On Second-order Nonlinearities of Some D₀ Type Bent Functions

Issue title: Cryptology in Progress: 10th Central European Conference on Cryptology, Będlewo Poland, 2010

Article type: Research Article

Authors: Gangopadhyay, Sugata | Singh, Brajesh Kumar

Affiliations: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667 India. [email protected] | Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667 India. [email protected]

Note: [] Address for correspondence: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667 India

Note: [] Research supported by CSIR, India

Abstract: In this paper we study the lower bounds of second-order nonlinearities of bent functions in the class D0 constructed by modifying certain cubic Maiorana-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.

Keywords: Second-order nonlinearity, bent functions, Maiorana-McFarland type bents, ${\rm D}_0$ type bents

DOI: 10.3233/FI-2012-628

Journal: Fundamenta Informaticae, vol. 114, no. 3-4, pp. 271-285, 2012