## Cryptology ePrint Archive: Report 2010/597

A New Class of Bent--Negabent Boolean Functions

Abstract: In this paper we develop a technique of constructing bent--negabent Boolean functions by using complete mapping polynomials. Using this technique we demonstrate that for each $\ell \ge 2$ there exits bent--negabent functions on $n = 12\ell$ variables with algebraic degree $\frac{n}{4}+1 = 3\ell + 1$. It is also demonstrated that there exist bent--negabent functions on $8$ variables with algebraic degrees $2$, $3$ and $4$.