<html>
<head>
<meta content="text/html; charset=ISO-8859-1"
http-equiv="Content-Type">
</head>
<body bgcolor="#FFFFFF" text="#000000">
Thinking more about the issue: <br>
<br>
As said, the quality of a random number generator is more a matter
of taste than a subject to in-depth discussion (as nearly everything
that is influenced by the way infinity word). <br>
<br>
Obviously a perfect random number generator (for integer numbers
0...n) <b>needs </b>to be able to create a series of a million
zeros. This is (seemingly) neither a nice Equal Distribution nor <b>obviously</b>
unpredictable.<br>
<br>
<br>
<br>
IMHO a very decent random generator is just the simple process<br>
<tt><br>
</tt><tt>r(n) = x(n) with x(n) = (a + b*x(n-1) ) mod c</tt> <br>
<br>
Here c should be a (big) prime, as you will get "less random"
sub-series of the length of any factor of c. <br>
<br>
OK let a and b be big primes, as well. That does not harm.<br>
<br>
<br>
Equal Distribution is granted, as the sequence will completely cover
all the numbers 0..c-1 and then start from the beginning.<br>
<br>
Of course it is perfectly predictable if you know the numbers a, b,
and c. and I suppose you can detect them from watching the series
for a rather short time. <br>
<br>
<br>
You can reduce the predictability by doing a much smaller
non-process from the big cyclic process <br>
<br>
maybe just <br>
<br>
<tt>r(n) = x(n) mod d with x(n) = (a + b*x(n-1) ) mod c</tt>
with d being a prime several orders of magnitude lower than c (and a
and b)<br>
<br>
could work (I did not try a proof or disproof). Maybe d needs not be
a prime but just 2^n if you want an appropriately long key. <br>
<br>
But for cryptology all this needs really large integer numbers. That
should not be an unsolvable problem. Finding a really large Prime is
a standard task, anyway.<br>
<br>
<br>
Of course x(0) should be created using a nice entropy method. <br>
<br>
-Michael<br>
</body>
</html>