 #endif // OPENSSL_HEADER_BN_INTERNAL_H