Hash function construction based on time average moiré
Minvydas Ragulskis Zenonas Navickas
Discrete & Continuous Dynamical Systems - B 2007, 8(4): 1007-1020 doi: 10.3934/dcdsb.2007.8.1007
An algorithm for the construction of hash function based on optical time average moirè experimental technique is proposed in this paper. Algebraic structures of grayscale color functions and time average operators are constructed. Properties of time average operators and effects of digital image representation are explored. The fact that the inverse problem of identification of the original grayscale color function from its time averaged image is an ill-posed problem helps to construct an efficient algorithm for the construction of a new class of one-way collision free hash functions.
keywords: algebraic structure. Time average moire hash function
The logistic map of matrices
Zenonas Navickas Rasa Smidtaite Alfonsas Vainoras Minvydas Ragulskis
Discrete & Continuous Dynamical Systems - B 2011, 16(3): 927-944 doi: 10.3934/dcdsb.2011.16.927
The standard iterative logistic map is extended by replacing the scalar variable by a square matrix of variables. Dynamical properties of such an iterative map are explored in detail when the order of matrices is 2. It is shown that the evolution of the logistic map depends not only on the control parameter but also on the eigenvalues of the matrix of initial conditions. Several computational examples are used to demonstrate the convergence to periodic attractors and the sensitivity of chaotic processes to initials conditions.
keywords: idempotent The logistic map attractor nilpotent.

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