mbed TLS v2.16.12
bignum.h
Go to the documentation of this file.
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  *
47  * **********
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 
66 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
67 
68 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
69 
70 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
71 
72 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
73 
74 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
75 
76 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
77 
78 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
79 
80 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
81 
82 #define MBEDTLS_MPI_CHK(f) \
83  do \
84  { \
85  if( ( ret = (f) ) != 0 ) \
86  goto cleanup; \
87  } while( 0 )
88 
89 /*
90  * Maximum size MPIs are allowed to grow to in number of limbs.
91  */
92 #define MBEDTLS_MPI_MAX_LIMBS 10000
93 
94 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
95 /*
96  * Maximum window size used for modular exponentiation. Default: 6
97  * Minimum value: 1. Maximum value: 6.
98  *
99  * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
100  * for the sliding window calculation. (So 64 by default)
101  *
102  * Reduction in size, reduces speed.
103  */
104 #define MBEDTLS_MPI_WINDOW_SIZE 6
105 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
106 
107 #if !defined(MBEDTLS_MPI_MAX_SIZE)
108 /*
109  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
110  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
111  *
112  * Note: Calculations can temporarily result in larger MPIs. So the number
113  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
114  */
115 #define MBEDTLS_MPI_MAX_SIZE 1024
116 #endif /* !MBEDTLS_MPI_MAX_SIZE */
117 
118 #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE )
120 /*
121  * When reading from files with mbedtls_mpi_read_file() and writing to files with
122  * mbedtls_mpi_write_file() the buffer should have space
123  * for a (short) label, the MPI (in the provided radix), the newline
124  * characters and the '\0'.
125  *
126  * By default we assume at least a 10 char label, a minimum radix of 10
127  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
128  * Autosized at compile time for at least a 10 char label, a minimum radix
129  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
130  *
131  * This used to be statically sized to 1250 for a maximum of 4096 bit
132  * numbers (1234 decimal chars).
133  *
134  * Calculate using the formula:
135  * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
136  * LabelSize + 6
137  */
138 #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS )
139 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
140 #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 )
141 
142 /*
143  * Define the base integer type, architecture-wise.
144  *
145  * 32 or 64-bit integer types can be forced regardless of the underlying
146  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
147  * respectively and undefining MBEDTLS_HAVE_ASM.
148  *
149  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
150  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
151  */
152 #if !defined(MBEDTLS_HAVE_INT32)
153  #if defined(_MSC_VER) && defined(_M_AMD64)
154  /* Always choose 64-bit when using MSC */
155  #if !defined(MBEDTLS_HAVE_INT64)
156  #define MBEDTLS_HAVE_INT64
157  #endif /* !MBEDTLS_HAVE_INT64 */
158  typedef int64_t mbedtls_mpi_sint;
159  typedef uint64_t mbedtls_mpi_uint;
160  #elif defined(__GNUC__) && ( \
161  defined(__amd64__) || defined(__x86_64__) || \
162  defined(__ppc64__) || defined(__powerpc64__) || \
163  defined(__ia64__) || defined(__alpha__) || \
164  ( defined(__sparc__) && defined(__arch64__) ) || \
165  defined(__s390x__) || defined(__mips64) )
166  #if !defined(MBEDTLS_HAVE_INT64)
167  #define MBEDTLS_HAVE_INT64
168  #endif /* MBEDTLS_HAVE_INT64 */
169  typedef int64_t mbedtls_mpi_sint;
170  typedef uint64_t mbedtls_mpi_uint;
171  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
172  /* mbedtls_t_udbl defined as 128-bit unsigned int */
173  typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
174  #define MBEDTLS_HAVE_UDBL
175  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
176  #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
177  /*
178  * __ARMCC_VERSION is defined for both armcc and armclang and
179  * __aarch64__ is only defined by armclang when compiling 64-bit code
180  */
181  #if !defined(MBEDTLS_HAVE_INT64)
182  #define MBEDTLS_HAVE_INT64
183  #endif /* !MBEDTLS_HAVE_INT64 */
184  typedef int64_t mbedtls_mpi_sint;
185  typedef uint64_t mbedtls_mpi_uint;
186  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
187  /* mbedtls_t_udbl defined as 128-bit unsigned int */
188  typedef __uint128_t mbedtls_t_udbl;
189  #define MBEDTLS_HAVE_UDBL
190  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
191  #elif defined(MBEDTLS_HAVE_INT64)
192  /* Force 64-bit integers with unknown compiler */
193  typedef int64_t mbedtls_mpi_sint;
194  typedef uint64_t mbedtls_mpi_uint;
195  #endif
196 #endif /* !MBEDTLS_HAVE_INT32 */
197 
198 #if !defined(MBEDTLS_HAVE_INT64)
199  /* Default to 32-bit compilation */
200  #if !defined(MBEDTLS_HAVE_INT32)
201  #define MBEDTLS_HAVE_INT32
202  #endif /* !MBEDTLS_HAVE_INT32 */
203  typedef int32_t mbedtls_mpi_sint;
204  typedef uint32_t mbedtls_mpi_uint;
205  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
206  typedef uint64_t mbedtls_t_udbl;
207  #define MBEDTLS_HAVE_UDBL
208  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
209 #endif /* !MBEDTLS_HAVE_INT64 */
210 
211 #ifdef __cplusplus
212 extern "C" {
213 #endif
214 
218 typedef struct mbedtls_mpi
219 {
220  int s;
221  size_t n;
223 }
225 
234 void mbedtls_mpi_init( mbedtls_mpi *X );
235 
243 void mbedtls_mpi_free( mbedtls_mpi *X );
244 
258 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
259 
275 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
276 
290 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
291 
299 
324 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
325 
349 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
350 
362 
373 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
374 
390 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
391 
404 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
405 
418 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
419 
433 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
434 
445 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
446 
469 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
470  char *buf, size_t buflen, size_t *olen );
471 
472 #if defined(MBEDTLS_FS_IO)
473 
494 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
495 
511 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
512  int radix, FILE *fout );
513 #endif /* MBEDTLS_FS_IO */
514 
527 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
528  size_t buflen );
529 
544 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
545  size_t buflen );
546 
557 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
558 
569 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
570 
581 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
582 
593 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
594 
610 int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
611  unsigned *ret );
612 
624 
637  const mbedtls_mpi *B );
638 
652  const mbedtls_mpi *B );
653 
666  const mbedtls_mpi *B );
667 
680  const mbedtls_mpi *B );
681 
694  mbedtls_mpi_sint b );
695 
709  mbedtls_mpi_sint b );
710 
724  const mbedtls_mpi *B );
725 
740  mbedtls_mpi_uint b );
741 
761  const mbedtls_mpi *B );
762 
782  mbedtls_mpi_sint b );
783 
802  const mbedtls_mpi *B );
803 
821  mbedtls_mpi_sint b );
822 
850  const mbedtls_mpi *E, const mbedtls_mpi *N,
851  mbedtls_mpi *prec_RR );
852 
870 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
871  int (*f_rng)(void *, unsigned char *, size_t),
872  void *p_rng );
873 
885 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A,
886  const mbedtls_mpi *B );
887 
905  const mbedtls_mpi *N );
906 
907 #if !defined(MBEDTLS_DEPRECATED_REMOVED)
908 #if defined(MBEDTLS_DEPRECATED_WARNING)
909 #define MBEDTLS_DEPRECATED __attribute__((deprecated))
910 #else
911 #define MBEDTLS_DEPRECATED
912 #endif
913 
933  int (*f_rng)(void *, unsigned char *, size_t),
934  void *p_rng );
935 #undef MBEDTLS_DEPRECATED
936 #endif /* !MBEDTLS_DEPRECATED_REMOVED */
937 
965 int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
966  int (*f_rng)(void *, unsigned char *, size_t),
967  void *p_rng );
974 typedef enum {
978 
998 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
999  int (*f_rng)(void *, unsigned char *, size_t),
1000  void *p_rng );
1001 
1002 #if defined(MBEDTLS_SELF_TEST)
1003 
1009 int mbedtls_mpi_self_test( int verbose );
1010 
1011 #endif /* MBEDTLS_SELF_TEST */
1012 
1013 #ifdef __cplusplus
1014 }
1015 #endif
1016 
1017 #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.
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.
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.
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. ...
#define MBEDTLS_DEPRECATED
Definition: bignum.h:911
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&#39;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.
int32_t mbedtls_mpi_sint
Definition: bignum.h:203
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|.
Configuration options (set of defines)
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:206
int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val)
Modify a specific bit in an MPI.
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:222
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.
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.
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.
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.
uint32_t mbedtls_mpi_uint
Definition: bignum.h:204
int mbedtls_mpi_self_test(int verbose)
Checkup routine.
int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign)
Perform a safe conditional swap which doesn&#39;t reveal whether the condition was true or not...
void mbedtls_mpi_init(mbedtls_mpi *X)
Initialize an MPI context.
void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y)
Swap the contents of two MPIs.
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.
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:218
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.
int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin)
Read an MPI from a line in an opened file.
int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X, int radix, FILE *fout)
Export an MPI into an opened file.
size_t n
Definition: bignum.h:221
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_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *prec_RR)
Perform a sliding-window exponentiation: X = A^E mod N.
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:974
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.
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.
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.