2005, Volume 7, Issue 12
Strategic Study of CAE >> 2005, Volume 7, Issue 12
The Strict Avalanche Criterion of Order k Spectral Properties of m-Valued Logical Functions
Department of Information Research , PLA Information Engineering College,Information Engineering Institute, Zhengzhou 450002, China
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Abstract
Many cryptographic properties of m - valued logical functions are often described by their Chrestenson cyclic spectrums and auto-correlation functions, so Chrestenson cyclic spectrums and autocorrelation functions play important roles in properties and construct ions for m-valued logical functions. In this paper, in residue class ring Zm, the concept of the strict avalanche criterion of order k of m-valued logical functions is presented. Then, by applying probabilistic thought and methods, the rule that a w-valued logical function fulfills the SAC of lower order if it fulfills the SAC of higher order is proved. Finally, by Chrestenson cyclic spectrums, a necessary and sufficient condition on a m-valued logical function is given, which fulfills the strict avalanche criterion of order k.
Keywords
m-valued logical function ; Chrestenson cyclic spectrum ; auto-correlation function ; the strict avalanche criterion
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References
[ 1 ] Webster A F, Tavares S E.On the design of S-boxes[A].Advances in Cryptology, Crypto’85[C].Springer-Verlag, 1986.523~534
[ 2 ] Forre'R.The strict avalanche criterion:properties ofBoolean functions and extended definition[A].Advances in Crytology-Crypt’88[C].Springer-Verlag, 1990.450~468
[ 3 ] Cusick W.Boolean functions satisfying a higher orderstrict avalanche criterion[A].Advances in Crytology-Eurocrypt’93[C].Springer-Verlag, 1994.86~95
[ 4 ] Youssef A M, Cusick T W, Stanica P, Tavares S E.Newbounds on the number of functions satisfying the strictavalanche criterion[A].In Third Annual Workshop onSelected Areas in Cryptography[C].1996
[ 5 ] 冯登国, 肖国镇.满足k次扩散准则的布尔函数的谱特征[J].电子科学学刊, 1996, (4) :385~390 link1
[ 6 ] 冯登国.频谱理论及其在密码学中的应用[M].北京:科学出版社, 2000 link1
[ 7 ] 李世取, 曾本胜.密码学中的逻辑函数[M].北京:中软电子出版社, 2003
[ 8 ] 丁存生, 肖国镇.流密码学及其应用[M].北京:国防工业出版社, 1994 link1
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