Self-Parameterized Chaotic Map: A Hardware-efficient Scheme Providing Wide Chaotic Range

Paul, Partha Sarathi; Dhungel, Anurag; Sadia, Maisha; Hossain, Md Razuan; Muldrey, Barry; Hasan, Sakib

doi:10.1109/icecs53924.2021.9665500

Cited by 6 publications

(2 citation statements)

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“…The sensitive dependence on the initial state can be verified by correlation coefficient measurement, as well [25]. Equations ( 4) and ( 5) analytically express two schemes of our correlation coefficient measurements.…”

Section: Correlation-coefficientmentioning

confidence: 61%

A 2D Chaotic Oscillator for Analog IC

Paul

Hardy

Sadia

et al. 2022

IEEE Open J. Circuits Syst.

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In this paper, we have proposed the design of an analog two-dimensional (2D) discretetime chaotic oscillator. 2D chaotic systems are studied because of their more complex chaotic behavior compared to one-dimensional (1D) chaotic systems. The already published works on 2D chaotic systems are mainly focused either on the complex analytical combinations of familiar 1D chaotic maps such as Sine map, Logistic map, Tent map, and so on, or off-the-shelf component-based analog circuits. Due to complex hardware requirements, neither of them is feasible for hardware-efficient integrated circuit (IC) implementations. To the best of our knowledge, this proposed work is the first-ever report of an analog 2D discrete-time chaotic oscillator design that is suitable for hardware-constrained IC implementations. The chaotic performance of the proposed design is analyzed with bifurcation plots, the transient response, 2D Lyapunov exponent, and correlation coefficient measurements. It is demonstrated that the proposed design exhibits promising chaotic behavior with low hardware cost. The real-world application of the proposed 2D chaotic oscillator is presented in a random number generator (RNG) design. The applicability of the RNG in cryptography is verified by passing the generated random sequence through four standard statistical tests namely, NIST, FIPS, TestU01, and Diehard.INDEX TERMS Discrete-time chaos, chaotic IC, chaotic oscillator, 2D chaotic system, random number generator.

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Section: Correlation-coefficientmentioning

confidence: 61%

A 2D Chaotic Oscillator for Analog IC

Paul

Hardy

Sadia

et al. 2022

IEEE Open J. Circuits Syst.

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“…Researchers have been exploring various schemes for an improved chaotic map by manipulating multiple existing 1-D maps (henceforth referred to as seed maps). The schemes include dynamic reconfiguration of control parameter [19], [20], cascading of multiple seed maps [21], [6], use of discrete wheel-switching technique [22], averaging of multiple seed maps [23], sine transformation of a combination of multiple maps [24], modulation and coupling [25], exponential chaotic model [15] and so on. Recently, a new paradigm of designing hyperchaotic maps based on discrete memristor model has attracted the interest of the research community.…”

Section: Introductionmentioning

confidence: 99%

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

Hasan,

Dhungel,

Paul

et al. 2023

IEEE Open J. Ind. Electron. Soc.

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This work presents a general framework for developing a multi-parameter 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 (FPGA)-based implementation and validate its chaotic properties using comparison between simulation and experimental results. Cascaded NLCS exhibits ALE (Average LE), CR (chaotic ratio), and CPS(chaotic parameter space) of 1.364, 100%, and 1.1×10 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 multi-parameter Pseudo Random Number Generator (PRNG) and validate its randomness using two standard statistical tests, namely, NIST SP 800-22 and FIPS PUB 140-2. . Finally, we outline six potential applications where NLCS will be useful.

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