Cryptology ePrint Archive: Report 2013/332

A method for obtaining lower bounds on the higher order nonlinearity of Boolean function

Mikhail S. Lobanov

Abstract: Obtainment of exact value or high lower bound on the $r$-th order nonlinearity of Boolean function is a very complicated problem (especial if $r > 1$). In a number of papers lower bounds on the $r$-th order nonlinearity of Boolean function via its algebraic immunity were obtain for different $r$. This bounds is rather high for function with maximum near maximum possible algebraic immunity. In this paper we prove theorem, which try to obtain rather high lower bound on the $r$-th order nonlinearity for many functions with small algebraic immunity.

Category / Keywords: Boolean function, algebraic immunity, algebraic degree, nonlinearity, higher order nonlinearity, annihilator

Date: received 29 May 2013

Contact author: misha_msu at mail ru

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Version: 20130603:132727 (All versions of this report)

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