On 5/17/06, Kuehn, Ulrich <[EMAIL PROTECTED]> wrote:

Given known plaintext and corresponding ciphertext, there should not be too many keys that map the plaintext to the ciphertext. I don't have the probability at hand how many such 'collisions' you would expect from 256 random permutations, but intuitively I would not expect too many. However, I could be wrong here and would like to be corrected in this case.

I'm a little rusty but I'll give it a shot. Well we have a byte x and a mapping f_k(x) = y, with f selected at random (for now I'll assume with replacement since 256 << 256!) from the set of all permutations, x and y from 0..255. The questions is what fraction of permutations have f_k(x) = y, I think the answer is 1/256. There's 255 "other" permutations, so the chance that there is at least one k' such that f_k'(x)=y is 255/256 = 99.6%. The chance that there is exactly one such k' is sampling with replacement and if I am not mistaken P(|K|=1) = (255/256)^255 = 0.36. Along those same lines, P(|K|=2) = (255/256)^253 * 254 / 256^2 = 0.001, so it looks like the expected number of equivocating keys is very small. I suspect that's why Terry Ritter's "Dynamic Substitution" algorithms, which are meant to replace XOR combiner in stream ciphers, maintain state. -- "Curiousity killed the cat, but for a while I was a suspect" -- Steven Wright Security Guru for Hire http://www.lightconsulting.com/~travis/ -><- GPG fingerprint: 9D3F 395A DAC5 5CCC 9066 151D 0A6B 4098 0C55 1484 --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to [EMAIL PROTECTED]