We present a group key exchange protocol that naturally expands the Diffie-Hellman protocol. Our protocol is scalable: it has two towers (for n>2 parts) and the number of modular exposures per user is constant. It`s safe against a passive opponent if the Diffie-Hellman problem is intractable. The minutes of this document were presented to Eurocrypt `94 and appeared in [Proc. Eurocrypt `94, in Reading Notes in Comput. Sci., 950, Springer-Verlag, Berlin, 1995, 275-286]. The proof of safety for groups with an even number of parties appeared in [Preproceedings of Eurocrypt `94, Scuola Superiore Guglielmo Reiss Romoli (SSGRR), Perugia, Italy, 9-12 May 1994, p. 279-290]. After submitting this contribution, Yvo Desmedt is at University College, London, UK.
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