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基于多目标遗传算法的8 × 8 S盒的优化设计方法

王永 王明月 龚建

王永, 王明月, 龚建. 基于多目标遗传算法的8 × 8 S盒的优化设计方法[J]. 西南交通大学学报. doi: 10.3969/j.issn.0258-2724.20210377
引用本文: 王永, 王明月, 龚建. 基于多目标遗传算法的8 × 8 S盒的优化设计方法[J]. 西南交通大学学报. doi: 10.3969/j.issn.0258-2724.20210377
WANG Yong, WANG Mingyue, GONG Jian. Optimal Design Method of 8 × 8 S-box Based on Multi-objective Genetic Algorithm[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20210377
Citation: WANG Yong, WANG Mingyue, GONG Jian. Optimal Design Method of 8 × 8 S-box Based on Multi-objective Genetic Algorithm[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20210377

基于多目标遗传算法的8 × 8 S盒的优化设计方法

doi: 10.3969/j.issn.0258-2724.20210377
基金项目: 国家自然科学基金(61472464);重庆市自然科学基金(cstc2021jcyj-msxmX0557)
详细信息
    作者简介:

    王永(1977—),男,教授,研究方向为信息安全、混沌密码、隐私保护,E-mail:wangyong1@cqupt.edu.cn

  • 中图分类号: TP18;TN918.1

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

  • 摘要:

    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.

     

  • 图 1  算法流程

    Figure 1.  Algorithm flowchart

    图 2  数组A

    Figure 2.  Array A

    图 3  每代中最佳10% S盒的非线性分布

    Figure 3.  Nonlinearity distributions of best 10% S-boxes in each generation

    图 4  每代中最佳10% S盒的差分均匀度分布

    Figure 4.  Difference uniformity distributions of best 10% S-boxes in each generation

    图 5  S盒种群的性能分布情况

    Figure 5.  Performance distribution of S-box populations

    图 6  S盒示例

    Figure 6.  Example of S-box

    图 7  示例S盒的差分分布矩阵元素

    Figure 7.  Difference distribution matrix of exemplified S-box

    图 8  示例S盒BIC-Nonlinearity

    Figure 8.  BIC-Nonlinearity of exemplified S-box

    图 9  示例S盒的BIC-SAC

    Figure 9.  BIC-SAC of exemplified S-box

    图 10  示例S盒的依赖矩阵元素

    Figure 10.  Dependency matrix of exemplified S-box

    表  1  S盒性能对比

    Table  1.   Comparison of S-box performances

    S 盒 非线性度 DU SAC BIC-SAC BIC-Nonlinearity LAP 透明阶 代数次数/次
    最小值 最大值 平均值
    本文方案 110 112 111.50 6 0.5000 0.5043 109.71 0.0859 7.840 6
    AES 112 112 112.00 4 0.5058 0.5040 112.00 0.0625 7.860 7
    文献[9] 96 108 102.50 12 0.5059 0.5050 103.50 0.0625 7.799 6
    文献[10] 110 112 110.25 10 0.5000 0.5052 104.00 0.1250 7.824 7
    文献[11] 106 108 107.00 10 0.4960 0.4974 104.64 0.0811 7.809 7
    文献[12] 110 112 110.25 10 0.4953 0.5021 104.07 0.1250 7.842 6
    文献[15] 106 110 107.75 12 0.5034 0.4980 105.29 0.1328 7.833 6
    文献[18] 98 106 103.75 8 0.5056 0.5068 103.57 0.1250 7.799 7
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出版历程
  • 收稿日期:  2021-05-10
  • 修回日期:  2022-03-03
  • 网络出版日期:  2024-04-19

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