Dynamic analysis of new two-dimensional fractional-order discrete chaotic map and its application in cryptosystem

被引:2
|
作者
Liu, Ze-Yu [1 ]
Xia, Tie-Cheng [2 ]
Hu, Ye [3 ]
机构
[1] Northwest A&F Univ, Coll Sci, Yangling 712100, Shaanxi, Peoples R China
[2] Shanghai Univ, Coll Sci, Shanghai, Peoples R China
[3] Lvliang Univ, Dept Math, Lishi, Peoples R China
基金
中国国家自然科学基金;
关键词
bifurcation; Caputo fractional derivative; cryptology design; elliptic curve cryptosystem; fractional discrete map; CRYPTANALYSIS;
D O I
10.1002/mma.8779
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A new fractional difference equation two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) based on Caputo derivative is proposed. Using the bifurcation diagram, the maximum Lyapunov exponent, and the phase diagram, the numerical solutions of the fractional difference equations are obtained, and the chaotic behavior is observed numerically. After encrypting the key with elliptic curve cryptosystem, the fractional map is developed as an encryption algorithm and applied to color image encryption. Finally, the proposed encryption system is systematically analyzed from five main aspects, and the results show that the proposed encryption system has a good encryption effect.
引用
收藏
页码:12319 / 12339
页数:21
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