Abstract: The S-box is the only nonlinear component of block cipher, and its merit determines the security strength of the cryptographic algorithm. In order to efficiently construct S-boxes with excellent and stable cryptographic properties, an 8-bits S-box construction and optimization method based on composite chaotic system is proposed. Firstly, an extended tent mapping is given by extending the value domain of the tent chaotic mapping, and a composite chaotic system with excellent chaotic properties is constructed by combining the extended tent mapping with the extended logistic mapping. Subsequently, after 50 iterations to eliminate the transient effects of chaotic systems, the composite chaotic system is used to generate random sequences to construct initial 8-bits S-boxes. Furthermore, for the initial S-boxes with poor cryptographic properties, an optimization objective constraint function is designed to trade-off the relationship between the differential uniformity and linearity of the S-boxes, and the iterative optimization methods, searching for the data that make the differential distribution and linear distribution of the S-boxes more uniform according to the differential and linear distributions of the S-boxes, are carried out to lower the differential uniformity and linearity of the S-boxes as much as possible, and improve the ability of S-box to resist differential analysis and linear analysis. The experimental results show that the method can optimize all the initial S-boxes with poor cryptographic properties, the differential uniformity reaches 8, and the nonlinearity reaches 102. And the proposed method has a fast optimization speed, requiring at least 33 iterations to complete the optimization.

Key words: S-box, Chaos Map, differential uniformity, nonlinearity, linearity

摘要： S盒是分组密码算法的唯一非线性部件，其优劣决定了密码算法的安全强度。为高效构造密码学性质优良且稳定的S盒，提出一种基于复合混沌系统的8比特S盒构造及优化方法。首先，通过扩展tent混沌映射的值域给出扩展的tent映射，并与扩展的logistic映射结合构造了一个具有优秀混沌特性的复合混沌系统；其次，在迭代50次消除混沌系统暂态效应后，利用复合混沌系统产生随机序列构造初始8比特S盒；进一步地，针对密码学性质较差的初始S盒，设计一个用于权衡S盒差分均匀度和线性度的优化目标约束函数，分别根据S盒的差分分布和线性分布情况，搜索使得S盒差分分布和线性分布更均匀的数据进行迭代优化，尽可能地降低S盒的差分均匀度和线性度，提高S盒抵抗差分分析和线性分析的能力。试验测试结果表明，该方法能够对所有密码学性质较差的初始S盒进行性质优化提升，优化后的差分均匀度可以达到8，非线性度达到102；且该方法的优化速度快，最少仅需要33次迭代就可以完成优化。

关键词: S盒, 混沌映射, 差分均匀度, 非线性度, 线性度