New bent functions from permutations and linear translators

Date

2017-04-12

Author

MESNAGER, sihem
ONGAN, pınar
Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

86
views

0
downloads

Starting from the secondary construction originally introduced by Carlet ["On Bent and Highly Nonlinear Balanced/Resilient Functions and Their Algebraic Immunities", Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 2006], that we shall call "Carlet` ssecondary construction", Mesnager has showed how one can construct several new primary constructions of bent functions. In particular, she has showed that three tuples of permutations over the finite field F2m such that the inverse of their sum equals the sum of their inverses give rise to a construction of a bent function given with its dual. It is not quite easy to find permutations satisfying such a strong condition (Am). Nevertheless, Mesnager has derived several candidates of such permutations in 2015, and showed in 2016 that in the case of involutions, the problem of construction of bent functions amounts to solve arithmetical and algebraic problems over finite fields. This paper is in the line of those previous works. We present new families of permutations satisfying (Am) as well as new infinite families of permutations constructed from permutations in both lower and higher dimensions. Our results involve linear translators and give rise to new primary constructions of bent functions given with their dual. And also, we show that our new families are not in the class of Maiorana-McFarland in general.

Subject Keywords

Boolean Functions, Bent Functions, Linear Translators, Permutations

URI

https://hdl.handle.net/11511/40578

DOI

https://doi.org/10.1007/978-3-319-55589-8_19

Collections

Department of Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

FORCED HARMONIC RESPONSE ANALYSIS OF NONLINEAR STRUCTURES USING DESCRIBING FUNCTIONS TANRIKULU, O; KURAN, B; Özgüven, Hasan Nevzat; IMREGUN, M (1993-07-01) The dynamic response of multiple-degree-of-freedom nonlinear structures is usually determined by numerical integration of the equations of motion, an approach which is computationally very expensive for steady-state response analysis of large structures. In this paper, an alternative semianalytical quasilinear method based on the describing function formulation is proposed for the harmonic response analysis of structures with symmetrical nonlinearities. The equations of motion are converted to a set of nonl...
Improved p-ary codes and sequence families from Galois rings Ling, San; Özbudak, Ferruh (2005-01-01) In this paper, a recent bound on some Weil-type exponential sums over Galois rings is used in the construction of codes and sequences. The bound on these type of exponential sums provides a lower bound for the minimum distance of a family of codes over F-p, mostly nonlinear, of length p(m+1) and size p(2) (.) p(m)((D-[D/p2])), where 1 <= D <= p(m/2). Several families of pairwise cyclically distinct p-ary sequences of period p(p(m) - 1) of low correlation are also constructed. They compare favorably with cer...
Studies on non-weakly regular bent functions and related structures Pelen, Rumi Melih; Özbudak, Ferruh; Department of Mathematics (2020) Interest in bent functions over finite fields arises both from mathematical theory and practical applications. There has been lots of literature addressing various properties of bent functions. They have a number of applications consisting of coding theory, cryptography, and sequence designs. They’re divided into four subclasses: regular bent functions that are contained within the class of weakly regular bent functions that are contained within the class of dual-bent functions. Additionally, there are non-...
Characterisation and enumeration of a class of semi bent quadratic Boolean functions KOÇAK, Neşe; Koçak, Onur Ozan; Özbudak, Ferruh; SAYGI, ZÜLFÜKAR (2015-01-01) In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for 6|n. Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous ...
Improved cost function in the design of Boolean functions satisfying multiple criteria Kavut, S; Yucel, MD (2003-01-01) We develop an improved cost function, to be used, in simulated annealing followed by hill-climbing to find Boolean functions satisfying multiple desirable criteria such as high nonlinearity, low autocorrelation, balancedness, and high algebraic degree. Using this cost function that does not necessitate experimental search for parameter tuning, the annealing-based algorithm reaches the desired function profiles more rapidly. Some Boolean functions of eight and nine variables have been found, which are unatta...

Citation Formats

s. MESNAGER, p. ONGAN, and F. Özbudak, “New bent functions from permutations and linear translators,” 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40578.