Construction of subsets of bent functions satisfying restrictions in the Reed-Muller domain

Abstract

Our society greatly depends on services and applications provided by mobile communication networks. As billions of people and devices become connected, it becomes increasingly important to guarantee security of interactions of all players. In this talk we address several aspects of this important, many-folded problem. First, we show how to design cryptographic primitives which can assure integrity and confidentiality of transmitted messages while satisfying resource constrains of low-end low-cost wireless devices such as sensors or RFID tags. Second, we describe countermeasures which can enhance the resistance of hardware implementing cryptographic algorithms to hardware Trojans.

Construction of Multiple-Valued Bent Functions Using Subsets of Coefficients in GF and RMF Domains

“…It was shown that using restrictions of binary functions in the Reed-Muller (RM) domain, the set of functions can be split into the spectral subset with respect to three different criteria related to the properties of RM-spectra of bent functions. The vertical, horizontal, and grid RM subsets are defined [8]. Experimental results showed some interesting properties of different subsets in the spectral RM domain which can be helpful in designing construction methods for obtaining bent functions.…”

“…Since the algebraic degree of n-variable p-valued bent functions in the polynomial form is at most ⌈n/2⌉ for n > 2, the possible positions of the non-zero coefficients in the spectrum of bent functions are restricted. By using the same feature in the case of binary bent functions, we proposed in [8] splitting the set of all Boolean bent functions with respect to three different criteria related to the properties of their RM spectra. In this paper, the approach is generalized to ternary and quaternary functions.…”

“…We consider the number and the order of non-zero coefficients for bent functions of different degree. Depending on that, as in the binary case, [8], [9], we define three different subsets: vertical, horizontal, and grid, for multiple-valued functions. Another difference is that we are using coefficients of two different transforms, the GF and RMF spectra.…”