New Enhanced Chaotic Number Generators Lozi René1,* 1Laboratoire J.A. Dicudonné, UMR du CNRS N° 6621, University of Nice-Sophia-Antipolis Parc Valrose. 136108 Nice Cedex 02, France and Institu Universitaire de Formation des Maîtres Célestin Freinet-académie de Nice, 89 Avenue George V, 06046 Nice Cedex 1, France *Author for Correspondence. E-mail: rlozi@unice.fr
Abstract New families of enhanced chaotic number generators are introduced in order to compute very fast long series of pseudorandom numbers. Generation of random or pseudorandom numbers, nowadays, is a key feature of industrial mathematics. Pseudorandom or chaotic numbers are used in many areas of contemporary technology such as modern communication systems and engineering applications. Everything we do to achieve privacy and security in the computer age depends on random numbers. More and more patents using discrete mappings for this purpose are being obtained by researchers of discrete dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) applying discrete chaotic dynamical systems intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. Recently, it has been found that the very weak coupling of many symmetric tent maps (and logistic maps) can generate chaotic numbers in good conditions. Moreover, these numbers are equally distributed over a given Unite interval. Numerical computations show that this distribution is obtained with a very good approximation. They also have the property that the length of the periods of the numerically observed orbits is very large. However, chaotic numbers are not pseudorandom numbers, because the plot of the couples of iterated points (xn, xn+1) in the phase plane shows up the symmetric tent map used to generate them. Now, new families of enhanced chaotic number generators are introduced to hide the generating function. The key feature of enhanced chaotic number generators is that they use chaotic numbers themselves to sample chaotic subsequences of chaotic numbers. The properties of the new families are explored numerically. Their very high qualities and usefulness as CPRNG when series are computed up to 1013 iterations are underlined. Top AMS Subject Classification 65C10, 65P20, 37E05, 37M10. Top Keywords Enhanced chaotic number, Pseudorandom number, PRNG, CPRNG, Coupled tent map. Top |