A key-exchange protocol using real quadratic fields

Abstract

In 1976 Diffie and Hellman first introduced their well-known key-exchange protocol which is based on exponentiation in the multiplicative group GF(p)* of integers relatively prime to a large prime p (see [8]). Since then, this scheme has been extended to numerous other finite groups. Recently, Buchmann and Williams [2] introduced a version of the Diffie-Hellman protocol which uses the infrastructure of a real quadratic field. Theirs is the first such system not to require an underlying group structure, but rather a structure which is "almost" like that of a group. We give here a more detailed description of this scheme as well as state the required algorithms and considerations for their implementation. © 1994 International Association for Cryptologic Research.