release/src/router/dropbear/libtommath/bn_fast_mp_invmod.c

   1 #include <tommath.h>
   2 #ifdef BN_FAST_MP_INVMOD_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@gmail.com, http://math.libtomcrypt.com
  16  */
  17
  18 /* computes the modular inverse via binary extended euclidean algorithm,
  19  * that is c = 1/a mod b
  20  *
  21  * Based on slow invmod except this is optimized for the case where b is
  22  * odd as per HAC Note 14.64 on pp. 610
  23  */
  24 int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
  25 {
  26   mp_int  x, y, u, v, B, D;
  27   int     res, neg;
  28
  29   /* 2. [modified] b must be odd   */
  30   if (mp_iseven (b) == 1) {
  31     return MP_VAL;
  32   }
  33
  34   /* init all our temps */
  35   if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
  36      return res;
  37   }
  38
  39   /* x == modulus, y == value to invert */
  40   if ((res = mp_copy (b, &x)) != MP_OKAY) {
  41     goto LBL_ERR;
  42   }
  43
  44   /* we need y = |a| */
  45   if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
  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 (&D, 1);
  57
  58 top:
  59   /* 4.  while u is even do */
  60   while (mp_iseven (&u) == 1) {
  61     /* 4.1 u = u/2 */
  62     if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
  63       goto LBL_ERR;
  64     }
  65     /* 4.2 if B is odd then */
  66     if (mp_isodd (&B) == 1) {
  67       if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
  68         goto LBL_ERR;
  69       }
  70     }
  71     /* B = B/2 */
  72     if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
  73       goto LBL_ERR;
  74     }
  75   }
  76
  77   /* 5.  while v is even do */
  78   while (mp_iseven (&v) == 1) {
  79     /* 5.1 v = v/2 */
  80     if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
  81       goto LBL_ERR;
  82     }
  83     /* 5.2 if D is odd then */
  84     if (mp_isodd (&D) == 1) {
  85       /* D = (D-x)/2 */
  86       if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
  87         goto LBL_ERR;
  88       }
  89     }
  90     /* D = D/2 */
  91     if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
  92       goto LBL_ERR;
  93     }
  94   }
  95
  96   /* 6.  if u >= v then */
  97   if (mp_cmp (&u, &v) != MP_LT) {
  98     /* u = u - v, B = B - D */
  99     if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
 100       goto LBL_ERR;
 101     }
 102
 103     if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
 104       goto LBL_ERR;
 105     }
 106   } else {
 107     /* v - v - u, D = D - B */
 108     if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
 109       goto LBL_ERR;
 110     }
 111
 112     if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
 113       goto LBL_ERR;
 114     }
 115   }
 116
 117   /* if not zero goto step 4 */
 118   if (mp_iszero (&u) == 0) {
 119     goto top;
 120   }
 121
 122   /* now a = C, b = D, gcd == g*v */
 123
 124   /* if v != 1 then there is no inverse */
 125   if (mp_cmp_d (&v, 1) != MP_EQ) {
 126     res = MP_VAL;
 127     goto LBL_ERR;
 128   }
 129
 130   /* b is now the inverse */
 131   neg = a->sign;
 132   while (D.sign == MP_NEG) {
 133     if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
 134       goto LBL_ERR;
 135     }
 136   }
 137   mp_exch (&D, c);
 138   c->sign = neg;
 139   res = MP_OKAY;
 140
 141 LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
 142   return res;
 143 }
 144 #endif
 145
 146 /* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */
 147 /* $Revision: 1.3 $ */
 148 /* $Date: 2006/03/31 14:18:44 $ */