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

   1 #include <tommath.h>
   2 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_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 xR**-1 == x (mod N) via Montgomery Reduction
  19  *
  20  * This is an optimized implementation of montgomery_reduce
  21  * which uses the comba method to quickly calculate the columns of the
  22  * reduction.
  23  *
  24  * Based on Algorithm 14.32 on pp.601 of HAC.
  25 */
  26 int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
  27 {
  28   int     ix, res, olduse;
  29   mp_word W[MP_WARRAY];
  30
  31   /* get old used count */
  32   olduse = x->used;
  33
  34   /* grow a as required */
  35   if (x->alloc < n->used + 1) {
  36     if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
  37       return res;
  38     }
  39   }
  40
  41   /* first we have to get the digits of the input into
  42    * an array of double precision words W[...]
  43    */
  44   {
  45     register mp_word *_W;
  46     register mp_digit *tmpx;
  47
  48     /* alias for the W[] array */
  49     _W   = W;
  50
  51     /* alias for the digits of  x*/
  52     tmpx = x->dp;
  53
  54     /* copy the digits of a into W[0..a->used-1] */
  55     for (ix = 0; ix < x->used; ix++) {
  56       *_W++ = *tmpx++;
  57     }
  58
  59     /* zero the high words of W[a->used..m->used*2] */
  60     for (; ix < n->used * 2 + 1; ix++) {
  61       *_W++ = 0;
  62     }
  63   }
  64
  65   /* now we proceed to zero successive digits
  66    * from the least significant upwards
  67    */
  68   for (ix = 0; ix < n->used; ix++) {
  69     /* mu = ai * m' mod b
  70      *
  71      * We avoid a double precision multiplication (which isn't required)
  72      * by casting the value down to a mp_digit.  Note this requires
  73      * that W[ix-1] have  the carry cleared (see after the inner loop)
  74      */
  75     register mp_digit mu;
  76     mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
  77
  78     /* a = a + mu * m * b**i
  79      *
  80      * This is computed in place and on the fly.  The multiplication
  81      * by b**i is handled by offseting which columns the results
  82      * are added to.
  83      *
  84      * Note the comba method normally doesn't handle carries in the
  85      * inner loop In this case we fix the carry from the previous
  86      * column since the Montgomery reduction requires digits of the
  87      * result (so far) [see above] to work.  This is
  88      * handled by fixing up one carry after the inner loop.  The
  89      * carry fixups are done in order so after these loops the
  90      * first m->used words of W[] have the carries fixed
  91      */
  92     {
  93       register int iy;
  94       register mp_digit *tmpn;
  95       register mp_word *_W;
  96
  97       /* alias for the digits of the modulus */
  98       tmpn = n->dp;
  99
 100       /* Alias for the columns set by an offset of ix */
 101       _W = W + ix;
 102
 103       /* inner loop */
 104       for (iy = 0; iy < n->used; iy++) {
 105           *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
 106       }
 107     }
 108
 109     /* now fix carry for next digit, W[ix+1] */
 110     W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
 111   }
 112
 113   /* now we have to propagate the carries and
 114    * shift the words downward [all those least
 115    * significant digits we zeroed].
 116    */
 117   {
 118     register mp_digit *tmpx;
 119     register mp_word *_W, *_W1;
 120
 121     /* nox fix rest of carries */
 122
 123     /* alias for current word */
 124     _W1 = W + ix;
 125
 126     /* alias for next word, where the carry goes */
 127     _W = W + ++ix;
 128
 129     for (; ix <= n->used * 2 + 1; ix++) {
 130       *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
 131     }
 132
 133     /* copy out, A = A/b**n
 134      *
 135      * The result is A/b**n but instead of converting from an
 136      * array of mp_word to mp_digit than calling mp_rshd
 137      * we just copy them in the right order
 138      */
 139
 140     /* alias for destination word */
 141     tmpx = x->dp;
 142
 143     /* alias for shifted double precision result */
 144     _W = W + n->used;
 145
 146     for (ix = 0; ix < n->used + 1; ix++) {
 147       *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
 148     }
 149
 150     /* zero oldused digits, if the input a was larger than
 151      * m->used+1 we'll have to clear the digits
 152      */
 153     for (; ix < olduse; ix++) {
 154       *tmpx++ = 0;
 155     }
 156   }
 157
 158   /* set the max used and clamp */
 159   x->used = n->used + 1;
 160   mp_clamp (x);
 161
 162   /* if A >= m then A = A - m */
 163   if (mp_cmp_mag (x, n) != MP_LT) {
 164     return s_mp_sub (x, n, x);
 165   }
 166   return MP_OKAY;
 167 }
 168 #endif
 169
 170 /* $Source: /cvs/libtom/libtommath/bn_fast_mp_montgomery_reduce.c,v $ */
 171 /* $Revision: 1.3 $ */
 172 /* $Date: 2006/03/31 14:18:44 $ */