南京大学学报（自然科学版）2018，Vol.54Issue(3)：543-547,5.DOI:10.13232/j.cnki.jnju.2018.03.008
基于动态复合混沌系统的S盒设计
A novel method of designing S-box based on dynamic compound chaotic system
摘要
Abstract
Substitution box(S-box)is one of the important non-linear components in the block cipher.In recent years, many scholars have proposed relevant methods based on chaotic S-box.However,these methods mostly exploit the randomness of chaotic maps which is relatively simple.To address this problem,we propose a method of combining multi-chaotic system and linear congruence generators(LCGs)based on chaotic maps.Firstly,several chaotic equations are introduced to form a new compound chaotic system.Autocorrelation and cross-correlation of these equations are studied to prove that they are adequate to generate pseudorandom sequences.This system makes it possible to generate chaotic sequences dynamically.When the iteration value is below 0,we choose f0,or we choose f1.Then,linear congruence generator is used to exclusive-OR with chaotic sequences to make them much more chaotic and nonlinear.We also import the Lewis-Goosman-Miller minimal standard which is a kind of method to get longest LCGs cycle length.Thus,new pseudo-random sequences are developed.Subsequently,the continuous sequences are discretized to integer sequences which are formed into a temporary S-box.Finally,the S-box is scrambled to a new one by using Arnold map.The elements in the sequence change from an old position to a new position.In the experimental part,the S-box is compared with the algorithm proposed by the predecessors.By validating nonlinearity and Output Bits Independence Criterion-Strict Avalanche Criterion(BIC-SAC),we can know that the S-box proposed in this paper has strong cryptography characteristics.It shows that it could be a good resistance to linear attacks and differential attacks.The design of S-box takes advantage of multi-chaotic system and the pseudo-randomness of linear congruence generator.In a word,this S-box has a good application prospects in the space network security and lightweight cipher.关键词
S盒/多混沌系统/线性同余随机数发生器/Arnold置乱Key words
S-box/multi-chaotic system/linear congruence generator/Arnold scrambling分类
信息技术与安全科学引用本文复制引用
朱虹宏,佟晓筠,张淼,刘杨..基于动态复合混沌系统的S盒设计[J].南京大学学报（自然科学版）,2018,54(3):543-547,5.基金项目
2017年威海市大学共建项目,山东省自然科学基金(ZR2014FM026) （ZR2014FM026）
