>> - You cannot determine the key from the encrypted & decrypted text (by
key I
>> mean the 'session' key)
>Any secure cipher would qualify (unless you're describing a known-plaintext
attack).

Essentially, yes. Any cipher that is vulnerable to this would reveal keys a
and b, since the encrypted and unencrypted versions of each are transmitted,
and if you know a or b, you can work out the original message, M.

>> - You can decrypt in a 'nested' fashion - eg, if E(M,x) means encrypting
M
>> with key x and D(M,x) means decrypt M with key x, then the algorithm
should
>> satisfy D(E(E(M,a),b),a) == E(M,b)
>I doubt such a thing is possible.  Of course, we need the mathmatical proof
to be sure.

Well, XOR meets this requirement. Unfortunately, it doesn't meet the first
requirement of not being able to get the keys/session keys.

>In any case, what's wrong with the public key crypto? Sure it's slow, but
you only do it
>once.

Just interest, really - if something like this is possible, it could be much
easier to implement than any public-key system. See
http://ciphersaber.gurus.com if you're curious why a really-simple key
exchange protocol would be useful. :)


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