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Improved One-Dimensional Piecewise Chaotic Maps for Information Security

Ichraf Aouissaoui 1, Toufik Bakir2, Anis Sakly 1, and Smain Femmam 3
1. Laboratory LAESE, ENIM, University of Monastir, Monastir 5000, Tunisia
2. Laboratory ImVia, EA 7535, Dijon 21000, France
3. Haute-Alsace University, Strasbourg, France

Abstract—Chaos represents interesting features that are suitable for the cryptography domain. One-dimensional chaotic maps are widely used for security issues due to their simplicity and chaotic behavior versus other multidimensional chaotic maps that can be complex for hardware implementation and hard to analyze. However, classical one-dimensional chaotic maps present a reduced range of chaotic behavior. In this paper, we propose two new piecewise compound one-dimensional chaotic maps; an Altered Sine-Logistic map based on Tent map (ASLT) and a combined Cubic-Tent map (CT). The proposed compound maps combine classical and simple one-dimensional chaotic maps to produce an extensive range of chaotic behavior. The ASLT system comprises a combined Sine-Tent map in the first piece of the function and a combined Logistic-Tent map in the second piece of the function. Then, the CT map is based on the nonlinear fusion operation between the Cubic map and the piecewise Tent map. Simulation results and chaotic behavior analysis are provided using the bifurcation diagram, Lyapunov exponent, initial sensitivity, and Shannon entropy measure. The evaluation results demonstrate the effectiveness of the proposed 1D maps with better chaotic performances, chaotic range, and complexity compared to their corresponding classical chaotic maps. The simple structure and effectiveness of the proposed systems make them suitable for chaos-based cryptography providing better security strength and more randomness.
Index Terms—Chaotic map, chaotic range, Lyapunov exponent, bifurcation diagram, Initial sensitivity

Cite: Ichraf Aouissaoui, Toufik Bakir, Anis Sakly, and Smain Femmam, "Improved One-Dimensional Piecewise Chaotic Maps for Information Security," Journal of Communications vol. 17, no. 1, pp. 11-16, January 2022. Doi: 10.12720/jcm.17.1.11-16

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