Design, Analysis, and Application of Flipped Product Chaotic System
In this paper, a novel method is proposed to build an improved 1-D discrete chaotic map called flipped product chaotic system (FPCS) by multiplying the output of one map with the output of a vertically flipped second map. Two variants, each with nine combinations, are shown with trade-off between co...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2022-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9966563/ |
| _version_ | 1811311495587299328 |
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| author | Md Sakib Hasan Partha Sarathi Paul Anurag Dhungel Maisha Sadia Md Razuan Hossain |
| author_facet | Md Sakib Hasan Partha Sarathi Paul Anurag Dhungel Maisha Sadia Md Razuan Hossain |
| author_sort | Md Sakib Hasan |
| collection | DOAJ |
| description | In this paper, a novel method is proposed to build an improved 1-D discrete chaotic map called flipped product chaotic system (FPCS) by multiplying the output of one map with the output of a vertically flipped second map. Two variants, each with nine combinations, are shown with trade-off between computational cost and performance. The chaotic properties are explored using the bifurcation diagram, Lyapunov exponent, Kolmogorov entropy, and correlation coefficient. The proposed schemes offer a wider chaotic range and improved chaotic performance compared to the constituent maps and several prior works of similar nature. Wide chaotic window and improved chaotic complexity are two desired characteristics for several security applications as these two characteristics ensure enhanced design space with elevated entropic properties. We present a general Field-Programmable Gate Array (FPGA) design framework for the hardware implementation of the proposed flipped-product schemes and the results show good qualitative agreement with the numerical results from MATLAB simulation. Finally, we present a new Pseudo Random Number Generator (PRNG) using the two variants of the proposed chaotic map and validate their excellent randomness property using four standard statistical tests, namely NIST, FIPS, TestU01, and Diehard. |
| first_indexed | 2024-04-13T10:18:45Z |
| format | Article |
| id | doaj.art-a97d7d9738ba42bdad347941a2eed013 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-13T10:18:45Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-a97d7d9738ba42bdad347941a2eed0132022-12-22T02:50:34ZengIEEEIEEE Access2169-35362022-01-011012518112519310.1109/ACCESS.2022.32256619966563Design, Analysis, and Application of Flipped Product Chaotic SystemMd Sakib Hasan0https://orcid.org/0000-0002-4792-6236Partha Sarathi Paul1https://orcid.org/0000-0002-8868-5854Anurag Dhungel2Maisha Sadia3https://orcid.org/0000-0003-1854-8739Md Razuan Hossain4Department of Electrical and Computer Engineering, University of Mississippi, Oxford, MS, USADepartment of Electrical and Computer Engineering, University of Mississippi, Oxford, MS, USADepartment of Electrical and Computer Engineering, University of Mississippi, Oxford, MS, USADepartment of Electrical and Computer Engineering, University of Mississippi, Oxford, MS, USADepartment of Electrical and Computer Engineering, University of Mississippi, Oxford, MS, USAIn this paper, a novel method is proposed to build an improved 1-D discrete chaotic map called flipped product chaotic system (FPCS) by multiplying the output of one map with the output of a vertically flipped second map. Two variants, each with nine combinations, are shown with trade-off between computational cost and performance. The chaotic properties are explored using the bifurcation diagram, Lyapunov exponent, Kolmogorov entropy, and correlation coefficient. The proposed schemes offer a wider chaotic range and improved chaotic performance compared to the constituent maps and several prior works of similar nature. Wide chaotic window and improved chaotic complexity are two desired characteristics for several security applications as these two characteristics ensure enhanced design space with elevated entropic properties. We present a general Field-Programmable Gate Array (FPGA) design framework for the hardware implementation of the proposed flipped-product schemes and the results show good qualitative agreement with the numerical results from MATLAB simulation. Finally, we present a new Pseudo Random Number Generator (PRNG) using the two variants of the proposed chaotic map and validate their excellent randomness property using four standard statistical tests, namely NIST, FIPS, TestU01, and Diehard.https://ieeexplore.ieee.org/document/9966563/Nonlinear dynamical systemschaosfield-programmable gate arrays (FPGA)bifurcation diagramlyapunov exponentdiscrete-time map |
| spellingShingle | Md Sakib Hasan Partha Sarathi Paul Anurag Dhungel Maisha Sadia Md Razuan Hossain Design, Analysis, and Application of Flipped Product Chaotic System IEEE Access Nonlinear dynamical systems chaos field-programmable gate arrays (FPGA) bifurcation diagram lyapunov exponent discrete-time map |
| title | Design, Analysis, and Application of Flipped Product Chaotic System |
| title_full | Design, Analysis, and Application of Flipped Product Chaotic System |
| title_fullStr | Design, Analysis, and Application of Flipped Product Chaotic System |
| title_full_unstemmed | Design, Analysis, and Application of Flipped Product Chaotic System |
| title_short | Design, Analysis, and Application of Flipped Product Chaotic System |
| title_sort | design analysis and application of flipped product chaotic system |
| topic | Nonlinear dynamical systems chaos field-programmable gate arrays (FPGA) bifurcation diagram lyapunov exponent discrete-time map |
| url | https://ieeexplore.ieee.org/document/9966563/ |
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