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