Résumé.

Boolean functions play an important role in many symmetric cryptosystems and are crucial for their security. It is important to design boolean functions with reliable cryptographic properties such as balancedness and nonlinearity. Most of these properties are based on specific structures such as Mobius transform and Algebraic Normal Form. In this talk, we present an introduction to the theory of boolean functions and their main properties. In addition, we introduce the notion of Dirichlet product and use it to study the arithmetical properties of boolean functions.