Information-content of ciphertext

[wet!naga (Peter Davidson)]

>From: Mike Johnson <exabyte!smtplink!mikej@uunet.uu.net>
>To: cypherpunks@toad.com
>Subject: Information theory and cryptography
>
>Robert W. Clark asks:
>> ...
>> Is this affected by whether or not the key is known?  If the
>> key has been irretrievably lost, does this lessen the amount
>> of information, or does the 'potential' informational content
>> remain the same?
>
>If you have the proper algorithm and key, then the same information can be
>derived from both.  ...
>the information in the plain text is conveyed by the combination of
>the ciphertext, the key, and the algorithm used.  Take any of these away, and
>you lose information.  In most cases, loss of the algorithm is not an issue,
>but if you forget, lose, or damage either the key or the ciphertext, you have
>reduced the useful information content, possibly to zero.
 
Yes.  Remember what information is (in the real world): it is what
reduces our uncertainty about things, it is what allows us to exclude
some things from the realm of what we take to be the case.  An object
contains information only in the context of some method to use that
object to reduce uncertainty.  Thus a piece of ciphertext may contain
information for Joe if he knows how to convert it to plaintext. If
Fred does not know this then for Fred the ciphertext contains no
information, since he is just as uncertain about the world after
receiving the ciphertext as he was before.
 
Information is information only if you can access it.  What was not
informative may become informative, and vice-versa.  It makes no sense
to think of information independently of a representational agent
(something which represents a state-of-affairs to itself) who is or
can be informed by it.
 
Mathematicians have a mathematical definition of information, but
mathematicians live in an ideal world, so their definition of
information is different from that of the rest of us.