Paper 2016/673

Dirichlet Product for Boolean Functions

Abderrahmane Nitaj, Willy Susilo, and Joseph Tonien

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.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Journal of Applied Mathematics and Computing
DOI
10.1007/s12190-016-1037-4
Keywords
Boolean FunctionsMobius TransformDirichlet ProductCoincident Functions
Contact author(s)
abderrahmane nitaj @ unicane fr
History
2016-07-06: received
Short URL
https://ia.cr/2016/673
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2016/673,
      author = {Abderrahmane Nitaj and Willy Susilo and Joseph Tonien},
      title = {Dirichlet Product for Boolean Functions},
      howpublished = {Cryptology ePrint Archive, Paper 2016/673},
      year = {2016},
      doi = {10.1007/s12190-016-1037-4},
      note = {\url{https://eprint.iacr.org/2016/673}},
      url = {https://eprint.iacr.org/2016/673}
}
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