integer.h

00001 /* integer.h
00002  *
00003  * Copyright (C) 2006-2016 wolfSSL Inc.
00004  *
00005  * This file is part of wolfSSL.
00006  *
00007  * wolfSSL is free software; you can redistribute it and/or modify
00008  * it under the terms of the GNU General Public License as published by
00009  * the Free Software Foundation; either version 2 of the License, or
00010  * (at your option) any later version.
00011  *
00012  * wolfSSL is distributed in the hope that it will be useful,
00013  * but WITHOUT ANY WARRANTY; without even the implied warranty of
00014  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00015  * GNU General Public License for more details.
00016  *
00017  * You should have received a copy of the GNU General Public License
00018  * along with this program; if not, write to the Free Software
00019  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
00020  */
00021 
00022 
00023 /*
00024  * Based on public domain LibTomMath 0.38 by Tom St Denis, tomstdenis@iahu.ca,
00025  * http://math.libtomcrypt.com
00026  */
00027 
00028 
00029 #ifndef WOLF_CRYPT_INTEGER_H
00030 #define WOLF_CRYPT_INTEGER_H
00031 
00032 /* may optionally use fast math instead, not yet supported on all platforms and
00033    may not be faster on all
00034 */
00035 #include <wolfssl/wolfcrypt/types.h>       /* will set MP_xxBIT if not default */
00036 #ifdef USE_FAST_MATH
00037     #include <wolfssl/wolfcrypt/tfm.h>
00038 #else
00039 
00040 #include <wolfssl/wolfcrypt/random.h>
00041 
00042 #ifndef CHAR_BIT
00043     #include <limits.h>
00044 #endif
00045 
00046 #include <wolfssl/wolfcrypt/mpi_class.h>
00047 
00048 /* wolf big int and common functions */
00049 #include <wolfssl/wolfcrypt/wolfmath.h>
00050 
00051 
00052 #ifdef WOLFSSL_PUBLIC_MP
00053     #define MP_API   WOLFSSL_API
00054 #else
00055     #define MP_API
00056 #endif
00057 
00058 #ifndef MIN
00059    #define MIN(x,y) ((x)<(y)?(x):(y))
00060 #endif
00061 
00062 #ifndef MAX
00063    #define MAX(x,y) ((x)>(y)?(x):(y))
00064 #endif
00065 
00066 #ifdef __cplusplus
00067 extern "C" {
00068 
00069 /* C++ compilers don't like assigning void * to mp_digit * */
00070 #define  OPT_CAST(x)  (x *)
00071 
00072 #else
00073 
00074 /* C on the other hand doesn't care */
00075 #define  OPT_CAST(x)
00076 
00077 #endif /* __cplusplus */
00078 
00079 
00080 /* detect 64-bit mode if possible */
00081 #if defined(__x86_64__)
00082    #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
00083       #define MP_64BIT
00084    #endif
00085 #endif
00086 /* if intel compiler doesn't provide 128 bit type don't turn on 64bit */
00087 #if defined(MP_64BIT) && defined(__INTEL_COMPILER) && !defined(HAVE___UINT128_T)
00088     #undef MP_64BIT
00089 #endif
00090 
00091 
00092 /* allow user to define on mp_digit, mp_word, DIGIT_BIT types */
00093 #ifndef WOLFSSL_BIGINT_TYPES
00094 
00095 /* some default configurations.
00096  *
00097  * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
00098  * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
00099  *
00100  * At the very least a mp_digit must be able to hold 7 bits
00101  * [any size beyond that is ok provided it doesn't overflow the data type]
00102  */
00103 #ifdef MP_8BIT
00104    typedef unsigned char      mp_digit;
00105    typedef unsigned short     mp_word;
00106 #elif defined(MP_16BIT) || defined(NO_64BIT)
00107    typedef unsigned short     mp_digit;
00108    typedef unsigned int       mp_word;
00109    #define DIGIT_BIT          12
00110 #elif defined(MP_64BIT)
00111    /* for GCC only on supported platforms */
00112    typedef unsigned long long mp_digit;  /* 64 bit type, 128 uses mode(TI) */
00113    typedef unsigned long      mp_word __attribute__ ((mode(TI)));
00114 
00115    #define DIGIT_BIT          60
00116 #else
00117    /* this is the default case, 28-bit digits */
00118 
00119    #if defined(_MSC_VER) || defined(__BORLANDC__)
00120       typedef unsigned __int64   ulong64;
00121    #else
00122       typedef unsigned long long ulong64;
00123    #endif
00124 
00125    typedef unsigned int       mp_digit;  /* long could be 64 now, changed TAO */
00126    typedef ulong64            mp_word;
00127 
00128 #ifdef MP_31BIT
00129    /* this is an extension that uses 31-bit digits */
00130    #define DIGIT_BIT          31
00131 #else
00132    /* default case is 28-bit digits, defines MP_28BIT as a handy test macro */
00133    #define DIGIT_BIT          28
00134    #define MP_28BIT
00135 #endif
00136 #endif
00137 
00138 #endif /* WOLFSSL_BIGINT_TYPES */
00139 
00140 /* otherwise the bits per digit is calculated automatically from the size of
00141    a mp_digit */
00142 #ifndef DIGIT_BIT
00143    #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))
00144       /* bits per digit */
00145 #endif
00146 
00147 #define MP_DIGIT_BIT     DIGIT_BIT
00148 #define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
00149 #define MP_DIGIT_MAX     MP_MASK
00150 
00151 /* equalities */
00152 #define MP_LT        -1   /* less than */
00153 #define MP_EQ         0   /* equal to */
00154 #define MP_GT         1   /* greater than */
00155 
00156 #define MP_ZPOS       0   /* positive integer */
00157 #define MP_NEG        1   /* negative */
00158 
00159 #define MP_OKAY       0   /* ok result */
00160 #define MP_MEM        -2  /* out of mem */
00161 #define MP_VAL        -3  /* invalid input */
00162 #define MP_NOT_INF    -4  /* point not at infinity */
00163 #define MP_RANGE      MP_NOT_INF
00164 
00165 #define MP_YES        1   /* yes response */
00166 #define MP_NO         0   /* no response */
00167 
00168 /* Primality generation flags */
00169 #define LTM_PRIME_BBS      0x0001 /* BBS style prime */
00170 #define LTM_PRIME_SAFE     0x0002 /* Safe prime (p-1)/2 == prime */
00171 #define LTM_PRIME_2MSB_ON  0x0008 /* force 2nd MSB to 1 */
00172 
00173 typedef int           mp_err;
00174 
00175 /* define this to use lower memory usage routines (exptmods mostly) */
00176 #define MP_LOW_MEM
00177 
00178 /* default precision */
00179 #ifndef MP_PREC
00180    #ifndef MP_LOW_MEM
00181       #define MP_PREC                 32     /* default digits of precision */
00182    #else
00183       #define MP_PREC                 1      /* default digits of precision */
00184    #endif
00185 #endif
00186 
00187 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD -
00188    BITS_PER_DIGIT*2) */
00189 #define MP_WARRAY  (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
00190 
00191 #ifdef HAVE_WOLF_BIGINT
00192     struct WC_BIGINT;
00193 #endif
00194 
00195 /* the mp_int structure */
00196 typedef struct mp_int {
00197     int used, alloc, sign;
00198     mp_digit *dp;
00199 
00200 #ifdef HAVE_WOLF_BIGINT
00201     struct WC_BIGINT raw; /* unsigned binary (big endian) */
00202 #endif
00203 } mp_int;
00204 #define MP_INT_DEFINED
00205 
00206 /* callback for mp_prime_random, should fill dst with random bytes and return
00207    how many read [up to len] */
00208 typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
00209 
00210 
00211 #define USED(m)    ((m)->used)
00212 #define DIGIT(m,k) ((m)->dp[(k)])
00213 #define SIGN(m)    ((m)->sign)
00214 
00215 
00216 /* ---> Basic Manipulations <--- */
00217 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
00218 #define mp_isone(a) \
00219     (((((a)->used == 1)) && ((a)->dp[0] == 1u)) ? MP_YES : MP_NO)
00220 #define mp_iseven(a) \
00221     (((a)->used > 0 && (((a)->dp[0] & 1u) == 0u)) ? MP_YES : MP_NO)
00222 #define mp_isodd(a) \
00223     (((a)->used > 0 && (((a)->dp[0] & 1u) == 1u)) ? MP_YES : MP_NO)
00224 #define mp_isneg(a)  (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)
00225 
00226 /* number of primes */
00227 #ifdef MP_8BIT
00228    #define PRIME_SIZE      31
00229 #else
00230    #define PRIME_SIZE      256
00231 #endif
00232 
00233 #define mp_prime_random(a, t, size, bbs, cb, dat) \
00234    mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
00235 
00236 #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
00237 #define mp_raw_size(mp)           mp_signed_bin_size(mp)
00238 #define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
00239 #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
00240 #define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
00241 #define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))
00242 
00243 #define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
00244 #define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
00245 #define mp_todecimal(M, S) mp_toradix((M), (S), 10)
00246 #define mp_tohex(M, S)     mp_toradix((M), (S), 16)
00247 
00248 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
00249 
00250 extern const char *mp_s_rmap;
00251 
00252 /* 6 functions needed by Rsa */
00253 MP_API int  mp_init (mp_int * a);
00254 MP_API void mp_clear (mp_int * a);
00255 MP_API void mp_free (mp_int * a);
00256 MP_API void mp_forcezero(mp_int * a);
00257 MP_API int  mp_unsigned_bin_size(mp_int * a);
00258 MP_API int  mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c);
00259 MP_API int  mp_to_unsigned_bin_at_pos(int x, mp_int *t, unsigned char *b);
00260 MP_API int  mp_to_unsigned_bin (mp_int * a, unsigned char *b);
00261 MP_API int  mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
00262 /* end functions needed by Rsa */
00263 
00264 /* functions added to support above needed, removed TOOM and KARATSUBA */
00265 MP_API int  mp_count_bits (mp_int * a);
00266 MP_API int  mp_leading_bit (mp_int * a);
00267 MP_API int  mp_init_copy (mp_int * a, mp_int * b);
00268 MP_API int  mp_copy (mp_int * a, mp_int * b);
00269 MP_API int  mp_grow (mp_int * a, int size);
00270 MP_API int  mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
00271 MP_API void mp_zero (mp_int * a);
00272 MP_API void mp_clamp (mp_int * a);
00273 MP_API void mp_exch (mp_int * a, mp_int * b);
00274 MP_API void mp_rshd (mp_int * a, int b);
00275 MP_API void mp_rshb (mp_int * a, int b);
00276 MP_API int  mp_mod_2d (mp_int * a, int b, mp_int * c);
00277 MP_API int  mp_mul_2d (mp_int * a, int b, mp_int * c);
00278 MP_API int  mp_lshd (mp_int * a, int b);
00279 MP_API int  mp_abs (mp_int * a, mp_int * b);
00280 MP_API int  mp_invmod (mp_int * a, mp_int * b, mp_int * c);
00281 int  fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c);
00282 MP_API int  mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
00283 MP_API int  mp_cmp_mag (mp_int * a, mp_int * b);
00284 MP_API int  mp_cmp (mp_int * a, mp_int * b);
00285 MP_API int  mp_cmp_d(mp_int * a, mp_digit b);
00286 MP_API int  mp_set (mp_int * a, mp_digit b);
00287 MP_API int  mp_is_bit_set (mp_int * a, mp_digit b);
00288 MP_API int  mp_mod (mp_int * a, mp_int * b, mp_int * c);
00289 MP_API int  mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
00290 MP_API int  mp_div_2(mp_int * a, mp_int * b);
00291 MP_API int  mp_add (mp_int * a, mp_int * b, mp_int * c);
00292 int  s_mp_add (mp_int * a, mp_int * b, mp_int * c);
00293 int  s_mp_sub (mp_int * a, mp_int * b, mp_int * c);
00294 MP_API int  mp_sub (mp_int * a, mp_int * b, mp_int * c);
00295 MP_API int  mp_reduce_is_2k_l(mp_int *a);
00296 MP_API int  mp_reduce_is_2k(mp_int *a);
00297 MP_API int  mp_dr_is_modulus(mp_int *a);
00298 MP_API int  mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y,
00299                              int);
00300 MP_API int  mp_montgomery_setup (mp_int * n, mp_digit * rho);
00301 int  fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
00302 MP_API int  mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
00303 MP_API void mp_dr_setup(mp_int *a, mp_digit *d);
00304 MP_API int  mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k);
00305 MP_API int  mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
00306 int  fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
00307 int  s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
00308 MP_API int  mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
00309 MP_API int  mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
00310 MP_API int  mp_reduce (mp_int * x, mp_int * m, mp_int * mu);
00311 MP_API int  mp_reduce_setup (mp_int * a, mp_int * b);
00312 int  s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
00313 MP_API int  mp_montgomery_calc_normalization (mp_int * a, mp_int * b);
00314 int  s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
00315 int  s_mp_sqr (mp_int * a, mp_int * b);
00316 int  fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
00317 int  fast_s_mp_sqr (mp_int * a, mp_int * b);
00318 MP_API int  mp_init_size (mp_int * a, int size);
00319 MP_API int  mp_div_3 (mp_int * a, mp_int *c, mp_digit * d);
00320 MP_API int  mp_mul_2(mp_int * a, mp_int * b);
00321 MP_API int  mp_mul (mp_int * a, mp_int * b, mp_int * c);
00322 MP_API int  mp_sqr (mp_int * a, mp_int * b);
00323 MP_API int  mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
00324 MP_API int  mp_submod (mp_int* a, mp_int* b, mp_int* c, mp_int* d);
00325 MP_API int  mp_addmod (mp_int* a, mp_int* b, mp_int* c, mp_int* d);
00326 MP_API int  mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
00327 MP_API int  mp_2expt (mp_int * a, int b);
00328 MP_API int  mp_set_bit (mp_int * a, int b);
00329 MP_API int  mp_reduce_2k_setup(mp_int *a, mp_digit *d);
00330 MP_API int  mp_add_d (mp_int* a, mp_digit b, mp_int* c);
00331 MP_API int  mp_set_int (mp_int * a, unsigned long b);
00332 MP_API int  mp_sub_d (mp_int * a, mp_digit b, mp_int * c);
00333 /* end support added functions */
00334 
00335 /* added */
00336 MP_API int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e,
00337                          mp_int* f);
00338 MP_API int mp_toradix (mp_int *a, char *str, int radix);
00339 MP_API int mp_radix_size (mp_int * a, int radix, int *size);
00340 
00341 #ifdef WOLFSSL_DEBUG_MATH
00342     MP_API void mp_dump(const char* desc, mp_int* a, byte verbose);
00343 #else
00344     #define mp_dump(desc, a, verbose)
00345 #endif
00346 
00347 #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN)
00348     MP_API int mp_sqrmod(mp_int* a, mp_int* b, mp_int* c);
00349 #endif
00350 #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN)
00351     MP_API int mp_read_radix(mp_int* a, const char* str, int radix);
00352 #endif
00353 
00354 #ifdef WOLFSSL_KEY_GEN
00355     MP_API int mp_prime_is_prime (mp_int * a, int t, int *result);
00356     MP_API int mp_gcd (mp_int * a, mp_int * b, mp_int * c);
00357     MP_API int mp_lcm (mp_int * a, mp_int * b, mp_int * c);
00358     MP_API int mp_rand_prime(mp_int* N, int len, WC_RNG* rng, void* heap);
00359 #endif
00360 
00361 MP_API int mp_cnt_lsb(mp_int *a);
00362 MP_API int mp_mod_d(mp_int* a, mp_digit b, mp_digit* c);
00363 
00364 
00365 /* wolf big int and common functions */
00366 #include <wolfssl/wolfcrypt/wolfmath.h>
00367 
00368 
00369 #ifdef __cplusplus
00370    }
00371 #endif
00372 
00373 
00374 #endif /* USE_FAST_MATH */
00375 
00376 #endif  /* WOLF_CRYPT_INTEGER_H */
00377 
00378