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在分组密码的设计中 ,提高分组密码的抗差分攻击性能是一个重要的课题。论文提出了一种基于矩阵的代替置换网络模型。基于这一模型 ,设计了一个称为基于全非奇异矩阵的代替置换网络的密码结构。给出了基于全非奇异矩阵的代替置换网络的差分概率上界。证明了当使用大规模的基于全奇异矩阵的代替置换网络时 ,i圈基于全奇异矩阵的代替置换网络的差分概率上界迅速减小。指出了使用大规模的基于全奇异矩阵的代替置换网络可有效地提高分组密码抗差分密码分析的安全性。
In the design of block cipher, improving the performance of block cipher against differential attack is an important issue. This paper presents a matrix-based replacement permutation network model. Based on this model, we design a cryptographic structure called an alternative permutation network based on an all-non-singular matrix. The upper bound of differential probability based on all nonsingular matrices is given. It is proved that the upper bound of differential probability of i-cycle surrogate replacement network based on all-singular matrices decreases rapidly when using large-scale all-singular matrix-based displacement networks. It is pointed out that the use of a large-scale all-singular matrix-based replacement permutation network can effectively improve the security of block cipher against differential cryptanalysis.