Abstract
In this paper, a new 4D hyperchaotic system is generated. The dynamic properties of attractor phase space, local stability, poincare section, periodic attractor, quasi-periodic attractor, chaotic attractor, bifurcation diagram, and Lyapunov index are analyzed. The hyperchaotic system is normalized and binary serialized, and the binary hyperchaotic stream generated by the system is statistically tested and entropy analyzed. Finally, the hyperchaotic binary stream is applied to the gray image encryption. The histogram, correlation coefficient, entropy test, and security analysis show that the hyperchaotic system has good random characteristics and can be applied to the gray image encryption.
Highlights
Since Lorenz [1] discovered the first three-dimensional chaos model, chaos theory has grown with the development of computer science
The certainty of a dynamic system is a concept defined in mathematics, which means that the state of the system at any time can be determined by the initial state of the system
The main contributions of this paper are shown as follows: (1) A new 4D hyperchaotic system is generated, and the dynamic properties of the attractor such as phase space, local stability, poincare section, periodic attractor, quasi-periodic attractor, chaotic attractor, bifurcation diagram, and Lyapunov index are analyzed; (2) the new hyperchaotic system is normalized and binary serialized, and the binary hyperchaotic stream generated by the system is statistically tested and entropy analyzed; (3) The hyperchaotic binary stream is applied to the gray image encryption; (4) The histogram, correlation coefficient, entropy test, and security analysis show that the hyperchaotic system has good random characteristics and can be applied to the gray image encryption
Summary
Since Lorenz [1] discovered the first three-dimensional chaos model, chaos theory has grown with the development of computer science. The above image encryption methods using chaotic systems are based on low-dimensional chaotic systems with at most one positive Lyapunov exponent, which have many advantages, such as simple format, few control parameters, and ease of implementation. The main contributions of this paper are shown as follows: (1) A new 4D hyperchaotic system is generated, and the dynamic properties of the attractor such as phase space, local stability, poincare section, periodic attractor, quasi-periodic attractor, chaotic attractor, bifurcation diagram, and Lyapunov index are analyzed; (2) the new hyperchaotic system is normalized and binary serialized, and the binary hyperchaotic stream generated by the system is statistically tested and entropy analyzed; (3) The hyperchaotic binary stream is applied to the gray image encryption; (4) The histogram, correlation coefficient, entropy test, and security analysis show that the hyperchaotic system has good random characteristics and can be applied to the gray image encryption.
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