mbed TLS v2.24.0
bignum.h
Go to the documentation of this file.
1 
6 /*
7  * Copyright The Mbed TLS Contributors
8  * SPDX-License-Identifier: Apache-2.0
9  *
10  * Licensed under the Apache License, Version 2.0 (the "License"); you may
11  * not use this file except in compliance with the License.
12  * You may obtain a copy of the License at
13  *
14  * http://www.apache.org/licenses/LICENSE-2.0
15  *
16  * Unless required by applicable law or agreed to in writing, software
17  * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
18  * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
19  * See the License for the specific language governing permissions and
20  * limitations under the License.
21  */
22 #ifndef MBEDTLS_BIGNUM_H
23 #define MBEDTLS_BIGNUM_H
24 
25 #if !defined(MBEDTLS_CONFIG_FILE)
26 #include "mbedtls/config.h"
27 #else
28 #include MBEDTLS_CONFIG_FILE
29 #endif
30 
31 #include <stddef.h>
32 #include <stdint.h>
33 
34 #if defined(MBEDTLS_FS_IO)
35 #include <stdio.h>
36 #endif
37 
38 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
39 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
40 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
41 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
42 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
43 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
44 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
45 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
47 #define MBEDTLS_MPI_CHK(f) \
48  do \
49  { \
50  if( ( ret = (f) ) != 0 ) \
51  goto cleanup; \
52  } while( 0 )
53 
54 /*
55  * Maximum size MPIs are allowed to grow to in number of limbs.
56  */
57 #define MBEDTLS_MPI_MAX_LIMBS 10000
58 
59 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
60 /*
61  * Maximum window size used for modular exponentiation. Default: 6
62  * Minimum value: 1. Maximum value: 6.
63  *
64  * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
65  * for the sliding window calculation. (So 64 by default)
66  *
67  * Reduction in size, reduces speed.
68  */
69 #define MBEDTLS_MPI_WINDOW_SIZE 6
70 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
71 
72 #if !defined(MBEDTLS_MPI_MAX_SIZE)
73 /*
74  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
75  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
76  *
77  * Note: Calculations can temporarily result in larger MPIs. So the number
78  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
79  */
80 #define MBEDTLS_MPI_MAX_SIZE 1024
81 #endif /* !MBEDTLS_MPI_MAX_SIZE */
82 
83 #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE )
85 /*
86  * When reading from files with mbedtls_mpi_read_file() and writing to files with
87  * mbedtls_mpi_write_file() the buffer should have space
88  * for a (short) label, the MPI (in the provided radix), the newline
89  * characters and the '\0'.
90  *
91  * By default we assume at least a 10 char label, a minimum radix of 10
92  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
93  * Autosized at compile time for at least a 10 char label, a minimum radix
94  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
95  *
96  * This used to be statically sized to 1250 for a maximum of 4096 bit
97  * numbers (1234 decimal chars).
98  *
99  * Calculate using the formula:
100  * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
101  * LabelSize + 6
102  */
103 #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS )
104 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
105 #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 )
106 
107 /*
108  * Define the base integer type, architecture-wise.
109  *
110  * 32 or 64-bit integer types can be forced regardless of the underlying
111  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
112  * respectively and undefining MBEDTLS_HAVE_ASM.
113  *
114  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
115  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
116  */
117 #if !defined(MBEDTLS_HAVE_INT32)
118  #if defined(_MSC_VER) && defined(_M_AMD64)
119  /* Always choose 64-bit when using MSC */
120  #if !defined(MBEDTLS_HAVE_INT64)
121  #define MBEDTLS_HAVE_INT64
122  #endif /* !MBEDTLS_HAVE_INT64 */
123  typedef int64_t mbedtls_mpi_sint;
124  typedef uint64_t mbedtls_mpi_uint;
125  #elif defined(__GNUC__) && ( \
126  defined(__amd64__) || defined(__x86_64__) || \
127  defined(__ppc64__) || defined(__powerpc64__) || \
128  defined(__ia64__) || defined(__alpha__) || \
129  ( defined(__sparc__) && defined(__arch64__) ) || \
130  defined(__s390x__) || defined(__mips64) || \
131  defined(__aarch64__) )
132  #if !defined(MBEDTLS_HAVE_INT64)
133  #define MBEDTLS_HAVE_INT64
134  #endif /* MBEDTLS_HAVE_INT64 */
135  typedef int64_t mbedtls_mpi_sint;
136  typedef uint64_t mbedtls_mpi_uint;
137  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
138  /* mbedtls_t_udbl defined as 128-bit unsigned int */
139  typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
140  #define MBEDTLS_HAVE_UDBL
141  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
142  #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
143  /*
144  * __ARMCC_VERSION is defined for both armcc and armclang and
145  * __aarch64__ is only defined by armclang when compiling 64-bit code
146  */
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  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
153  /* mbedtls_t_udbl defined as 128-bit unsigned int */
154  typedef __uint128_t mbedtls_t_udbl;
155  #define MBEDTLS_HAVE_UDBL
156  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
157  #elif defined(MBEDTLS_HAVE_INT64)
158  /* Force 64-bit integers with unknown compiler */
159  typedef int64_t mbedtls_mpi_sint;
160  typedef uint64_t mbedtls_mpi_uint;
161  #endif
162 #endif /* !MBEDTLS_HAVE_INT32 */
163 
164 #if !defined(MBEDTLS_HAVE_INT64)
165  /* Default to 32-bit compilation */
166  #if !defined(MBEDTLS_HAVE_INT32)
167  #define MBEDTLS_HAVE_INT32
168  #endif /* !MBEDTLS_HAVE_INT32 */
169  typedef int32_t mbedtls_mpi_sint;
170  typedef uint32_t mbedtls_mpi_uint;
171  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
172  typedef uint64_t mbedtls_t_udbl;
173  #define MBEDTLS_HAVE_UDBL
174  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
175 #endif /* !MBEDTLS_HAVE_INT64 */
176 
177 #ifdef __cplusplus
178 extern "C" {
179 #endif
180 
184 typedef struct mbedtls_mpi
185 {
186  int s;
187  size_t n;
188  mbedtls_mpi_uint *p;
189 }
191 
200 void mbedtls_mpi_init( mbedtls_mpi *X );
201 
209 void mbedtls_mpi_free( mbedtls_mpi *X );
210 
224 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
225 
241 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
242 
256 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
257 
265 
290 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
291 
315 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
316 
327 int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
328 
339 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
340 
356 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
357 
370 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
371 
384 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
385 
399 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
400 
411 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
412 
435 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
436  char *buf, size_t buflen, size_t *olen );
437 
438 #if defined(MBEDTLS_FS_IO)
439 
460 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
461 
477 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
478  int radix, FILE *fout );
479 #endif /* MBEDTLS_FS_IO */
480 
493 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
494  size_t buflen );
495 
509  const unsigned char *buf, size_t buflen );
510 
526 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
527  size_t buflen );
528 
545  unsigned char *buf, 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 
623 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
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 
820 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A,
821  mbedtls_mpi_sint b );
822 
850  const mbedtls_mpi *E, const mbedtls_mpi *N,
851  mbedtls_mpi *_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 
932 MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
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. ...
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:169
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.
int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val)
Modify a specific bit in an MPI.
#define MBEDTLS_DEPRECATED
Definition: pkcs11.h:60
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:188
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.
int mbedtls_mpi_read_binary_le(mbedtls_mpi *X, const unsigned char *buf, size_t buflen)
Import X from unsigned binary data, little endian.
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_write_binary_le(const mbedtls_mpi *X, unsigned char *buf, size_t buflen)
Export X into unsigned binary data, little endian. Always fills the whole buffer, which will end with...
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:170
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:184
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:187
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 X into unsigned binary data, big endian. Always fills the whole buffer, which will start with ...
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.