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      1 #include <tommath.h>
      2 #ifdef BN_MP_INVMOD_SLOW_C
      3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
      4  *
      5  * LibTomMath is a library that provides multiple-precision
      6  * integer arithmetic as well as number theoretic functionality.
      7  *
      8  * The library was designed directly after the MPI library by
      9  * Michael Fromberger but has been written from scratch with
     10  * additional optimizations in place.
     11  *
     12  * The library is free for all purposes without any express
     13  * guarantee it works.
     14  *
     15  * Tom St Denis, tomstdenis (at) gmail.com, http://math.libtomcrypt.com
     16  */
     17 
     18 /* hac 14.61, pp608 */
     19 int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
     20 {
     21   mp_int  x, y, u, v, A, B, C, D;
     22   int     res;
     23 
     24   /* b cannot be negative */
     25   if (b->sign == MP_NEG || mp_iszero(b) == 1) {
     26     return MP_VAL;
     27   }
     28 
     29   /* init temps */
     30   if ((res = mp_init_multi(&x, &y, &u, &v,
     31                            &A, &B, &C, &D, NULL)) != MP_OKAY) {
     32      return res;
     33   }
     34 
     35   /* x = a, y = b */
     36   if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
     37       goto LBL_ERR;
     38   }
     39   if ((res = mp_copy (b, &y)) != MP_OKAY) {
     40     goto LBL_ERR;
     41   }
     42 
     43   /* 2. [modified] if x,y are both even then return an error! */
     44   if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
     45     res = MP_VAL;
     46     goto LBL_ERR;
     47   }
     48 
     49   /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
     50   if ((res = mp_copy (&x, &u)) != MP_OKAY) {
     51     goto LBL_ERR;
     52   }
     53   if ((res = mp_copy (&y, &v)) != MP_OKAY) {
     54     goto LBL_ERR;
     55   }
     56   mp_set (&A, 1);
     57   mp_set (&D, 1);
     58 
     59 top:
     60   /* 4.  while u is even do */
     61   while (mp_iseven (&u) == 1) {
     62     /* 4.1 u = u/2 */
     63     if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
     64       goto LBL_ERR;
     65     }
     66     /* 4.2 if A or B is odd then */
     67     if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
     68       /* A = (A+y)/2, B = (B-x)/2 */
     69       if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
     70          goto LBL_ERR;
     71       }
     72       if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
     73          goto LBL_ERR;
     74       }
     75     }
     76     /* A = A/2, B = B/2 */
     77     if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
     78       goto LBL_ERR;
     79     }
     80     if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
     81       goto LBL_ERR;
     82     }
     83   }
     84 
     85   /* 5.  while v is even do */
     86   while (mp_iseven (&v) == 1) {
     87     /* 5.1 v = v/2 */
     88     if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
     89       goto LBL_ERR;
     90     }
     91     /* 5.2 if C or D is odd then */
     92     if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
     93       /* C = (C+y)/2, D = (D-x)/2 */
     94       if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
     95          goto LBL_ERR;
     96       }
     97       if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
     98          goto LBL_ERR;
     99       }
    100     }
    101     /* C = C/2, D = D/2 */
    102     if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
    103       goto LBL_ERR;
    104     }
    105     if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
    106       goto LBL_ERR;
    107     }
    108   }
    109 
    110   /* 6.  if u >= v then */
    111   if (mp_cmp (&u, &v) != MP_LT) {
    112     /* u = u - v, A = A - C, B = B - D */
    113     if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
    114       goto LBL_ERR;
    115     }
    116 
    117     if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
    118       goto LBL_ERR;
    119     }
    120 
    121     if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
    122       goto LBL_ERR;
    123     }
    124   } else {
    125     /* v - v - u, C = C - A, D = D - B */
    126     if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
    127       goto LBL_ERR;
    128     }
    129 
    130     if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
    131       goto LBL_ERR;
    132     }
    133 
    134     if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
    135       goto LBL_ERR;
    136     }
    137   }
    138 
    139   /* if not zero goto step 4 */
    140   if (mp_iszero (&u) == 0)
    141     goto top;
    142 
    143   /* now a = C, b = D, gcd == g*v */
    144 
    145   /* if v != 1 then there is no inverse */
    146   if (mp_cmp_d (&v, 1) != MP_EQ) {
    147     res = MP_VAL;
    148     goto LBL_ERR;
    149   }
    150 
    151   /* if its too low */
    152   while (mp_cmp_d(&C, 0) == MP_LT) {
    153       if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
    154          goto LBL_ERR;
    155       }
    156   }
    157 
    158   /* too big */
    159   while (mp_cmp_mag(&C, b) != MP_LT) {
    160       if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
    161          goto LBL_ERR;
    162       }
    163   }
    164 
    165   /* C is now the inverse */
    166   mp_exch (&C, c);
    167   res = MP_OKAY;
    168 LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
    169   return res;
    170 }
    171 #endif
    172 
    173 /* $Source: /cvs/libtom/libtommath/bn_mp_invmod_slow.c,v $ */
    174 /* $Revision: 1.3 $ */
    175 /* $Date: 2006/03/31 14:18:44 $ */
    176