中国物理B ›› 2024, Vol. 33 ›› Issue (5): 50505-050505.doi: 10.1088/1674-1056/ad2a69

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Two-dimensional-lag complex logistic map with complex parameters and its encryption application

Fangfang Zhang(张芳芳)1, Jinbo Wu(武金波)1, Lei Kou(寇磊)2, Fengying Ma(马凤英)1,†, Liming Wu(吴黎明)1, and Xue Zhang(张雪)1   

  1. 1 School of Information and Automation Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China;
    2 Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Sciences), Qingdao 266000, China
  • 收稿日期:2023-10-06 修回日期:2024-02-08 接受日期:2024-02-19 出版日期:2024-05-20 发布日期:2024-05-20
  • 通讯作者: Fengying Ma E-mail:mafengy@163.com
  • 基金资助:
    Project supported by the Shandong Province Natural Science Foundation (Grant Nos. ZR2023MF089, R2023QF036, and ZR2021MF073), the Industry-University-Research Collaborative Innovation Fund Project of Qilu University of Technology (Shandong Academy of Sciences) (Grant Nos. 2021CXY-13 and 2021CXY-14), the Major Scientific and Technological Innovation Projects of Shandong Province (Grant No. 2020CXGC010901), the Talent Research Project of Qilu University of Technology (Shandong Academy of Sciences) (Grant No. 2023RCKY054), and the Basic Research Projects of Science, Education and Industry Integration Pilot Project of Qilu University of Technology (Shandong Academy of Sciences) (Grant No. 2023PX081).

Two-dimensional-lag complex logistic map with complex parameters and its encryption application

Fangfang Zhang(张芳芳)1, Jinbo Wu(武金波)1, Lei Kou(寇磊)2, Fengying Ma(马凤英)1,†, Liming Wu(吴黎明)1, and Xue Zhang(张雪)1   

  1. 1 School of Information and Automation Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China;
    2 Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Sciences), Qingdao 266000, China
  • Received:2023-10-06 Revised:2024-02-08 Accepted:2024-02-19 Online:2024-05-20 Published:2024-05-20
  • Contact: Fengying Ma E-mail:mafengy@163.com
  • Supported by:
    Project supported by the Shandong Province Natural Science Foundation (Grant Nos. ZR2023MF089, R2023QF036, and ZR2021MF073), the Industry-University-Research Collaborative Innovation Fund Project of Qilu University of Technology (Shandong Academy of Sciences) (Grant Nos. 2021CXY-13 and 2021CXY-14), the Major Scientific and Technological Innovation Projects of Shandong Province (Grant No. 2020CXGC010901), the Talent Research Project of Qilu University of Technology (Shandong Academy of Sciences) (Grant No. 2023RCKY054), and the Basic Research Projects of Science, Education and Industry Integration Pilot Project of Qilu University of Technology (Shandong Academy of Sciences) (Grant No. 2023PX081).

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摘要： With the rapid development of internet technology, security protection of information has become more and more prominent, especially information encryption. Considering the great advantages of chaotic encryption, we propose a 2D-lag complex logistic map with complex parameters (2D-LCLMCP) and corresponding encryption schemes. Firstly, we present the model of the 2D-LCLMCP and analyze its chaotic properties and system stability through fixed points, Lyapunov exponent, bifurcation diagram, phase diagram, etc. Secondly, a block cipher algorithm based on the 2D-LCLMCP is proposed, the plaintext data is preprocessed using a pseudorandom sequence generated by the 2D-LCLMCP. Based on the generalized Feistel cipher structure, a round function $F$ is constructed using dynamic S-box and DNA encoding rules as the core of the block cipher algorithm. The generalized Feistel cipher structure consists of two $F$ functions, four XOR operations, and one permutation operation per round. The symmetric dynamic round keys that change with the plaintext are generated by the 2D-LCLMCP. Finally, experimental simulation and performance analysis tests are conducted. The results show that the block cipher algorithm has low complexit, good diffusion and a large key space. When the block length is 64 bits, only six rounds of encryption are required to provide sufficient security and robustness against cryptographic attacks.

关键词: logistic map, block ciphers, chaotic system, encryption

Abstract: With the rapid development of internet technology, security protection of information has become more and more prominent, especially information encryption. Considering the great advantages of chaotic encryption, we propose a 2D-lag complex logistic map with complex parameters (2D-LCLMCP) and corresponding encryption schemes. Firstly, we present the model of the 2D-LCLMCP and analyze its chaotic properties and system stability through fixed points, Lyapunov exponent, bifurcation diagram, phase diagram, etc. Secondly, a block cipher algorithm based on the 2D-LCLMCP is proposed, the plaintext data is preprocessed using a pseudorandom sequence generated by the 2D-LCLMCP. Based on the generalized Feistel cipher structure, a round function $F$ is constructed using dynamic S-box and DNA encoding rules as the core of the block cipher algorithm. The generalized Feistel cipher structure consists of two $F$ functions, four XOR operations, and one permutation operation per round. The symmetric dynamic round keys that change with the plaintext are generated by the 2D-LCLMCP. Finally, experimental simulation and performance analysis tests are conducted. The results show that the block cipher algorithm has low complexit, good diffusion and a large key space. When the block length is 64 bits, only six rounds of encryption are required to provide sufficient security and robustness against cryptographic attacks.

Key words: logistic map, block ciphers, chaotic system, encryption

中图分类号:  (Numerical simulations of chaotic systems)

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