基于矩阵的代替置换网络抗差分密码分析

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。

Matrix-based substitution-permutation network against differential cryptanalysis

An important problem in the design of the block cipher is to improve the performance of the resisting differential cryptanalysis. This paper proposes a matrix based substitution permutation network as the model of block cipher. Based on this model, a new crypt structure called completely nonsingular matrix based substitution permutation network is designed. The upper bound of the differential probability is developed for the completely nonsingular matrix based substitution permutation network. The analysis proves that the upper bound of the differential probability of the i rounds completely nonsingular matrix based substitution permutation network is greatly reduced when a large completely nonsingular matrix based substitution permutation network is used. Therefore, using large completely nonsingular matrix based substitution permutation networks can effectively improve cipher security in relation to differential cryptanalysis.