Cryptographic Aspects Of Real Quadratic Congruence Function Fields

Andreas Stein

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.

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