ON THE DISTRIBUTION OF AUTO-CORRELATION VALUE OF BALANCED BOOLEAN FUNCTIONS
In this paper, we study the lower bound on the sum-of-square indicator of balanced Boolean functions obtained by Son, et al. in 1998, and give a sufficient and necessary condition under which balanced Boolean functions achieve this lower bound. We introduce a new general class of balanced Boolean functions in n variables (n >= 4) with optimal auto-correlation distribution, and we study two sub-classes more explicitely. Finally, we study the sets of Boolean functions having a same auto-correlation distribution, and derive a lower bound on the number of elements in such set.
balanced boolean functions auto-correlation distribution global avalanche characteristics linear structure