Table of Contents
International Journal of Engineering Mathematics
Volume 2014, Article ID 937386, 7 pages
Research Article

On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions

Department of Mathematics, School of Allied Sciences, Graphic Era Hill University, Dehradun, Uttarakhand 248002, India

Received 30 January 2014; Accepted 28 February 2014; Published 1 April 2014

Academic Editor: J. A. Tenreiro Machado

Copyright © 2014 Brajesh Kumar Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The th-order nonlinearity of Boolean function plays a central role against several known attacks on stream and block ciphers. Because of the fact that its maximum equals the covering radius of the th-order Reed-Muller code, it also plays an important role in coding theory. The computation of exact value or high lower bound on the th-order nonlinearity of a Boolean function is very complicated problem, especially when . This paper is concerned with the computation of the lower bounds for third-order nonlinearities of two classes of Boolean functions of the form for all , , where , where , , and are integers such that and , and , where is a positive integer such that and .