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Open AccessArticle

Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

1
Laboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
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Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
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Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72000, Mexico
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Department of Electrical Engineering, University of Dschang, Dschang P.O. Box 134, Cameroon
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Center for Nonlinear dynamics, Defence University, Mekelle 1020, Ethiopia
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Institute of Energy, Mekelle University, Mekelle 6330, Ethiopia
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(4), 474; https://doi.org/10.3390/e22040474
Received: 29 March 2020 / Revised: 15 April 2020 / Accepted: 16 April 2020 / Published: 20 April 2020
A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption. View Full-Text
Keywords: chaos; logistic map; bifurcation analysis; fuzzy numbers; RBG; image encryption chaos; logistic map; bifurcation analysis; fuzzy numbers; RBG; image encryption
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MDPI and ACS Style

Moysis, L.; Volos, C.; Jafari, S.; Munoz-Pacheco, J.M.; Kengne, J.; Rajagopal, K.; Stouboulos, I. Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption. Entropy 2020, 22, 474.

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