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bignum.h
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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 
16 #include <stddef.h>
17 #include <stdint.h>
18 
19 #if defined(MBEDTLS_FS_IO)
20 #include <stdio.h>
21 #endif
22 
24 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
25 
26 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
27 
28 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
29 
30 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
31 
32 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
33 
34 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
35 
36 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
37 
38 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
39 
40 #define MBEDTLS_MPI_CHK(f) \
41  do \
42  { \
43  if ((ret = (f)) != 0) \
44  goto cleanup; \
45  } while (0)
46 
47 /*
48  * Maximum size MPIs are allowed to grow to in number of limbs.
49  */
50 #define MBEDTLS_MPI_MAX_LIMBS 10000
51 
52 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
53 /*
54  * Maximum window size used for modular exponentiation. Default: 3
55  * Minimum value: 1. Maximum value: 6.
56  *
57  * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
58  * for the sliding window calculation. (So 8 by default)
59  *
60  * Reduction in size, reduces speed.
61  */
62 #define MBEDTLS_MPI_WINDOW_SIZE 3
63 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
64 
65 #if !defined(MBEDTLS_MPI_MAX_SIZE)
66 /*
67  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
68  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
69  *
70  * Note: Calculations can temporarily result in larger MPIs. So the number
71  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
72  */
73 #define MBEDTLS_MPI_MAX_SIZE 1024
74 #endif /* !MBEDTLS_MPI_MAX_SIZE */
75 
76 #define MBEDTLS_MPI_MAX_BITS (8 * MBEDTLS_MPI_MAX_SIZE)
78 /*
79  * When reading from files with mbedtls_mpi_read_file() and writing to files with
80  * mbedtls_mpi_write_file() the buffer should have space
81  * for a (short) label, the MPI (in the provided radix), the newline
82  * characters and the '\0'.
83  *
84  * By default we assume at least a 10 char label, a minimum radix of 10
85  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
86  * Autosized at compile time for at least a 10 char label, a minimum radix
87  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
88  *
89  * This used to be statically sized to 1250 for a maximum of 4096 bit
90  * numbers (1234 decimal chars).
91  *
92  * Calculate using the formula:
93  * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
94  * LabelSize + 6
95  */
96 #define MBEDTLS_MPI_MAX_BITS_SCALE100 (100 * MBEDTLS_MPI_MAX_BITS)
97 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
98 #define MBEDTLS_MPI_RW_BUFFER_SIZE (((MBEDTLS_MPI_MAX_BITS_SCALE100 + \
99  MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / \
100  MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6)
101 
102 /*
103  * Define the base integer type, architecture-wise.
104  *
105  * 32 or 64-bit integer types can be forced regardless of the underlying
106  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
107  * respectively and undefining MBEDTLS_HAVE_ASM.
108  *
109  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
110  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
111  */
112 #if !defined(MBEDTLS_HAVE_INT32)
113  #if defined(_MSC_VER) && defined(_M_AMD64)
114 /* Always choose 64-bit when using MSC */
115  #if !defined(MBEDTLS_HAVE_INT64)
116  #define MBEDTLS_HAVE_INT64
117  #endif /* !MBEDTLS_HAVE_INT64 */
118 typedef int64_t mbedtls_mpi_sint;
119 typedef uint64_t mbedtls_mpi_uint;
120 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
121  #elif defined(__GNUC__) && ( \
122  defined(__amd64__) || defined(__x86_64__) || \
123  defined(__ppc64__) || defined(__powerpc64__) || \
124  defined(__ia64__) || defined(__alpha__) || \
125  (defined(__sparc__) && defined(__arch64__)) || \
126  defined(__s390x__) || defined(__mips64) || \
127  defined(__aarch64__))
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 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
134  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
135 /* mbedtls_t_udbl defined as 128-bit unsigned int */
136 typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
137  #define MBEDTLS_HAVE_UDBL
138  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
139  #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
140 /*
141  * __ARMCC_VERSION is defined for both armcc and armclang and
142  * __aarch64__ is only defined by armclang when compiling 64-bit code
143  */
144  #if !defined(MBEDTLS_HAVE_INT64)
145  #define MBEDTLS_HAVE_INT64
146  #endif /* !MBEDTLS_HAVE_INT64 */
147 typedef int64_t mbedtls_mpi_sint;
148 typedef uint64_t mbedtls_mpi_uint;
149 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
150  #if !defined(MBEDTLS_NO_UDBL_DIVISION)
151 /* mbedtls_t_udbl defined as 128-bit unsigned int */
152 typedef __uint128_t mbedtls_t_udbl;
153  #define MBEDTLS_HAVE_UDBL
154  #endif /* !MBEDTLS_NO_UDBL_DIVISION */
155  #elif defined(MBEDTLS_HAVE_INT64)
156 /* Force 64-bit integers with unknown compiler */
157 typedef int64_t mbedtls_mpi_sint;
158 typedef uint64_t mbedtls_mpi_uint;
159 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX
160  #endif
161 #endif /* !MBEDTLS_HAVE_INT32 */
162 
163 #if !defined(MBEDTLS_HAVE_INT64)
164 /* Default to 32-bit compilation */
165  #if !defined(MBEDTLS_HAVE_INT32)
166  #define MBEDTLS_HAVE_INT32
167  #endif /* !MBEDTLS_HAVE_INT32 */
168 typedef int32_t mbedtls_mpi_sint;
169 typedef uint32_t mbedtls_mpi_uint;
170 #define MBEDTLS_MPI_UINT_MAX UINT32_MAX
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 /*
178  * Sanity check that exactly one of MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 is defined,
179  * so that code elsewhere doesn't have to check.
180  */
181 #if (!(defined(MBEDTLS_HAVE_INT32) || defined(MBEDTLS_HAVE_INT64))) || \
182  (defined(MBEDTLS_HAVE_INT32) && defined(MBEDTLS_HAVE_INT64))
183 #error "Only 32-bit or 64-bit limbs are supported in bignum"
184 #endif
185 
200 #ifdef __cplusplus
201 extern "C" {
202 #endif
203 
207 typedef struct mbedtls_mpi {
212  mbedtls_mpi_uint *MBEDTLS_PRIVATE(p);
213 
225  signed short MBEDTLS_PRIVATE(s);
226 
228  unsigned short MBEDTLS_PRIVATE(n);
229  /* Make sure that MBEDTLS_MPI_MAX_LIMBS fits in n.
230  * Use the same limit value on all platforms so that we don't have to
231  * think about different behavior on the rare platforms where
232  * unsigned short can store values larger than the minimum required by
233  * the C language, which is 65535.
234  */
235 #if MBEDTLS_MPI_MAX_LIMBS > 65535
236 #error "MBEDTLS_MPI_MAX_LIMBS > 65535 is not supported"
237 #endif
238 }
240 
250 
259 
273 int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs);
274 
290 int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs);
291 
305 int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y);
306 
314 
343 int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign);
344 
372 int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap);
373 
384 int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z);
385 
396 int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos);
397 
413 int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val);
414 
427 size_t mbedtls_mpi_lsb(const mbedtls_mpi *X);
428 
441 size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X);
442 
456 size_t mbedtls_mpi_size(const mbedtls_mpi *X);
457 
468 int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s);
469 
492 int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix,
493  char *buf, size_t buflen, size_t *olen);
494 
495 #if defined(MBEDTLS_FS_IO)
496 
517 int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin);
518 
534 int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X,
535  int radix, FILE *fout);
536 #endif /* MBEDTLS_FS_IO */
537 
550 int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf,
551  size_t buflen);
552 
566  const unsigned char *buf, size_t buflen);
567 
583 int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf,
584  size_t buflen);
585 
602  unsigned char *buf, size_t buflen);
603 
616 int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count);
617 
628 int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count);
629 
640 int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y);
641 
652 int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y);
653 
669 int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X, const mbedtls_mpi *Y,
670  unsigned *ret);
671 
682 int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z);
683 
696  const mbedtls_mpi *B);
697 
711  const mbedtls_mpi *B);
712 
725  const mbedtls_mpi *B);
726 
739  const mbedtls_mpi *B);
740 
753  mbedtls_mpi_sint b);
754 
768  mbedtls_mpi_sint b);
769 
783  const mbedtls_mpi *B);
784 
799  mbedtls_mpi_uint b);
800 
820  const mbedtls_mpi *B);
821 
841  mbedtls_mpi_sint b);
842 
861  const mbedtls_mpi *B);
862 
879 int mbedtls_mpi_mod_int(mbedtls_mpi_uint *r, const mbedtls_mpi *A,
880  mbedtls_mpi_sint b);
881 
910  const mbedtls_mpi *E, const mbedtls_mpi *N,
911  mbedtls_mpi *prec_RR);
912 
930 int mbedtls_mpi_fill_random(mbedtls_mpi *X, size_t size,
931  int (*f_rng)(void *, unsigned char *, size_t),
932  void *p_rng);
933 
967  mbedtls_mpi_sint min,
968  const mbedtls_mpi *N,
969  int (*f_rng)(void *, unsigned char *, size_t),
970  void *p_rng);
971 
983 int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A,
984  const mbedtls_mpi *B);
985 
1003  const mbedtls_mpi *N);
1004 
1032 int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds,
1033  int (*f_rng)(void *, unsigned char *, size_t),
1034  void *p_rng);
1041 typedef enum {
1045 
1065 int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags,
1066  int (*f_rng)(void *, unsigned char *, size_t),
1067  void *p_rng);
1068 
1069 #if defined(MBEDTLS_SELF_TEST)
1070 
1076 int mbedtls_mpi_self_test(int verbose);
1077 
1078 #endif /* MBEDTLS_SELF_TEST */
1079 
1080 #ifdef __cplusplus
1081 }
1082 #endif
1083 
1084 #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.
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.
#define MBEDTLS_PRIVATE(member)
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_read_string(mbedtls_mpi *X, int radix, const char *s)
Import an MPI from an ASCII string.
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.
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...
int32_t mbedtls_mpi_sint
The signed type corresponding to mbedtls_mpi_uint.
Definition: bignum.h:168
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.
uint32_t mbedtls_mpi_uint
The type of machine digits in a bignum, called limbs.
Definition: bignum.h:169
int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count)
Perform a left-shift on an MPI: X <<= count.
Macro wrapper for struct's members.
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_self_test(int verbose)
Checkup routine.
Build-time configuration info.
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:207
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.
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 modular 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:1041
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_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_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.