Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Results on characterizations of plateaued functions in arbitrary characteristic
Date
2016-01-01
Author
Mesnager, Sihem
Özbudak, Ferruh
Sınak, Ahmet
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
340
views
0
downloads
Cite This
Bent and plateaued functions play a significant role in cryptography since they can have various desirable cryptographic properties. In this work, we first provide the characterizations of plateaued functions in terms of the moments of their Walsh transforms. Next, we generalize the characterizations of Boolean bent and plateaued functions in terms of their second-order derivatives to arbitrary characteristic. Moreover, we present a new characterization of plateaued functions in terms of fourth power moments of their Walsh transforms. Furthermore, we give a new proof of the characterization of vectorial bent functions. Finally, we present the characterizations of vectorial s-plateaued functions in terms of moments of their Walsh transforms and the zeros of their second-order derivatives.
Subject Keywords
Bent functions
,
Plateaued functions
,
Vectorial functions
URI
https://hdl.handle.net/11511/45019
DOI
https://doi.org/10.1007/978-3-319-29172-7_2
Collections
Department of Mathematics, Conference / Seminar
Suggestions
OpenMETU
Core
Some characterizations of generalized s-plateaued functions
Çelik, Emircan; Özbudak, Ferruh; Department of Cryptography (2017)
Plateaued functions play important role in cryptography because of their various desirable cryptographic features. Due to this characteristics they have been widely studied in the literature. This studies include p-ary functions and some generalizations of the boolean functions. In this thesis, we present some of this important work and show that plateaued functions can be generalized much more general framework naturally. Characterizations of generalized plateaued functions using Walsh power moments are al...
Some Studies on CCZ-Equivalence of the Inverse Function
Fidan, Mehtap; ÖZBUDAK, Ferruh; Department of Cryptography (2021-9-28)
Most cryptographic systems, like block ciphers, depend heavily on vectorial Boolean functions. A function with good cryptological properties should have low differential uniformity which is invariant under some equivalence classes. The more general one of these is CCZ-equivalence which is introduced by Carlet, Charpin and Zinoviev in 1998. In cryptography, CCZ-equivalence gained an interest since it preserves many significant properties like differential uniformity. Looking for permutations within the CCZ-c...
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 ...
A new approach to mathematical water quality modeling in reservoirs: Neural networks
Karul, C; Soyupak, S; Germen, E (1998-01-01)
Neural Networks are becoming more and more valuable tools for system modeling and function approximation as computing power of microcomputers increase. Modeling of complex ecological systems such as reservoir limnology is very difficult since the ecological interactions within a reservoir are difficult to define mathematically and are usually system specific. To illustrate the potential use of Neural Networks in ecological modeling, a software was developed to train the data from Keban Dam Reservoir by back...
Characterizations of Partially Bent and Plateaued Functions over Finite Fields
Mesnager, Sihem; Özbudak, Ferruh; SINAK, AHMET (2018-12-30)
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 prim...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. Mesnager, F. Özbudak, and A. Sınak, “Results on characterizations of plateaued functions in arbitrary characteristic,” 2016, vol. 9540, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45019.