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en:group:seminars:20080528 [2016/06/23 11:26] (current)
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 +---- 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
 +===================
 +template:​datatemplates:​seminar
 +-----------------------
 +
 +
 +=== 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.