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 predescribed 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.