Normalized Linearly-Combined Chaotic System: Design, Analysis, Implementation, and Application

Abstract

This work presents a general framework for developing a multiparameter 1-D chaotic system for uniform and robust chaotic operation across the parameter space. This is important for diverse practical applications where parameter disturbance may cause degradation or even complete disappearance of chaotic properties. The wide uninterrupted chaotic range and improved chaotic properties are demonstrated with the aid of stability analysis, bifurcation diagram, Lyapunov exponent (LE), Kolmogorov entropy, Shannon entropy, and correlation coefficient. We also demonstrate the proposed system's amenability to cascading for further performance improvement. We introduce an efficient field-programmable gate array-based implementation and validate its chaotic properties using comparison between simulation and experimental results. Cascaded normalized linearly-combined chaotic system (NLCS) exhibits average LE, chaotic ratio, and chaotic parameter space of 1.364, 100%, and $1.1\times 10^{12}$, respectively, for 10-bit parameter values. We provide a thorough comparison of our system with prior works both in terms of performance and hardware cost. We also introduce a simple extension scheme to build 2-D robust, hyperchaotic NLCS maps. We present a novel reconfigurable multiparameter pseudorandom number generator and validate its randomness using two standard statistical tests, namely, National Institute of Standards and Technology SP 800-22 and FIPS PUB 140-2. Finally, we outline six potential applications where NLCS will be useful.

Keywords

• Chaos
• chaotic map
• encryption
• field-programmable gate array (FPGA)
• Lyapunov exponent (LE)
• reconfigurable random number generator