An asymptotically perfect pseudorandom generator
Marcela Mejía J. Urías
A transformation of binary sequences that is ergodic and mixing with respect to the equidistributed measure is constructed with the help of a cellular automaton. The transformation is the basic element for a pseudorandom number generator. The ratio of the number of seeds that generate equidistributed sequences to the number of all words goes to one as the length of words is increased. The evaluation of a hardware implementation of the generator confirms the statistical behavior of sequences as determined from the ergodic properties of the mathematical model of the generator. Unpredictability under random search attacks is attained by means of three coupled transformations.
keywords: pseudorandom sequences. Cellular automata ergodic transformations
Spectrum of dimensions for Poincaré recurrences of Markov maps
B. Fernandez E. Ugalde J. Urías
The spectrum of dimensions for Poincaré recurrences of Markov maps is obtained by constructing a sequence of approximating maps whose spectra are known to be solution of non-homogeneous Bowen equations. We prove that the spectrum of the Markov map also satisfies such an equation.
keywords: Markov maps Poincaré recurrences spectra of dimensions.

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