Pi

[Steve Schear]

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