mbed TLS v2.28.0
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 
39 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
40 
41 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
42 
43 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
44 
45 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
46 
47 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
48 
49 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
50 
51 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
52 
53 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
54 
55 #define MBEDTLS_MPI_CHK(f) \
56  do \
57  { \
58  if( ( ret = (f) ) != 0 ) \
59  goto cleanup; \
60  } while( 0 )
61 
62 /*
63  * Maximum size MPIs are allowed to grow to in number of limbs.
64  */
65 #define MBEDTLS_MPI_MAX_LIMBS 10000
66 
67 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
68 /*
69  * Maximum window size used for modular exponentiation. Default: 6
70  * Minimum value: 1. Maximum value: 6.
71  *
72  * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
73  * for the sliding window calculation. (So 64 by default)
74  *
75  * Reduction in size, reduces speed.
76  */
77 #define MBEDTLS_MPI_WINDOW_SIZE 6
78 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
79 
80 #if !defined(MBEDTLS_MPI_MAX_SIZE)
81 /*
82  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
83  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
84  *
85  * Note: Calculations can temporarily result in larger MPIs. So the number
86  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
87  */
88 #define MBEDTLS_MPI_MAX_SIZE 1024
89 #endif /* !MBEDTLS_MPI_MAX_SIZE */
90 
91 #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE )
93 /*
94  * When reading from files with mbedtls_mpi_read_file() and writing to files with
95  * mbedtls_mpi_write_file() the buffer should have space
96  * for a (short) label, the MPI (in the provided radix), the newline
97  * characters and the '\0'.
98  *
99  * By default we assume at least a 10 char label, a minimum radix of 10
100  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
101  * Autosized at compile time for at least a 10 char label, a minimum radix
102  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
103  *
104  * This used to be statically sized to 1250 for a maximum of 4096 bit
105  * numbers (1234 decimal chars).
106  *
107  * Calculate using the formula:
108  * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
109  * LabelSize + 6
110  */
111 #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS )
112 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
113 #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 )
114 
115 /*
116  * Define the base integer type, architecture-wise.
117  *
118  * 32 or 64-bit integer types can be forced regardless of the underlying
119  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
120  * respectively and undefining MBEDTLS_HAVE_ASM.
121  *
122  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
123  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
124  */
125 #if !defined(MBEDTLS_HAVE_INT32)
126  #if defined(_MSC_VER) && defined(_M_AMD64)
127  /* Always choose 64-bit when using MSC */
128  #if !defined(MBEDTLS_HAVE_INT64)
129  #define MBEDTLS_HAVE_INT64
130  #endif /* !MBEDTLS_HAVE_INT64 */
131  typedef int64_t mbedtls_mpi_sint;
132  typedef uint64_t mbedtls_mpi_uint;
133  #elif defined(__GNUC__) && ( \
134  defined(__amd64__) || defined(__x86_64__) || \
135  defined(__ppc64__) || defined(__powerpc64__) || \
136  defined(__ia64__) || defined(__alpha__) || \
137  ( defined(__sparc__) && defined(__arch64__) ) || \
138  defined(__s390x__) || defined(__mips64) || \
139  defined(__aarch64__) )
140  #if !defined(MBEDTLS_HAVE_INT64)
141  #define MBEDTLS_HAVE_INT64
142  #endif /* MBEDTLS_HAVE_INT64 */
143  typedef int64_t mbedtls_mpi_sint;
144  typedef uint64_t mbedtls_mpi_uint;
145  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
146  /* mbedtls_t_udbl defined as 128-bit unsigned int */
147  typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
148  #define MBEDTLS_HAVE_UDBL
149  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
150  #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
151  /*
152  * __ARMCC_VERSION is defined for both armcc and armclang and
153  * __aarch64__ is only defined by armclang when compiling 64-bit code
154  */
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  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
161  /* mbedtls_t_udbl defined as 128-bit unsigned int */
162  typedef __uint128_t mbedtls_t_udbl;
163  #define MBEDTLS_HAVE_UDBL
164  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
165  #elif defined(MBEDTLS_HAVE_INT64)
166  /* Force 64-bit integers with unknown compiler */
167  typedef int64_t mbedtls_mpi_sint;
168  typedef uint64_t mbedtls_mpi_uint;
169  #endif
170 #endif /* !MBEDTLS_HAVE_INT32 */
171 
172 #if !defined(MBEDTLS_HAVE_INT64)
173  /* Default to 32-bit compilation */
174  #if !defined(MBEDTLS_HAVE_INT32)
175  #define MBEDTLS_HAVE_INT32
176  #endif /* !MBEDTLS_HAVE_INT32 */
177  typedef int32_t mbedtls_mpi_sint;
178  typedef uint32_t mbedtls_mpi_uint;
179  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
180  typedef uint64_t mbedtls_t_udbl;
181  #define MBEDTLS_HAVE_UDBL
182  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
183 #endif /* !MBEDTLS_HAVE_INT64 */
184 
185 #ifdef __cplusplus
186 extern "C" {
187 #endif
188 
192 typedef struct mbedtls_mpi
193 {
194  int s;
195  size_t n;
197 }
199 
208 void mbedtls_mpi_init( mbedtls_mpi *X );
209 
217 void mbedtls_mpi_free( mbedtls_mpi *X );
218 
232 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
233 
249 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
250 
264 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
265 
273 
298 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
299 
323 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
324 
336 
347 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
348 
364 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
365 
378 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
379 
392 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
393 
407 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
408 
419 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
420 
443 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
444  char *buf, size_t buflen, size_t *olen );
445 
446 #if defined(MBEDTLS_FS_IO)
447 
468 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
469 
485 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
486  int radix, FILE *fout );
487 #endif /* MBEDTLS_FS_IO */
488 
501 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
502  size_t buflen );
503 
517  const unsigned char *buf, size_t buflen );
518 
534 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
535  size_t buflen );
536 
553  unsigned char *buf, size_t buflen );
554 
565 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
566 
577 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
578 
589 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
590 
601 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
602 
618 int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
619  unsigned *ret );
620 
632 
645  const mbedtls_mpi *B );
646 
660  const mbedtls_mpi *B );
661 
674  const mbedtls_mpi *B );
675 
688  const mbedtls_mpi *B );
689 
702  mbedtls_mpi_sint b );
703 
717  mbedtls_mpi_sint b );
718 
732  const mbedtls_mpi *B );
733 
748  mbedtls_mpi_uint b );
749 
769  const mbedtls_mpi *B );
770 
790  mbedtls_mpi_sint b );
791 
810  const mbedtls_mpi *B );
811 
829  mbedtls_mpi_sint b );
830 
858  const mbedtls_mpi *E, const mbedtls_mpi *N,
859  mbedtls_mpi *prec_RR );
860 
878 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
879  int (*f_rng)(void *, unsigned char *, size_t),
880  void *p_rng );
881 
915  mbedtls_mpi_sint min,
916  const mbedtls_mpi *N,
917  int (*f_rng)(void *, unsigned char *, size_t),
918  void *p_rng );
919 
931 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A,
932  const mbedtls_mpi *B );
933 
951  const mbedtls_mpi *N );
952 
953 #if !defined(MBEDTLS_DEPRECATED_REMOVED)
954 #if defined(MBEDTLS_DEPRECATED_WARNING)
955 #define MBEDTLS_DEPRECATED __attribute__((deprecated))
956 #else
957 #define MBEDTLS_DEPRECATED
958 #endif
959 
979  int (*f_rng)(void *, unsigned char *, size_t),
980  void *p_rng );
981 #undef MBEDTLS_DEPRECATED
982 #endif /* !MBEDTLS_DEPRECATED_REMOVED */
983 
1011 int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
1012  int (*f_rng)(void *, unsigned char *, size_t),
1013  void *p_rng );
1020 typedef enum {
1024 
1044 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
1045  int (*f_rng)(void *, unsigned char *, size_t),
1046  void *p_rng );
1047 
1048 #if defined(MBEDTLS_SELF_TEST)
1049 
1055 int mbedtls_mpi_self_test( int verbose );
1056 
1057 #endif /* MBEDTLS_SELF_TEST */
1058 
1059 #ifdef __cplusplus
1060 }
1061 #endif
1062 
1063 #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:957
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:177
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:180
int mbedtls_mpi_random(mbedtls_mpi *X, mbedtls_mpi_sint min, const mbedtls_mpi *N, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
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:196
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.
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_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:178
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:192
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:195
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 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:1020
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.