Nonlinearity of Boolean functions: an algorithmic approach based on multivariate polynomials

E. Bellini; I. Simonetti; M. Sala

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arXiv · 1404.2741

Nonlinearity of Boolean functions: an algorithmic approach based on multivariate polynomials

E. Bellini·I. Simonetti·M. Sala

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Abstract

We compute the nonlinearity of Boolean functions with Groebner basis techniques, providing two algorithms: one over the binary field and the other over the rationals. We also estimate their complexity. Then we show how to improve our rational algorithm, arriving at a worst-case complexity of $O(n2^n)$ operations over the integers, that is, sums and doublings. This way, with a different approach, we reach the same complexity of established algorithms, such as those based on the fast Walsh transform.

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E. Bellini, I. Simonetti, M. Sala. 2014-04-10. Nonlinearity of Boolean functions: an algorithmic approach based on multivariate polynomials. https://arxiv.org/abs/1404.2741

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