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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 769108, 10 pages
Research Article

Study of a New Chaotic Dynamical System and Its Usage in a Novel Pseudorandom Bit Generator

1IT&C Department, Lumina-The University of South-East Europe, 021187 Bucharest, Romania
2Faculty of Informatics, University “Titu Maiorescu”, 0400511 Bucharest, Romania
3ETTI Faculty, University Politehnica of Bucharest, 061071 Bucharest, Romania

Received 8 July 2013; Revised 14 September 2013; Accepted 16 September 2013

Academic Editor: Zhan Shu

Copyright © 2013 Ana-Cristina Dăscălescu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.