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Dirichlet product for boolean functions

Journal Article


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 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.

Publication Date


  • 2017

Citation


  • Nitaj, A., Susilo, W. & Tonien, J. (2017). Dirichlet product for boolean functions. Journal of Applied Mathematics and Computing, 55 293-312.

Scopus Eid


  • 2-s2.0-84978100513

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5739

Number Of Pages


  • 19

Start Page


  • 293

End Page


  • 312

Volume


  • 55

Place Of Publication


  • Germany

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 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.

Publication Date


  • 2017

Citation


  • Nitaj, A., Susilo, W. & Tonien, J. (2017). Dirichlet product for boolean functions. Journal of Applied Mathematics and Computing, 55 293-312.

Scopus Eid


  • 2-s2.0-84978100513

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5739

Number Of Pages


  • 19

Start Page


  • 293

End Page


  • 312

Volume


  • 55

Place Of Publication


  • Germany