integer.h
1 /* integer.h
2  *
3  * Copyright (C) 2006-2020 wolfSSL Inc.
4  *
5  * This file is part of wolfSSL.
6  *
7  * wolfSSL is free software; you can redistribute it and/or modify
8  * it under the terms of the GNU General Public License as published by
9  * the Free Software Foundation; either version 2 of the License, or
10  * (at your option) any later version.
11  *
12  * wolfSSL is distributed in the hope that it will be useful,
13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15  * GNU General Public License for more details.
16  *
17  * You should have received a copy of the GNU General Public License
18  * along with this program; if not, write to the Free Software
19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
20  */
21 
22 
23 /*
24  * Based on public domain LibTomMath 0.38 by Tom St Denis, tomstdenis@iahu.ca,
25  * http://math.libtomcrypt.com
26  */
27 
28 
29 #ifndef WOLF_CRYPT_INTEGER_H
30 #define WOLF_CRYPT_INTEGER_H
31 
32 /* may optionally use fast math instead, not yet supported on all platforms and
33  may not be faster on all
34 */
35 #include <wolfssl/wolfcrypt/types.h> /* will set MP_xxBIT if not default */
36 #ifdef WOLFSSL_SP_MATH
37  #include <wolfssl/wolfcrypt/sp_int.h>
38 #elif defined(USE_FAST_MATH)
39  #include <wolfssl/wolfcrypt/tfm.h>
40 #else
41 
42 #include <wolfssl/wolfcrypt/random.h>
43 
44 #ifndef CHAR_BIT
45  #include <limits.h>
46 #endif
47 
48 #include <wolfssl/wolfcrypt/mpi_class.h>
49 
50 
51 #ifdef __cplusplus
52 extern "C" {
53 
54 /* C++ compilers don't like assigning void * to mp_digit * */
55 #define OPT_CAST(x) (x *)
56 
57 #elif defined(_SH3)
58 
59 /* SuperH SH3 compiler doesn't like assigning voi* to mp_digit* */
60 #define OPT_CAST(x) (x *)
61 
62 #else
63 
64 /* C on the other hand doesn't care */
65 #define OPT_CAST(x)
66 
67 #endif /* __cplusplus */
68 
69 
70 /* detect 64-bit mode if possible */
71 #if defined(__x86_64__) && !(defined (_MSC_VER) && defined(__clang__))
72  #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
73  #define MP_64BIT
74  #endif
75 #endif
76 /* if intel compiler doesn't provide 128 bit type don't turn on 64bit */
77 #if defined(MP_64BIT) && defined(__INTEL_COMPILER) && !defined(HAVE___UINT128_T)
78  #undef MP_64BIT
79 #endif
80 
81 
82 /* allow user to define on mp_digit, mp_word, DIGIT_BIT types */
83 #ifndef WOLFSSL_BIGINT_TYPES
84 
85 /* some default configurations.
86  *
87  * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
88  * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
89  *
90  * At the very least a mp_digit must be able to hold 7 bits
91  * [any size beyond that is ok provided it doesn't overflow the data type]
92  */
93 #ifdef MP_8BIT
94  /* 8-bit */
95  typedef unsigned char mp_digit;
96  typedef unsigned short mp_word;
97  /* don't define DIGIT_BIT, so its calculated below */
98 #elif defined(MP_16BIT)
99  /* 16-bit */
100  typedef unsigned int mp_digit;
101  typedef unsigned long mp_word;
102  /* don't define DIGIT_BIT, so its calculated below */
103 #elif defined(NO_64BIT)
104  /* 32-bit forced to 16-bit */
105  typedef unsigned short mp_digit;
106  typedef unsigned int mp_word;
107  #define DIGIT_BIT 12
108 #elif defined(MP_64BIT)
109  /* 64-bit */
110  /* for GCC only on supported platforms */
111  typedef unsigned long long mp_digit; /* 64 bit type, 128 uses mode(TI) */
112  typedef unsigned long mp_word __attribute__ ((mode(TI)));
113  #define DIGIT_BIT 60
114 #else
115  /* 32-bit default case */
116 
117  #if defined(_MSC_VER) || defined(__BORLANDC__)
118  typedef unsigned __int64 ulong64;
119  #else
120  typedef unsigned long long ulong64;
121  #endif
122 
123  typedef unsigned int mp_digit; /* long could be 64 now, changed TAO */
124  typedef ulong64 mp_word;
125 
126  #ifdef MP_31BIT
127  /* this is an extension that uses 31-bit digits */
128  #define DIGIT_BIT 31
129  #else
130  /* default case is 28-bit digits, defines MP_28BIT as a handy test macro */
131  #define DIGIT_BIT 28
132  #define MP_28BIT
133  #endif
134 #endif
135 
136 #endif /* WOLFSSL_BIGINT_TYPES */
137 
138 /* otherwise the bits per digit is calculated automatically from the size of
139  a mp_digit */
140 #ifndef DIGIT_BIT
141  #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))
142  /* bits per digit */
143 #endif
144 
145 #define MP_DIGIT_BIT DIGIT_BIT
146 #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
147 #define MP_DIGIT_MAX MP_MASK
148 
149 /* equalities */
150 #define MP_LT -1 /* less than */
151 #define MP_EQ 0 /* equal to */
152 #define MP_GT 1 /* greater than */
153 
154 #define MP_ZPOS 0 /* positive integer */
155 #define MP_NEG 1 /* negative */
156 
157 #define MP_OKAY 0 /* ok result */
158 #define MP_MEM -2 /* out of mem */
159 #define MP_VAL -3 /* invalid input */
160 #define MP_NOT_INF -4 /* point not at infinity */
161 #define MP_RANGE MP_NOT_INF
162 
163 #define MP_YES 1 /* yes response */
164 #define MP_NO 0 /* no response */
165 
166 /* Primality generation flags */
167 #define LTM_PRIME_BBS 0x0001 /* BBS style prime */
168 #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
169 #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
170 
171 typedef int mp_err;
172 
173 /* define this to use lower memory usage routines (exptmods mostly) */
174 #define MP_LOW_MEM
175 
176 /* default precision */
177 #ifndef MP_PREC
178  #ifndef MP_LOW_MEM
179  #define MP_PREC 32 /* default digits of precision */
180  #else
181  #define MP_PREC 1 /* default digits of precision */
182  #endif
183 #endif
184 
185 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD -
186  BITS_PER_DIGIT*2) */
187 #define MP_WARRAY ((mp_word)1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
188 
189 #ifdef HAVE_WOLF_BIGINT
190  /* raw big integer */
191  typedef struct WC_BIGINT {
192  byte* buf;
193  word32 len;
194  void* heap;
195  } WC_BIGINT;
196  #define WOLF_BIGINT_DEFINED
197 #endif
198 
199 /* the mp_int structure */
200 typedef struct mp_int {
201  int used, alloc, sign;
202  mp_digit *dp;
203 
204 #ifdef HAVE_WOLF_BIGINT
205  struct WC_BIGINT raw; /* unsigned binary (big endian) */
206 #endif
207 } mp_int;
208 
209 /* wolf big int and common functions */
210 #include <wolfssl/wolfcrypt/wolfmath.h>
211 
212 
213 /* callback for mp_prime_random, should fill dst with random bytes and return
214  how many read [up to len] */
215 typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
216 
217 
218 #define USED(m) ((m)->used)
219 #define DIGIT(m,k) ((m)->dp[(k)])
220 #define SIGN(m) ((m)->sign)
221 
222 
223 /* ---> Basic Manipulations <--- */
224 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
225 #define mp_isone(a) \
226  (((((a)->used == 1)) && ((a)->dp[0] == 1u)) ? MP_YES : MP_NO)
227 #define mp_iseven(a) \
228  (((a)->used > 0 && (((a)->dp[0] & 1u) == 0u)) ? MP_YES : MP_NO)
229 #define mp_isodd(a) \
230  (((a)->used > 0 && (((a)->dp[0] & 1u) == 1u)) ? MP_YES : MP_NO)
231 #define mp_isneg(a) (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)
232 #define mp_isword(a, w) \
233  ((((a)->used == 1) && ((a)->dp[0] == w)) || ((w == 0) && ((a)->used == 0)) \
234  ? MP_YES : MP_NO)
235 
236 /* number of primes */
237 #ifdef MP_8BIT
238  #define PRIME_SIZE 31
239 #else
240  #define PRIME_SIZE 256
241 #endif
242 
243 #ifndef MAX_INVMOD_SZ
244  #if defined(WOLFSSL_MYSQL_COMPATIBLE)
245  #define MAX_INVMOD_SZ 8192
246  #else
247  #define MAX_INVMOD_SZ 4096
248  #endif
249 #endif
250 
251 #define mp_prime_random(a, t, size, bbs, cb, dat) \
252  mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
253 
254 #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
255 #define mp_raw_size(mp) mp_signed_bin_size(mp)
256 #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
257 #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
258 #define mp_mag_size(mp) mp_unsigned_bin_size(mp)
259 #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
260 
261 #define MP_RADIX_BIN 2
262 #define MP_RADIX_OCT 8
263 #define MP_RADIX_DEC 10
264 #define MP_RADIX_HEX 16
265 #define MP_RADIX_MAX 64
266 
267 #define mp_tobinary(M, S) mp_toradix((M), (S), MP_RADIX_BIN)
268 #define mp_tooctal(M, S) mp_toradix((M), (S), MP_RADIX_OCT)
269 #define mp_todecimal(M, S) mp_toradix((M), (S), MP_RADIX_DEC)
270 #define mp_tohex(M, S) mp_toradix((M), (S), MP_RADIX_HEX)
271 
272 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
273 
274 #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY) || \
275  defined(WOLFSSL_DEBUG_MATH) || defined(DEBUG_WOLFSSL)
276 extern const char *mp_s_rmap;
277 #endif
278 
279 /* 6 functions needed by Rsa */
280 MP_API int mp_init (mp_int * a);
281 MP_API void mp_clear (mp_int * a);
282 MP_API void mp_free (mp_int * a);
283 MP_API void mp_forcezero(mp_int * a);
284 MP_API int mp_unsigned_bin_size(mp_int * a);
285 MP_API int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c);
286 MP_API int mp_to_unsigned_bin_at_pos(int x, mp_int *t, unsigned char *b);
287 MP_API int mp_to_unsigned_bin (mp_int * a, unsigned char *b);
288 MP_API int mp_to_unsigned_bin_len(mp_int * a, unsigned char *b, int c);
289 MP_API int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
290 MP_API int mp_exptmod_ex (mp_int * G, mp_int * X, int digits, mp_int * P,
291  mp_int * Y);
292 /* end functions needed by Rsa */
293 
294 /* functions added to support above needed, removed TOOM and KARATSUBA */
295 MP_API int mp_count_bits (mp_int * a);
296 MP_API int mp_leading_bit (mp_int * a);
297 MP_API int mp_init_copy (mp_int * a, mp_int * b);
298 MP_API int mp_copy (mp_int * a, mp_int * b);
299 MP_API int mp_grow (mp_int * a, int size);
300 MP_API int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
301 MP_API void mp_zero (mp_int * a);
302 MP_API void mp_clamp (mp_int * a);
303 MP_API void mp_exch (mp_int * a, mp_int * b);
304 MP_API void mp_rshd (mp_int * a, int b);
305 MP_API void mp_rshb (mp_int * a, int b);
306 MP_API int mp_mod_2d (mp_int * a, int b, mp_int * c);
307 MP_API int mp_mul_2d (mp_int * a, int b, mp_int * c);
308 MP_API int mp_lshd (mp_int * a, int b);
309 MP_API int mp_abs (mp_int * a, mp_int * b);
310 MP_API int mp_invmod (mp_int * a, mp_int * b, mp_int * c);
311 int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c);
312 MP_API int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
313 MP_API int mp_cmp_mag (mp_int * a, mp_int * b);
314 MP_API int mp_cmp (mp_int * a, mp_int * b);
315 MP_API int mp_cmp_d(mp_int * a, mp_digit b);
316 MP_API int mp_set (mp_int * a, mp_digit b);
317 MP_API int mp_is_bit_set (mp_int * a, mp_digit b);
318 MP_API int mp_mod (mp_int * a, mp_int * b, mp_int * c);
319 MP_API int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
320 MP_API int mp_div_2(mp_int * a, mp_int * b);
321 MP_API int mp_add (mp_int * a, mp_int * b, mp_int * c);
322 int s_mp_add (mp_int * a, mp_int * b, mp_int * c);
323 int s_mp_sub (mp_int * a, mp_int * b, mp_int * c);
324 MP_API int mp_sub (mp_int * a, mp_int * b, mp_int * c);
325 MP_API int mp_reduce_is_2k_l(mp_int *a);
326 MP_API int mp_reduce_is_2k(mp_int *a);
327 MP_API int mp_dr_is_modulus(mp_int *a);
328 MP_API int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y,
329  int);
330 MP_API int mp_exptmod_base_2 (mp_int * X, mp_int * P, mp_int * Y);
331 #define mp_exptmod_nct(G,X,P,Y) mp_exptmod_fast(G,X,P,Y,0)
332 MP_API int mp_montgomery_setup (mp_int * n, mp_digit * rho);
333 int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
334 MP_API int mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
335 MP_API void mp_dr_setup(mp_int *a, mp_digit *d);
336 MP_API int mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k);
337 MP_API int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
338 int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
339 int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
340 MP_API int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
341 MP_API int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
342 MP_API int mp_reduce (mp_int * x, mp_int * m, mp_int * mu);
343 MP_API int mp_reduce_setup (mp_int * a, mp_int * b);
344 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
345 MP_API int mp_montgomery_calc_normalization (mp_int * a, mp_int * b);
346 int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
347 int s_mp_sqr (mp_int * a, mp_int * b);
348 int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
349 int fast_s_mp_sqr (mp_int * a, mp_int * b);
350 MP_API int mp_init_size (mp_int * a, int size);
351 MP_API int mp_div_3 (mp_int * a, mp_int *c, mp_digit * d);
352 MP_API int mp_mul_2(mp_int * a, mp_int * b);
353 MP_API int mp_mul (mp_int * a, mp_int * b, mp_int * c);
354 MP_API int mp_sqr (mp_int * a, mp_int * b);
355 MP_API int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
356 MP_API int mp_submod (mp_int* a, mp_int* b, mp_int* c, mp_int* d);
357 MP_API int mp_addmod (mp_int* a, mp_int* b, mp_int* c, mp_int* d);
358 MP_API int mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
359 MP_API int mp_2expt (mp_int * a, int b);
360 MP_API int mp_set_bit (mp_int * a, int b);
361 MP_API int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
362 MP_API int mp_add_d (mp_int* a, mp_digit b, mp_int* c);
363 MP_API int mp_set_int (mp_int * a, unsigned long b);
364 MP_API int mp_sub_d (mp_int * a, mp_digit b, mp_int * c);
365 /* end support added functions */
366 
367 /* added */
368 MP_API int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e,
369  mp_int* f);
370 MP_API int mp_toradix (mp_int *a, char *str, int radix);
371 MP_API int mp_radix_size (mp_int * a, int radix, int *size);
372 
373 #ifdef WOLFSSL_DEBUG_MATH
374  MP_API void mp_dump(const char* desc, mp_int* a, byte verbose);
375 #else
376  #define mp_dump(desc, a, verbose)
377 #endif
378 
379 #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN) || !defined(NO_RSA) || \
380  !defined(NO_DSA) || !defined(NO_DH)
381  MP_API int mp_sqrmod(mp_int* a, mp_int* b, mp_int* c);
382 #endif
383 #if !defined(NO_DSA) || defined(HAVE_ECC)
384  MP_API int mp_read_radix(mp_int* a, const char* str, int radix);
385 #endif
386 
387 #if defined(WOLFSSL_KEY_GEN) || !defined(NO_RSA) || !defined(NO_DSA) || !defined(NO_DH)
388  MP_API int mp_prime_is_prime (mp_int * a, int t, int *result);
389  MP_API int mp_prime_is_prime_ex (mp_int * a, int t, int *result, WC_RNG*);
390 #endif /* WOLFSSL_KEY_GEN NO_RSA NO_DSA NO_DH */
391 #ifdef WOLFSSL_KEY_GEN
392  MP_API int mp_gcd (mp_int * a, mp_int * b, mp_int * c);
393  MP_API int mp_lcm (mp_int * a, mp_int * b, mp_int * c);
394  MP_API int mp_rand_prime(mp_int* N, int len, WC_RNG* rng, void* heap);
395 #endif
396 
397 MP_API int mp_cnt_lsb(mp_int *a);
398 MP_API int mp_mod_d(mp_int* a, mp_digit b, mp_digit* c);
399 
400 
401 #ifdef __cplusplus
402  }
403 #endif
404 
405 
406 #endif /* USE_FAST_MATH */
407 
408 #endif /* WOLF_CRYPT_INTEGER_H */
409 
mp_int
Definition: integer.h:200
WC_BIGINT
Definition: integer.h:191
WC_RNG
Definition: random.h:153