Some Studies on CCZ-Equivalence of the Inverse Function

Download

Mehtap-Thesis.pdf

Date

2021-9-28

Author

Fidan, Mehtap

Metadata

Show full item record

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

Item Usage Stats

719
views

164
downloads

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-class of a function for the construction of S-boxes used in block ciphers is also intriguing. In this thesis, we presented a detailed description on the results of Kölsch's paper about nonexistence of permutation polynomials in the form $L_m(x^{-1})+L_{m'}(x)$ over binary finite field. This proves that every permutation CCZ-equivalent to the inverse function is also affine equivalent to it. We also gave a criterian to be a permutation polynomial which is verified by using Kloosterman sums.

Subject Keywords

CCZ-equivalence, kloosterman sum, permutation polynomial, inverse function

URI

https://hdl.handle.net/11511/92890

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Results on characterizations of plateaued functions in arbitrary characteristic Mesnager, Sihem; Özbudak, Ferruh; Sınak, Ahmet (2016-01-01) 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 moment...
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...
Constructions of bent functions Sulak, Fatih; Doğanaksoy, Ali; Department of Cryptography (2006) In cryptography especially in block cipher design, Boolean functions are the basic elements. A cryptographic function should have high nonlinearity as it can be attacked by linear attack. In this thesis the highest possible nonlinear boolean functions in the even dimension, that is bent functions, basic properties and construction methods of bent functions are studied. Also normal bent functions and generalized bent functions are presented.
Joint linear complexity of multisequences consisting of linear recurring sequences Fu, Fang-Wei; Niederreiter, Harald; Özbudak, Ferruh (Springer Science and Business Media LLC, 2009-04-01) The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. In this paper, we study the joint linear complexity of multisequences consisting of linear recurring sequences. The expectation and variance of the joint linear complexity of random multisequences consisting of linear recurring sequences are determined. These results extend the ...
Hybrid classes of balanced Boolean functions with good cryptographic properties Khan, Mansoor Ahmed; Özbudak, Ferruh (2014-07-20) Cryptographically strong Boolean functions play an imperative role in the design of almost every modern symmetric cipher. In this context, the cryptographic properties of Boolean functions, such as non-linearity, algebraic degree, correlation immunity and propagation criteria, are critically considered in the process of designing these ciphers. More recently, with the emergence of algebraic and fast algebraic attacks, algebraic immunity has also been included as an integral property to be considered. As a r...

Citation Formats

M. Fidan, “Some Studies on CCZ-Equivalence of the Inverse Function,” M.S. - Master of Science, Middle East Technical University, 2021.