Cryptographic Aspects Of Real Quadratic Congruence Function Fields
Date: July 19th (Friday)
Time: 15:00-15:30
Abstract
We show how the theory of real quadratic congruence function fields can be used
to produce a secure key distribution protocol. The technique is similar to that advocated by
Diffie and Hellman in 1976, but instead of making use of a group for its underlying
structure, makes use of a structure which is ``almost'' a group. The method is an extension of
the recent ideas of Scheidler, Buchmann and Williams, but, because it is implemented in
these function fields, several of the difficulties with their protocol can be eliminated. A
description of the protocol is provided, together with a discussion of the difficulty of the
so-called discrete logarithm problem (DLP) in real quadratic congruence function fields. In
this context, we will point out that the DLP for real quadratic congruence function fields of
genus one is equivalent to the DLP for elliptic curves over finite fields.
