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Nonlinearity of Boolean functions: an algorithmic approach based on multivariate polynomials by Bellini, E.; Simonetti, I.; Sala, M. is a scholarly article available to read on EtoBox.

What is Nonlinearity of Boolean functions: an algorithmic approach based on multivariate polynomials about?

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.

Author

Bellini, E.; Simonetti, I.; Sala, M.

Published

2014

Language

EN