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This paper introduces a new family of group key establishment protocols suit-able for small or medium-sized groups. Five protocols are presented, using a semi-trustedserver, with varying security service. The first one is a non-authenticated key agreement pro-tocol suitable for applications with low security requirements. The second protocol adds anauthenticated key agreement to provide collaborative authentication. The third and the fourthprotocols provide key establishment with integrity and confirmation services, and the fifth pro-tocol is the member adding protocol. A major advantage of the protocols is that they reducethe numbers of rounds from n to 5.