Oberwolfach Seminar: Arithmetic Geometry and Public Key Cryptography

Date:

November 7th - 13th, 2004

Organizers:

Gerhard Frey, Duisburg-Essen

Tanja Lange, Bochum

Subject:

Public key crypto systems are an important part of data security. They rely on one way functions. For the construction of such functions one looks for ``hard computational problems'' and so number theory and the theory of varieties over finite fields enter the scene. The study of the action of the Frobenius automorphism plays a central role and a main attraction of public key cryptography for mathematicians is that the most beautiful and deepest results on the arithmetic of Galois representations lead to the most efficient algorithms both for constructing and attacking systems.

Program:

Protocols, RSA and the factorization of numbers, Discrete Logarithms and their realizations as ideal class groups, constructive and destructive applications of Galois theory: efficient scalar multiplication, point counting, Tate dualiy and scalar restriction.

Prerequisites:

Basic algebra, number theory, and algebraic geometry, including Galois theory and the theory of curves and their Jacobian varieties, especially over finite fields. Some experience with algorithmic approaches to problems is helpful but not necessary.

Deadline for applications:

September 24, 2004

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.