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On Second-order Nonlinearities of Some D_0 Type Bent Functions

Gangopadhyay S., Singh B. K.

Fundamenta Informaticae

2012

Vol. 114, nr 3/4

271-285

In this paper we study the lower bounds of second-order nonlinearities of bent functions in the class D_0 constructed by modifying certain cubicMaiorana-McFarland (MMF) type bent functions. We also obtain improvements on existing results on second-order nonlinearities of some cubic MMF type bent functions having no affine derivative.

A Lower Bound of the Second-order Nonlinearities of Boolean Bent Functions

Garg M., Gangopadhyay S.

Fundamenta Informaticae

2011

Vol. 111, nr 4

413-422

In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form f(x) = [formula], where d1 and d2 are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a recent result of Li, Hu and Gao (eprint.iacr.org/2010 /009.pdf). It is shown in Section 3, by a direct computation, that for large values of n, the lower bound obtained in this paper are better than the lower bound obtained by Li, Hu and Gao.