Design And Application Of S-box Based On Chaos

There are two main branches of traditional encryption algorithms: stream cipher encryption and block cipher.In the block encryption algorithm,S-box(substitution box,S-box)also known as replacement box plays an important role in algorithm security,because it is a rare non-linear element in the whole algorithm,and its performance determines the security of the whole encryption algorithm to a certain extent.Therefore,how to design an S-box with excellent performance has always been the top priority in the research of packet encryption algorithm.However,chaos has natural cryptographic properties,such as non-linearity,pseudo-randomness,initial value sensitivity and repeatability,and there is some corresponding relationship between chaos and the performance of S-box,which provides a new research idea and direction for the design of S-box.Based on different chaotic maps,combined with multi-objective genetic algorithm and finite field,this thesis mainly completes the following work:1.Aiming at the optimization of single performance index of static S-box,this thesis analyzes the related theorems about the non-linearity and difference uniformity of S-box in detail.On the basis of chaotic mapping and multi-objective genetic algorithm,an algorithm that can produce S-box with excellent non-linearity and differential uniformity is proposed.The initial population is generated by using Logistic chaotic mapping,and the operation is preliminarily optimized according to the existing theorems.The mutation operator is designed by using the model formula of Arnold chaotic mapping to complete the mutation operation.The performance analysis of S-box verifies the effectiveness of the above algorithm.2.Aiming at the problems of slow generation speed and trivial performance of dynamic S-boxes.This thesis designs and optimizes a new linear formula based on the model formula of Arnold chaotic map,and completes the calculation operation with the help of the calculation rules of irreducible polynomials in the finite field.By combining the calculation parameters of linear formula and the selection parameters of irreducible polynomials generated by Logistic chaotic mapping,the modular N operation in Arnold formula is replaced by the modular operation of selected irreducible polynomials.Experimental results show that the algorithm can produce S-boxes with outstanding performance in a short time.3 Because the dynamic S-box has the problems of slow generation speed and poor cryptographic characteristics,the image encryption algorithm based on the dynamic S-box has the problems of low encryption efficiency and poor security.Based on the algorithm proposed in 2,this thesis proposes a new image encryption algorithm.The algorithm applies the dynamic S-box to the grouping,permutation and confusion of image pixel values,and selects the S-box participating in the next round of encryption according to the sum of all pixel values in each group and the different iteration value of Logistic chaotic map.The evaluation indexes show that the encryption algorithm can effectively resist various cryptographic attacks.