唐灯教授, 上海交通大学

In this talk we consider the maximum absolute value in the autocorrelation spectrum (not considering the zero point) of balanced Boolean function. The long-standing open question in this area is to obtain a theoretical construction of balanced functions with absolute value strictly lesser than 2n/2. In this talk, we introduce our constructions on several infinite class of balanced Boolean functions in n variables with maximum absolute value strictly lesser than 2n/2, which is also infinite classes of counterexamples against the Zhang-Zheng conjecture proposed in 1995. We also introduce applications of Boolean functions with good autocorrelation spectra to design substitution-boxes with good behavior against differential-linear attacks and construct binary locally repairable codes with locality two and multiple repair alternatives.