Abstract
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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 Möbius transform and Algebraic
Normal Form. In this paper, we introduce the notion of Dirichlet product and use it to
study the arithmetical properties of boolean functions.We showthat,with theDirichlet
product, the set of boolean functions is an Abelian monoid with interesting algebraic
structure. In addition, we apply the Dirichlet product to the sub-family of coincident
functions and exhibit many properties satisfied by such functions.