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...

In this paper, we study boolean monomial dynamical systems. Colón-Reyes, Jarrah, Laubenbacher, and Sturmfels(2006) studied fixed point structure of boolean monomial dynamical systems of f by associating the dynamical systems of f with its dependency graph χ f and Jarrah, Laubenbacher, and Veliz-Cuba(2010) extended it and presented lower and upper bound for the number of cycles of a given length...

Consider a family of boolean circuits C~, C2,..., C,,..., constructed by some uniform, effective procedure operating on input n. Such a procedure provides a concise representation of a family of parallel algorithms for computing boolean values. A formula of first-order logic may also be viewed as a concise representation of a family of parallel algorithms for evaluating boolean functions. The p...

This paper presents a new functional computation model for developing a class of two-variable Lambda-Boolean functions, and describes the properties of the duality principle on this model. With respect to this aim, some definitions and theorems which construct the model of the two-variable Lambda-Boolean functions are given. The simulation of the model is implemented in the programming language...

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...