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
"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]

Reply via email to