Short Course on APN Functions and Related Structures

Faculty of Engineering and Natural Sciences

SEMINAR ANNOUNCEMENT

Short Course on APN Functions and Related Structures

Gary McGuire, UCD, Claude Shannon Institute

In the last fifteen years or so, interest in APN (Almost Perfect Nonlinear) functions has grown

and grown.These functions are mappings between finite fields having certain extremal

properties. In these lectures we will give an introduction to APN functions, and a survey of

the area. In particular, we will explain the connections to areas such as cryptography, coding

theory, sequences, and geometry.

We will discuss the important tools in the study of APN functions, such as quadratic forms,linearized polynomials,and the Fourier transform. We will explain how these arise, and give  some applications.The theory of polynomials over finite fields is heavily used. Along the way  we will mention various open problems, and ideas for future research.

In the final lecture we will outline some connections to algebraic geometry and number theory, particularly curves over finite fields.

15-17 March, 2010, FENS 2019

Schedule:
15 March, Monday
16:00-17:30

16 March, Tuesday
13:00-14:00