Modifying Maiorana--McFarland Type Bent Functions for Good Cryptographic Properties and Efficient Implementation

Abstract

Very recently, a class of cryptographically significant Boolean functions were constructed by Tang and Maitra [IEEE Trans. Inform. Theory, 64 (2018), pp. 393--402] by modifying the $\mathcal{PS}_{ap}$ class of bent functions. The basic ideas used in Tang--Maitra construction were derived from a modification of a subclass of bent functions which is defined over the finite field, and a concern was raised in the same paper whether the implementation of such functions will be as efficient as that of Maiorana--McFarland type bent functions. In this paper, we look at the concrete realization of such functions over a vector space and answer the question positively. The first part of this paper investigates how the finite field implementation of the functions can be viewed as simple truth tables. Next, we present a completely new construction that itself starts from Maiorana--McFarland bent functions which are straightforward concatenations of linear functions.