Information-content of ciphertext

From: Mike Johnson 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.