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
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 */
130typedef int64_t mbedtls_mpi_sint;
131typedef 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 */
143typedef int64_t mbedtls_mpi_sint;
144typedef 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 */
148typedef 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 */
159typedef int64_t mbedtls_mpi_sint;
160typedef 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 */
164typedef __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 */
169typedef int64_t mbedtls_mpi_sint;
170typedef 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 */
180typedef int32_t mbedtls_mpi_sint;
181typedef uint32_t mbedtls_mpi_uint;
182#define MBEDTLS_MPI_UINT_MAX UINT32_MAX
183 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
184typedef 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
213extern "C" {
214#endif
215
219typedef 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
285int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs);
286
302int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs);
303
318
326
355int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign);
356
384int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap);
385
397
408int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos);
409
425int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val);
426
440
454
469
480int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s);
481
504int 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)
529int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin);
530
546int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X,
547 int radix, FILE *fout);
548#endif /* MBEDTLS_FS_IO */
549
562int 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
595int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf,
596 size_t buflen);
597
614 unsigned char *buf, size_t buflen);
615
628int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count);
629
640int 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
766
781
795 const mbedtls_mpi *B);
796
812
832 const mbedtls_mpi *B);
833
854
873 const mbedtls_mpi *B);
874
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
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
1044int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds,
1045 int (*f_rng)(void *, unsigned char *, size_t),
1046 void *p_rng);
1053typedef enum {
1057
1077int 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
1088int 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