[Turkmath:8238] SU General Seminar, Osmanbey Uzunkol, 21.03.2012

[Alp Bassa]

*Sabanci University General Seminar*

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*Speaker:* Osmanbey Uzunkol (Carl von Ossietzky University Oldenburg)

*Date/Time:* 21 March 2012, Wednesday, 16:00

*Place:* Sabanci University, FENS G 015

*Title:* *Complex Multiplication with its applications*

*Abstract:* In the first part of my talk I am going to introduce
the classical theory of complex multiplication (CM-theory), and
its applications in primality proving, group, curve and pairing
based cryptography. Furthermore, the use of class invariants will
be explained which enables to construct groups with desired
properties. (More concretely elliptic curves over finite fields with given
number of points and some predesribed properties that realize all of
above applications.)

In the second part I will show that the classical class invariants can be
computed more efficiently using "Thetanullwerte". Moreover, we show that
most of the invariants are units in the corresponding field extensions,
which allows to obtain better class invariants in some cases. The
optimality of class invariants and some open questions will be
also discussed at the end of the talk.


Tea, coffee and cookies will be served in FENS G 015 from 15:30.


For information on how to reach Sabanci University, please see

http://www.sabanciuniv.edu/eng/?kampus_hayati/hizmet_ve_olanaklar/ulasim.html
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