Relation between number theory and cryptography

[J. Michael Diehl]

According to hfinney at shell.portal.com:
> Clark Reynard, <clark at metal.psu.edu>, asks about information and cryptography.
> 
> As I see it, a cyphertext has at most the same information as the sum of
> the original message, the key, and the encryption algorithm.  Without
> knowing the key a cyphertext may appear random, but actually it is not.
> If it is the encryption of a lower-information plaintext (such as English
> text) then it still basically possesses that low level of information, it's
> just not obvious how to compress it.

Well, you may have placed an upper-limit on the amount of information in an
encrypted message.  I will try to place a lower limit.  Consider the case where
there is less information in the ciphertext than in the plaintext.  Clearly, in
this case, there is no way to retrieve the entire plaintext from the ciphertext
since we no longer have enough information.  So we have to have at least as much
information in the CT as we do in the PT.  If I bought your original arguement,
I'd have to say there is no net change in information content.  Unfortunately,
I don't buy your arguement.

What if we were to add some noise in the process of crypting the PT?  If we did
it algorithmicly, we have added some kind of information to your CP, totally 
unrelated to the actuall message.  But nontheless, it is information of SOME
type; it may simply be 0xFE if the message was writen in the daytime or 0xAC
if not.  This is information in a very "uncompressed" form.  Strictly speaking
this is only 1 bit of information encoded into a byte, but the net result is a 
gain in information content in our CT.

I don't know, is there a flaw in my reasoning?

Laters.

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