Abstract
In this paper, a method to enhance the dynamic characteristics of one-dimension (1D) chaotic maps is first presented. Linear combinations and nonlinear transform based on existing chaotic systems (LNECS) are introduced. Then, a numerical chaotic map (LCLS), based on Logistic map and Sine map, is given. Through the analysis of a bifurcation diagram, Lyapunov exponent (LE), and Sample entropy (SE), we can see that CLS has overcome the shortcomings of a low-dimensional chaotic system and can be used in the field of cryptology. In addition, the construction of eight functions is designed to obtain an S-box. Finally, five security criteria of the S-box are shown, which indicate the S-box based on the proposed in this paper has strong encryption characteristics. The research of this paper is helpful for the development of cryptography study such as dynamic construction methods based on chaotic systems.
Highlights
Substitution box (S-box) is an important nonlinear module, used to substitute and permutate elements in block cipher, which ensures the security of the block cipher to a large extent
We have presented the generation method S-box based on CLS
The chaotic characteristics of the system are further enhanced by the nonlinear variation of the linear combination of the values
Summary
Substitution box (S-box) is an important nonlinear module, used to substitute and permutate elements in block cipher, which ensures the security of the block cipher to a large extent. In order to overcome the above weakness of the low dimensional discrete-time chaotic map, linear combinations of the output values of existing chaotic systems are proposed to enhance the chaotic characteristics in [23,24,25,26,27]. Through the analysis of the bifurcation diagram, LE and SE, we can see that CLS has overcome the shortcomings of the low-dimensional chaotic system and can be used in the field of cryptology Another innovation in this article is the construction of eight functions designed to convert a decimal number into eight binary numbers.
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