Algebra Seminar: On the Walsh spectrum of recent APN functions

Algebra Seminar: On the Walsh spectrum of recent APN functions

Speaker: Nurdagül Anbar, Sabancı University

Title: On the Walsh spectrum of recent APN functions  

Date/Time: October 2, 2019  /  13.40-14.30

Place: FENS G035

Abstract: Almost perfect nonlinear functions (APN) are of central interest in many mathematical areas such as coding theory and cryptography. In particular, having optimal differential properties, they provide good resistance against differential attack in cryptography. Therefore, many constructions of “infinite classes” of APN functions were introduced in the last years. For example, among those are the functions of Carlet (2011), Zhou–Pott (2013) and Taniguchi (2019), all of which are APN under certain conditions. Another important concept, which plays an essential role against linear attack in cryptography, is the nonlinearity of a function. Therefore, Tan–Qu–Ling– Tan (2013) determined the nonlinearity of the functions given by Carlet, and Zhou–Pott. In this talk, I describe a new method based on Bezout’s theorem to determine the nonlinearity of some classes of quadratic functions, which contain all the classes of APN functions mentioned above. In particular, this approach helps to understand why the majority of the functions in those classes have solely bent and semibent components, which in the case of APN functions is called the classical spectrum.

This is a joint work with Tekgül Kalaycı and Wilfried Meidl.

BIO: Nurdagül Anbar earned her B.S degree in Mathematics at Middle East Technical University (METU), Ankara, Turkey in 2007. Then she earned her Master degree on the subject “Ramification in extensions of rational function fields” and Ph.D. degree on the subject “Algebraic curves in prime characteristic” with Prof. Henning Stichtenoth at Sabancı University. During her Ph.D. (March 2011-February 2012), she visited the University of Perugia in Italy to work with Prof. Massimo Gulietti. After obtaining her Ph.D., she worked as a post-doctoral researcher at Sabancı University (July 2012-February 2014), Max Planck Institute for Mathematics (March 2014-May 2014) in Bonn, Germany, the Technical University of Denmark (November 2014-September 2016) in Lyngby, Denmark, Otto-von-Guericke-Universitat (October 2016-March 2017) in Magdeburg, Germany, RICAM (May 2017-January 2018) and Johannes Kepler University (February 2018-Au-gust 2018) in Linz, Austria. Since September 2018, she works as an assistant professor in Faculty of Engineering and Natural Sciences at Sabancı University.

Contact: Michel Lavrauw