A Practical Hybrid Group Key Establishment for Secure Group Communications

A group key establishment enables a group key shared among all group members. In this paper, we proposed a novel group key establishment, which is a hybrid of the Diffie–Hellman (DH) public-key scheme and the secret sharing scheme. Our protocol takes the advantages of the DH scheme, which does not need a mutually trusted key generation center (KGC) and the secret sharing scheme, which reduces the computational time. Employing the DH scheme allows any group member to act as a KGC to distribute a secret key to all group members. The secret sharing scheme is used as the encryption tool to transfer a group key to group members. Since public-key encryption involves modular exponentiations using a larger modulus (say at least 1024 bits) as compared with the secret sharing encryption involves polynomial operations using a smaller modulus (say only 160 bits), our proposed approach is faster than the broadcast encryption in public-key setting. We show that our protocol can provide key secrecy, key authentication and key independence.