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)
129OPENSSL_MSVC_PRAGMA(warning(push, 3))
130#include <intrin.h>
131OPENSSL_MSVC_PRAGMA(warning(pop))
132#pragma intrinsic(__umulh, _umul128)
133#endif
134
135#include "../../internal.h"
136
137#if defined(__cplusplus)
138extern "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#if !defined(OPENSSL_NO_ASM) && (defined(__GNUC__) || defined(__clang__))
189#define BN_CAN_USE_INLINE_ASM
190#endif
191
192// |BN_mod_exp_mont_consttime| is based on the assumption that the L1 data
193// cache line width of the target processor is at least the following value.
194#define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH 64
195
196// The number of |BN_ULONG|s needed for the |BN_mod_exp_mont_consttime| stack-
197// allocated storage buffer. The buffer is just the right size for the RSAZ
198// and is about ~1KB larger than what's necessary (4480 bytes) for 1024-bit
199// inputs.
200#define MOD_EXP_CTIME_STORAGE_LEN \
201 (((320u * 3u) + (32u * 9u * 16u)) / sizeof(BN_ULONG))
202
203#define STATIC_BIGNUM(x) \
204 { \
205 (BN_ULONG *)(x), sizeof(x) / sizeof(BN_ULONG), \
206 sizeof(x) / sizeof(BN_ULONG), 0, BN_FLG_STATIC_DATA \
207 }
208
209#if defined(BN_ULLONG)
210#define Lw(t) ((BN_ULONG)(t))
211#define Hw(t) ((BN_ULONG)((t) >> BN_BITS2))
212#endif
213
214// bn_minimal_width returns the minimal value of |bn->top| which fits the
215// value of |bn|.
216int bn_minimal_width(const BIGNUM *bn);
217
218// bn_set_minimal_width sets |bn->width| to |bn_minimal_width(bn)|. If |bn| is
219// zero, |bn->neg| is set to zero.
220void bn_set_minimal_width(BIGNUM *bn);
221
222// bn_wexpand ensures that |bn| has at least |words| works of space without
223// altering its value. It returns one on success or zero on allocation
224// failure.
225int bn_wexpand(BIGNUM *bn, size_t words);
226
227// bn_expand acts the same as |bn_wexpand|, but takes a number of bits rather
228// than a number of words.
229int bn_expand(BIGNUM *bn, size_t bits);
230
231// bn_resize_words adjusts |bn->top| to be |words|. It returns one on success
232// and zero on allocation error or if |bn|'s value is too large.
233OPENSSL_EXPORT int bn_resize_words(BIGNUM *bn, size_t words);
234
235// bn_select_words sets |r| to |a| if |mask| is all ones or |b| if |mask| is
236// all zeros.
237void bn_select_words(BN_ULONG *r, BN_ULONG mask, const BN_ULONG *a,
238 const BN_ULONG *b, size_t num);
239
240// bn_set_words sets |bn| to the value encoded in the |num| words in |words|,
241// least significant word first.
242int bn_set_words(BIGNUM *bn, const BN_ULONG *words, size_t num);
243
244// bn_fits_in_words returns one if |bn| may be represented in |num| words, plus
245// a sign bit, and zero otherwise.
246int bn_fits_in_words(const BIGNUM *bn, size_t num);
247
248// bn_copy_words copies the value of |bn| to |out| and returns one if the value
249// is representable in |num| words. Otherwise, it returns zero.
250int bn_copy_words(BN_ULONG *out, size_t num, const BIGNUM *bn);
251
252// bn_mul_add_words multiples |ap| by |w|, adds the result to |rp|, and places
253// the result in |rp|. |ap| and |rp| must both be |num| words long. It returns
254// the carry word of the operation. |ap| and |rp| may be equal but otherwise may
255// not alias.
256BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num,
257 BN_ULONG w);
258
259// bn_mul_words multiples |ap| by |w| and places the result in |rp|. |ap| and
260// |rp| must both be |num| words long. It returns the carry word of the
261// operation. |ap| and |rp| may be equal but otherwise may not alias.
262BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num, BN_ULONG w);
263
264// bn_sqr_words sets |rp[2*i]| and |rp[2*i+1]| to |ap[i]|'s square, for all |i|
265// up to |num|. |ap| is an array of |num| words and |rp| an array of |2*num|
266// words. |ap| and |rp| may not alias.
267//
268// This gives the contribution of the |ap[i]*ap[i]| terms when squaring |ap|.
269void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num);
270
271// bn_add_words adds |ap| to |bp| and places the result in |rp|, each of which
272// are |num| words long. It returns the carry bit, which is one if the operation
273// overflowed and zero otherwise. Any pair of |ap|, |bp|, and |rp| may be equal
274// to each other but otherwise may not alias.
275BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
276 size_t num);
277
278// bn_sub_words subtracts |bp| from |ap| and places the result in |rp|. It
279// returns the borrow bit, which is one if the computation underflowed and zero
280// otherwise. Any pair of |ap|, |bp|, and |rp| may be equal to each other but
281// otherwise may not alias.
282BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
283 size_t num);
284
285// bn_mul_comba4 sets |r| to the product of |a| and |b|.
286void bn_mul_comba4(BN_ULONG r[8], const BN_ULONG a[4], const BN_ULONG b[4]);
287
288// bn_mul_comba8 sets |r| to the product of |a| and |b|.
289void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]);
290
291// bn_sqr_comba8 sets |r| to |a|^2.
292void bn_sqr_comba8(BN_ULONG r[16], const BN_ULONG a[4]);
293
294// bn_sqr_comba4 sets |r| to |a|^2.
295void bn_sqr_comba4(BN_ULONG r[8], const BN_ULONG a[4]);
296
297// bn_less_than_words returns one if |a| < |b| and zero otherwise, where |a|
298// and |b| both are |len| words long. It runs in constant time.
299int bn_less_than_words(const BN_ULONG *a, const BN_ULONG *b, size_t len);
300
301// bn_in_range_words returns one if |min_inclusive| <= |a| < |max_exclusive|,
302// where |a| and |max_exclusive| both are |len| words long. |a| and
303// |max_exclusive| are treated as secret.
304int bn_in_range_words(const BN_ULONG *a, BN_ULONG min_inclusive,
305 const BN_ULONG *max_exclusive, size_t len);
306
307// bn_rand_range_words sets |out| to a uniformly distributed random number from
308// |min_inclusive| to |max_exclusive|. Both |out| and |max_exclusive| are |len|
309// words long.
310//
311// This function runs in time independent of the result, but |min_inclusive| and
312// |max_exclusive| are public data. (Information about the range is unavoidably
313// leaked by how many iterations it took to select a number.)
314int bn_rand_range_words(BN_ULONG *out, BN_ULONG min_inclusive,
315 const BN_ULONG *max_exclusive, size_t len,
316 const uint8_t additional_data[32]);
317
318// bn_range_secret_range behaves like |BN_rand_range_ex|, but treats
319// |max_exclusive| as secret. Because of this constraint, the distribution of
320// values returned is more complex.
321//
322// Rather than repeatedly generating values until one is in range, which would
323// leak information, it generates one value. If the value is in range, it sets
324// |*out_is_uniform| to one. Otherwise, it sets |*out_is_uniform| to zero,
325// fixing up the value to force it in range.
326//
327// The subset of calls to |bn_rand_secret_range| which set |*out_is_uniform| to
328// one are uniformly distributed in the target range. Calls overall are not.
329// This function is intended for use in situations where the extra values are
330// still usable and where the number of iterations needed to reach the target
331// number of uniform outputs may be blinded for negligible probabilities of
332// timing leaks.
333//
334// Although this function treats |max_exclusive| as secret, it treats the number
335// of bits in |max_exclusive| as public.
336int bn_rand_secret_range(BIGNUM *r, int *out_is_uniform, BN_ULONG min_inclusive,
337 const BIGNUM *max_exclusive);
338
339#if !defined(OPENSSL_NO_ASM) && \
340 (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \
341 defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64))
342#define OPENSSL_BN_ASM_MONT
343// bn_mul_mont writes |ap| * |bp| mod |np| to |rp|, each |num| words
344// long. Inputs and outputs are in Montgomery form. |n0| is a pointer to the
345// corresponding field in |BN_MONT_CTX|. It returns one if |bn_mul_mont| handles
346// inputs of this size and zero otherwise.
347//
348// TODO(davidben): The x86_64 implementation expects a 32-bit input and masks
349// off upper bits. The aarch64 implementation expects a 64-bit input and does
350// not. |size_t| is the safer option but not strictly correct for x86_64. But
351// this function implicitly already has a bound on the size of |num| because it
352// internally creates |num|-sized stack allocation.
353//
354// See also discussion in |ToWord| in abi_test.h for notes on smaller-than-word
355// inputs.
356int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
357 const BN_ULONG *np, const BN_ULONG *n0, size_t num);
358#endif
359
360#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64)
361#define OPENSSL_BN_ASM_MONT5
362
363// bn_mul_mont_gather5 multiples loads index |power| of |table|, multiplies it
364// by |ap| modulo |np|, and stores the result in |rp|. The values are |num|
365// words long and represented in Montgomery form. |n0| is a pointer to the
366// corresponding field in |BN_MONT_CTX|.
367void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
368 const BN_ULONG *table, const BN_ULONG *np,
369 const BN_ULONG *n0, int num, int power);
370
371// bn_scatter5 stores |inp| to index |power| of |table|. |inp| and each entry of
372// |table| are |num| words long. |power| must be less than 32. |table| must be
373// 32*|num| words long.
374void bn_scatter5(const BN_ULONG *inp, size_t num, BN_ULONG *table,
375 size_t power);
376
377// bn_gather5 loads index |power| of |table| and stores it in |out|. |out| and
378// each entry of |table| are |num| words long. |power| must be less than 32.
379void bn_gather5(BN_ULONG *out, size_t num, BN_ULONG *table, size_t power);
380
381// bn_power5 squares |ap| five times and multiplies it by the value stored at
382// index |power| of |table|, modulo |np|. It stores the result in |rp|. The
383// values are |num| words long and represented in Montgomery form. |n0| is a
384// pointer to the corresponding field in |BN_MONT_CTX|. |num| must be divisible
385// by 8.
386void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *table,
387 const BN_ULONG *np, const BN_ULONG *n0, int num, int power);
388
389// bn_from_montgomery converts |ap| from Montgomery form modulo |np| and writes
390// the result in |rp|, each of which is |num| words long. It returns one on
391// success and zero if it cannot handle inputs of length |num|. |n0| is a
392// pointer to the corresponding field in |BN_MONT_CTX|.
393int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
394 const BN_ULONG *not_used, const BN_ULONG *np,
395 const BN_ULONG *n0, int num);
396#endif // !OPENSSL_NO_ASM && OPENSSL_X86_64
397
398uint64_t bn_mont_n0(const BIGNUM *n);
399
400// bn_mod_exp_base_2_consttime calculates r = 2**p (mod n). |p| must be larger
401// than log_2(n); i.e. 2**p must be larger than |n|. |n| must be positive and
402// odd. |p| and the bit width of |n| are assumed public, but |n| is otherwise
403// treated as secret.
404int bn_mod_exp_base_2_consttime(BIGNUM *r, unsigned p, const BIGNUM *n,
405 BN_CTX *ctx);
406
407#if defined(OPENSSL_X86_64) && defined(_MSC_VER)
408#define BN_UMULT_LOHI(low, high, a, b) ((low) = _umul128((a), (b), &(high)))
409#endif
410
411#if !defined(BN_ULLONG) && !defined(BN_UMULT_LOHI)
412#error "Either BN_ULLONG or BN_UMULT_LOHI must be defined on every platform."
413#endif
414
415// bn_jacobi returns the Jacobi symbol of |a| and |b| (which is -1, 0 or 1), or
416// -2 on error.
417int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
418
419// bn_is_bit_set_words returns one if bit |bit| is set in |a| and zero
420// otherwise.
421int bn_is_bit_set_words(const BN_ULONG *a, size_t num, unsigned bit);
422
423// bn_one_to_montgomery sets |r| to one in Montgomery form. It returns one on
424// success and zero on error. This function treats the bit width of the modulus
425// as public.
426int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx);
427
428// bn_less_than_montgomery_R returns one if |bn| is less than the Montgomery R
429// value for |mont| and zero otherwise.
430int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont);
431
432// bn_mod_u16_consttime returns |bn| mod |d|, ignoring |bn|'s sign bit. It runs
433// in time independent of the value of |bn|, but it treats |d| as public.
434OPENSSL_EXPORT uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d);
435
436// bn_odd_number_is_obviously_composite returns one if |bn| is divisible by one
437// of the first several odd primes and zero otherwise.
438int bn_odd_number_is_obviously_composite(const BIGNUM *bn);
439
440// bn_rshift1_words sets |r| to |a| >> 1, where both arrays are |num| bits wide.
441void bn_rshift1_words(BN_ULONG *r, const BN_ULONG *a, size_t num);
442
443// bn_rshift_words sets |r| to |a| >> |shift|, where both arrays are |num| bits
444// wide.
445void bn_rshift_words(BN_ULONG *r, const BN_ULONG *a, unsigned shift,
446 size_t num);
447
448// bn_rshift_secret_shift behaves like |BN_rshift| but runs in time independent
449// of both |a| and |n|.
450OPENSSL_EXPORT int bn_rshift_secret_shift(BIGNUM *r, const BIGNUM *a,
451 unsigned n, BN_CTX *ctx);
452
453// bn_reduce_once sets |r| to |a| mod |m| where 0 <= |a| < 2*|m|. It returns
454// zero if |a| < |m| and a mask of all ones if |a| >= |m|. Each array is |num|
455// words long, but |a| has an additional word specified by |carry|. |carry| must
456// be zero or one, as implied by the bounds on |a|.
457//
458// |r|, |a|, and |m| may not alias. Use |bn_reduce_once_in_place| if |r| and |a|
459// must alias.
460BN_ULONG bn_reduce_once(BN_ULONG *r, const BN_ULONG *a, BN_ULONG carry,
461 const BN_ULONG *m, size_t num);
462
463// bn_reduce_once_in_place behaves like |bn_reduce_once| but acts in-place on
464// |r|, using |tmp| as scratch space. |r|, |tmp|, and |m| may not alias.
465BN_ULONG bn_reduce_once_in_place(BN_ULONG *r, BN_ULONG carry, const BN_ULONG *m,
466 BN_ULONG *tmp, size_t num);
467
468
469// Constant-time non-modular arithmetic.
470//
471// The following functions implement non-modular arithmetic in constant-time
472// and pessimally set |r->width| to the largest possible word size.
473//
474// Note this means that, e.g., repeatedly multiplying by one will cause widths
475// to increase without bound. The corresponding public API functions minimize
476// their outputs to avoid regressing calculator consumers.
477
478// bn_uadd_consttime behaves like |BN_uadd|, but it pessimally sets
479// |r->width| = |a->width| + |b->width| + 1.
480int bn_uadd_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
481
482// bn_usub_consttime behaves like |BN_usub|, but it pessimally sets
483// |r->width| = |a->width|.
484int bn_usub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
485
486// bn_abs_sub_consttime sets |r| to the absolute value of |a| - |b|, treating
487// both inputs as secret. It returns one on success and zero on error.
488OPENSSL_EXPORT int bn_abs_sub_consttime(BIGNUM *r, const BIGNUM *a,
489 const BIGNUM *b, BN_CTX *ctx);
490
491// bn_mul_consttime behaves like |BN_mul|, but it rejects negative inputs and
492// pessimally sets |r->width| to |a->width| + |b->width|, to avoid leaking
493// information about |a| and |b|.
494int bn_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
495
496// bn_sqrt_consttime behaves like |BN_sqrt|, but it pessimally sets |r->width|
497// to 2*|a->width|, to avoid leaking information about |a| and |b|.
498int bn_sqr_consttime(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
499
500// bn_div_consttime behaves like |BN_div|, but it rejects negative inputs and
501// treats both inputs, including their magnitudes, as secret. It is, as a
502// result, much slower than |BN_div| and should only be used for rare operations
503// where Montgomery reduction is not available.
504//
505// Note that |quotient->width| will be set pessimally to |numerator->width|.
506OPENSSL_EXPORT int bn_div_consttime(BIGNUM *quotient, BIGNUM *remainder,
507 const BIGNUM *numerator,
508 const BIGNUM *divisor, BN_CTX *ctx);
509
510// bn_is_relatively_prime checks whether GCD(|x|, |y|) is one. On success, it
511// returns one and sets |*out_relatively_prime| to one if the GCD was one and
512// zero otherwise. On error, it returns zero.
513OPENSSL_EXPORT int bn_is_relatively_prime(int *out_relatively_prime,
514 const BIGNUM *x, const BIGNUM *y,
515 BN_CTX *ctx);
516
517// bn_lcm_consttime sets |r| to LCM(|a|, |b|). It returns one and success and
518// zero on error. |a| and |b| are both treated as secret.
519OPENSSL_EXPORT int bn_lcm_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
520 BN_CTX *ctx);
521
522
523// Constant-time modular arithmetic.
524//
525// The following functions implement basic constant-time modular arithmetic.
526
527// bn_mod_add_words sets |r| to |a| + |b| (mod |m|), using |tmp| as scratch
528// space. Each array is |num| words long. |a| and |b| must be < |m|. Any pair of
529// |r|, |a|, and |b| may alias.
530void bn_mod_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
531 const BN_ULONG *m, BN_ULONG *tmp, size_t num);
532
533// bn_mod_add_consttime acts like |BN_mod_add_quick| but takes a |BN_CTX|.
534int bn_mod_add_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
535 const BIGNUM *m, BN_CTX *ctx);
536
537// bn_mod_sub_words sets |r| to |a| - |b| (mod |m|), using |tmp| as scratch
538// space. Each array is |num| words long. |a| and |b| must be < |m|. Any pair of
539// |r|, |a|, and |b| may alias.
540void bn_mod_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
541 const BN_ULONG *m, BN_ULONG *tmp, size_t num);
542
543// bn_mod_sub_consttime acts like |BN_mod_sub_quick| but takes a |BN_CTX|.
544int bn_mod_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
545 const BIGNUM *m, BN_CTX *ctx);
546
547// bn_mod_lshift1_consttime acts like |BN_mod_lshift1_quick| but takes a
548// |BN_CTX|.
549int bn_mod_lshift1_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
550 BN_CTX *ctx);
551
552// bn_mod_lshift_consttime acts like |BN_mod_lshift_quick| but takes a |BN_CTX|.
553int bn_mod_lshift_consttime(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
554 BN_CTX *ctx);
555
556// bn_mod_inverse_consttime sets |r| to |a|^-1, mod |n|. |a| must be non-
557// negative and less than |n|. It returns one on success and zero on error. On
558// failure, if the failure was caused by |a| having no inverse mod |n| then
559// |*out_no_inverse| will be set to one; otherwise it will be set to zero.
560//
561// This function treats both |a| and |n| as secret, provided they are both non-
562// zero and the inverse exists. It should only be used for even moduli where
563// none of the less general implementations are applicable.
564OPENSSL_EXPORT int bn_mod_inverse_consttime(BIGNUM *r, int *out_no_inverse,
565 const BIGNUM *a, const BIGNUM *n,
566 BN_CTX *ctx);
567
568// bn_mod_inverse_prime sets |out| to the modular inverse of |a| modulo |p|,
569// computed with Fermat's Little Theorem. It returns one on success and zero on
570// error. If |mont_p| is NULL, one will be computed temporarily.
571int bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
572 BN_CTX *ctx, const BN_MONT_CTX *mont_p);
573
574// bn_mod_inverse_secret_prime behaves like |bn_mod_inverse_prime| but uses
575// |BN_mod_exp_mont_consttime| instead of |BN_mod_exp_mont| in hopes of
576// protecting the exponent.
577int bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
578 BN_CTX *ctx, const BN_MONT_CTX *mont_p);
579
580
581// Low-level operations for small numbers.
582//
583// The following functions implement algorithms suitable for use with scalars
584// and field elements in elliptic curves. They rely on the number being small
585// both to stack-allocate various temporaries and because they do not implement
586// optimizations useful for the larger values used in RSA.
587
588// BN_SMALL_MAX_WORDS is the largest size input these functions handle. This
589// limit allows temporaries to be more easily stack-allocated. This limit is set
590// to accommodate P-521.
591#if defined(OPENSSL_32_BIT)
592#define BN_SMALL_MAX_WORDS 17
593#else
594#define BN_SMALL_MAX_WORDS 9
595#endif
596
597// bn_mul_small sets |r| to |a|*|b|. |num_r| must be |num_a| + |num_b|. |r| may
598// not alias with |a| or |b|.
599void bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a,
600 const BN_ULONG *b, size_t num_b);
601
602// bn_sqr_small sets |r| to |a|^2. |num_a| must be at most |BN_SMALL_MAX_WORDS|.
603// |num_r| must be |num_a|*2. |r| and |a| may not alias.
604void bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a);
605
606// In the following functions, the modulus must be at most |BN_SMALL_MAX_WORDS|
607// words long.
608
609// bn_to_montgomery_small sets |r| to |a| translated to the Montgomery domain.
610// |r| and |a| are |num| words long, which must be |mont->N.width|. |a| must be
611// fully reduced and may alias |r|.
612void bn_to_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num,
613 const BN_MONT_CTX *mont);
614
615// bn_from_montgomery_small sets |r| to |a| translated out of the Montgomery
616// domain. |r| and |a| are |num| words long, which must be |mont->N.width|. |a|
617// must be fully-reduced and may alias |r|.
618void bn_from_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num,
619 const BN_MONT_CTX *mont);
620
621// bn_mod_mul_montgomery_small sets |r| to |a| * |b| mod |mont->N|. Both inputs
622// and outputs are in the Montgomery domain. Each array is |num| words long,
623// which must be |mont->N.width|. Any two of |r|, |a|, and |b| may alias. |a|
624// and |b| must be reduced on input.
625void bn_mod_mul_montgomery_small(BN_ULONG *r, const BN_ULONG *a,
626 const BN_ULONG *b, size_t num,
627 const BN_MONT_CTX *mont);
628
629// bn_mod_exp_mont_small sets |r| to |a|^|p| mod |mont->N|. It returns one on
630// success and zero on programmer or internal error. Both inputs and outputs are
631// in the Montgomery domain. |r| and |a| are |num| words long, which must be
632// |mont->N.width| and at most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced.
633// This function runs in time independent of |a|, but |p| and |mont->N| are
634// public values. |a| must be fully-reduced and may alias with |r|.
635//
636// Note this function differs from |BN_mod_exp_mont| which uses Montgomery
637// reduction but takes input and output outside the Montgomery domain. Combine
638// this function with |bn_from_montgomery_small| and |bn_to_montgomery_small|
639// if necessary.
640void bn_mod_exp_mont_small(BN_ULONG *r, const BN_ULONG *a, size_t num,
641 const BN_ULONG *p, size_t num_p,
642 const BN_MONT_CTX *mont);
643
644// bn_mod_inverse_prime_mont_small sets |r| to |a|^-1 mod |mont->N|. |mont->N|
645// must be a prime. |r| and |a| are |num| words long, which must be
646// |mont->N.width| and at most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced
647// and may alias |r|. This function runs in time independent of |a|, but
648// |mont->N| is a public value.
649void bn_mod_inverse_prime_mont_small(BN_ULONG *r, const BN_ULONG *a, size_t num,
650 const BN_MONT_CTX *mont);
651
652
653#if defined(__cplusplus)
654} // extern C
655#endif
656
657#endif // OPENSSL_HEADER_BN_INTERNAL_H
658