Summary: A multi-party key establishment protocol based on the difficulty of calculating discrete logarithms in a finite field is proposed with the following features. It requires a constant number (independent of the number of participants) of rounds. All messages have the same constant size. All participants perform a constant number of exponential operations. All participants agree on a key together with two random integers simultaneously. Furthermore, to establish a new key when the set of participants is changed is easy. We also show that this new scheme is secure against passive attacks provided that the Diffie-Hellman key agreement protocol is secure in the sense that the established key is computationally indistinguishable from a random value.