In 2010, Harn et al. proposed an authenticated group key transfer protocol-based secret sharing. In their protocol, for distributing a secret group key involving t group members, the key generation center (KGC) needs to broadcast a message containing (t + 1) elements to all group members, whereas each group member needs to compute a tth-degree interpolating polynomial to recover the secret group key. Thus, the protocol of Harn et al. is only suitable for small-size groups. We propose an improved protocol from the protocol of Harn et al. In our protocol, the size of a broadcasted message from the KGC is fixed, and each group member only needs to compute a fixed-degree interpolating polynomial to recover the group key. Thus, our protocol can be suitable for large-size groups. On the other hand, in the protocol of Harn et al., the KGC should be mutually trusted because it knows all group keys for every communication. If the KGC is untrustworthy, it can bring great threats to the group communications. In this paper, we also propose another improved group key transfer protocol based on untrustworthy KGC. Copyright © 2012 John Wiley & Sons, Ltd.