On the algebraic immunity of direct sum constructions

In this paper, we study sufficient conditions to improve the lower bound on algebraic immunity of a direct sum Boolean functions. We exhibit three properties component functions such that satisfying one them is ensure their exceeds maximum immunities. These can be checked while computing and they allow determine better security provided by central in different cryptographic constructions as stream ciphers, pseudorandom generators, weak provide examples for each property exact candidate constructions.