| The applications of chaotic systems and fractals to cryptology are examined. Several methods are proposed with the intention to produce better pseudorandom numbers and increase the level of confusion and diffusion in encoded messages. A complexity measure is adopted as a means to assess the performance of each method. The proposed schemes are compared against each other and against the results of the crypt algorithm, available from the Unix operating system.; The schemes are divided into pseudorandom number generators, permutation matrix generators, substitution schemes, and secret sharing schemes. Computer simulations suggest that, in the case of pseudorandom generators, a technique we call indirect thresholding should be favored against a more straightforward approach called direct thresholding. Also, the proposed substitution schemes, from the viewpoint of our complexity measure, compare favorably against the crypt command. Permutation matrix generators are found to produce weaker results when used directly for encoding purposes and simulations suggest their proper role in cryptography is that of cryptographic primitives whose function is to increase the diffusion in the ciphertext.; Iterated function systems are used in both permutation matrix generation and secret sharing schemes. In the latter, a method is devised by which a secret is broken into shares (represented by functions of an iterated function system) in such a manner that only when the shareholders agree on combining their information, it is possible to decode the secret message. Examples are shown in which individual attempts by a single shareholder to decode the secret are unfruitful.; Some other issues are also treated, such as the assignment of a dimension to structured languages, the general concepts of fractals and chaotic systems, and how unpredictability in these systems suggest their application to cryptography. |
