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bignum.h
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1 
6 /*
7  * Copyright The Mbed TLS Contributors
8  * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
9  *
10  * This file is provided under the Apache License 2.0, or the
11  * GNU General Public License v2.0 or later.
12  *
13  * **********
14  * Apache License 2.0:
15  *
16  * Licensed under the Apache License, Version 2.0 (the "License"); you may
17  * not use this file except in compliance with the License.
18  * You may obtain a copy of the License at
19  *
20  * http://www.apache.org/licenses/LICENSE-2.0
21  *
22  * Unless required by applicable law or agreed to in writing, software
23  * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
24  * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
25  * See the License for the specific language governing permissions and
26  * limitations under the License.
27  *
28  * **********
29  *
30  * **********
31  * GNU General Public License v2.0 or later:
32  *
33  * This program is free software; you can redistribute it and/or modify
34  * it under the terms of the GNU General Public License as published by
35  * the Free Software Foundation; either version 2 of the License, or
36  * (at your option) any later version.
37  *
38  * This program is distributed in the hope that it will be useful,
39  * but WITHOUT ANY WARRANTY; without even the implied warranty of
40  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
41  * GNU General Public License for more details.
42  *
43  * You should have received a copy of the GNU General Public License along
44  * with this program; if not, write to the Free Software Foundation, Inc.,
45  * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
46  *
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48  */
49 #ifndef MBEDTLS_BIGNUM_H
50 #define MBEDTLS_BIGNUM_H
51 
52 #if !defined(MBEDTLS_CONFIG_FILE)
53 #include "config.h"
54 #else
55 #include MBEDTLS_CONFIG_FILE
56 #endif
57 
58 #include <stddef.h>
59 #include <stdint.h>
60 
61 #if defined(MBEDTLS_FS_IO)
62 #include <stdio.h>
63 #endif
64 
65 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
66 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
67 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
68 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
69 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
70 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
71 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
72 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
74 #define MBEDTLS_MPI_CHK(f) \
75  do \
76  { \
77  if( ( ret = (f) ) != 0 ) \
78  goto cleanup; \
79  } while( 0 )
80 
81 /*
82  * Maximum size MPIs are allowed to grow to in number of limbs.
83  */
84 #define MBEDTLS_MPI_MAX_LIMBS 10000
85 
86 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
87 /*
88  * Maximum window size used for modular exponentiation. Default: 6
89  * Minimum value: 1. Maximum value: 6.
90  *
91  * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
92  * for the sliding window calculation. (So 64 by default)
93  *
94  * Reduction in size, reduces speed.
95  */
96 #define MBEDTLS_MPI_WINDOW_SIZE 6
97 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
98 
99 #if !defined(MBEDTLS_MPI_MAX_SIZE)
100 /*
101  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
102  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
103  *
104  * Note: Calculations can temporarily result in larger MPIs. So the number
105  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
106  */
107 #define MBEDTLS_MPI_MAX_SIZE 1024
108 #endif /* !MBEDTLS_MPI_MAX_SIZE */
109 
110 #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE )
112 /*
113  * When reading from files with mbedtls_mpi_read_file() and writing to files with
114  * mbedtls_mpi_write_file() the buffer should have space
115  * for a (short) label, the MPI (in the provided radix), the newline
116  * characters and the '\0'.
117  *
118  * By default we assume at least a 10 char label, a minimum radix of 10
119  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
120  * Autosized at compile time for at least a 10 char label, a minimum radix
121  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
122  *
123  * This used to be statically sized to 1250 for a maximum of 4096 bit
124  * numbers (1234 decimal chars).
125  *
126  * Calculate using the formula:
127  * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
128  * LabelSize + 6
129  */
130 #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS )
131 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
132 #define MBEDTLS_MPI_RW_BUFFER_SIZE ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 )
133 
134 /*
135  * Define the base integer type, architecture-wise.
136  *
137  * 32 or 64-bit integer types can be forced regardless of the underlying
138  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
139  * respectively and undefining MBEDTLS_HAVE_ASM.
140  *
141  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
142  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
143  */
144 #if !defined(MBEDTLS_HAVE_INT32)
145  #if defined(_MSC_VER) && defined(_M_AMD64)
146  /* Always choose 64-bit when using MSC */
147  #if !defined(MBEDTLS_HAVE_INT64)
148  #define MBEDTLS_HAVE_INT64
149  #endif /* !MBEDTLS_HAVE_INT64 */
150  typedef int64_t mbedtls_mpi_sint;
151  typedef uint64_t mbedtls_mpi_uint;
152  #elif defined(__GNUC__) && ( \
153  defined(__amd64__) || defined(__x86_64__) || \
154  defined(__ppc64__) || defined(__powerpc64__) || \
155  defined(__ia64__) || defined(__alpha__) || \
156  ( defined(__sparc__) && defined(__arch64__) ) || \
157  defined(__s390x__) || defined(__mips64) )
158  #if !defined(MBEDTLS_HAVE_INT64)
159  #define MBEDTLS_HAVE_INT64
160  #endif /* MBEDTLS_HAVE_INT64 */
161  typedef int64_t mbedtls_mpi_sint;
162  typedef uint64_t mbedtls_mpi_uint;
163  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
164  /* mbedtls_t_udbl defined as 128-bit unsigned int */
165  typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
166  #define MBEDTLS_HAVE_UDBL
167  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
168  #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
169  /*
170  * __ARMCC_VERSION is defined for both armcc and armclang and
171  * __aarch64__ is only defined by armclang when compiling 64-bit code
172  */
173  #if !defined(MBEDTLS_HAVE_INT64)
174  #define MBEDTLS_HAVE_INT64
175  #endif /* !MBEDTLS_HAVE_INT64 */
176  typedef int64_t mbedtls_mpi_sint;
177  typedef uint64_t mbedtls_mpi_uint;
178  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
179  /* mbedtls_t_udbl defined as 128-bit unsigned int */
180  typedef __uint128_t mbedtls_t_udbl;
181  #define MBEDTLS_HAVE_UDBL
182  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
183  #elif defined(MBEDTLS_HAVE_INT64)
184  /* Force 64-bit integers with unknown compiler */
185  typedef int64_t mbedtls_mpi_sint;
186  typedef uint64_t mbedtls_mpi_uint;
187  #endif
188 #endif /* !MBEDTLS_HAVE_INT32 */
189 
190 #if !defined(MBEDTLS_HAVE_INT64)
191  /* Default to 32-bit compilation */
192  #if !defined(MBEDTLS_HAVE_INT32)
193  #define MBEDTLS_HAVE_INT32
194  #endif /* !MBEDTLS_HAVE_INT32 */
197  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
199  #define MBEDTLS_HAVE_UDBL
200  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
201 #endif /* !MBEDTLS_HAVE_INT64 */
202 
203 #ifdef __cplusplus
204 extern "C" {
205 #endif
206 
210 typedef struct mbedtls_mpi
211 {
212  int s;
213  size_t n;
215 }
217 
227 
236 
250 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
251 
267 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
268 
282 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
283 
291 
316 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
317 
341 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
342 
354 
365 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
366 
382 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
383 
396 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
397 
410 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
411 
425 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
426 
437 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
438 
461 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
462  char *buf, size_t buflen, size_t *olen );
463 
464 #if defined(MBEDTLS_FS_IO)
465 
486 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
487 
503 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
504  int radix, FILE *fout );
505 #endif /* MBEDTLS_FS_IO */
506 
519 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
520  size_t buflen );
521 
536 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
537  size_t buflen );
538 
549 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
550 
561 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
562 
573 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
574 
585 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
586 
602 int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
603  unsigned *ret );
604 
616 
629  const mbedtls_mpi *B );
630 
644  const mbedtls_mpi *B );
645 
658  const mbedtls_mpi *B );
659 
672  const mbedtls_mpi *B );
673 
687 
702 
716  const mbedtls_mpi *B );
717 
733 
753  const mbedtls_mpi *B );
754 
775 
794  const mbedtls_mpi *B );
795 
814 
842  const mbedtls_mpi *E, const mbedtls_mpi *N,
843  mbedtls_mpi *_RR );
844 
863  int (*f_rng)(void *, unsigned char *, size_t),
864  void *p_rng );
865 
878  const mbedtls_mpi *B );
879 
897  const mbedtls_mpi *N );
898 
899 #if !defined(MBEDTLS_DEPRECATED_REMOVED)
900 #if defined(MBEDTLS_DEPRECATED_WARNING)
901 #define MBEDTLS_DEPRECATED __attribute__((deprecated))
902 #else
903 #define MBEDTLS_DEPRECATED
904 #endif
905 
925  int (*f_rng)(void *, unsigned char *, size_t),
926  void *p_rng );
927 #undef MBEDTLS_DEPRECATED
928 #endif /* !MBEDTLS_DEPRECATED_REMOVED */
929 
957 int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
958  int (*f_rng)(void *, unsigned char *, size_t),
959  void *p_rng );
966 typedef enum {
970 
990 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
991  int (*f_rng)(void *, unsigned char *, size_t),
992  void *p_rng );
993 
994 #if defined(MBEDTLS_SELF_TEST)
995 
1001 int mbedtls_mpi_self_test( int verbose );
1002 
1003 #endif /* MBEDTLS_SELF_TEST */
1004 
1005 #ifdef __cplusplus
1006 }
1007 #endif
1008 
1009 #endif /* bignum.h */
int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform a division with remainder of two MPIs: A = Q * B + R.
void mbedtls_mpi_free(mbedtls_mpi *X)
This function frees the components of an MPI context.
int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B)
Compute the greatest common divisor: G = gcd(A, B)
int mbedtls_mpi_fill_random(mbedtls_mpi *X, size_t size, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
Fill an MPI with a number of random bytes.
#define R(b, x)
Definition: sha2.c:134
int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
Miller-Rabin primality test.
Definition: ehthrow.cxx:53
int mbedtls_mpi_sub_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b)
Perform a signed subtraction of an MPI and an integer: X = A - b.
#define Y(I)
size_t mbedtls_mpi_lsb(const mbedtls_mpi *X)
Return the number of bits of value 0 before the least significant bit of value 1.
GLdouble GLdouble GLdouble r
Definition: gl.h:2055
GLuint GLuint GLsizei count
Definition: gl.h:1545
#define MBEDTLS_DEPRECATED
Definition: bignum.h:903
int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs)
Enlarge an MPI to the specified number of limbs.
int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign)
Perform a safe conditional copy of MPI which doesn't reveal whether the condition was true or not.
int mbedtls_mpi_mod_mpi(mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform a modular reduction. R = A mod B.
int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR)
Perform a sliding-window exponentiation: X = A^E mod N.
int32_t mbedtls_mpi_sint
Definition: bignum.h:195
size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X)
Return the number of bits up to and including the most significant bit of value 1.
int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y)
Compare two MPIs.
size_t mbedtls_mpi_size(const mbedtls_mpi *X)
Return the total size of an MPI value in bytes.
int mbedtls_mpi_sub_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform a signed subtraction of MPIs: X = A - B.
int mbedtls_mpi_sub_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform an unsigned subtraction of MPIs: X = |A| - |B|.
ULONG G
Definition: xcpt4u.c:549
int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s)
Import an MPI from an ASCII string.
uint64_t mbedtls_t_udbl
Definition: bignum.h:198
Definition: ehthrow.cxx:92
int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val)
Modify a specific bit in an MPI.
#define verbose
Definition: rosglue.h:36
GLenum GLuint GLenum GLsizei const GLchar * buf
Definition: glext.h:7751
#define __attribute__(x)
Definition: wpp_private.h:207
int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z)
Store integer value in MPI.
int mbedtls_mpi_div_int(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b)
Perform a division with remainder of an MPI by an integer: A = Q * b + R.
int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf, size_t buflen)
Import an MPI from unsigned big endian binary data.
mbedtls_mpi_uint * p
Definition: bignum.h:214
int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs)
This function resizes an MPI downwards, keeping at least the specified number of limbs.
int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned *ret)
Check if an MPI is less than the other in constant time.
GLdouble GLdouble z
Definition: glext.h:5874
MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime(const mbedtls_mpi *X, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
Perform a Miller-Rabin primality test with error probability of 2-80.
int mbedtls_mpi_add_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b)
Perform a signed addition of an MPI and an integer: X = A + b.
int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count)
Perform a right-shift on an MPI: X >>= count.
GLuint GLfloat * val
Definition: glext.h:7180
int mbedtls_mpi_mod_int(mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b)
Perform a modular reduction with respect to an integer. r = A mod b.
GLboolean GLboolean GLboolean b
Definition: glext.h:6204
GLsizeiptr size
Definition: glext.h:5919
int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count)
Perform a left-shift on an MPI: X <<= count.
int mbedtls_mpi_mul_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b)
Perform a multiplication of an MPI with an unsigned integer: X = A * b.
GLbitfield flags
Definition: glext.h:7161
uint32_t mbedtls_mpi_uint
Definition: bignum.h:196
int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign)
Perform a safe conditional swap which doesn't reveal whether the condition was true or not.
int ret
void mbedtls_mpi_init(mbedtls_mpi *X)
Initialize an MPI context.
GLdouble s
Definition: gl.h:2039
GLenum mode
Definition: glext.h:6217
void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y)
Swap the contents of two MPIs.
INT32 int32_t
Definition: types.h:71
int mbedtls_mpi_add_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform a signed addition of MPIs: X = A + B.
static const WCHAR E[]
Definition: oid.c:1253
UINT64 uint64_t
Definition: types.h:77
int mbedtls_mpi_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N)
Compute the modular inverse: X = A^-1 mod N.
MPI structure.
Definition: bignum.h:210
int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y)
Make a copy of an MPI.
int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix, char *buf, size_t buflen, size_t *olen)
Export an MPI to an ASCII string.
size_t n
Definition: bignum.h:213
UINT32 uint32_t
Definition: types.h:75
int mbedtls_mpi_add_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform an unsigned addition of MPIs: X = |A| + |B|.
int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y)
Compare the absolute values of two MPIs.
int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf, size_t buflen)
Export an MPI into unsigned big endian binary data of fixed size.
mbedtls_mpi_gen_prime_flag_t
Flags for mbedtls_mpi_gen_prime()
Definition: bignum.h:966
int mbedtls_mpi_mul_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform a multiplication of two MPIs: X = A * B.
int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z)
Compare an MPI with an integer.
GLfloat GLfloat p
Definition: glext.h:8902
int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos)
Get a specific bit from an MPI.
struct mbedtls_mpi mbedtls_mpi
MPI structure.
INT64 int64_t
Definition: types.h:72
int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
Generate a prime number.