---- dataentry seminar ----
date_dt : 2008-05-28
title : Advances on APN Functions
speaker : Dr. Eimear Byrne
affiliation :  School of Mathematical Sciences, University College Dublin, Ireland
time : 16h15-17h15
room : BC129
table : seminars
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template:datatemplates:seminar
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=== Abstract ===
A function f defined on a finite field L is called almost perfect nonlinear (
APN) if there are at most two solutions to the equation f(x+a)-f(x) = b for each
 a,b in L with a nonzero. APN functions arise in coding theory, cryptography and
 sequences, especially for fields of characteristic 2. Monomial APN functions co
rrespond to m-sequences and cyclic codes of minimum distance 5. Many APN functio
ns are useful as substitution boxes of block-ciphers, having optimal resistance 
to a differential attack (by definition) and to a linear attack when defined on 
a field of odd degree over GF(2). For some time, it was conjectured that any APN
 function was equivalent to one of a short list of monomials and much work has b
een done towards a full classification. However, since 2006, a number of new fam
ilies of APN functions have been discovered, inequivalent to any of the known po
wer functions. In this talk we discuss these new results and related open proble
ms.