Re: Toaster to Generate Random Numbers

From: Carlos Moreno (moreno_at_mochima_dot_com@xx.xxx)
Date: 01/10/03 

From: Carlos Moreno <moreno_at_mochima_dot_com@xx.xxx>
Date: Fri, 10 Jan 2003 10:52:39 -0500

Bill Unruh wrote:

> Carlos Moreno <moreno_at_mochima_dot_com@xx.xxx> writes:
>
> ]Omar Bohsali wrote:
>
> ]The discussion is mostly philosophical. Most (sane) people
> ]should agree that thermal noise can be considered random
> ]for all practical purposes from any conceivable point of
> ]view.
>
> No, it is not. The noise structure of "thermal noise"-- eg the noise
> coming from a resistor with a constant current source across it, has
> correlations, especially at long times (1/f noise). Furthermore, stray
> capacitances, inductances, etc, also introduce correlations into the
> noise. All physical systems have such correlations. Some are well
> understood, some not. Such correlations mean that the source is NOT
> "random" (ie, uncorrelated white noise-- or each bit value equal
> probablility 1 and 0 and no correlations between bits).

I think you have a misconception here... (though I wonder if it
is me who has the misconception).

To me, the definition of "random" (if there is one), involves
*only* unpredictability and lack of any fixed pattern.

Uniformly distributed and uncorrelated are different things
(they imply stronger requirements).

In other words, having a higher probability of taking one
particular value still doesn't make it predictable. (i.e.,
you still can not predict if three consecutive coin tosses
will produce at least one head -- you could systematically
state it as your "prediction", and you will be right more
often than wrong... But you did not *predict* the outcome,
and the fact that you get three tails or not *is still* a
random variable).

Now, of course, for many applications (including particularly
cryptography), non-uniformly distributed random sources are
useless (unless you can process them and extract as much
uniformly-distributed data as possible). But that's a
practical consideration; despite thermal noise exhibiting
certain correlation characteristics, *it is* still random
(well, philosophical discussions aside :-)). And of course,
as you say, in most practical cases, the correlation exhibited
by thermal noise is almost sure below the practical limit
of observability, and/or would not affect the system for
which we're using it on.

Carlos 

--

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