Image Encryption Schemes Based on a Class of Uniformly Distributed Chaotic Systems

This paper proposes a method to construct a one-dimensional discrete chaotic system. First, we define a generalized distance function to control the boundedness of the one-dimensional discrete system. Based on Marotto’s theorem, one-dimensional discrete systems are proven to be chaotic in the sense...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-04, Vol.10 (7), p.1027
Main Authors: Zang, Hongyan, Tai, Mengdan, Wei, Xinyuan
Format: Article
Language:English
Subjects:
Algorithms
Chaos theory
chaotic image encryption
chaotic system
Cryptography
Discrete systems
DNA coding
Dynamical systems
Food science
Theorems
uniform distribution
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Summary:This paper proposes a method to construct a one-dimensional discrete chaotic system. First, we define a generalized distance function to control the boundedness of the one-dimensional discrete system. Based on Marotto’s theorem, one-dimensional discrete systems are proven to be chaotic in the sense of Li–Yorke, and the corresponding chaos criterion theorem is proposed. The system can be distributed uniformly by adjusting the parameters. In this paper, we propose an image encryption scheme based on a uniformly distributed discrete chaotic system and DNA encoding. DNA encoding and decoding rules are determined by plain text. The experimental results demonstrate that our encryption algorithm has a large key space, high key sensitivity, and fast encryption speed and can resist differential and statistical attacks.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10071027