Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem

doi:10.1088/1674-1056/27/3/030502

中国物理B ›› 2018, Vol. 27 ›› Issue (3): 30502-030502.doi: 10.1088/1674-1056/27/3/030502

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem

Zeyu Liu(刘泽宇), Tiecheng Xia(夏铁成), Jinbo Wang(王金波)

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

收稿日期:2017-09-29 修回日期:2017-11-11 出版日期:2018-03-05 发布日期:2018-03-05
通讯作者: Tiecheng Xia E-mail:xiatc@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem

Zeyu Liu(刘泽宇)¹, Tiecheng Xia(夏铁成)¹, Jinbo Wang(王金波)²

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

Received:2017-09-29 Revised:2017-11-11 Online:2018-03-05 Published:2018-03-05
Contact: Tiecheng Xia E-mail:xiatc@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).

摘要/Abstract

摘要： We propose a new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference. Moreover, the chaos behaviors of the proposed map are observed and the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits are derived, respectively. Finally, with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem, we apply the discrete fractional map into color image encryption. After that, the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.

关键词: chaos, fractional two-dimensional triangle function combination discrete chaotic map, image encryption, Menezes-Vanstone elliptic curve cryptosystem

Abstract: We propose a new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference. Moreover, the chaos behaviors of the proposed map are observed and the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits are derived, respectively. Finally, with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem, we apply the discrete fractional map into color image encryption. After that, the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.

Key words: chaos, fractional two-dimensional triangle function combination discrete chaotic map, image encryption, Menezes-Vanstone elliptic curve cryptosystem

中图分类号: (Low-dimensional chaos)

05.45.Ac

05.45.Df (Fractals) 05.45.Gg (Control of chaos, applications of chaos)

刘泽宇, 夏铁成, 王金波. Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem[J]. 中国物理B, 2018, 27(3): 30502-030502.

Zeyu Liu(刘泽宇), Tiecheng Xia(夏铁成), Jinbo Wang(王金波). Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem[J]. Chin. Phys. B, 2018, 27(3): 30502-030502.

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Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem

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