Cryptology ePrint Archive: Report 2010/597

A New Class of Bent--Negabent Boolean Functions

Sugata Gangopadhyay and Ankita Chaturvedi

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 $4$.

Category / Keywords: secret-key cryptography / Boolean function, bent function, bent - negabent function, nega-Hadamard tranform, complete mapping polynomial.

Date: received 22 Nov 2010, last revised 21 Dec 2010

Contact author: gsugata at gmail com

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Version: 20101222:034906 (All versions of this report)

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