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With the growth of Internet, many applications are based on a group communication model where members of the group would like to communicate among themselves over a public channel securely. To carry out the group communication confidentially over a public channel, a group key is required. In this paper we propose a new group key computation technique for secure group communication. The scheme is based on contributory key agreement approach, allows the users to verify the consistency of the shares used for computing the group key, and is applicable to dynamic groups. The paper also addresses periodic group rekeying.