April 23, 2024

Fall 2006
Thematic Program in Cryptography

Cryptography Participants Seminar
Tuesdays 2-3 p.m., held at the Fields Institute, Room 230

Times and dates of courses will be announced when finalized.

October 10, 2006
2:00 PM
room 230
Andreas Stein
Approximating Euler Products and an Algorithm for Computing the Class Number of an Algebraic Function Field
A fundamental problem in the theory of function fields and curves over finite fields is the effective computation of the class number h and thus the order of the Jacobian of an algebraic function field. If the characteristic of the finite field is small, various recent algorithms solve this problem. Our main focus will be algebraic function fields of large characteristic, in which case not much is known about effective computation of the order of the Jacobian. However, our methods are very general for any genus and any characteristic. In our talk, we will first discuss how to perform arithmetic in an algebraic function fields based on recent results. Then we will provide tight estimates for the class number via truncated Euler products, and show how these estimates can be used to develop an effective method of computing h.
Thursday, October 5, 2006
2:00 - 3:00
Fields Library
Felix Fontain (University of Zurich)
Computing in Divisor Class Groups of Global Function Fields
In this talk, I will present an algorithm from Florian Hess to effectively compute Riemann-Roch spaces of divisors in global function fields. Then I will describe a unique representation of divisor classes and an algorithm to effectively compute in the divisor class group.