Eric Cordian wrote:

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."

This would let us "whiten" entropy with confidence. Now we just assume without really knowing that feeding everything through SHA1 is a good idea; that is, the mapping of input strings to the resulting hash string is even. (This is different from the "can't find a collision" property. Even if that property doesn't hold, so long as the probability of each resulting hash is about the same, it will work fine as an entropy whitener.) The term "random" may be misleading. What they are likely close to proving is that the occurences of any given string of bits is evenly distributed. This does not mean it is a good encryption algorithm. For example, if it turns out that given a sequence of bits it's easy to find the places in pi where they appear, you have a good known plaintext attack. However, if in addition it was shown to be impossible to do this, we would have something neat and very important - a provably strong encryption algorithm. My guess is that this is a ways off, if it's even possible.