The expressiveness of Boolean Algebras is significantly extended by the Boolean Differential Calculus (BDC). The additionally defined differentials of Boolean variables, differentials and further differential operators of Boolean functions as well as several derivative operations of Boolean functions allow to model changes of function values together with changes of the values of variables and ...

Since 2003, Algebraic Attacks have received a lot of attention in the cryptography literature. In this context, algebraic immunity quantifies the resistance of a Boolean function to the standard algebraic attack of the pseudo-random generators using it as a nonlinear Boolean function. A high value of algebraic immunity is now an absolutely necessary cryptographic criterion for a resistance to a...

The Forward Problem (FB) of Boolean equations consists of finding solutions of a system of Boolean equations, or equivalently, a single Boolean equation of the form f(X) = 0 where f(X): B n → B and B is an arbitrary Boolean algebra. By contrast, the Inverse Problem (IB) of Boolean equations aims to reconstruct the equation f (X) = 0 given the set of solutions and hence to verify the correctness...