中文摘要：

扩散层的扩散性能影响整个密码结构的抗攻击能力,而衡量扩散性的一个重要指标是扩散层的线性分支数,分支数越大则抵抗差分和线性分析的能力就越强.由循环矩阵构成的最优扩散层能够循环利用已有资源,因此实现性能更优越.分支数达到最大的充要条件是各阶子式均不为0,由此构造了能够生成最优扩散循环矩阵的算法,首次得到大量8阶最优扩散循环矩阵;提出了一类最优扩散的4阶循环矩阵的构造方法,同时证明参考文献中的一个主要定理是错误的;实验结果说明当矩阵元素满足一定条件时,达到最优扩散性的循环矩阵的个数近似于均匀分布.

英文摘要：

The diffusion performance of diffusion layer affects the anti-attack ability of all the cipher structure, and the linear branch number is an important indicator to measure the diffusion performance; the bigger the branch number is, the stronger the ability to resist differential and linear cryptanalysis. The optimal diffusion layer composed by cyclic matrix can recycle the existing resources, so the implementa- tion performance is more superior. As the necessary and sufficient condition of branch number to achieve maximum is that each sub-determinant is not zero, the paper constructs an algorithm based on this condition which can generate cyclic matirx with optimal diffusion and verify whether a matrix meets the optimal diffusion. A lot of eight order cyclic matrixes with optimal diffusion are obtained for the first time. A construction method of a class of four order cyclic matrix with the optimal diffusion is presented,and an error in reference is also Corrected. The experiment results show that the number of the cyclic matrix with optimal diffusion is distributed evenly.