基于多目标遗传算法的8×8 S盒的优化设计方法

Optimal Design Method of 8×8 S-box Based on Multi-objective Genetic Algorithm

混沌系统具有非线性、伪随机性、初始值敏感等特性,为基于动力系统构造性能良好的S盒提供了基础,进一步保证了分组加密算法安全性.目前,基于混沌构造S盒的方法大多数针对单个性能指标进行优化,难以获得全面的性能提升.针对此问题,结合混沌映射与多目标遗传算法,提出了一种新的S盒设计方法.首先,利用混沌映射的特性产生初始S盒种群;然后,以S盒的非线性度和差分均匀性为优化目标,基于遗传算法框架对上述两指标进行优化.针对S盒的特点,在优化算法中引入了交换操作,设计了新的变异操作以及非支配序集计算,有效提升了S盒的非线性度和差分均匀性.实验结果表明该算法产生的S盒其差分均匀度为6,非线性度值至少为110,有效提升了S盒的综合性能.

Chaotic systems have the characteristics of nonlinearity,pseudo-randomness and sensitivity to initial values,which provides an anchor to construct S-boxes based on dynamic system and secures block encryption algorithms.At present,most chaos-based S-box construction methods is designed to optimize single performance index,making it hard to improve the overall performance.To solve this,a new S-box design method is proposed by combining chaotic mapping and multi-objective genetic algorithm.Firstly,the initial S-box population is generated according to the characteristics of chaotic mapping;then,nonlinearity and difference uniformity of Sboxes are optimized under the framework of the genetic algorithm.According to the characteristics of the Sboxes,the exchange operation is introduced into the optimization algorithm,and a new mutation operation and calculation of non-dominated ordered sets are designed,effectively improving the nonlinearity and difference uniformity of the S-boxes.The experimental results show that the difference uniformity of the generated S-box is 6 and its nonlinearity is at least 110,demonstrating an improvement in the overall performance of the S-boxes.