Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyap...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2019-10, Vol.21 (10), p.958
Main Authors: Farhan, Alaa Kadhim, Al-Saidi, Nadia M.G., Maolood, Abeer Tariq, Nazarimehr, Fahimeh, Hussain, Iqtadar
Format: Article
Language:English
Subjects:
bifurcation
Bifurcations
Chaos theory
chaotic flow
complexity
Correlation coefficients
cylinder
Cylinders
Data encryption
Dynamical systems
Eigenvalues
encryption
Entropy
Entropy (Information theory)
Equilibrium
Histograms
Hypotheses
Investigations
Liapunov exponents
Methods
multistability
Nonlinear dynamics
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Summary:Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents’ spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system’s efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shuffle the rows and columns of the image, and then the shuffled image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance.
ISSN:1099-4300
1099-4300
DOI:10.3390/e21100958