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

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...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2020-04, Vol.22 (4), p.474
Main Authors: Moysis, Lazaros, Volos, Christos, Jafari, Sajad, Munoz-Pacheco, Jesus M, Kengne, Jacques, Rajagopal, Karthikeyan, Stouboulos, Ioannis
Format: Article
Language:English
Subjects:
bifurcation analysis
Bifurcations
chaos
Chaos theory
Dynamical systems
Encryption
fuzzy numbers
Fuzzy sets
image encryption
Liapunov exponents
logistic map
Pseudorandom
RBG
Statistical tests
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Summary: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.
ISSN:1099-4300
1099-4300
DOI:10.3390/E22040474