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   1 /* -*-c-*-
   2  *
   3  * $Id: mprand.c,v 1.5 2004/04/08 01:36:15 mdw Exp $
   4  *
   5  * Generate a random multiprecision integer
   6  *
   7  * (c) 1999 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Header files ------------------------------------------------------*/
  31
  32 #include <mLib/alloc.h>
  33
  34 #include "grand.h"
  35 #include "mp.h"
  36 #include "mprand.h"
  37
  38 /*----- Main code ---------------------------------------------------------*/
  39
  40 /* --- @mprand@ --- *
  41  *
  42  * Arguments:   @mp *d@ = destination integer
  43  *              @unsigned b@ = number of bits
  44  *              @grand *r@ = pointer to random number source
  45  *              @mpw or@ = mask to OR with low-order bits
  46  *
  47  * Returns:     A random integer with the requested number of bits.
  48  *
  49  * Use:         Constructs an arbitrarily large pseudorandom integer.
  50  *              Assuming that the generator @r@ is good, the result is
  51  *              uniformly distributed in the interval %$[2^{b - 1}, 2^b)$%.
  52  *              The result is then ORred with the given @or@ value.  This
  53  *              will often be 1, to make the result odd.
  54  */
  55
  56 mp *mprand(mp *d, unsigned b, grand *r, mpw or)
  57 {
  58   size_t sz = (b + 7) >> 3;
  59   arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global;
  60   octet *v = x_alloc(a, sz);
  61   unsigned m;
  62
  63   /* --- Fill buffer with random data --- */
  64
  65   r->ops->fill(r, v, sz);
  66
  67   /* --- Force into the correct range --- *
  68    *
  69    * This is slightly tricky.  Oh, well.
  70    */
  71
  72   b = (b - 1) & 7;
  73   m = (1 << b);
  74   v[0] = (v[0] & (m - 1)) | m;
  75
  76   /* --- Mask, load and return --- */
  77
  78   d = mp_loadb(d, v, sz);
  79   d->v[0] |= or;
  80   memset(v, 0, sz);
  81   x_free(a, v);
  82   return (d);
  83 }
  84
  85 /* --- @mprand_range@ --- *
  86  *
  87  * Arguments:   @mp *d@ = destination integer
  88  *              @mp *l@ = limit for random number
  89  *              @grand *r@ = random number source
  90  *              @mpw or@ = mask for low-order bits
  91  *
  92  * Returns:     A pseudorandom integer, unformly distributed over the
  93  *              interval %$[0, l)$%.
  94  *
  95  * Use:         Generates a uniformly-distributed pseudorandom number in the
  96  *              appropriate range.
  97  */
  98
  99 mp *mprand_range(mp *d, mp *l, grand *r, mpw or)
 100 {
 101   size_t b = mp_bits(l);
 102   size_t sz = (b + 7) >> 3;
 103   arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global;
 104   octet *v = x_alloc(a, sz);
 105   unsigned m;
 106
 107   /* --- The algorithm --- *
 108    *
 109    * Rather simpler than most.  Find the number of bits in the number %$l$%
 110    * (i.e., the integer %$b$% such that %$2^{b - 1} \le l < 2^b$%), and
 111    * generate pseudorandom integers with %$n$% bits (but not, unlike in the
 112    * function above, with the top bit forced to 1).  If the integer is
 113    * greater than or equal to %$l$%, try again.
 114    *
 115    * This is similar to the algorithms used in @lcrand_range@ and friends,
 116    * except that I've forced the `raw' range of the random numbers such that
 117    * %$l$% itself is the largest multiple of %$l$% in the range (since, by
 118    * the inequality above, %$2^b \le 2l$%).  This removes the need for costly
 119    * division and remainder operations.
 120    *
 121    * As usual, the number of iterations expected is two.
 122    */
 123
 124   b = ((b - 1) & 7) + 1;
 125   m = (1 << b) - 1;
 126   do {
 127     r->ops->fill(r, v, sz);
 128     v[0] &= m;
 129     d = mp_loadb(d, v, sz);
 130     d->v[0] |= or;
 131   } while (MP_CMP(d, >=, l));
 132
 133   /* --- Done --- */
 134
 135   memset(v, 0, sz);
 136   x_free(a, v);
 137   return (d);
 138 }
 139
 140 /*----- That's all, folks -------------------------------------------------*/