IMAGE ENCRYPTION BASED ON TWO-DIMENSIONAL FRACTIONAL QUADRIC POLYNOMIAL MAP

Ze-Yu Liu, Tie-Cheng Xia (), Hua-Rong Feng and Chang-You Ma
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Ze-Yu Liu: College of Science, Northwest A&F University, Yangling District 712100, Shaanxi, P. R. China
Tie-Cheng Xia: Department of Mathematics, Shanghai University, Shanghai 200444, Shanghai, P. R. China
Hua-Rong Feng: School of Computer Science, Sichuan Technology and Business University, Chengdu 611745, Sichuan, P. R. China
Chang-You Ma: Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, Sichuan, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-16

Abstract: A new fractional two-dimensional quadric polynomial discrete chaotic map (2D-QPDM) with the discrete fractional difference is proposed. Afterwards, the new dynamical behaviors are observed, so that the bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits of the proposed map are given, respectively. The new discrete fractional map is exploited into color image encryption algorithm and it is illustrated with several examples. The proposed image encryption algorithm is analyzed in six aspects which indicates that the proposed algorithm is superior to other known algorithms as a conclusion.

Keywords: Chaos; Discrete Fractional Calculus; Fractional 2D-QPDM; Image Encryption (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21400417

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