# 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.

• 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

### Web Of Science Accession Number

• http://ro.uow.edu.au/eispapers/5739

• 19

• 293

• 312

• 55

• 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.

• 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

### Web Of Science Accession Number

• http://ro.uow.edu.au/eispapers/5739

• 19

• 293

• 312

• 55

• Germany