Pi
Steve Schear
schear at lvcm.com
Thu Aug 2 16:25:40 PDT 2001
At 11:34 AM 8/2/2001 -0700, Eric Cordian wrote:
>Interesting article recently posted on the Nature Web site about the
>normality of Pi.
>
>http://www.nature.com/nsu/010802/010802-9.html
>
>"David Bailey of Lawrence Berkeley National Laboratory in California and
> Richard Crandall of Reed College in Portland, Oregon, present evidence
> that pi's decimal expansion contains every string of whole numbers. They
> also suggest that all strings of the same length appear in pi with the
> same frequency: 87,435 appears as often as 30,752, and 451 as often as
> 862, a property known as normality."
>
>Of cryptographic interest.
>
>"While there may be no cosmic message lurking in pi's digits, if they are
> random they could be used to encrypt other messages as follows:
>
>"Convert a message into zeros and ones, choose a string of digits
> somewhere in the decimal expansion of pi, and encode the message by
> adding the digits of pi to the digits of the message string, one after
> another. Only a person who knows the chosen starting point in pi's
> expansion will be able to decode the message."
>
>While there's presently no known formula which generates decimal digits of
>Pi starting from a particular point, there's a clever formula which can be
>used to generate HEX digits of Pi starting from anywhere, which Bailey et
>al discovered in 1996, using the PSLQ linear relation algorithm.
I tried to something like this in the late '80s to allow efficient
loss-less compression using "conditioned" PRNs which could generate
suitable auto correlated streams. Unfortunately, I did not discover a
similar method of locating the desired sequences. The search during the
compression phase was to computationally difficult and I abandoned the effort.
steve
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