> At 06:24 AM 3/12/1998 -0500, you wrote:

> Many simple hardware and software integer random number generators are of
> the pseudo-random number generator (PRNG) variety.   PRNG generators,
> usually are implemented with shift registers (serial in, parallel out type)
> with feedback (some of the shift register outputs are exclusive OR'ed
> together and exclusive OR'ed with the input to the shift register).  As
> noted, this can easily be achieved in either software or hardware.  The
> PRNG number sequences (generated via this technique) pass many statistical
> tests for randomness that truly random number sequences would also pass,
> but with one undesirable feature - the sequence of "random" numbers
> eventually will repeat.

If you use some sort of time varying-random input, from external
world, changing its value before random sequence is complete  then
you should get rid off repeating - predictability problem.

> To obtain truly random number sequences, analog noise sources are usually
> employed.  These noise sources generate amplitude (and bandwidth)
> limited white noise.  Suppose that a white noise source (band-width
> limited) generates uniformly distributed amplitudes, when sampled at
> a frequency fs,

There are many natural random events having different distributions
such as gaussian in some heat related events, which are not suitable
for this purpose but used because of  its unpredictable nature. It
sounds like what you mean with truly random generator is to have a
uniform distribution in a random event. At least for casino type of
games I am agree on that.  I am not sure for the analog schemes but I
know you can implement PRNG in a quite uniform manner.

To me long sequence PRNG with an additional external random input is
the best technique. If you are going to use a micro with ALU
recursive (dynamic) difference equations will give you more options
to get there.

> Gary Pepper

Aydin