On cryptographic properties of the cosets of R(1, m)

Abstract

Abstract-We introduce a new approach for the study of weight distributions of cosets of the Reed-Muller code of order 1. Our approach is based on the method introduced by Kasami in [1], using Pless identities. By interpreting some equations, we obtain a necessary condition for a coset to have a "high" minimum weight. Most notably, we are able to distinguish such cosets which have three weights only. We then apply our results to the problem of the nonlinearity of Boolean functions. We particularly study the links between this criterion and the propagation characteristics of a function.

On sets determining the differential spectrum of mappings

“…The statement of Theorem 2 is related with Theorems V.2 and V.3 from [7]. These results show that for checking that a given Boolean function is bent (resp.…”

Decomposing bent functions

“…The properties of the restrictions of a bent function to a subspace of codimension and (and to its cosets) have been investigated in [1]. This study points out the major role played by the functions whose extended Fourier spectrum takes on exactly three values.…”

“…Note that the following proposition includes both three-valued and bent functions. [10], are notably studied in [1]. These functions are three valued and could be almost optimal.…”

“…Then (1) where the function is the indicator of . Moreover, for any , let be the Boolean function in defined by .…”

On Plateaued Functions and Their Constructions

“…Annex A.2) and by Canteaut, Carlet, Charpin and Fontaine [5,6]. In the standard model of stream ciphers, a Boolean function is used to combine the outputs of n linear feedback shift registers.…”