Increasing Average Period Lengths by Switching of Robust Chaos Maps in Finite Precision

Details Increasing Average Period Lengths by Switching of Robust Chaos Maps in Finite Precision Increasing Average Period Lengths by Switching of Robust Chaos Maps in Finite Precision

2008-11-12

arxiv.org/abs/0811.1823v3

European Physical Journal Special Topics, Vol. 165, pp. 73--83, 2008

Nonlinear Sciences

Chaotic Dynamics

10 pages, 5 figures, 2 tables. This paper will be published in European Physical Journal Special Topics, Vol. 165, pp. 73--83,

Scientific paper

10.1140/epjst/e2008-00850-4

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits ($T$) of a dynamical system scales as a function of computer precision ($\epsilon$) and the correlation dimension ($d$) of the chaotic attractor: $T \sim \epsilon^{-d/2}$. In this work, we are concerned with increasing the average period length which is desirable for chaotic cryptography applications. Our experiments reveal that random and chaotic switching of deterministic chaotic dynamical systems yield higher average length of periodic orbits as compared to simple sequential switching or absence of switching. To illustrate the application of switching, a novel generalization of the Logistic map that exhibits Robust Chaos (absence of attracting periodic orbits) is first introduced. We then propose a pseudo-random number generator based on chaotic switching between Robust Chaos maps which is found to successfully pass stringent statistical tests of randomness.

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