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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. | ||