[Turkmath:7442] Seminar by Alexander Pott on 8 February 2011

[Cem Güneri]

Degerli Meslektaslar,

Alexander Pott'un Sabanci Universitesi Karakoy Iletisim Merkezinde 
verecegi seminerin bilgilerini asagida bulabilirsiniz.

Saygilarimla,

Cem Guneri

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Dear Colleagues,

Please find below the information about an upcoming seminar of Alexander 
Pott at Sabanci University Karakoy Communication Center.

Sincerely,

Cem Guneri

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Speaker: Alexander Pott* (Magdeburg University, Germany)
Title: On the equivalence of functions that occur in cryptography and in 
finite geometry.
Time: Tuesday, 8 February 2011, 15:00.
Place: Sabanci University Karakoy Communication Center (location 
<http://www.sabanciuniv.edu/tr/?kampus_hayati/hizmet_ve_olanaklar/karakoy_iletisim_merkezi_adres_ve_ulasim_krokisi.html>)

(*Alexander Pott's visit is partly supported by Tubitak.)

Abstract: Difference constructions are very common in Discrete 
Mathematics: They are used to construct interesting combinatorial 
objects. One of the most famous examples are the Singer cycles which 
represent the classical Desarguesian projective planes: If you take the 
elements in the cyclic group G={0,1,2,3,4,5,6} of order 7 as points, and 
the cyclic shifts of the set D={0,1,3} as lines, you get the projective 
plane of order 2. The reson is that the list of non-zero differences 
formed by the elements in D cover every element in G exactly once.

There are more and less trivial constructions of other objects: 
symmetric designs, strongly regular graphs, partial geometries, to name 
just a few. From the point of view of the Discrete mathematician, the 
interesting question is to decide whether the combinatorial objects are 
isomorphic, no matter how they are constructed.

Difference constructions also occur in applied topics like cryptography, 
codes, multiple access communication systems or navigation systems. In 
contrast to the mathematical point of view described above, one is not 
interested in the combinatorics but rather the difference properties of 
the objects. As an example, there are four bent functions on six symbols 
which are considered to be "different" in cryptography. However, there 
are only three combinatorial designs which are described by these four 
bent functions. Another recent example is the wonderful discovery of a 
bijective almost perfect nonlinear function by John F. Dillon and his 
colleagues. This function is "equivalent" to one of the previously known 
functions, so it is not really "new", it is just a new description of 
something which was already known.

In my talk, I will describe the idea of difference constructions and the 
problem how to distinguish them. In particular, I will look at

-- bent functions
-- perfect nonlinear functions