Summary
International Symposium on Nonlinear Theory and its Applications
2005
Session Number:2-4-1
Session:
Number:2-4-1-3
Discrete Chaos and Cryptography
J.M. Amigo, J. Szczepanski, L. Kocarev,
pp.461-464
Publication Date:2005/10/18
Online ISSN:2188-5079
Summary:
We propose definitions of discrete Lyapunov exponent and discrete entropy for permutations on a finite set. We justify our definitions by proving that in the ‘infinite limit’, i.e., when the cardinality M of the set goes to infinity, the discrete concepts converge to their continuous counterparts for a large class of chaotic maps. Consequently, we say that a discrete-time dynamical system on a finite-state phase space is discretely chaotic if its discrete Lyapunov exponent tends to a positive number (or to ∞) when M → ∞. Possible applications of discrete chaos to cryptography are also discussed.