Generalized bent functions with perfect nonlinear functions on arbitrary groups

Yılmaz, Emrah Sercan
This thesis depends on the paper ‘Non-Boolean Almost Perfect Nonlinear Functions on Non- Abelian Groups’ by Laurent Poinsot and Alexander Pott and we have no new costructions here. We give an introduction about character theory and the paper of Poinsot and Pott, and we also compare previous definitions of bent functions with the definition of the bent function in the paper. As a conclusion, we give new theoretical definitions of bent, PN, APN ana maximum nonlinearity. Moreover, we show that bent and PN functions are not always same in the non-abelian cases.


On planar functions
Hamidli, Fuad; Özbudak, Ferruh; Department of Cryptography (2011)
The notion of ”Planar functions” goes back to Dembowski and Ostrom, who introduced it in 1968 first time to describe projective planes with special properties in finite geometry. Recently, they attracted an interest from cryptography because of having an optimal resistance to differential cryptanalysis.This thesis is based on the paper ”New semifields, PN and APN functions” by Jürgen Bierbrauer. The whole purpose of this thesis is to understand and present a detailed description of the results of the paper ...
On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields
Özbudak, Ferruh; YAYLA, OĞUZ (2014-09-18)
We determined the number of rational points of fibre products of two Kummer covers over a rational point of the projective line in a recent work of F. Ozbudak and B. G. Temur (Des Codes Cryptogr 70(3): 385-404, 2014), where we also constructed explicit examples, including a record and two new entries for the current Table of Curves with Many Points (manYPoints: Table of curves with many points. (2014). Accessed 30 Sep 2014). Using the methods given in Ozbudak and Gulmez Temur (Des ...
Classification of function fields with class number three
BİLHAN, Mehpare; Buyruk, Dilek; Özbudak, Ferruh (2015-11-01)
We give the full list of all algebraic function fields over a finite field with class number three up to isomorphism. Our list consists of explicit equations of algebraic function fields which are mutually non-isomorphic over the full constant field.
Hilbert functions of gorenstein monomial curves
Topaloğlu Mete, Pınar; Arslan, Sefa Feza; Department of Mathematics (2005)
The aim of this thesis is to study the Hilbert function of a one-dimensional Gorenstein local ring of embedding dimension four in the case of monomial curves. We show that the Hilbert function is non-decreasing for some families of Gorenstein monomial curves in affine 4-space. In order to prove this result, under some arithmetic assumptions on generators of the defining ideal, we determine the minimal generators of their tangent cones by using the standard basis and check the Cohen-Macaulayness of them. Lat...
Efficient multiplications in F(5)5n and F(7)7n
Cenk, Murat; Özbudak, Ferruh (2011-08-15)
Efficient multiplications in finite fields of characteristics 5 and 7 are used for computing the Eta pairing over divisor class groups of the hyperelliptic curves Lee et al. (2008) [1]. In this paper, using the recent methods for multiplication in finite fields, the explicit formulas for multiplication in F(5)5n and F(7)7n are obtained with 10 multiplications in F(5)n for F(5)5n and 15 multiplications in F(7)n for F(7)7n improving the results in Cenk and Ozbudak (2008) [4], Cenk et al. (2009) [5], Lee et al...
Citation Formats
E. S. Yılmaz, “Generalized bent functions with perfect nonlinear functions on arbitrary groups,” M.S. - Master of Science, Middle East Technical University, 2012.