## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - B
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DCDS-B

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.

DCDS-B

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.

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