Beefy Boxes and Bandwidth Generously Provided by pair Networks
Problems? Is your data what you think it is?
 
PerlMonks  

Comment on

( #3333=superdoc: print w/ replies, xml ) Need Help??

If you liked that, here's another way to discover the internal state of a linear congruential pseudorandom number generator. It's only effective when the internal state of the PRNG is small enough. As long as that's true, it's fairly fast, since it doesn't need to use any BigInts.

This code is set up to use the same constants as the rand() function in ActiveState Perl for Windows. It can be modified for other generators, but there are some magic numbers that need to be tweaked. It takes four output bytes from the PRNG, and comes up with a small number of possible seeds (often just one). If that bothers you, give it a fifth byte to work with, and that will narrow it down to one almost every time.

It works by looking at the first two output bytes from the PRNG, and checking each of the roughly 2**15 seed values that would produce them. This is one of the steps in the cryptanalysis of the PKZIP cipher by Biham and Kocher, which is implemented (though somewhat differently) in pkcrack.

use strict; use warnings; use integer; # PRNG parameters my $m = 0x343fd; my $b = 0x269ec3; my $m1 = 0x39b33155; # multiplicative inverse of $m mod 2**31 # build the lookup tables my (@diff_tbl, @prod_tbl); for my $x (0 .. 0x2bc) { # 0x2bc is a magic number... see below my $p = ($x * $m1) & 0x7fffffff; my $e = ($p >> 22) & 0x1ff; for ($e, ($e-1)&0x1ff, ($e-2)&0x1ff) { push @{$diff_tbl[$_]}, $x; push @{$prod_tbl[$_]}, $p; } } # "Unknown" values: internal states of the PRNG my $X0 = int(rand 2**31); my $X1 = ($X0 * $m + $b) & 0x7fffffff; my $X2 = ($X1 * $m + $b) & 0x7fffffff; my $X3 = ($X2 * $m + $b) & 0x7fffffff; # "Known" values: a few bytes of output from the PRNG my $x0 = $X0 & 0x7f800000; my $x1 = $X1 & 0x7f800000; my $x2 = $X2 & 0x7f800000; my $x3 = $X3 & 0x7f800000; # find the lowest nonnegative $d such that # $x0 == ((($x1 + $d - $b) * $m1) & 0x7f800000) my $prev = (($x1 - $b) * $m1) & 0x7fffffff; my $ent = (($x0 - $prev) >> 22) & 0x1ff; my ($d, $p); for (0 .. $#{$prod_tbl[$ent]}) { $p = $prev + $prod_tbl[$ent][$_]; if (($p & 0x7f800000) == $x0) { $d = $diff_tbl[$ent][$_]; last } } die "can't happen\n" unless defined $d; $p &= 0x7fffff; my $q = ($x1 + $d) * $m + $b; # modest (about 2**15 steps) brute-force search for the right $d while ($d < 0x800000) { # invariant: $p == ((($x1 + $d - $b) * $m1) & 0x7fffff) # invariant: $q == ($x1 + $d) * $m + $b # is this a solution? if (($q & 0x7f800000) == $x2) { my $r = $q * $m + $b; if (($r & 0x7f800000) == $x3) { printf "guessed x0 = %08x\n", (($x1 + $d - $b) * $m1) & 0x7fffff +ff; } } # find the next admissible value of $d # there is much magic here... see below for a hint if ($p < 0x67ceeb) { $d += 0x0c1; $p += 0x183115; $q += 0x27641b +d } elsif ($p >= 0x6a1b54) { $d += 0x1fc; $p -= 0x6a1b54; $q += 0x67aea0 +c } else { $d += 0x2bd; $p -= 0x51ea3f; $q += 0x8f12bc +9 } } printf "actual X0 = %08x\n", $X0; # calculate the magic numbers my $low = 0; my $high = 0x800000; my $x = 0; while ($low < $high) { $x++; my $y = ($x * $m1) & 0x7fffffff; my $yhi = ($y >> 23) & 0xff; my $yneg = (-$y) & 0x7fffff; if ($yhi == 0 && $yneg > $low) { printf "if y < 0x%x then x += 0x%x, y += 0x%x\n", $yneg, $x, $y; $low = $yneg; } elsif ($yhi == 0xff && $yneg < $high) { printf "if y >= 0x%x then x += 0x%x, y -= 0x%x\n", $yneg, $x, $yne +g; $high = $yneg; } }

In reply to Re: Predict Random Numbers by no_slogan
in thread Predict Random Numbers by no_slogan

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":



  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • Outside of code tags, you may need to use entities for some characters:
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.
  • Log In?
    Username:
    Password:

    What's my password?
    Create A New User
    Chatterbox?
    and the web crawler heard nothing...

    How do I use this? | Other CB clients
    Other Users?
    Others about the Monastery: (8)
    As of 2014-10-24 16:54 GMT
    Sections?
    Information?
    Find Nodes?
    Leftovers?
      Voting Booth?

      For retirement, I am banking on:










      Results (133 votes), past polls