It is well known that the algebraic expression of AES S-box is very simple and only 9 terms are involved. Hence, AES security is suspected although there is no vulnerability on it so far. To eliminate the weakness of ...It is well known that the algebraic expression of AES S-box is very simple and only 9 terms are involved. Hence, AES security is suspected although there is no vulnerability on it so far. To eliminate the weakness of extremely small terms in the algebraic expression of AES S-box, one improved AES S-box is proposed, which preserves the algebraic degree invariable but significantly increases the number of its algebraic expression terms from 9 to 255. At the same times Boolean function has good characters in balance and strict avalanche criterion （SAC）, etc. Finally, it is proved that the improved AES S-box scheme is secure against the powerful known differential and linear cryptanalysis.展开更多
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 gene...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.展开更多
基金the National Natural Science Foundation of China (90604009).
文摘It is well known that the algebraic expression of AES S-box is very simple and only 9 terms are involved. Hence, AES security is suspected although there is no vulnerability on it so far. To eliminate the weakness of extremely small terms in the algebraic expression of AES S-box, one improved AES S-box is proposed, which preserves the algebraic degree invariable but significantly increases the number of its algebraic expression terms from 9 to 255. At the same times Boolean function has good characters in balance and strict avalanche criterion （SAC）, etc. Finally, it is proved that the improved AES S-box scheme is secure against the powerful known differential and linear cryptanalysis.
文摘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.
