Permutation polynomials and construction of bent functions

Download

12626173.pdf

Date

2021-3-03

Author

Ongan, Pınar

Metadata

Show full item record

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

Item Usage Stats

298
views

543
downloads

This thesis consists of two main parts: In the first part, a study of several classes ofpermutation and complete permutation polynomials is given, while in the second part,a method of construction of several new classes of bent functions is described.The first part consists of the study of several classes of binomials and trinomialsover finite fields. A complete list of permutation polynomials of the formf(x) =xqn−1q−1+1+bx∈Fqn[x]is obtained for the casen= 5, and a criterion on permutationpolynomials of the same type is derived for the general case. Furthermore, it is shownthat whenqis odd, trinomials of the formf(x) =x5h(xq−1)∈Fq2[x], whereh(x) =x5+x+ 1never permutesFq2.A method of constructing several new classes of bent functions via linear translatorsand permutation polynomials forms the second part of the thesis. First, a way to lifta permutation overF2tto a permutation overF2mis described, wheret|m. Then,via this method,3-tuples of particular permutations that lead to new classes of bentfunctions are obtained. As a last step, the fact that none of the bent functions obtainedhere will be contained in Maiorana-McFarland class is proved.

Subject Keywords

Finite fields, Permutation polynomials, Complete permutation polynomials, Bent functions, Linear translators

URI

https://hdl.handle.net/11511/89801

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

On plateaued functions, linear structures and permutation polynomials Mesnager, Sihem; Kaytancı, Kübra; Özbudak, Ferruh (2019-01-01) We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some app...
Some permutations and complete permutation polynomials over finite fields Ongan, Pinar; GÜLMEZ TEMÜR, BURCU (2019-01-01) In this paper we determine b is an element of F-qn*. for which the polynomial f(x) = x(s+1) + bx is an element of F-qn[x] is a permutation polynomial and determine b is an element of F-gn* for which the polynomial f(x) = x(s+1)+ bx is an element of F(q)n [x] is a complete permutation polynomial where s = q(n)-1/t, t is an element of Z(+) such that t vertical bar q(n) - 1.
Hierarchical control with partial observations: Sufficient conditions Boutin, Olivier; Komenda, Jan; Masopust, Tomas; Schmidt, Klaus Verner; Van Schuppen, Jan H. (2011-12-01) In this paper, hierarchical control of both monolithic and modular discrete-event systems under partial observations is studied. Two new conditions, called observation consistency and local observation consistency, are proposed. These conditions are sufficient for the preservation of observability between the original and the abstracted plant. Moreover, it is shown that both conditions are compositional, that is, they are preserved by the synchronous product. This property makes it possible to use hierarchi...
NONCOMMUTATIVE HOLOMORPHIC FUNCTIONAL CALCULUS, AFFINE AND PROJECTIVE SPACES FROM NC-COMPLETE ALGEBRAS Dosi, A. (American Mathematical Society (AMS), 2020-01-01) The paper is devoted to a noncommutative holomorphic functional calculus and its application to noncommutative algebraic geometry. A description is given for the noncommutative (infinite-dimensional) affine spaces A(q)(x), 1 = 0, are calculated.
Semi-Bayesian Inference of Time Series Chain Graphical Models in Biological Networks Farnoudkia, Hajar; Purutçuoğlu Gazi, Vilda (null; 2018-09-20) The construction of biological networks via time-course datasets can be performed both deterministic models such as ordinary differential equations and stochastic models such as diffusion approximation. Between these two branches, the former has wider application since more data can be available. In this study, we particularly deal with the probabilistic approaches for the steady-state or deterministic description of the biological systems when the systems are observed though time. Hence, we consider time s...

Citation Formats

P. Ongan, “Permutation polynomials and construction of bent functions,” Ph.D. - Doctoral Program, Middle East Technical University, 2021.