We describe new families of efficiently implementable Boolean functions achieving provable trade-offs between resiliency, nonlinearity, and algebraic immunity. Compared to one direction of research on balanced and 1-resilient functions with optimal algebraic immunity, the new functions provide lower algebraic immunity, but much lower -- in fact, almost optimal -- linear bias and importantly are much more efficient to implement. Compared to another direction of research based on constructions using direct sum, the new functions while achieving similar efficiency, has less number of variables for the same order of resiliency, same lower bound on algebraic immunity, and similar nonlinearity.

翻译：暂无翻译