Optimal Design Method of 8 × 8 S-box Based on Multi-objective Genetic Algorithm
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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.
Abstract: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 S-boxes are optimized under the framework of the genetic algorithm. According to the characteristics of the S-boxes, 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.
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Key words:
- S-box /
- nonlinearity /
- difference uniformity /
- multi-objective genetic algorithm /
- chaotic map
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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
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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