-----BEGIN PGP SIGNED MESSAGE----- This is a supplement to the fine answer to your question which has already provided by Scott Collins.
How do we measure the entropy of a random number, or a series of random numbers?
Give a particular set of data used to generate a random key, such as, a unix box's /dev/mem, how can one measure the number of bits of entropy?
Actually, it can't be done. The consistent measure of entropy for finite objects like a string or a (finite) series of random numbers is the so-called ``program length complexity''. This is defined as the length of the shortest program for some given universal Turing machine which computes the string. It's consistent in the sense that it has the familiar properties of ``ordinary'' (Shannon) entropy. Unfortunately, it's uncomputable: there's no algorithm which, given an arbitrary finite string S, computes the program-length complexity of S. Program-length complexity is well-studied in the literature. A good introductory paper is ``A Theory of Program Size Formally Identical to Information Theory'' by G. J. Chaitin, _Journal of the ACM_, 22 (1975) reprinted in Chaitin's book _Information Randomness & Incompleteness_, World Scientific Publishing Co., 1990. John E. Kreznar | Relations among people to be by jkreznar@ininx.com | mutual consent, or not at all. -----BEGIN PGP SIGNATURE----- Version: 2.3a iQCVAgUBLP6iDsDhz44ugybJAQH9IwP/V2EZ/crPIENnkWAYFbCKfNrPuStkb7U9 kQurAUc0xgIzcGjYYw6KFAwJ2zMYgGAmtUlbBbkEaJnAjQJc6AT2Q3PBWitWG5Fk +p2YJwSV00TtSxVXqiu7IWUpK2zlbCDzYq0hdoabe4GOoYgdYd96y6WV62AqFb39 MifNcQF5XMQ= =quUv -----END PGP SIGNATURE-----