On Fri, May 19, 2006 at 06:51:55AM -0500, Travis H. wrote: > 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)?

You could do this with relatively simple Bayesian classification. Start with a prior assumption like "As far as I know it is 50/50 that it is source A or B" and then for the output you see you calculate P(A|output) and P(B|outout) using Bayes rule, your probabilistic model for the source and P(A) = P(B) = 0.5. P(X|O) = P(O|X) P(X)/P(O) A finite number of sources is not required here, as long as you're willing to provide a prior distribution over all possible sources that you can do calculations with. > 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. I think you're still going to run into the problem of deciding what is random, and that problem will be tied up in your choice of prior distribution on the sources. > 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. I guess the usual proviso: these sort of calculations require assumptions to make them possible, and the results should not be confidently applied outside situations where those assumptions are valid. David. --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to [EMAIL PROTECTED]