次數(shù)最大的平衡相關(guān)免疫函數(shù)的構(gòu)造
Construction of Balanced Correlation-Immune Functions with Highest Degree
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摘要: Maitra和Sarkar于1999年提出了一種遞歸構(gòu)造n元平衡相關(guān)免疫布爾函數(shù)的方法。該文給出了一種新的遞歸構(gòu)造方法，構(gòu)造出非線性度很高的n元m階n- m-1次的平衡相關(guān)免疫函數(shù)。與原構(gòu)造方法相比，該文構(gòu)造方法得到的函數(shù)性質(zhì)相同，數(shù)量更大。Abstract: Maitra and Sarkar provided a recursive construction method of balanced correlation-immune Boolean functions on n variables in 1999. In this paper, a new method is provided to construct balanced m-th order correlation-immune Boolean functions on n variables with high nonlinearity and algebraic degree n -m- 1. Compared with the original one, this method can get more functions with the same characteristics.
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Siegenthaler T. Correlation-immunity of nonlinear combining functions for cryptographic applications[J].IEEE Trans. on Information Theory.1984, 30(5):776-[2]Maitra S, Sarkar P. Highly nonlinear resilient functions optimizing Siegenthaler's inequality. In Advances in Cryptology - CRYPTO'99, LNCS.1666, Springer Verlag, 1999: 198－215.[3]Xiao Guo-Zhen, Massey J. A spectral characterization of correlation immune combining functions[J].IEEE Trans. on Information Theory.1988, 34(3):569-[4]Camion P, Carlet C, Charpin P, Sendrier N. On correlation immune functions. In Advances in Cryptology - CRYPTO'91, LNCS.576, Springer-Verlag, 1991: 86－100. -
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