full-disclosure - Random number prediction

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Date: Thu Jun 30 15:50:42 2005
From: avosani.gabriele at libero.it (Gabriele Avosani)
Subject: Random number prediction

Hello there folks,
take a look at this source, its called sidis.c
/*****************************************************************************************************/
/* Sidis                                                                                             */
/* CRT rand() function random number predictor                                                       */
/*                                                                                                   */
/* works with every windows and unix random generator                                                */
/*                                                                                                   */
/* this is a full service random number predictor                                                    */
/* the function of CRT rand is the following                                                         */
/* int rand (void)                                                                                   */
/* {                                                                                                 */
/*      _ptiddata ptd = _getptd();                                                                   */
/*        return( ((ptd->_holdrand = ptd->_holdrand * 214013L + 2531011L) >> 16) & 0x7fff );         */
/* }                                                                                                 */
/* As you can see the seed starts to set the variable that is returned from the pointer              */
/* then we have a little mathematic and we get 15 bits                                               */
/* ......                                                                                            */
/* but, from what i discovered, you can read the explaination in sci.math, i have made a post there, */
/* we can do this operation                                                                          */
/* x1 = (seed * y + z)                                                                               */
/* x2 = (x1 * y + z)                                                                                 */
/* x3 = (x2 * y + z)                                                                                 */
/* the random numbers are: x1 >> 15, x2 >> 15, x3 >> 15                                              */
/* now .... if we apply a little phormula, i can assure you that:                                    */
/* (x2 >> 15 - z >> 15) * y >> 15 gives us x1 >> 15                                                  */
/* now we can easily brute force the remaining 17 bits                                               */
/*                                                                                                   */
/* Zuc                                                                                               */
/*                                                                                                   */
/*****************************************************************************************************/

#include <stdlib.h>
#include <stdio.h>

#define rand1 666
#define rand2 32767

unsigned long next=-1,w;

void main(void)
{
 unsigned long x = (((rand2 >> 15) - (2531011 >> 15) >> 15) * 214013 >> 15) >> 15;
 for(long y=0;y<2^17;y++)
 {
  w = y * 2^17 + x;
  next = (w * 214013 + 2531011) >> 32;
  if( (( next * 214013 + 2531011)>> 15 ) == rand1 )break;
 }
 if(next==-1)
 {
  printf("Sorry, number not found.\n");
  return;
 }
 for(unsigned short i=0;i<10;i++)
 {
  printf("Next number n.%i --- %i\n",i,(next*214013+2531011)>>15);
  next=next*214013+2531011;
 }
 printf("Sic transit gloria mundi.\n");
}

Zuc
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