statistical inferences and PRNG characterization

Travis H. solinym at gmail.com
Fri May 19 07:51:55 EDT 2006


Hi,

I've been wondering about the proper application of statistics with
regard to comparing PRNGs and encrypted text to truly random sources.

As I understand it, when looking at output, one can take a
hypothetical source model (e.g. "P(0) = 0.3, P(1) = 0.7, all bits
independent") and come up with a probability that the source may have
generated that output.  One cannot, however, say what probability such
a source had generated the output, because there is an infinite number
of sources (e.g. "P(0) = 0.29999.., P(1) = 7.000...").  Can one say
that, if the source must be A or B, what probability it actually was A
(and if so, how)?

Also, it strikes me that it may not be possible to prove something
cannot be distinguished from random, but that proofs must be of the
opposite form, i.e. that some source is distinguishable from random.

Am I correct?  Are there any other subtleties in the application of
statistics to crypto that anyone wishes to describe?  I have yet to
find a good book on statistics in these kinds of situations, or for
that matter in any.

As an aside, it's amusing to see the abuse of statistics and
probability in the media.  For example, when people ask "what's the
probability of <some non-repeating event or condition>?"
-- 
"Curiousity killed the cat, but for a while I was a suspect" -- Steven Wright
Security Guru for Hire http://www.lightconsulting.com/~travis/ -><-
GPG fingerprint: 9D3F 395A DAC5 5CCC 9066  151D 0A6B 4098 0C55 1484

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