基于仿射非正型σ变换的Lai-Massey模型的密码学缺陷

The Cryptographic Weakness of Lai-Massey Scheme with an Affine but not Orthomorphic Bijection σ

Vaudenay(1999)从伪随机性的角度出发,证明了Lai-Massey模型中的σ变换应设计为正型置换或几乎正型置换。该文从抗差分攻击和线性攻击的角度重新考察了Lai-Massey模型双射σ的设计问题。证明了基于任意有限交换群设计的Lai-Massey模型,如果σ变换设计为该群上的仿射变换,则必须为正型置换,否则该算法将分别存在概率为1的差分对应和线性逼近,结论表明仿射的几乎正型置换并不适用于Lai-Massey模型的设计。此外,该文借助有限群的特征标引入了一种新的线性逼近方式,收集和刻画了一般有限交换群上Lai-Massey模型输入和输出的线性逼近关系。

Vaudenay （1999） proved that the permutationσin Lai -Massey scheme should be an orthomorphism or almost orthomorphism. This paper mainly focuses on the principle of the functionsin Lai-Massey scheme, which is described by its resistance to differential and linear attack. It shows that no matter how the group G is defined, if sis an affine function on G, then it should be defined as an orthomorphism, or else there exists a differentially characteristic with probability 1 and a linearly approximation with correlation coefficient 1, therefore it has potential security risk. Moreover, by the characteristic spectrum in finite group, a new linear relationship between the input and output of Lai-Massey scheme is introduced, which is used to describe the linear relationship lying between the input and the output of Lai-Massey scheme.