摘要
In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functionsF(x)=x d over field GF(2 n ), withW(d)=n?1, have desirable cryptographic properties. Therefore we generalize an important result of Nyberg. As application, we use these conclusions to analyze cryptographic property of the S-box of AES (the Advanced Encryption Standard) and give its several equivalent representations, proving that the composition of inversion function of AES and any invertible affine transformations is impossible to satisfy strict avalanche criterion, any order propagation criteria and any order correlation immunity. Key words trace function - nonlinearity - differentially uniform - strict avalanche criterion CLC number TP 309 Foundation item: Supported by the National Natural Science Foundation of China (60373089, 60373041), Natural Science Foundation of Hubei Province (2002AB0037) and Chen-guang Plan of Wuhan City (20025001007).Biography: Zeng Xiang-yong (1973-), male, A postdoctoral fellow, research direction: cryptology and the representation theory of algebra.
In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functionsF(x)=x d over field GF(2 n ), withW(d)=n?1, have desirable cryptographic properties. Therefore we generalize an important result of Nyberg. As application, we use these conclusions to analyze cryptographic property of the S-box of AES (the Advanced Encryption Standard) and give its several equivalent representations, proving that the composition of inversion function of AES and any invertible affine transformations is impossible to satisfy strict avalanche criterion, any order propagation criteria and any order correlation immunity. Key words trace function - nonlinearity - differentially uniform - strict avalanche criterion CLC number TP 309 Foundation item: Supported by the National Natural Science Foundation of China (60373089, 60373041), Natural Science Foundation of Hubei Province (2002AB0037) and Chen-guang Plan of Wuhan City (20025001007).Biography: Zeng Xiang-yong (1973-), male, A postdoctoral fellow, research direction: cryptology and the representation theory of algebra.
基金
upportedbytheNationalNaturalScienceFoundationofChina (60 3730 89,60 3730 4 1 ) ,NaturalScienceFoundationofHubeiProvince (2 0 0 2AB0 0 37)andChenguangPlanofWuhanCity(2 0 0 2 50 0 1 0 0 7) .
