基于遗传粒子群算法的超混沌S盒设计  

Hyperchaotic S-box design based on genetic particle swarm algorithm

作　　者：陆雅雯 李正权 谭立容[3] 顾斌[3] 邢松[4] LU Yawen;LI Zhengquan;TAN Lirong;GU Bin;XING Song(School of Internet of Things Engineering,Jiangnan University,Wuxi,Jiangsu 214122,China;Jiangsu Future Networks Innovation Institute,Nanjing,Jiangsu 211111,China;School of Electronic Information,Nanjing Vocational College of Information Technology,Nanjing,Jiangsu 210023,China;Information Systems Department,California State University,Los Angeles,CA 90032,USA)

机构地区：[1]江南大学物联网工程学院,江苏无锡214122 [2]江苏省未来网络创新研究院,江苏南京211111 [3]南京信息职业技术学院电子信息学院,江苏南京210023 [4]加利福尼亚州立大学信息系统系,美国洛杉矶90032

出　　处：《江苏大学学报（自然科学版）》2024年第6期701-708,共8页Journal of Jiangsu University：Natural Science Edition

基　　金：未来网络科研基金资助项目(FNSRFP-2021-YB-11);111引智计划基金资助项目(B12018);无锡市科技发展资金资助项目(G20213001)。

摘　　要：针对目前基于混沌系统所构造的S盒难以拥有良好密码学性能的问题,提出一种基于超混沌系统及遗传粒子群优化算法的S盒设计方案.在一维混沌映射基础上,引入正余弦函数以及指数因子,构造一个二维超混沌系统,从系统分叉图、相图、Lyapunov指数图进行性能分析,该混沌系统在参数范围内有着连续的超混沌区间,混沌行为复杂.通过改变混沌系统的初值、参数以及迭代次数可以动态生成S盒,随后结合粒子群优化算法和遗传算法提出一种针对S盒的遗传粒子群优化算法,将混沌系统生成的S盒作为初始种群,利用粒子群算法改进遗传算法中的交叉操作,同时结合爬山算法提出一种新的变异策略.为验证所生成S盒性能,对S盒的双射特性、非线性度、严格雪崩准则、差分均匀性及输出比特间独立性进行仿真测试,仿真结果表明:所提出的优化算法能够生成非线性度、差分均匀性、输出比特间独立性方面表现良好的S盒.To solve the problem that the previously constructed S-boxes based on chaotic systems were difficult to achieve good cryptographic performance,the design scheme for S-boxes was proposed based on hyperchaotic system and genetic particle swarm optimization algorithm.Introducing sine and cosine functions and exponential factors,the two-dimensional hyperchaotic system was constructed based on the one-dimensional chaotic mapping.The performance analysis was conducted by system bifurcation diagram,phase diagram and Lyapunov exponent diagram to reveal that the chaotic system exhibited continuous hyper-chaotic intervals in the parameter range with complex chaotic behavior.By varying initial values,parameters and iteration times of the chaotic system,S-boxes were dynamically generated.Combining particle swarm optimization algorithm and genetic algorithm,the genetic particle swarm optimization algorithm for S-boxes was proposed,and the S-boxes generated by chaotic system were used as initial population.The particle swarm optimization algorithm was leveraged to enhance the crossover operation in the genetic algorithm,and a new mutation strategy was introduced in conjunction with hill-climbing algorithm.To verify the performance of the generated S-box,the simulation tests were conducted on bijective property,nonlinearity,strict avalanche criterion,differential probability and bit independence criterion.The simulation results show that the proposed optimization algorithm can generate S-boxes with good performance in terms of nonlinearity,differential uniformity and bit independence criterion.

关 键 词：S盒 超混沌系统 LYAPUNOV指数 粒子群优化算法 遗传算法 爬山算法 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]