一类SP结构的不可能差分区分器证明

Proof of class of SP structure for impossible differential cryptanalysis

针对分组密码SP结构的不可能差分区分器轮数的下界进行证明,提出的方法使用线性代数的理论,对系数矩阵P及P-1进行分析,提出了系数矩阵部分子空间存在两个行向量线性相关时,可证明至少存在四轮不可能差分区分器。uBlock算法是SPN结构,提出的方法对uBlock算法进行了分析验证,说明了结论的正确性,进一步,使用该算法搜索到比uBlock算法设计文档更多的不可能差分区分器。针对SPN结构线性扩散层P,使用了本原指数的概念,使用线性扩散层P的本原指数对SPN结构不可能差分的轮数进行论证。分析结果表明,分组密码SP结构至少存在四轮不可能差分区分器。

This paper gave the proof of the lower bound of the impossible differential round for a class of SP structure based on block cipher.Presented method used the theory of linear algebra to analyze the coefficient matrix of P and P-1.The algorithm proved that there were at least four rounds of impossible differential when two row vectors were linearly correlated in the subspaces of the coefficient matrix.uBlock is a SPN structure,the proposed method verified and analyzed the uBlock algorithm,which showed the correctness of the conclusion.Furthermore,it used the algorithm to search for more impossible differential cryptanalysis than the uBlock design document.For the linear diffusion layer P of SPN structure,this paper used the concept of primitive index,and demonstrated the rounds of SPN structure impossible differential by using primitive index of linear diffusion layer P.The results show that there are at least four rounds of impossible differential in the block cipher SP structure.