The weight, balancedness and nonlinearity are important properties of Boolean functions, but they can be difficult to determine in general. In this paper, we study how to compute them for two classes of functions where these problems are more tractable. In particular, we study functions of degree three and the so-called "splitting" functions. The latter are functions that can be written as the sum of two functions defined over disjoint sets of variables. We show how, for splitting functions, studying these properties reduces to the study of simpler functions. We provide then a procedure to compute the weight of a cubic Boolean function. We show computationally that, for a cubic Boolean function with limited number of terms, this procedure is on average significantly more efficient than some other methods.

On cryptographic properties of cubic and splitting Boolean functions / Musukwa, A; Sala, M; Villa, I; Zaninelli, M. - In: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING. - ISSN 0938-1279. - 2022:(2022). [10.1007/s00200-022-00575-2]

### On cryptographic properties of cubic and splitting Boolean functions

#### Abstract

The weight, balancedness and nonlinearity are important properties of Boolean functions, but they can be difficult to determine in general. In this paper, we study how to compute them for two classes of functions where these problems are more tractable. In particular, we study functions of degree three and the so-called "splitting" functions. The latter are functions that can be written as the sum of two functions defined over disjoint sets of variables. We show how, for splitting functions, studying these properties reduces to the study of simpler functions. We provide then a procedure to compute the weight of a cubic Boolean function. We show computationally that, for a cubic Boolean function with limited number of terms, this procedure is on average significantly more efficient than some other methods.
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2022
Musukwa, A; Sala, M; Villa, I; Zaninelli, M
On cryptographic properties of cubic and splitting Boolean functions / Musukwa, A; Sala, M; Villa, I; Zaninelli, M. - In: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING. - ISSN 0938-1279. - 2022:(2022). [10.1007/s00200-022-00575-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11572/390770`
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