Bent, resilient functions and the numerical normal form

p-Ary and q-ary versions of certain results about bent functions and resilient functions

“…for all ð1; y; 1ÞauAU: Theorem 1.1 is a combination of Proposition 1 of [4] and a result of [3]. A binary function f AFðF n 2 ; F 2 Þ is called t-resilient if fðcÞ ¼ 0 for all cAF n 2 with jcjpt:…”

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

“…For example, quadratic bent functions have an important place in bent function construction. All bent functions from this class are known and they can be obtained by applying the affine transformations to the variables of the function [7].…”

“…As noticed above, in this paper, we use the so-called Hadamard ordering of RM coefficients originating in the Kronecker product structure of the Reed-Muller matrix in (4). In this ordering, for a given n, we can determine positions of coefficients which cannot be 1 by referring to (7). Definition 6 A bent function belongs to the Horizontal (k min , k max )-subset H(k min , k max ) iff it has the minimum k min and the maximum k max order of RM coefficients.…”

Funciones perfectamente no-lineales, casi-bent, esquemas de compartición de secretos y autenticación

“…En esta sección se definen las funciones bent f : F n 2 → F 2 . La definición de función bent así como varias de sus propiedades podemos encontrarlas en varias referencias, por ejemplo [4], [5], [23]…”

“…No está demás mencionar que para n = 2 y n = 4 en B n existen 8 y 896 funciones bent respectivamente. Es un problema abierto contar estas funciones para valores grandes de n ( [5]).…”