1 | /* integer.h
|
---|
2 | *
|
---|
3 | * Copyright (C) 2006-2015 wolfSSL Inc.
|
---|
4 | *
|
---|
5 | * This file is part of wolfSSL. (formerly known as CyaSSL)
|
---|
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 02110-1301, USA
|
---|
20 | */
|
---|
21 |
|
---|
22 | /*
|
---|
23 | * Based on public domain LibTomMath 0.38 by Tom St Denis, tomstdenis@iahu.ca,
|
---|
24 | * http://math.libtomcrypt.com
|
---|
25 | */
|
---|
26 |
|
---|
27 |
|
---|
28 | #ifndef WOLF_CRYPT_INTEGER_H
|
---|
29 | #define WOLF_CRYPT_INTEGER_H
|
---|
30 |
|
---|
31 | /* may optionally use fast math instead, not yet supported on all platforms and
|
---|
32 | may not be faster on all
|
---|
33 | */
|
---|
34 | #include <wolfssl/wolfcrypt/types.h> /* will set MP_xxBIT if not default */
|
---|
35 | #ifdef USE_FAST_MATH
|
---|
36 | #include <wolfssl/wolfcrypt/tfm.h>
|
---|
37 | #else
|
---|
38 |
|
---|
39 | #include <wolfssl/wolfcrypt/random.h>
|
---|
40 |
|
---|
41 | #ifndef CHAR_BIT
|
---|
42 | #include <limits.h>
|
---|
43 | #endif
|
---|
44 |
|
---|
45 | #include <wolfssl/wolfcrypt/mpi_class.h>
|
---|
46 |
|
---|
47 | #ifndef MIN
|
---|
48 | #define MIN(x,y) ((x)<(y)?(x):(y))
|
---|
49 | #endif
|
---|
50 |
|
---|
51 | #ifndef MAX
|
---|
52 | #define MAX(x,y) ((x)>(y)?(x):(y))
|
---|
53 | #endif
|
---|
54 |
|
---|
55 | #ifdef __cplusplus
|
---|
56 | extern "C" {
|
---|
57 |
|
---|
58 | /* C++ compilers don't like assigning void * to mp_digit * */
|
---|
59 | #define OPT_CAST(x) (x *)
|
---|
60 |
|
---|
61 | #else
|
---|
62 |
|
---|
63 | /* C on the other hand doesn't care */
|
---|
64 | #define OPT_CAST(x)
|
---|
65 |
|
---|
66 | #endif
|
---|
67 |
|
---|
68 |
|
---|
69 | /* detect 64-bit mode if possible */
|
---|
70 | #if defined(__x86_64__)
|
---|
71 | #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
|
---|
72 | #define MP_64BIT
|
---|
73 | #endif
|
---|
74 | #endif
|
---|
75 | /* if intel compiler doesn't provide 128 bit type don't turn on 64bit */
|
---|
76 | #if defined(MP_64BIT) && defined(__INTEL_COMPILER) && !defined(HAVE___UINT128_T)
|
---|
77 | #undef MP_64BIT
|
---|
78 | #endif
|
---|
79 |
|
---|
80 |
|
---|
81 | /* allow user to define on mp_digit, mp_word, DIGIT_BIT types */
|
---|
82 | #ifndef WOLFSSL_BIGINT_TYPES
|
---|
83 |
|
---|
84 | /* some default configurations.
|
---|
85 | *
|
---|
86 | * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
|
---|
87 | * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
|
---|
88 | *
|
---|
89 | * At the very least a mp_digit must be able to hold 7 bits
|
---|
90 | * [any size beyond that is ok provided it doesn't overflow the data type]
|
---|
91 | */
|
---|
92 | #ifdef MP_8BIT
|
---|
93 | typedef unsigned char mp_digit;
|
---|
94 | typedef unsigned short mp_word;
|
---|
95 | #elif defined(MP_16BIT) || defined(NO_64BIT)
|
---|
96 | typedef unsigned short mp_digit;
|
---|
97 | typedef unsigned int mp_word;
|
---|
98 | #elif defined(MP_64BIT)
|
---|
99 | /* for GCC only on supported platforms */
|
---|
100 | typedef unsigned long long mp_digit; /* 64 bit type, 128 uses mode(TI) */
|
---|
101 | typedef unsigned long mp_word __attribute__ ((mode(TI)));
|
---|
102 |
|
---|
103 | #define DIGIT_BIT 60
|
---|
104 | #else
|
---|
105 | /* this is the default case, 28-bit digits */
|
---|
106 |
|
---|
107 | #if defined(_MSC_VER) || defined(__BORLANDC__)
|
---|
108 | typedef unsigned __int64 ulong64;
|
---|
109 | #else
|
---|
110 | typedef unsigned long long ulong64;
|
---|
111 | #endif
|
---|
112 |
|
---|
113 | typedef unsigned int mp_digit; /* long could be 64 now, changed TAO */
|
---|
114 | typedef ulong64 mp_word;
|
---|
115 |
|
---|
116 | #ifdef MP_31BIT
|
---|
117 | /* this is an extension that uses 31-bit digits */
|
---|
118 | #define DIGIT_BIT 31
|
---|
119 | #else
|
---|
120 | /* default case is 28-bit digits, defines MP_28BIT as a handy test macro */
|
---|
121 | #define DIGIT_BIT 28
|
---|
122 | #define MP_28BIT
|
---|
123 | #endif
|
---|
124 | #endif
|
---|
125 |
|
---|
126 | #endif /* WOLFSSL_BIGINT_TYPES */
|
---|
127 |
|
---|
128 | /* otherwise the bits per digit is calculated automatically from the size of
|
---|
129 | a mp_digit */
|
---|
130 | #ifndef DIGIT_BIT
|
---|
131 | #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))
|
---|
132 | /* bits per digit */
|
---|
133 | #endif
|
---|
134 |
|
---|
135 | #define MP_DIGIT_BIT DIGIT_BIT
|
---|
136 | #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
|
---|
137 | #define MP_DIGIT_MAX MP_MASK
|
---|
138 |
|
---|
139 | /* equalities */
|
---|
140 | #define MP_LT -1 /* less than */
|
---|
141 | #define MP_EQ 0 /* equal to */
|
---|
142 | #define MP_GT 1 /* greater than */
|
---|
143 |
|
---|
144 | #define MP_ZPOS 0 /* positive integer */
|
---|
145 | #define MP_NEG 1 /* negative */
|
---|
146 |
|
---|
147 | #define MP_OKAY 0 /* ok result */
|
---|
148 | #define MP_MEM -2 /* out of mem */
|
---|
149 | #define MP_VAL -3 /* invalid input */
|
---|
150 | #define MP_NOT_INF -4 /* point not at infinity */
|
---|
151 | #define MP_RANGE MP_NOT_INF
|
---|
152 |
|
---|
153 | #define MP_YES 1 /* yes response */
|
---|
154 | #define MP_NO 0 /* no response */
|
---|
155 |
|
---|
156 | /* Primality generation flags */
|
---|
157 | #define LTM_PRIME_BBS 0x0001 /* BBS style prime */
|
---|
158 | #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
|
---|
159 | #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
|
---|
160 |
|
---|
161 | typedef int mp_err;
|
---|
162 |
|
---|
163 | /* define this to use lower memory usage routines (exptmods mostly) */
|
---|
164 | #define MP_LOW_MEM
|
---|
165 |
|
---|
166 | /* default precision */
|
---|
167 | #ifndef MP_PREC
|
---|
168 | #ifndef MP_LOW_MEM
|
---|
169 | #define MP_PREC 32 /* default digits of precision */
|
---|
170 | #else
|
---|
171 | #define MP_PREC 1 /* default digits of precision */
|
---|
172 | #endif
|
---|
173 | #endif
|
---|
174 |
|
---|
175 | /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD -
|
---|
176 | BITS_PER_DIGIT*2) */
|
---|
177 | #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
|
---|
178 |
|
---|
179 | /* the infamous mp_int structure */
|
---|
180 | typedef struct {
|
---|
181 | int used, alloc, sign;
|
---|
182 | mp_digit *dp;
|
---|
183 | } mp_int;
|
---|
184 |
|
---|
185 | /* callback for mp_prime_random, should fill dst with random bytes and return
|
---|
186 | how many read [upto len] */
|
---|
187 | typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
|
---|
188 |
|
---|
189 |
|
---|
190 | #define USED(m) ((m)->used)
|
---|
191 | #define DIGIT(m,k) ((m)->dp[(k)])
|
---|
192 | #define SIGN(m) ((m)->sign)
|
---|
193 |
|
---|
194 |
|
---|
195 | /* ---> Basic Manipulations <--- */
|
---|
196 | #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
|
---|
197 | #define mp_iseven(a) \
|
---|
198 | (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
|
---|
199 | #define mp_isodd(a) \
|
---|
200 | (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
|
---|
201 |
|
---|
202 |
|
---|
203 | /* number of primes */
|
---|
204 | #ifdef MP_8BIT
|
---|
205 | #define PRIME_SIZE 31
|
---|
206 | #else
|
---|
207 | #define PRIME_SIZE 256
|
---|
208 | #endif
|
---|
209 |
|
---|
210 | #define mp_prime_random(a, t, size, bbs, cb, dat) \
|
---|
211 | mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
|
---|
212 |
|
---|
213 | #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
|
---|
214 | #define mp_raw_size(mp) mp_signed_bin_size(mp)
|
---|
215 | #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
|
---|
216 | #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
|
---|
217 | #define mp_mag_size(mp) mp_unsigned_bin_size(mp)
|
---|
218 | #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
|
---|
219 |
|
---|
220 | #define mp_tobinary(M, S) mp_toradix((M), (S), 2)
|
---|
221 | #define mp_tooctal(M, S) mp_toradix((M), (S), 8)
|
---|
222 | #define mp_todecimal(M, S) mp_toradix((M), (S), 10)
|
---|
223 | #define mp_tohex(M, S) mp_toradix((M), (S), 16)
|
---|
224 |
|
---|
225 | #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
|
---|
226 |
|
---|
227 | extern const char *mp_s_rmap;
|
---|
228 |
|
---|
229 | /* 6 functions needed by Rsa */
|
---|
230 | int mp_init (mp_int * a);
|
---|
231 | void mp_clear (mp_int * a);
|
---|
232 | int mp_unsigned_bin_size(mp_int * a);
|
---|
233 | int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c);
|
---|
234 | int mp_to_unsigned_bin (mp_int * a, unsigned char *b);
|
---|
235 | int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
|
---|
236 | /* end functions needed by Rsa */
|
---|
237 |
|
---|
238 | /* functions added to support above needed, removed TOOM and KARATSUBA */
|
---|
239 | int mp_count_bits (mp_int * a);
|
---|
240 | int mp_leading_bit (mp_int * a);
|
---|
241 | int mp_init_copy (mp_int * a, mp_int * b);
|
---|
242 | int mp_copy (mp_int * a, mp_int * b);
|
---|
243 | int mp_grow (mp_int * a, int size);
|
---|
244 | int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
|
---|
245 | void mp_zero (mp_int * a);
|
---|
246 | void mp_clamp (mp_int * a);
|
---|
247 | void mp_exch (mp_int * a, mp_int * b);
|
---|
248 | void mp_rshd (mp_int * a, int b);
|
---|
249 | void mp_rshb (mp_int * a, int b);
|
---|
250 | int mp_mod_2d (mp_int * a, int b, mp_int * c);
|
---|
251 | int mp_mul_2d (mp_int * a, int b, mp_int * c);
|
---|
252 | int mp_lshd (mp_int * a, int b);
|
---|
253 | int mp_abs (mp_int * a, mp_int * b);
|
---|
254 | int mp_invmod (mp_int * a, mp_int * b, mp_int * c);
|
---|
255 | int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c);
|
---|
256 | int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
|
---|
257 | int mp_cmp_mag (mp_int * a, mp_int * b);
|
---|
258 | int mp_cmp (mp_int * a, mp_int * b);
|
---|
259 | int mp_cmp_d(mp_int * a, mp_digit b);
|
---|
260 | void mp_set (mp_int * a, mp_digit b);
|
---|
261 | int mp_is_bit_set (mp_int * a, mp_digit b);
|
---|
262 | int mp_mod (mp_int * a, mp_int * b, mp_int * c);
|
---|
263 | int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
|
---|
264 | int mp_div_2(mp_int * a, mp_int * b);
|
---|
265 | int mp_add (mp_int * a, mp_int * b, mp_int * c);
|
---|
266 | int s_mp_add (mp_int * a, mp_int * b, mp_int * c);
|
---|
267 | int s_mp_sub (mp_int * a, mp_int * b, mp_int * c);
|
---|
268 | int mp_sub (mp_int * a, mp_int * b, mp_int * c);
|
---|
269 | int mp_reduce_is_2k_l(mp_int *a);
|
---|
270 | int mp_reduce_is_2k(mp_int *a);
|
---|
271 | int mp_dr_is_modulus(mp_int *a);
|
---|
272 | int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int);
|
---|
273 | int mp_montgomery_setup (mp_int * n, mp_digit * rho);
|
---|
274 | int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
|
---|
275 | int mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
|
---|
276 | void mp_dr_setup(mp_int *a, mp_digit *d);
|
---|
277 | int mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k);
|
---|
278 | int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
|
---|
279 | int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
|
---|
280 | int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
|
---|
281 | int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
|
---|
282 | int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
|
---|
283 | int mp_reduce (mp_int * x, mp_int * m, mp_int * mu);
|
---|
284 | int mp_reduce_setup (mp_int * a, mp_int * b);
|
---|
285 | int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
|
---|
286 | int mp_montgomery_calc_normalization (mp_int * a, mp_int * b);
|
---|
287 | int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
|
---|
288 | int s_mp_sqr (mp_int * a, mp_int * b);
|
---|
289 | int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
|
---|
290 | int fast_s_mp_sqr (mp_int * a, mp_int * b);
|
---|
291 | int mp_init_size (mp_int * a, int size);
|
---|
292 | int mp_div_3 (mp_int * a, mp_int *c, mp_digit * d);
|
---|
293 | int mp_mul_2(mp_int * a, mp_int * b);
|
---|
294 | int mp_mul (mp_int * a, mp_int * b, mp_int * c);
|
---|
295 | int mp_sqr (mp_int * a, mp_int * b);
|
---|
296 | int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
|
---|
297 | int mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
|
---|
298 | int mp_2expt (mp_int * a, int b);
|
---|
299 | int mp_set_bit (mp_int * a, int b);
|
---|
300 | int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
|
---|
301 | int mp_add_d (mp_int* a, mp_digit b, mp_int* c);
|
---|
302 | int mp_set_int (mp_int * a, unsigned long b);
|
---|
303 | int mp_sub_d (mp_int * a, mp_digit b, mp_int * c);
|
---|
304 | /* end support added functions */
|
---|
305 |
|
---|
306 | /* added */
|
---|
307 | int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e,
|
---|
308 | mp_int* f);
|
---|
309 | int mp_toradix (mp_int *a, char *str, int radix);
|
---|
310 | int mp_radix_size (mp_int * a, int radix, int *size);
|
---|
311 |
|
---|
312 | #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN)
|
---|
313 | int mp_sqrmod(mp_int* a, mp_int* b, mp_int* c);
|
---|
314 | #endif
|
---|
315 | #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN)
|
---|
316 | int mp_read_radix(mp_int* a, const char* str, int radix);
|
---|
317 | #endif
|
---|
318 |
|
---|
319 | #ifdef WOLFSSL_KEY_GEN
|
---|
320 | int mp_prime_is_prime (mp_int * a, int t, int *result);
|
---|
321 | int mp_gcd (mp_int * a, mp_int * b, mp_int * c);
|
---|
322 | int mp_lcm (mp_int * a, mp_int * b, mp_int * c);
|
---|
323 | int mp_rand_prime(mp_int* N, int len, WC_RNG* rng, void* heap);
|
---|
324 | #endif
|
---|
325 |
|
---|
326 | int mp_cnt_lsb(mp_int *a);
|
---|
327 | int mp_mod_d(mp_int* a, mp_digit b, mp_digit* c);
|
---|
328 |
|
---|
329 | #ifdef __cplusplus
|
---|
330 | }
|
---|
331 | #endif
|
---|
332 |
|
---|
333 |
|
---|
334 | #endif /* USE_FAST_MATH */
|
---|
335 |
|
---|
336 | #endif /* WOLF_CRYPT_INTEGER_H */
|
---|
337 |
|
---|