Minimum Distance between Bent and Resilient Boolean Functions
نویسندگان
چکیده
The minimum distance between Bent functions and Resilient functions is studied. An algorithm for calculating the minimum distance betw een Bent functions and resilient functions is given. We give a new lower bound for the minimum distance be tween Bent functions and 1 resilient functions. This new lower bound is better than that presented by S. Maity etc in 2004, and their conjectures are proven to be true. The minimum distances between Bent functions and 1 resilient functions on 12 and 14 variables are also given.
منابع مشابه
Minimum Distance between Bent and 1-Resilient Boolean Functions
In this paper we study the minimum distance between the set of bent functions and the set of 1-resilient Boolean functions and present a lower bound on that. The bound is proved to be tight for functions up to 10 input variables. As a consequence, we present a strategy to modify the bent functions, by toggling some of its outputs, in getting a large class of 1-resilient functions with very good...
متن کاملConstruction of 1-Resilient Boolean Functions with Very Good Nonlinearity
In this paper we present a strategy to construct 1-resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct a 1-resilient function is based on modifying a bent function, by toggling some of its output bits. Two natural questions that arise in this context are “at least how many bits and which bits in the output of a bent function need to be changed ...
متن کاملA New Construction of Resilient Boolean Functions with High Nonlinearity
In this paper we develop a technique that allows us to obtain new effective construction of 1-resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct a 1-resilient function is based on modifying a bent function, by toggling some of its output bits. Two natural questions that arise in this context are “at least how many bits and which bits in the ou...
متن کاملOn Dillon's class H of Niho bent functions and o-polynomials
Bent functions (Dillon 1974; Rothaus 1976) are extremal objects in combinatorics and Boolean function theory. They have been studied for about 40 years; even more, under the name of difference sets in elementary Abelian 2-groups. The motivation for the study of these particular difference sets is mainly cryptographic (but bent functions play also a role in coding theory and sequences; and as di...
متن کاملAutomorphism group of the set of all bent functions
Boolean function in even number of variables is called bent if it is at the maximal possible Hamming distance from the class of all affine Boolean functions. We have proven that every isometric mapping of the set of all Boolean functions into itself that transforms bent functions into bent functions is a combination of an affine transform of coordinates and an affine shift.
متن کامل