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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 4585083, 24 pages
Research Article

Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2Science and Technology on Communication Security Laboratory, Chengdu, Sichuan 610041, China

Correspondence should be addressed to Tiecheng Xia; nc.ude.uhs@ctaix

Received 7 December 2017; Revised 10 February 2018; Accepted 22 February 2018; Published 23 April 2018

Academic Editor: Youssef N. Raffoul

Copyright © 2018 Zeyu Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC). Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algorithm is better than others.