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A new chaotic discrete dynamical system, built on trigonometric functions, is proposed. With intent to use this system within cryptographic applications, we proved with the aid of specific tools from chaos theory (e.g., Lyapunov exponent, attractor’s fractal dimension, and Kolmogorov-Smirnov test) and statistics (e.g., NIST suite of tests) that the newly proposed dynamical system has a chaotic behavior, for a large parameter’s value space, and very good statistical properties, respectively. Further, the proposed chaotic dynamical system is used, in conjunction with a binary operation, in the designing of a new pseudorandom bit generator (PRBG) model. The PRBG is subjected, by turns, to an assessment of statistical properties. Theoretical and practical arguments, rounded by good statistical results, confirm viability of the proposed chaotic dynamical system and newly designed PRBG, recommending them for usage within cryptographic applications.

We present a new one-dimensional chaotic map, suitable for real-time image encryption. Its theoretical analysis, performed using some specific tools from the chaos theory, shows that the proposed map has a chaotic regime and proves its ergodicity, for a large space of values of the control parameter. In addition, to argue for the good cryptographic properties of the proposed map, we have tested the randomness of the values generated by its orbit using NIST statistical suite. Moreover, we present a new image encryption scheme with a classic bimodular architecture, in which the confusion and the diffusion are assured by means of two maps of the previously proposed type. The very good cryptographic performances of the proposed scheme are proved by an extensive analysis, which was performed regarding the latest methodology in this field.

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