Date:	Mon, April 22, 2013
Time:	17:15
Place:	Research II Lecture Hall

Abstract: The main task of public key cryptography is to provide highly efficient tools to exchange keys, sign electronic messages, authenticate members of a net and, sometimes,encrypt and decrypt messages by using simple protocols with clear and easy to follow implementation rules. For many applications the basic crypto primitive is the discrete logarithm in groups, and it is the task of mathematicians to provide suitable groups. This task was solved rather successfully, and there are lists of standardized groups that can be used - even without knowledge of any background. But typically, these groups come from arithmetic geometry, and to construct them and to shape them such that they provide fast systems took the whole arsenal of this deep theory. At the same time it turned out that every constructive tool could be used as attack to some of the groups, and it is very important to describe preci- sely the "weak" cases. So to understand why the suggested groups are, to our best knowledge, secure it is necessary to understand a little bit of arithmetic geometry. It is the aim of the lecture to explain the relevant constructions and convince the audience that the problems risen from cryptography lead to exciting developments in theoretical and algorithmic arithmetic geometry, and for cryptographers the im- portant message from arithmetic geometry is: The range of candidates usable for cryptography is rather narrow, but there are still plenty of groups we can trust.