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      1 #include <tommath.h>
      2 #ifdef BN_MP_KARATSUBA_SQR_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 /* Karatsuba squaring, computes b = a*a using three
     19  * half size squarings
     20  *
     21  * See comments of karatsuba_mul for details.  It
     22  * is essentially the same algorithm but merely
     23  * tuned to perform recursive squarings.
     24  */
     25 int mp_karatsuba_sqr (mp_int * a, mp_int * b)
     26 {
     27   mp_int  x0, x1, t1, t2, x0x0, x1x1;
     28   int     B, err;
     29 
     30   err = MP_MEM;
     31 
     32   /* min # of digits */
     33   B = a->used;
     34 
     35   /* now divide in two */
     36   B = B >> 1;
     37 
     38   /* init copy all the temps */
     39   if (mp_init_size (&x0, B) != MP_OKAY)
     40     goto ERR;
     41   if (mp_init_size (&x1, a->used - B) != MP_OKAY)
     42     goto X0;
     43 
     44   /* init temps */
     45   if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
     46     goto X1;
     47   if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
     48     goto T1;
     49   if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
     50     goto T2;
     51   if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
     52     goto X0X0;
     53 
     54   {
     55     register int x;
     56     register mp_digit *dst, *src;
     57 
     58     src = a->dp;
     59 
     60     /* now shift the digits */
     61     dst = x0.dp;
     62     for (x = 0; x < B; x++) {
     63       *dst++ = *src++;
     64     }
     65 
     66     dst = x1.dp;
     67     for (x = B; x < a->used; x++) {
     68       *dst++ = *src++;
     69     }
     70   }
     71 
     72   x0.used = B;
     73   x1.used = a->used - B;
     74 
     75   mp_clamp (&x0);
     76 
     77   /* now calc the products x0*x0 and x1*x1 */
     78   if (mp_sqr (&x0, &x0x0) != MP_OKAY)
     79     goto X1X1;           /* x0x0 = x0*x0 */
     80   if (mp_sqr (&x1, &x1x1) != MP_OKAY)
     81     goto X1X1;           /* x1x1 = x1*x1 */
     82 
     83   /* now calc (x1+x0)**2 */
     84   if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
     85     goto X1X1;           /* t1 = x1 - x0 */
     86   if (mp_sqr (&t1, &t1) != MP_OKAY)
     87     goto X1X1;           /* t1 = (x1 - x0) * (x1 - x0) */
     88 
     89   /* add x0y0 */
     90   if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
     91     goto X1X1;           /* t2 = x0x0 + x1x1 */
     92   if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY)
     93     goto X1X1;           /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
     94 
     95   /* shift by B */
     96   if (mp_lshd (&t1, B) != MP_OKAY)
     97     goto X1X1;           /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
     98   if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
     99     goto X1X1;           /* x1x1 = x1x1 << 2*B */
    100 
    101   if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
    102     goto X1X1;           /* t1 = x0x0 + t1 */
    103   if (mp_add (&t1, &x1x1, b) != MP_OKAY)
    104     goto X1X1;           /* t1 = x0x0 + t1 + x1x1 */
    105 
    106   err = MP_OKAY;
    107 
    108 X1X1:mp_clear (&x1x1);
    109 X0X0:mp_clear (&x0x0);
    110 T2:mp_clear (&t2);
    111 T1:mp_clear (&t1);
    112 X1:mp_clear (&x1);
    113 X0:mp_clear (&x0);
    114 ERR:
    115   return err;
    116 }
    117 #endif
    118 
    119 /* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_sqr.c,v $ */
    120 /* $Revision: 1.5 $ */
    121 /* $Date: 2006/03/31 14:18:44 $ */
    122