Mbed TLS v3.6.4
bignum.h
Go to the documentation of this file.
1 
6 /*
7  * Copyright The Mbed TLS Contributors
8  * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
9  */
10 #ifndef MBEDTLS_BIGNUM_H
11 #define MBEDTLS_BIGNUM_H
12 #include "mbedtls/private_access.h"
13 
14 #include "mbedtls/build_info.h"
15 #include "mbedtls/platform_util.h"
16 
17 #include <stddef.h>
18 #include <stdint.h>
19 
20 #if defined(MBEDTLS_FS_IO)
21 #include <stdio.h>
22 #endif
23 
25 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
27 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
29 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
31 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
33 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
35 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
37 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
39 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
40 
41 #define MBEDTLS_MPI_CHK(f) \
42  do \
43  { \
44  if ((ret = (f)) != 0) \
45  goto cleanup; \
46  } while (0)
47 
48 /*
49  * Maximum size MPIs are allowed to grow to in number of limbs.
50  */
51 #define MBEDTLS_MPI_MAX_LIMBS 10000
52 
53 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
54 /*
55  * Maximum window size used for modular exponentiation. Default: 3
56  * Minimum value: 1. Maximum value: 6.
57  *
58  * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
59  * for the sliding window calculation. (So 8 by default)
60  *
61  * Reduction in size, reduces speed.
62  */
63 #define MBEDTLS_MPI_WINDOW_SIZE 3
64 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
65 
66 #if !defined(MBEDTLS_MPI_MAX_SIZE)
67 /*
68  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
69  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
70  *
71  * Note: Calculations can temporarily result in larger MPIs. So the number
72  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
73  */
74 #define MBEDTLS_MPI_MAX_SIZE 1024
75 #endif /* !MBEDTLS_MPI_MAX_SIZE */
76 
77 #define MBEDTLS_MPI_MAX_BITS (8 * MBEDTLS_MPI_MAX_SIZE)
79 /*
80  * When reading from files with mbedtls_mpi_read_file() and writing to files with
81  * mbedtls_mpi_write_file() the buffer should have space
82  * for a (short) label, the MPI (in the provided radix), the newline
83  * characters and the '\0'.
84  *
85  * By default we assume at least a 10 char label, a minimum radix of 10
86  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
87  * Autosized at compile time for at least a 10 char label, a minimum radix
88  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
89  *
90  * This used to be statically sized to 1250 for a maximum of 4096 bit
91  * numbers (1234 decimal chars).
92  *
93  * Calculate using the formula:
94  * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
95  * LabelSize + 6
96  */
97 #define MBEDTLS_MPI_MAX_BITS_SCALE100 (100 * MBEDTLS_MPI_MAX_BITS)
98 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
99 #define MBEDTLS_MPI_RW_BUFFER_SIZE (((MBEDTLS_MPI_MAX_BITS_SCALE100 + \
100  MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / \
101  MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6)
102 
103 /*
104  * Define the base integer type, architecture-wise.
105  *
106  * 32 or 64-bit integer types can be forced regardless of the underlying
107  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
108  * respectively and undefining MBEDTLS_HAVE_ASM.
109  *
110  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
111  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
112  */
113 #if !defined(MBEDTLS_HAVE_INT32)
114  #if defined(_MSC_VER) && defined(_M_AMD64)
115 /* Always choose 64-bit when using MSC */
116  #if !defined(MBEDTLS_HAVE_INT64)
117  #define MBEDTLS_HAVE_INT64
118  #endif /* !MBEDTLS_HAVE_INT64 */
119 typedef int64_t mbedtls_mpi_sint;
120 typedef uint64_t mbedtls_mpi_uint;
121 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
122  #elif defined(__GNUC__) && ( \
123  defined(__amd64__) || defined(__x86_64__) || \
124  defined(__ppc64__) || defined(__powerpc64__) || \
125  defined(__ia64__) || defined(__alpha__) || \
126  (defined(__sparc__) && defined(__arch64__)) || \
127  defined(__s390x__) || defined(__mips64) || \
128  defined(__aarch64__))
129  #if !defined(MBEDTLS_HAVE_INT64)
130  #define MBEDTLS_HAVE_INT64
131  #endif /* MBEDTLS_HAVE_INT64 */
132 typedef int64_t mbedtls_mpi_sint;
133 typedef uint64_t mbedtls_mpi_uint;
134 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
135  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
136 /* mbedtls_t_udbl defined as 128-bit unsigned int */
137 typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
138  #define MBEDTLS_HAVE_UDBL
139  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
140  #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
141 /*
142  * __ARMCC_VERSION is defined for both armcc and armclang and
143  * __aarch64__ is only defined by armclang when compiling 64-bit code
144  */
145  #if !defined(MBEDTLS_HAVE_INT64)
146  #define MBEDTLS_HAVE_INT64
147  #endif /* !MBEDTLS_HAVE_INT64 */
148 typedef int64_t mbedtls_mpi_sint;
149 typedef uint64_t mbedtls_mpi_uint;
150 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
151  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
152 /* mbedtls_t_udbl defined as 128-bit unsigned int */
153 typedef __uint128_t mbedtls_t_udbl;
154  #define MBEDTLS_HAVE_UDBL
155  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
156  #elif defined(MBEDTLS_HAVE_INT64)
157 /* Force 64-bit integers with unknown compiler */
158 typedef int64_t mbedtls_mpi_sint;
159 typedef uint64_t mbedtls_mpi_uint;
160 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
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 #define MBEDTLS_MPI_UINT_MAX UINT32_MAX
172  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
173 typedef uint64_t mbedtls_t_udbl;
174  #define MBEDTLS_HAVE_UDBL
175  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
176 #endif /* !MBEDTLS_HAVE_INT64 */
177 
178 /*
179  * Sanity check that exactly one of MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 is defined,
180  * so that code elsewhere doesn't have to check.
181  */
182 #if (!(defined(MBEDTLS_HAVE_INT32) || defined(MBEDTLS_HAVE_INT64))) || \
183  (defined(MBEDTLS_HAVE_INT32) && defined(MBEDTLS_HAVE_INT64))
184 #error "Only 32-bit or 64-bit limbs are supported in bignum"
185 #endif
186 
201 #ifdef __cplusplus
202 extern "C" {
203 #endif
204 
208 typedef struct mbedtls_mpi {
214 
226  signed short MBEDTLS_PRIVATE(s);
227 
229  unsigned short MBEDTLS_PRIVATE(n);
230  /* Make sure that MBEDTLS_MPI_MAX_LIMBS fits in n.
231  * Use the same limit value on all platforms so that we don't have to
232  * think about different behavior on the rare platforms where
233  * unsigned short can store values larger than the minimum required by
234  * the C language, which is 65535.
235  */
236 #if MBEDTLS_MPI_MAX_LIMBS > 65535
237 #error "MBEDTLS_MPI_MAX_LIMBS > 65535 is not supported"
238 #endif
239 }
241 
251 
260 
274 int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs);
275 
291 int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs);
292 
307 
315 
344 int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign);
345 
373 int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap);
374 
386 
397 int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos);
398 
414 int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val);
415 
428 size_t mbedtls_mpi_lsb(const mbedtls_mpi *X);
429 
443 
457 size_t mbedtls_mpi_size(const mbedtls_mpi *X);
458 
469 int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s);
470 
493 int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix,
494  char *buf, size_t buflen, size_t *olen);
495 
496 #if defined(MBEDTLS_FS_IO)
518 int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin);
519 
535 int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X,
536  int radix, FILE *fout);
537 #endif /* MBEDTLS_FS_IO */
538 
551 int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf,
552  size_t buflen);
553 
567  const unsigned char *buf, size_t buflen);
568 
584 int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf,
585  size_t buflen);
586 
603  unsigned char *buf, size_t buflen);
604 
617 int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count);
618 
629 int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count);
630 
642 
654 
671  unsigned *ret);
672 
684 
697  const mbedtls_mpi *B);
698 
712  const mbedtls_mpi *B);
713 
726  const mbedtls_mpi *B);
727 
740  const mbedtls_mpi *B);
741 
754  mbedtls_mpi_sint b);
755 
769  mbedtls_mpi_sint b);
770 
784  const mbedtls_mpi *B);
785 
800  mbedtls_mpi_uint b);
801 
821  const mbedtls_mpi *B);
822 
842  mbedtls_mpi_sint b);
843 
862  const mbedtls_mpi *B);
863 
881  mbedtls_mpi_sint b);
882 
911  const mbedtls_mpi *E, const mbedtls_mpi *N,
912  mbedtls_mpi *prec_RR);
913 
932  mbedtls_f_rng_t *f_rng,
933  void *p_rng);
934 
968  mbedtls_mpi_sint min,
969  const mbedtls_mpi *N,
970  mbedtls_f_rng_t *f_rng,
971  void *p_rng);
972 
985  const mbedtls_mpi *B);
986 
1004  const mbedtls_mpi *N);
1005 
1033 int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds,
1034  mbedtls_f_rng_t *f_rng,
1035  void *p_rng);
1042 typedef enum {
1046 
1066 int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags,
1067  mbedtls_f_rng_t *f_rng,
1068  void *p_rng);
1069 
1070 #if defined(MBEDTLS_SELF_TEST)
1071 
1077 int mbedtls_mpi_self_test(int verbose);
1078 
1079 #endif /* MBEDTLS_SELF_TEST */
1080 
1081 #ifdef __cplusplus
1082 }
1083 #endif
1084 
1085 #endif /* bignum.h */
int mbedtls_mpi_fill_random(mbedtls_mpi *X, size_t size, mbedtls_f_rng_t *f_rng, void *p_rng)
Fill an MPI with a number of random bytes.
int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags, mbedtls_f_rng_t *f_rng, void *p_rng)
Generate a prime number.
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 modular exponentiation: X = A^E mod N.
int32_t mbedtls_mpi_sint
The signed type corresponding to mbedtls_mpi_uint.
Definition: bignum.h:169
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:1042
@ MBEDTLS_MPI_GEN_PRIME_FLAG_DH
Definition: bignum.h:1043
@ MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR
Definition: bignum.h:1044
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_is_prime_ext(const mbedtls_mpi *X, int rounds, mbedtls_f_rng_t *f_rng, void *p_rng)
Miller-Rabin primality test.
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_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y)
Compare the absolute values of two MPIs.
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.
int mbedtls_mpi_random(mbedtls_mpi *X, mbedtls_mpi_sint min, const mbedtls_mpi *N, mbedtls_f_rng_t *f_rng, void *p_rng)
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:170
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_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:173
Build-time configuration info.
Common and shared functions used by multiple modules in the Mbed TLS library.
int mbedtls_f_rng_t(void *p_rng, unsigned char *output, size_t output_size)
The type of custom random generator (RNG) callbacks.
Macro wrapper for struct's members.
#define MBEDTLS_PRIVATE(member)
MPI structure.
Definition: bignum.h:208