mbed TLS v2.16.6
bignum.h
Go to the documentation of this file.
1 
6 /*
7  * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
8  * SPDX-License-Identifier: GPL-2.0
9  *
10  * This program is free software; you can redistribute it and/or modify
11  * it under the terms of the GNU General Public License as published by
12  * the Free Software Foundation; either version 2 of the License, or
13  * (at your option) any later version.
14  *
15  * This program is distributed in the hope that it will be useful,
16  * but WITHOUT ANY WARRANTY; without even the implied warranty of
17  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18  * GNU General Public License for more details.
19  *
20  * You should have received a copy of the GNU General Public License along
21  * with this program; if not, write to the Free Software Foundation, Inc.,
22  * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
23  *
24  * This file is part of mbed TLS (https://tls.mbed.org)
25  */
26 #ifndef MBEDTLS_BIGNUM_H
27 #define MBEDTLS_BIGNUM_H
28 
29 #if !defined(MBEDTLS_CONFIG_FILE)
30 #include "config.h"
31 #else
32 #include MBEDTLS_CONFIG_FILE
33 #endif
34 
35 #include <stddef.h>
36 #include <stdint.h>
37 
38 #if defined(MBEDTLS_FS_IO)
39 #include <stdio.h>
40 #endif
41 
42 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
43 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
44 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
45 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
46 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
47 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
48 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
49 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
51 #define MBEDTLS_MPI_CHK(f) \
52  do \
53  { \
54  if( ( ret = (f) ) != 0 ) \
55  goto cleanup; \
56  } while( 0 )
57 
58 /*
59  * Maximum size MPIs are allowed to grow to in number of limbs.
60  */
61 #define MBEDTLS_MPI_MAX_LIMBS 10000
62 
63 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
64 /*
65  * Maximum window size used for modular exponentiation. Default: 6
66  * Minimum value: 1. Maximum value: 6.
67  *
68  * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
69  * for the sliding window calculation. (So 64 by default)
70  *
71  * Reduction in size, reduces speed.
72  */
73 #define MBEDTLS_MPI_WINDOW_SIZE 6
74 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
75 
76 #if !defined(MBEDTLS_MPI_MAX_SIZE)
77 /*
78  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
79  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
80  *
81  * Note: Calculations can temporarily result in larger MPIs. So the number
82  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
83  */
84 #define MBEDTLS_MPI_MAX_SIZE 1024
85 #endif /* !MBEDTLS_MPI_MAX_SIZE */
86 
87 #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE )
89 /*
90  * When reading from files with mbedtls_mpi_read_file() and writing to files with
91  * mbedtls_mpi_write_file() the buffer should have space
92  * for a (short) label, the MPI (in the provided radix), the newline
93  * characters and the '\0'.
94  *
95  * By default we assume at least a 10 char label, a minimum radix of 10
96  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
97  * Autosized at compile time for at least a 10 char label, a minimum radix
98  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
99  *
100  * This used to be statically sized to 1250 for a maximum of 4096 bit
101  * numbers (1234 decimal chars).
102  *
103  * Calculate using the formula:
104  * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
105  * LabelSize + 6
106  */
107 #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS )
108 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
109 #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 )
110 
111 /*
112  * Define the base integer type, architecture-wise.
113  *
114  * 32 or 64-bit integer types can be forced regardless of the underlying
115  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
116  * respectively and undefining MBEDTLS_HAVE_ASM.
117  *
118  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
119  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
120  */
121 #if !defined(MBEDTLS_HAVE_INT32)
122  #if defined(_MSC_VER) && defined(_M_AMD64)
123  /* Always choose 64-bit when using MSC */
124  #if !defined(MBEDTLS_HAVE_INT64)
125  #define MBEDTLS_HAVE_INT64
126  #endif /* !MBEDTLS_HAVE_INT64 */
127  typedef int64_t mbedtls_mpi_sint;
128  typedef uint64_t mbedtls_mpi_uint;
129  #elif defined(__GNUC__) && ( \
130  defined(__amd64__) || defined(__x86_64__) || \
131  defined(__ppc64__) || defined(__powerpc64__) || \
132  defined(__ia64__) || defined(__alpha__) || \
133  ( defined(__sparc__) && defined(__arch64__) ) || \
134  defined(__s390x__) || defined(__mips64) )
135  #if !defined(MBEDTLS_HAVE_INT64)
136  #define MBEDTLS_HAVE_INT64
137  #endif /* MBEDTLS_HAVE_INT64 */
138  typedef int64_t mbedtls_mpi_sint;
139  typedef uint64_t mbedtls_mpi_uint;
140  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
141  /* mbedtls_t_udbl defined as 128-bit unsigned int */
142  typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
143  #define MBEDTLS_HAVE_UDBL
144  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
145  #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
146  /*
147  * __ARMCC_VERSION is defined for both armcc and armclang and
148  * __aarch64__ is only defined by armclang when compiling 64-bit code
149  */
150  #if !defined(MBEDTLS_HAVE_INT64)
151  #define MBEDTLS_HAVE_INT64
152  #endif /* !MBEDTLS_HAVE_INT64 */
153  typedef int64_t mbedtls_mpi_sint;
154  typedef uint64_t mbedtls_mpi_uint;
155  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
156  /* mbedtls_t_udbl defined as 128-bit unsigned int */
157  typedef __uint128_t mbedtls_t_udbl;
158  #define MBEDTLS_HAVE_UDBL
159  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
160  #elif defined(MBEDTLS_HAVE_INT64)
161  /* Force 64-bit integers with unknown compiler */
162  typedef int64_t mbedtls_mpi_sint;
163  typedef uint64_t mbedtls_mpi_uint;
164  #endif
165 #endif /* !MBEDTLS_HAVE_INT32 */
166 
167 #if !defined(MBEDTLS_HAVE_INT64)
168  /* Default to 32-bit compilation */
169  #if !defined(MBEDTLS_HAVE_INT32)
170  #define MBEDTLS_HAVE_INT32
171  #endif /* !MBEDTLS_HAVE_INT32 */
172  typedef int32_t mbedtls_mpi_sint;
173  typedef uint32_t mbedtls_mpi_uint;
174  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
175  typedef uint64_t mbedtls_t_udbl;
176  #define MBEDTLS_HAVE_UDBL
177  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
178 #endif /* !MBEDTLS_HAVE_INT64 */
179 
180 #ifdef __cplusplus
181 extern "C" {
182 #endif
183 
187 typedef struct mbedtls_mpi
188 {
189  int s;
190  size_t n;
191  mbedtls_mpi_uint *p;
192 }
194 
203 void mbedtls_mpi_init( mbedtls_mpi *X );
204 
212 void mbedtls_mpi_free( mbedtls_mpi *X );
213 
227 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
228 
244 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
245 
259 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
260 
268 
293 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
294 
318 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
319 
330 int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
331 
342 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
343 
359 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
360 
373 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
374 
387 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
388 
402 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
403 
414 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
415 
438 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
439  char *buf, size_t buflen, size_t *olen );
440 
441 #if defined(MBEDTLS_FS_IO)
442 
463 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
464 
480 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
481  int radix, FILE *fout );
482 #endif /* MBEDTLS_FS_IO */
483 
496 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
497  size_t buflen );
498 
513 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
514  size_t buflen );
515 
526 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
527 
538 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
539 
550 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
551 
562 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
563 
579 int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
580  unsigned *ret );
581 
592 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
593 
606  const mbedtls_mpi *B );
607 
621  const mbedtls_mpi *B );
622 
635  const mbedtls_mpi *B );
636 
649  const mbedtls_mpi *B );
650 
663  mbedtls_mpi_sint b );
664 
678  mbedtls_mpi_sint b );
679 
693  const mbedtls_mpi *B );
694 
709  mbedtls_mpi_uint b );
710 
730  const mbedtls_mpi *B );
731 
751  mbedtls_mpi_sint b );
752 
771  const mbedtls_mpi *B );
772 
789 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A,
790  mbedtls_mpi_sint b );
791 
819  const mbedtls_mpi *E, const mbedtls_mpi *N,
820  mbedtls_mpi *_RR );
821 
839 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
840  int (*f_rng)(void *, unsigned char *, size_t),
841  void *p_rng );
842 
854 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A,
855  const mbedtls_mpi *B );
856 
874  const mbedtls_mpi *N );
875 
876 #if !defined(MBEDTLS_DEPRECATED_REMOVED)
877 #if defined(MBEDTLS_DEPRECATED_WARNING)
878 #define MBEDTLS_DEPRECATED __attribute__((deprecated))
879 #else
880 #define MBEDTLS_DEPRECATED
881 #endif
882 
902  int (*f_rng)(void *, unsigned char *, size_t),
903  void *p_rng );
904 #undef MBEDTLS_DEPRECATED
905 #endif /* !MBEDTLS_DEPRECATED_REMOVED */
906 
934 int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
935  int (*f_rng)(void *, unsigned char *, size_t),
936  void *p_rng );
943 typedef enum {
947 
967 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
968  int (*f_rng)(void *, unsigned char *, size_t),
969  void *p_rng );
970 
971 #if defined(MBEDTLS_SELF_TEST)
972 
978 int mbedtls_mpi_self_test( int verbose );
979 
980 #endif /* MBEDTLS_SELF_TEST */
981 
982 #ifdef __cplusplus
983 }
984 #endif
985 
986 #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:880
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:172
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:175
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:191
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:173
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'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:187
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:190
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:943
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.