Welcome to the resource topic for 2012/093
Title:
Recent Results on Balanced Symmetric Boolean Functions
Authors: Yingming Guo, Guangpu Gao, Yaqun Zhao
Abstract:In this paper we prove all balanced symmetric Boolean functions of fixed degree are trivial when the number of variables grows large enough. We also present the nonexistence of trivial balanced elementary symmetric Boolean functions except for n=l\cdot2^{t+1}-1 and d=2^t, where t and l are any positive integers, which shows Cusick’s conjecture for balanced elementary symmetric Boolean functions is exactly the conjecture that all balanced elementary symmetric Boolean functions are trivial balanced. In additional, we obtain an integer n_0, which depends only on d, that Cusick’s conjecture holds for any n>n_0.
ePrint: https://eprint.iacr.org/2012/093
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