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- W2108860744 abstract "The global avalanche characteristics measure the overall avalanche properties of Boolean functions, an n-variable balanced Boolean function of the sum-of-square indicator reaching σƒ=22n+2n+3 is an open problem. In this paper, we prove that there does not exist a balanced Boolean function with σƒ=22n+2n+3 for n≥4, if the hamming weight of one decomposition function belongs to the interval Q*. Some upper bounds on the order of propagation criterion of balanced Boolean functions with n (3≤n≤100) variables are given, if the number of vectors of propagation criterion is equal and less than 7·2n-3-1. Two lower bounds on the sum-of-square indicator for balanced Boolean functions with optimal autocorrelation distribution are obtained. Furthermore, the relationship between the sum-of-squares indicator and nonlinearity of balanced Boolean functions is deduced, the new nonlinearity improves the previously known nonlinearity." @default.
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- W2108860744 date "2015-01-01" @default.
- W2108860744 modified "2023-10-16" @default.
- W2108860744 title "Balanced Boolean Functions of σ<sub>ƒ</sub>>2<sup>2<i>n</i></sup>+2<sup><i>n</i>+3</sup>(<i>n</i>≥4)" @default.
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- W2108860744 doi "https://doi.org/10.1587/transfun.e98.a.1313" @default.
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