Clark Reynard, <clark@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. It's not unusual for different compression algorithms to achieve very different levels of compression. In a sense, these different algorithms disagree about the amount of information in the original data. We discussed digitized speech here some time back. Ordinary compression algorithms such as Lempel- Ziv or Huffman encoding don't compress digitized speech much at all. Special algorithms such as linear predictive coding can achieve great compression. In the same way, there is no contradiction between the fact that an encrypted file looks random and incompressible, and the fact that knowing the key it becomes clear that the file actually can be compressed. Any calculation of the information content of a file can only be considered an upper bound. A more clever algorithm may always exist which will reveal the data to have much less information than was originally thought. This is basically the situation you have when faced with an encrypted file for which you don't have the key. Hal Finney hfinney@shell.portal.com