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   1 /* -*-c-*-
   2  *
   3  * $Id: mprand.c,v 1.3 2000/06/17 11:45:09 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 /*----- Revision history --------------------------------------------------*
  31  *
  32  * $Log: mprand.c,v $
  33  * Revision 1.3  2000/06/17 11:45:09  mdw
  34  * Major memory management overhaul.  Added arena support.  Use the secure
  35  * arena for secret integers.  Replace and improve the MP management macros
  36  * (e.g., replace MP_MODIFY by MP_DEST).
  37  *
  38  * Revision 1.2  1999/12/22 15:55:33  mdw
  39  * Modify `mprand' slightly.  Add `mprand_range'.
  40  *
  41  * Revision 1.1  1999/12/10 23:23:05  mdw
  42  * Support for generating random large integers.
  43  *
  44  */
  45
  46 /*----- Header files ------------------------------------------------------*/
  47
  48 #include <mLib/alloc.h>
  49
  50 #include "grand.h"
  51 #include "mp.h"
  52 #include "mprand.h"
  53
  54 /*----- Main code ---------------------------------------------------------*/
  55
  56 /* --- @mprand@ --- *
  57  *
  58  * Arguments:   @mp *d@ = destination integer
  59  *              @unsigned b@ = number of bits
  60  *              @grand *r@ = pointer to random number source
  61  *              @mpw or@ = mask to OR with low-order bits
  62  *
  63  * Returns:     A random integer with the requested number of bits.
  64  *
  65  * Use:         Constructs an arbitrarily large pseudorandom integer.
  66  *              Assuming that the generator @r@ is good, the result is
  67  *              uniformly distributed in the interval %$[2^{b - 1}, 2^b)$%.
  68  *              The result is then ORred with the given @or@ value.  This
  69  *              will often be 1, to make the result odd.
  70  */
  71
  72 mp *mprand(mp *d, unsigned b, grand *r, mpw or)
  73 {
  74   size_t sz = (b + 7) >> 3;
  75   arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global;
  76   octet *v = x_alloc(a, sz);
  77   unsigned m;
  78
  79   /* --- Fill buffer with random data --- */
  80
  81   r->ops->fill(r, v, sz);
  82
  83   /* --- Force into the correct range --- *
  84    *
  85    * This is slightly tricky.  Oh, well.
  86    */
  87
  88   b = (b - 1) & 7;
  89   m = (1 << b);
  90   v[0] = (v[0] & (m - 1)) | m;
  91
  92   /* --- Mask, load and return --- */
  93
  94   d = mp_loadb(d, v, sz);
  95   d->v[0] |= or;
  96   memset(v, 0, sz);
  97   x_free(a, v);
  98   return (d);
  99 }
 100
 101 /* --- @mprand_range@ --- *
 102  *
 103  * Arguments:   @mp *d@ = destination integer
 104  *              @mp *l@ = limit for random number
 105  *              @grand *r@ = random number source
 106  *              @mpw or@ = mask for low-order bits
 107  *
 108  * Returns:     A pseudorandom integer, unformly distributed over the
 109  *              interval %$[0, l)$%.
 110  *
 111  * Use:         Generates a uniformly-distributed pseudorandom number in the
 112  *              appropriate range.
 113  */
 114
 115 mp *mprand_range(mp *d, mp *l, grand *r, mpw or)
 116 {
 117   size_t b = mp_bits(l);
 118   size_t sz = (b + 7) >> 3;
 119   arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global;
 120   octet *v = x_alloc(a, sz);
 121   unsigned m;
 122
 123   /* --- The algorithm --- *
 124    *
 125    * Rather simpler than most.  Find the number of bits in the number %$l$%
 126    * (i.e., the integer %$b$% such that %$2^{b - 1} \le l < 2^b$%), and
 127    * generate pseudorandom integers with %$n$% bits (but not, unlike in the
 128    * function above, with the top bit forced to 1).  If the integer is
 129    * greater than or equal to %$l$%, try again.
 130    *
 131    * This is similar to the algorithms used in @lcrand_range@ and friends,
 132    * except that I've forced the `raw' range of the random numbers such that
 133    * %$l$% itself is the largest multiple of %$l$% in the range (since, by
 134    * the inequality above, %$2^b \le 2l$%).  This removes the need for costly
 135    * division and remainder operations.
 136    *
 137    * As usual, the number of iterations expected is two.
 138    */
 139
 140   b = (b - 1) & 7;
 141   m = (1 << b) - 1;
 142   do {
 143     r->ops->fill(r, v, sz);
 144     v[0] &= m;
 145     d = mp_loadb(d, v, sz);
 146     d->v[0] |= or;
 147   } while (MP_CMP(d, >=, l));
 148
 149   /* --- Done --- */
 150
 151   memset(v, 0, sz);
 152   x_free(a, v);
 153   return (d);
 154 }
 155
 156 /*----- That's all, folks -------------------------------------------------*/