The group Diffie-Hellman problems

Abstract

In this paper we study generalizations of the Diffie-Hellman problems recently used to construct cryptographic schemes for practical purposes. The Group Computational and the Group Decisional Diffie-Hellman assumptions not only enable one to construct efficient pseudorandom functions but also to naturally extend the Diffie-Hellman protocol to allow more than two parties to agree on a secret key. In this paper we provide results that add to our confidence in the GCDH problem. We reach this aim by showing exact relations among the GCDH, GDDH, CDH and DDH problems. © Springer-Verlag Berlin Heidelberg 2003.