Improved One-Dimensional Piecewise Chaotic Maps for Information Security

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.

BER Performance Improvement of Dual Chaotic Maps Based on STBC Communication System

“…Table (6) summarizes the values of LEs for presented chaotic maps From the above table, it is observed that the dual tent has the most randomness whereas the single logistic map has the least randomness.…”

“…A compound of two 1-D chaotic maps suggests by I. Aouissaoui et al [6] for information security. Which achieved a logistic-sine map based on a tent chaotic map as well as a cubic-tent map but for SISO channel.…”

“…12 = N 11 and 𝑁 22 = 𝑁 21 represent AWGN components and h 11 , h 21 , h 12 and h 22 are the channel coefficients for 2 × 2 scheme. The above formulas are derived in[6].…”

A Secure Transmission of Digital Images using Multiple Chaotic Maps and Elliptic Curve

“…By integrating features of the sine map, logistic map, and tent map author in [21] suggested a novel compound one-dimensional piece wise chaotic system which is hybrid in nature to overcome the issues inherent in theses maps. The proposed map provides more chaotic characteristics than either map alone.…”

Design and Analysis of New Version of Cryptographic Hash Function Based on Improved Chaotic Maps With Induced DNA Sequences

“…Bifurcation diagram displays how the behavior of a chaotic system changes with a dynamic control parameter. And, the chaotic maps initial parameter, located in the chaotic areas, is selected using the Lyapunov exponent [27][28][29][30][31][32][33][34][35][36][37][38][39][40]. The Lyapunov exponent signs, λ, provide a qualitative picture of a system's dynamics.…”