期刊
SYMMETRY-BASEL
卷 14, 期 5, 页码 -出版社
MDPI
DOI: 10.3390/sym14050895
关键词
discrete dynamical system; logistic map; tent map; sine map; chaos; Lyapunov exponent; image encryption
The present article discusses a new dynamical system called M-map and its properties, as well as proposes a new image encryption algorithm and conducts corresponding analysis and comparison.
One of the applications of dynamical systems with chaotic behavior is data encryption. Chaos-based cryptography uses chaotic dynamical systems as the basis for creating algorithms. The present article discusses a new dynamical system called M-map with its analysis: fixed points, bifurcation diagram, Lyapunov exponent, and invariant density. The obtained bifurcation diagram and the plot of the Lyapunov exponent (with a minimum value of In 2 and a maximum value of In 4) suggest that the so-called robust chaos characterizes this map. Moreover, the obtained results are compared with other dynamical systems used in cryptography. Additionally, the article proposes a new image encryption algorithm. It uses, among others, cyclically shifted S-box or saving encrypted pixels on the first or last free space in the cipher-image. The conducted analysis shows that the cipher-images are characterized by an entropy value close to 8, a correlation of adjacent pixels value close to 0, or values of Number of Pixel of Change Rate (NPCR) and Unified Average Changing Intensity (UACI) measures close to 100% and 33%, respectively.
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