Mbed TLS v3.5.0
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 #include "mbedtls/private_access.h"
25 
26 #include "mbedtls/build_info.h"
27 
28 #include <stddef.h>
29 #include <stdint.h>
30 
31 #if defined(MBEDTLS_FS_IO)
32 #include <stdio.h>
33 #endif
34 
36 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
38 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
40 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
42 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
44 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
46 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
48 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
50 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
51 
52 #define MBEDTLS_MPI_CHK(f) \
53  do \
54  { \
55  if ((ret = (f)) != 0) \
56  goto cleanup; \
57  } while (0)
58 
59 /*
60  * Maximum size MPIs are allowed to grow to in number of limbs.
61  */
62 #define MBEDTLS_MPI_MAX_LIMBS 10000
63 
64 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
65 /*
66  * Maximum window size used for modular exponentiation. Default: 2
67  * Minimum value: 1. Maximum value: 6.
68  *
69  * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
70  * for the sliding window calculation. (So 64 by default)
71  *
72  * Reduction in size, reduces speed.
73  */
74 #define MBEDTLS_MPI_WINDOW_SIZE 2
75 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
76 
77 #if !defined(MBEDTLS_MPI_MAX_SIZE)
78 /*
79  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
80  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
81  *
82  * Note: Calculations can temporarily result in larger MPIs. So the number
83  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
84  */
85 #define MBEDTLS_MPI_MAX_SIZE 1024
86 #endif /* !MBEDTLS_MPI_MAX_SIZE */
87 
88 #define MBEDTLS_MPI_MAX_BITS (8 * MBEDTLS_MPI_MAX_SIZE)
90 /*
91  * When reading from files with mbedtls_mpi_read_file() and writing to files with
92  * mbedtls_mpi_write_file() the buffer should have space
93  * for a (short) label, the MPI (in the provided radix), the newline
94  * characters and the '\0'.
95  *
96  * By default we assume at least a 10 char label, a minimum radix of 10
97  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
98  * Autosized at compile time for at least a 10 char label, a minimum radix
99  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
100  *
101  * This used to be statically sized to 1250 for a maximum of 4096 bit
102  * numbers (1234 decimal chars).
103  *
104  * Calculate using the formula:
105  * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
106  * LabelSize + 6
107  */
108 #define MBEDTLS_MPI_MAX_BITS_SCALE100 (100 * MBEDTLS_MPI_MAX_BITS)
109 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
110 #define MBEDTLS_MPI_RW_BUFFER_SIZE (((MBEDTLS_MPI_MAX_BITS_SCALE100 + \
111  MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / \
112  MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6)
113 
114 /*
115  * Define the base integer type, architecture-wise.
116  *
117  * 32 or 64-bit integer types can be forced regardless of the underlying
118  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
119  * respectively and undefining MBEDTLS_HAVE_ASM.
120  *
121  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
122  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
123  */
124 #if !defined(MBEDTLS_HAVE_INT32)
125  #if defined(_MSC_VER) && defined(_M_AMD64)
126 /* Always choose 64-bit when using MSC */
127  #if !defined(MBEDTLS_HAVE_INT64)
128  #define MBEDTLS_HAVE_INT64
129  #endif /* !MBEDTLS_HAVE_INT64 */
130 typedef int64_t mbedtls_mpi_sint;
131 typedef uint64_t mbedtls_mpi_uint;
132 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
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 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
146  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
147 /* mbedtls_t_udbl defined as 128-bit unsigned int */
148 typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
149  #define MBEDTLS_HAVE_UDBL
150  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
151  #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
152 /*
153  * __ARMCC_VERSION is defined for both armcc and armclang and
154  * __aarch64__ is only defined by armclang when compiling 64-bit code
155  */
156  #if !defined(MBEDTLS_HAVE_INT64)
157  #define MBEDTLS_HAVE_INT64
158  #endif /* !MBEDTLS_HAVE_INT64 */
159 typedef int64_t mbedtls_mpi_sint;
160 typedef uint64_t mbedtls_mpi_uint;
161 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
162  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
163 /* mbedtls_t_udbl defined as 128-bit unsigned int */
164 typedef __uint128_t mbedtls_t_udbl;
165  #define MBEDTLS_HAVE_UDBL
166  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
167  #elif defined(MBEDTLS_HAVE_INT64)
168 /* Force 64-bit integers with unknown compiler */
169 typedef int64_t mbedtls_mpi_sint;
170 typedef uint64_t mbedtls_mpi_uint;
171 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
172  #endif
173 #endif /* !MBEDTLS_HAVE_INT32 */
174 
175 #if !defined(MBEDTLS_HAVE_INT64)
176 /* Default to 32-bit compilation */
177  #if !defined(MBEDTLS_HAVE_INT32)
178  #define MBEDTLS_HAVE_INT32
179  #endif /* !MBEDTLS_HAVE_INT32 */
180 typedef int32_t mbedtls_mpi_sint;
181 typedef uint32_t mbedtls_mpi_uint;
182 #define MBEDTLS_MPI_UINT_MAX UINT32_MAX
183  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
184 typedef uint64_t mbedtls_t_udbl;
185  #define MBEDTLS_HAVE_UDBL
186  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
187 #endif /* !MBEDTLS_HAVE_INT64 */
188 
189 /*
190  * Sanity check that exactly one of MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 is defined,
191  * so that code elsewhere doesn't have to check.
192  */
193 #if (!(defined(MBEDTLS_HAVE_INT32) || defined(MBEDTLS_HAVE_INT64))) || \
194  (defined(MBEDTLS_HAVE_INT32) && defined(MBEDTLS_HAVE_INT64))
195 #error "Only 32-bit or 64-bit limbs are supported in bignum"
196 #endif
197 
212 #ifdef __cplusplus
213 extern "C" {
214 #endif
215 
219 typedef struct mbedtls_mpi {
225 
237  signed short MBEDTLS_PRIVATE(s);
238 
240  unsigned short MBEDTLS_PRIVATE(n);
241  /* Make sure that MBEDTLS_MPI_MAX_LIMBS fits in n.
242  * Use the same limit value on all platforms so that we don't have to
243  * think about different behavior on the rare platforms where
244  * unsigned short can store values larger than the minimum required by
245  * the C language, which is 65535.
246  */
247 #if MBEDTLS_MPI_MAX_LIMBS > 65535
248 #error "MBEDTLS_MPI_MAX_LIMBS > 65535 is not supported"
249 #endif
250 }
252 
262 
271 
285 int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs);
286 
302 int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs);
303 
318 
326 
355 int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign);
356 
384 int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap);
385 
397 
408 int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos);
409 
425 int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val);
426 
439 size_t mbedtls_mpi_lsb(const mbedtls_mpi *X);
440 
454 
468 size_t mbedtls_mpi_size(const mbedtls_mpi *X);
469 
480 int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s);
481 
504 int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix,
505  char *buf, size_t buflen, size_t *olen);
506 
507 #if defined(MBEDTLS_FS_IO)
529 int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin);
530 
546 int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X,
547  int radix, FILE *fout);
548 #endif /* MBEDTLS_FS_IO */
549 
562 int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf,
563  size_t buflen);
564 
578  const unsigned char *buf, size_t buflen);
579 
595 int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf,
596  size_t buflen);
597 
614  unsigned char *buf, size_t buflen);
615 
628 int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count);
629 
640 int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count);
641 
653 
665 
682  unsigned *ret);
683 
695 
708  const mbedtls_mpi *B);
709 
723  const mbedtls_mpi *B);
724 
737  const mbedtls_mpi *B);
738 
751  const mbedtls_mpi *B);
752 
765  mbedtls_mpi_sint b);
766 
780  mbedtls_mpi_sint b);
781 
795  const mbedtls_mpi *B);
796 
811  mbedtls_mpi_uint b);
812 
832  const mbedtls_mpi *B);
833 
853  mbedtls_mpi_sint b);
854 
873  const mbedtls_mpi *B);
874 
892  mbedtls_mpi_sint b);
893 
922  const mbedtls_mpi *E, const mbedtls_mpi *N,
923  mbedtls_mpi *prec_RR);
924 
943  int (*f_rng)(void *, unsigned char *, size_t),
944  void *p_rng);
945 
979  mbedtls_mpi_sint min,
980  const mbedtls_mpi *N,
981  int (*f_rng)(void *, unsigned char *, size_t),
982  void *p_rng);
983 
996  const mbedtls_mpi *B);
997 
1015  const mbedtls_mpi *N);
1016 
1044 int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds,
1045  int (*f_rng)(void *, unsigned char *, size_t),
1046  void *p_rng);
1053 typedef enum {
1057 
1077 int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags,
1078  int (*f_rng)(void *, unsigned char *, size_t),
1079  void *p_rng);
1080 
1081 #if defined(MBEDTLS_SELF_TEST)
1082 
1088 int mbedtls_mpi_self_test(int verbose);
1089 
1090 #endif /* MBEDTLS_SELF_TEST */
1091 
1092 #ifdef __cplusplus
1093 }
1094 #endif
1095 
1096 #endif /* bignum.h */
int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s)
Import an MPI from an ASCII string.
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_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.
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_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap)
Perform a safe conditional swap which doesn't reveal whether the condition was true or not.
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_grow(mbedtls_mpi *X, size_t nblimbs)
Enlarge an MPI to the specified number of limbs.
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_is_prime_ext(const mbedtls_mpi *X, int rounds, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
Miller-Rabin primality test.
int32_t mbedtls_mpi_sint
The signed type corresponding to mbedtls_mpi_uint.
Definition: bignum.h:180
int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y)
Make a copy of an MPI.
int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val)
Modify a specific bit in an MPI.
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.
mbedtls_mpi_gen_prime_flag_t
Flags for mbedtls_mpi_gen_prime()
Definition: bignum.h:1053
@ MBEDTLS_MPI_GEN_PRIME_FLAG_DH
Definition: bignum.h:1054
@ MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR
Definition: bignum.h:1055
size_t mbedtls_mpi_size(const mbedtls_mpi *X)
Return the total size of an MPI value in bytes.
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_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_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.
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.
void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y)
Swap the contents of two MPIs.
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_lset(mbedtls_mpi *X, mbedtls_mpi_sint z)
Store integer value in MPI.
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_read_binary(mbedtls_mpi *X, const unsigned char *buf, size_t buflen)
Import an MPI from unsigned big endian binary data.
int mbedtls_mpi_self_test(int verbose)
Checkup routine.
int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y)
Compare two MPIs.
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_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_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_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y)
Compare the absolute values of two MPIs.
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.
int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count)
Perform a left-shift on an MPI: X <<= count.
void mbedtls_mpi_init(mbedtls_mpi *X)
Initialize an MPI context.
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_mul_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform a multiplication of two MPIs: X = A * B.
uint32_t mbedtls_mpi_uint
The type of machine digits in a bignum, called limbs.
Definition: bignum.h:181
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_write_file(const char *p, const mbedtls_mpi *X, int radix, FILE *fout)
Export an MPI into an opened file.
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_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N)
Compute the modular inverse: X = A^-1 mod N.
int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos)
Get a specific bit from an MPI.
void mbedtls_mpi_free(mbedtls_mpi *X)
This function frees the components of an MPI context.
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.
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_file(mbedtls_mpi *X, int radix, FILE *fin)
Read an MPI from a line in an opened file.
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 ...
int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z)
Compare an MPI with an integer.
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|.
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_shift_r(mbedtls_mpi *X, size_t count)
Perform a right-shift on an MPI: X >>= count.
int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B)
Compute the greatest common divisor: G = gcd(A, B)
struct mbedtls_mpi mbedtls_mpi
MPI structure.
uint64_t mbedtls_t_udbl
Definition: bignum.h:184
Build-time configuration info.
Macro wrapper for struct's members.
#define MBEDTLS_PRIVATE(member)
MPI structure.
Definition: bignum.h:219