次数最大的平衡相关免疫函数的构造
Construction of Balanced Correlation-Immune Functions with Highest Degree
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摘要: Maitra和Sarkar于1999年提出了一种递归构造n元平衡相关免疫布尔函数的方法。该文给出了一种新的递归构造方法，构造出非线性度很高的n元m阶n- m-1次的平衡相关免疫函数。与原构造方法相比，该文构造方法得到的函数性质相同，数量更大。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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