Research On Non-degenerate Chaotic Block Cipher Algorithm

With development of information technology and increasing frequency of information exchange,the information security technology is becoming more and more important.The idea of using chaotic systems to design new ciphers has attracted more and more attention,as a novel technology in cryptography,it has attracted researcher dense interest and widely study.Chaos,as a kind of nonlinear phenomenon,has the complicated dynamic behavior characteristics,such as pseudo-random,unpredictability of evolution of its orbits,sensitivity to initial conditions and system parameters,these characteristics are in accordance with the requirements of cryptography.Recently,much more contributions are made to get many promising achievements,the study of chaotic block cipher is one of the most popular subjects in recent years,and many thorough analyses are made on chaotic block ciphers and its components in researches,which make cryptographic algorithms safe and practical.In this paper,the design and analysis of non-degenerate chaotic block cipher are studied,which mainly involves the following: the design of algorithm of non-degenerate chaotic system;the design of S-boxes based on non-degenerate chaotic system;the design of chaotic block cipher based on non-degenerate chaotic system.The main research contents and innovations of this paper are as follows:(1)This paper studies the theoretical knowledge of chaotic system and several typical chaotic systems,and then proposes an algorithm to configure the positive Lyapunov exponent for discrete-time chaotic dynamics system.Based on the inverse control method,this algorithm uses the eigenvalues and eigenvectors of the controlled system matrix to accurately configure the Lyapunov exponent.In theory,the boundedness of the system’s orbit and the finiteness of Lyapunov exponent are proved,the linear feedback operator and the perturbation feedback operator are simulated and analyzed,the performance of the algorithm is compared with other algorithms,and the analysis shows that the algorithm can realize the discrete chaotic system without degeneration and merger.(2)Based on the excellent characteristics of non-degenerate chaotic systems,a new method for constructing dynamic S-boxes is proposed.First,based on the invariant probability density,autocorrelation and cross-correlation of non-degenerate logistic map,equal probability quantization is carried out,and then,through the relationship between the initialvalue of the system,the number of iterations,and the quantization interval to confuse the initial S-box,and a dynamic S-box is generated.Finally,the correlation cryptography characteristics of the S-boxes are tested and compared,such as bijectivity,nonlinearity,strict avalanche effect and differential uniformity,etc.Compared with other algorithms,the results show that the S-boxes generated by the proposed algorithm can effectively resist a variety of attacks and has high security.(3)A chaotic block cipher is designed based on the non-degenerate chaotic system and Sboxes.Based on the structure of AES algorithm,firstly,using the seed key to generate the S-boxes and selected by the number of rounds of operation,and then by using one-way to propose a new key expansion algorithm.Finally,the structure of the algorithm is simplified by deformation function that to speed up the encryption and decryption of data.And the cryptographic characteristics of this chaotic block cipher are analyzed,such as key analysis,differential cryptanalysis,Square attack analysis,key and plaintext randomness test,etc.And compare the encryption and decryption speed and the attack strength of keys with the classic AES algorithm,the comparison of experimental analysis show that this cryptosystem not only improves the security and robustness of the algorithm,but also increases the speed of encryption and decryption,it has good cryptographic characteristics and has certain practical value.