Key-exchange in real quadratic congruence function elds

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 isan extension f the recent ideas of Scheidler, Buchmann a d Williams, but, because it is implemented in these function fields, several of the difficulties with their protocol can be eliminated. A detailed description f the protocol is provided, together with a discussion fthe algorithms needed to effect it. 1