Characterizations of Partially Bent and Plateaued Functions over Finite Fields

Date

2018-12-30

Author

Mesnager, Sihem
Özbudak, Ferruh
SINAK, AHMET

Metadata

Show full item record

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

Item Usage Stats

231
views

0
downloads

Partially bent and plateaued functions over finite fields have significant applications in cryptography, sequence theory, coding theory, design theory and combinatorics. They have been extensively studied due to their various desirable cryptographic properties. In this paper, we study on characterizations of partially bent and plateaued functions over finite fields, with the aim of clarifying their structure. We first redefine the notion of partially bent functions over any finite field Fq , with q a prime power, and then provide a few characterizations of these functions in terms of their derivatives, Walsh power moments and autocorrelation functions. We next characterize partially bent (vectorial) functions over Fp , with p a prime, by means of their derivatives and Walsh power moments. We finally characterize plateaued functions over Fp in terms of their Walsh power moments, derivatives and autocorrelation functions.

Subject Keywords

p-ary function, q-ary functions, Partially bent, Plateaued, Additive character

URI

https://hdl.handle.net/11511/33263

DOI

https://doi.org/10.1007/978-3-030-05153-2_12

Collections

Department of Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

On q-ary plateaued functions over F-q and their explicit characterizations Mesnager, Sihem; Özbudak, Ferruh; Sinak, Ahmet; Cohen, Gerard (Elsevier BV, 2019-08-01) Plateaued and bent functions play a significant role in cryptography, sequence theory, coding theory and combinatorics. In 1997, Coulter and Matthews redefined bent functions over any finite field F-q where q is a prime power, and established their properties. The objective of this work is to redefine the notion of plateaued functions over F-q, and to present several explicit characterizations of those functions. We first give, over F-q, the notion of q-ary plateaued functions, which relies on the concept o...
Analysis of boolean functions with respect to Walsh spectrum Uyan, Erdener; Doğanaksoy, Ali; Department of Cryptography (2013) Boolean functions appear in various scientific disciplines including coding theory, combinatorics, complexity theory, cryptography, graph theory, etc. In cryptography, the design and analysis of Boolean functions possessing a range of cryptographic characteristics has often been the focus of attention. A productive ground of research for most of these cryptographic characteristics is Walsh spectrum, one of the most common representations of a Boolean function. This thesis presents an analysis of Boolean fun...
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-...
On constructions and enumeration of bent and semi-bent functions Koçak, Neşe; Doğanaksoy, Ali; Saygı, Zülfükar; Department of Cryptography (2015) Bent and semi-bent functions play an important role in cryptography and coding theory. They are widely studied as parts of building blocks in symmetric key cryptosystems because they provide resistance to fast correlation attacks and linear cryptanalysis due to their high nonlinearity. Besides, they can possess other desirable cryptographic properties such as low autocorrelation, propagation criteria, resiliency and high algebraic degree. Therefore, parallel to the advances in cryptanalysis techniques, the ...
Contributions on plateaued (vectorial) functions for symmetric cryptography and coding theory Sınak, Ahmet; Özbudak, Ferruh; Mesnager, Sihem; Department of Cryptography (2017) Plateaued functions, used to construct nonlinear functions and linear codes, play a significant role in cryptography and coding theory. They can possess various desirable cryptographic properties such as high nonlinearity, low autocorrelation, resiliency, propagation criteria, balanced-ness and correlation immunity. In fact, they provide the best possible compromise between resiliency order and nonlinearity. Besides they resist against linear cryptanalysis and fast correlation attacks due to their low Walsh...

Citation Formats

S. Mesnager, F. Özbudak, and A. SINAK, “Characterizations of Partially Bent and Plateaued Functions over Finite Fields,” 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/33263.