A Complete Study of Two Classes of Boolean Functions: Direct Sums of Monomials and Threshold Functions

In this paper, we make a comprehensive study of two classes Boolean functions whose interest originally comes from hybrid symmetric-FHE encryption (with stream ciphers like FiLIP), but which also present much for general ciphers. The in these are cheap and easy to implement, they allow the resistance all classical attacks their guess determine variants as well. We exactly main cryptographic parameters (algebraic degree, resiliency order, nonlinearity, algebraic immunity) classes, give close bounds others (fast immunity, dimension space annihilators minimal degree). This is first time that done large interest.