基于模糊数对逻辑斯谛映射的改进及其在伪随机数生成和图像加密中的应用

Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption.

作者信息

Moysis Lazaros, Volos Christos, Jafari Sajad, Munoz-Pacheco Jesus M, Kengne Jacques, Rajagopal Karthikeyan, Stouboulos Ioannis

机构信息

Laboratory of Nonlinear Systems-Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece.

Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam.

出版信息

Entropy (Basel). 2020 Apr 20;22(4):474. doi: 10.3390/e22040474.

DOI:10.3390/e22040474

PMID:33286248

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7516958/

Abstract

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

摘要

提出了一种使用模糊三角数对经典逻辑斯谛映射的修改方法。通过其李雅普诺夫指数（LE）和分岔图对所得映射进行分析。与经典逻辑斯谛映射相比，它显示出更高的复杂性，并展示了诸如反单调性和危机等现象。然后，使用一个简单规则生成比特序列，将该映射应用于伪随机比特生成问题。所得的随机比特发生器（RBG）成功通过了美国国家标准与技术研究院（NIST）的统计测试，并随后成功应用于图像加密问题。