Dirichlet product for boolean functions

Original Research
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Abstract

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 show that, with the Dirichlet 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.

Keywords

Boolean functions Möbius transform Dirichlet product Coincident functions 

Mathematics Subject Classification

06E30 

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Copyright information

© Korean Society for Computational and Applied Mathematics 2016

Authors and Affiliations

  • Abderrahmane Nitaj
    • 1
  • Willy Susilo
    • 2
  • Joseph Tonien
    • 2
  1. 1.Laboratoire de Mathématiques Nicolas OresmeUniversité de Caen NormandieCaenFrance
  2. 2.Centre for Computer and Information Security Research, School of Computing and Information TechnologyUniversity of WollongongWollongongAustralia

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