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 #ifndef MIN
00049    #define MIN(x,y) ((x)<(y)?(x):(y))
00050 #endif
00051 
00052 #ifndef MAX
00053    #define MAX(x,y) ((x)>(y)?(x):(y))
00054 #endif
00055 
00056 #ifdef __cplusplus
00057 extern "C" {
00058 
00059 /* C++ compilers don't like assigning void * to mp_digit * */
00060 #define  OPT_CAST(x)  (x *)
00061 
00062 #else
00063 
00064 /* C on the other hand doesn't care */
00065 #define  OPT_CAST(x)
00066 
00067 #endif
00068 
00069 
00070 /* detect 64-bit mode if possible */
00071 #if defined(__x86_64__)
00072    #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
00073       #define MP_64BIT
00074    #endif
00075 #endif
00076 /* if intel compiler doesn't provide 128 bit type don't turn on 64bit */
00077 #if defined(MP_64BIT) && defined(__INTEL_COMPILER) && !defined(HAVE___UINT128_T)
00078     #undef MP_64BIT
00079 #endif
00080 
00081 
00082 /* allow user to define on mp_digit, mp_word, DIGIT_BIT types */
00083 #ifndef WOLFSSL_BIGINT_TYPES
00084 
00085 /* some default configurations.
00086  *
00087  * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
00088  * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
00089  *
00090  * At the very least a mp_digit must be able to hold 7 bits
00091  * [any size beyond that is ok provided it doesn't overflow the data type]
00092  */
00093 #ifdef MP_8BIT
00094    typedef unsigned char      mp_digit;
00095    typedef unsigned short     mp_word;
00096 #elif defined(MP_16BIT) || defined(NO_64BIT)
00097    typedef unsigned short     mp_digit;
00098    typedef unsigned int       mp_word;
00099 #elif defined(MP_64BIT)
00100    /* for GCC only on supported platforms */
00101    typedef unsigned long long mp_digit;  /* 64 bit type, 128 uses mode(TI) */
00102    typedef unsigned long      mp_word __attribute__ ((mode(TI)));
00103 
00104    #define DIGIT_BIT          60
00105 #else
00106    /* this is the default case, 28-bit digits */
00107 
00108    #if defined(_MSC_VER) || defined(__BORLANDC__)
00109       typedef unsigned __int64   ulong64;
00110    #else
00111       typedef unsigned long long ulong64;
00112    #endif
00113 
00114    typedef unsigned int       mp_digit;  /* long could be 64 now, changed TAO */
00115    typedef ulong64            mp_word;
00116 
00117 #ifdef MP_31BIT
00118    /* this is an extension that uses 31-bit digits */
00119    #define DIGIT_BIT          31
00120 #else
00121    /* default case is 28-bit digits, defines MP_28BIT as a handy test macro */
00122    #define DIGIT_BIT          28
00123    #define MP_28BIT
00124 #endif
00125 #endif
00126 
00127 #endif /* WOLFSSL_BIGINT_TYPES */
00128 
00129 /* otherwise the bits per digit is calculated automatically from the size of
00130    a mp_digit */
00131 #ifndef DIGIT_BIT
00132    #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))
00133       /* bits per digit */
00134 #endif
00135 
00136 #define MP_DIGIT_BIT     DIGIT_BIT
00137 #define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
00138 #define MP_DIGIT_MAX     MP_MASK
00139 
00140 /* equalities */
00141 #define MP_LT        -1   /* less than */
00142 #define MP_EQ         0   /* equal to */
00143 #define MP_GT         1   /* greater than */
00144 
00145 #define MP_ZPOS       0   /* positive integer */
00146 #define MP_NEG        1   /* negative */
00147 
00148 #define MP_OKAY       0   /* ok result */
00149 #define MP_MEM        -2  /* out of mem */
00150 #define MP_VAL        -3  /* invalid input */
00151 #define MP_NOT_INF    -4  /* point not at infinity */
00152 #define MP_RANGE      MP_NOT_INF
00153 
00154 #define MP_YES        1   /* yes response */
00155 #define MP_NO         0   /* no response */
00156 
00157 /* Primality generation flags */
00158 #define LTM_PRIME_BBS      0x0001 /* BBS style prime */
00159 #define LTM_PRIME_SAFE     0x0002 /* Safe prime (p-1)/2 == prime */
00160 #define LTM_PRIME_2MSB_ON  0x0008 /* force 2nd MSB to 1 */
00161 
00162 typedef int           mp_err;
00163 
00164 /* define this to use lower memory usage routines (exptmods mostly) */
00165 #define MP_LOW_MEM
00166 
00167 /* default precision */
00168 #ifndef MP_PREC
00169    #ifndef MP_LOW_MEM
00170       #define MP_PREC                 32     /* default digits of precision */
00171    #else
00172       #define MP_PREC                 1      /* default digits of precision */
00173    #endif
00174 #endif
00175 
00176 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD -
00177    BITS_PER_DIGIT*2) */
00178 #define MP_WARRAY  (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
00179 
00180 /* the infamous mp_int structure */
00181 typedef struct  {
00182     int used, alloc, sign;
00183     mp_digit *dp;
00184 } mp_int;
00185 
00186 /* callback for mp_prime_random, should fill dst with random bytes and return
00187    how many read [up to len] */
00188 typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
00189 
00190 
00191 #define USED(m)    ((m)->used)
00192 #define DIGIT(m,k) ((m)->dp[(k)])
00193 #define SIGN(m)    ((m)->sign)
00194 
00195 
00196 /* ---> Basic Manipulations <--- */
00197 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
00198 #define mp_iseven(a) \
00199     (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
00200 #define mp_isodd(a) \
00201     (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
00202 
00203 
00204 /* number of primes */
00205 #ifdef MP_8BIT
00206    #define PRIME_SIZE      31
00207 #else
00208    #define PRIME_SIZE      256
00209 #endif
00210 
00211 #define mp_prime_random(a, t, size, bbs, cb, dat) \
00212    mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
00213 
00214 #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
00215 #define mp_raw_size(mp)           mp_signed_bin_size(mp)
00216 #define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
00217 #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
00218 #define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
00219 #define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))
00220 
00221 #define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
00222 #define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
00223 #define mp_todecimal(M, S) mp_toradix((M), (S), 10)
00224 #define mp_tohex(M, S)     mp_toradix((M), (S), 16)
00225 
00226 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
00227 
00228 extern const char *mp_s_rmap;
00229 
00230 /* 6 functions needed by Rsa */
00231 int  mp_init (mp_int * a);
00232 void mp_clear (mp_int * a);
00233 int  mp_unsigned_bin_size(mp_int * a);
00234 int  mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c);
00235 int  mp_to_unsigned_bin (mp_int * a, unsigned char *b);
00236 int  mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
00237 /* end functions needed by Rsa */
00238 
00239 /* functions added to support above needed, removed TOOM and KARATSUBA */
00240 int  mp_count_bits (mp_int * a);
00241 int  mp_leading_bit (mp_int * a);
00242 int  mp_init_copy (mp_int * a, mp_int * b);
00243 int  mp_copy (mp_int * a, mp_int * b);
00244 int  mp_grow (mp_int * a, int size);
00245 int  mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
00246 void mp_zero (mp_int * a);
00247 void mp_clamp (mp_int * a);
00248 void mp_exch (mp_int * a, mp_int * b);
00249 void mp_rshd (mp_int * a, int b);
00250 void mp_rshb (mp_int * a, int b);
00251 int  mp_mod_2d (mp_int * a, int b, mp_int * c);
00252 int  mp_mul_2d (mp_int * a, int b, mp_int * c);
00253 int  mp_lshd (mp_int * a, int b);
00254 int  mp_abs (mp_int * a, mp_int * b);
00255 int  mp_invmod (mp_int * a, mp_int * b, mp_int * c);
00256 int  fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c);
00257 int  mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
00258 int  mp_cmp_mag (mp_int * a, mp_int * b);
00259 int  mp_cmp (mp_int * a, mp_int * b);
00260 int  mp_cmp_d(mp_int * a, mp_digit b);
00261 void mp_set (mp_int * a, mp_digit b);
00262 int  mp_is_bit_set (mp_int * a, mp_digit b);
00263 int  mp_mod (mp_int * a, mp_int * b, mp_int * c);
00264 int  mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
00265 int  mp_div_2(mp_int * a, mp_int * b);
00266 int  mp_add (mp_int * a, mp_int * b, mp_int * c);
00267 int  s_mp_add (mp_int * a, mp_int * b, mp_int * c);
00268 int  s_mp_sub (mp_int * a, mp_int * b, mp_int * c);
00269 int  mp_sub (mp_int * a, mp_int * b, mp_int * c);
00270 int  mp_reduce_is_2k_l(mp_int *a);
00271 int  mp_reduce_is_2k(mp_int *a);
00272 int  mp_dr_is_modulus(mp_int *a);
00273 int  mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int);
00274 int  mp_montgomery_setup (mp_int * n, mp_digit * rho);
00275 int  fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
00276 int  mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho);
00277 void mp_dr_setup(mp_int *a, mp_digit *d);
00278 int  mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k);
00279 int  mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
00280 int  fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
00281 int  s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
00282 int  mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
00283 int  mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
00284 int  mp_reduce (mp_int * x, mp_int * m, mp_int * mu);
00285 int  mp_reduce_setup (mp_int * a, mp_int * b);
00286 int  s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
00287 int  mp_montgomery_calc_normalization (mp_int * a, mp_int * b);
00288 int  s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
00289 int  s_mp_sqr (mp_int * a, mp_int * b);
00290 int  fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
00291 int  fast_s_mp_sqr (mp_int * a, mp_int * b);
00292 int  mp_init_size (mp_int * a, int size);
00293 int  mp_div_3 (mp_int * a, mp_int *c, mp_digit * d);
00294 int  mp_mul_2(mp_int * a, mp_int * b);
00295 int  mp_mul (mp_int * a, mp_int * b, mp_int * c);
00296 int  mp_sqr (mp_int * a, mp_int * b);
00297 int  mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
00298 int  mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
00299 int  mp_2expt (mp_int * a, int b);
00300 int  mp_set_bit (mp_int * a, int b);
00301 int  mp_reduce_2k_setup(mp_int *a, mp_digit *d);
00302 int  mp_add_d (mp_int* a, mp_digit b, mp_int* c);
00303 int mp_set_int (mp_int * a, unsigned long b);
00304 int mp_sub_d (mp_int * a, mp_digit b, mp_int * c);
00305 /* end support added functions */
00306 
00307 /* added */
00308 int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e,
00309                   mp_int* f);
00310 int mp_toradix (mp_int *a, char *str, int radix);
00311 int mp_radix_size (mp_int * a, int radix, int *size);
00312 
00313 #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN)
00314     int mp_sqrmod(mp_int* a, mp_int* b, mp_int* c);
00315 #endif
00316 #if defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN)
00317     int mp_read_radix(mp_int* a, const char* str, int radix);
00318 #endif
00319 
00320 #ifdef WOLFSSL_KEY_GEN
00321     int mp_prime_is_prime (mp_int * a, int t, int *result);
00322     int mp_gcd (mp_int * a, mp_int * b, mp_int * c);
00323     int mp_lcm (mp_int * a, mp_int * b, mp_int * c);
00324     int mp_rand_prime(mp_int* N, int len, WC_RNG* rng, void* heap);
00325 #endif
00326 
00327 int mp_cnt_lsb(mp_int *a);
00328 int mp_mod_d(mp_int* a, mp_digit b, mp_digit* c);
00329 
00330 #ifdef __cplusplus
00331    }
00332 #endif
00333 
00334 
00335 #endif /* USE_FAST_MATH */
00336 
00337 #endif  /* WOLF_CRYPT_INTEGER_H */
00338 
00339