Multicast is a preferred network communication technique in the case of multiple recipients, whose importance has been increasingly highlighted with the development of the Internet. IGMP, the multicastmanagement protocol, does not provide access control of the users. In order to protect communicationconfidentiality, traffic in secure multicast is encrypted with a Session Encryption Key (SEK) which is known only to the certificated group members. Whenever there is a change in the group membership, the SEK has to bedynamically updated, thus the key distribution becomes a key problem in the research of secure multicast. In designing key distribution algorithms, communication costs, key storage, protection against attacks and computation complexity are considered as the four important factors. A group key distribution scheme utilizing a polynomial expansion is proposed, which features in no traditional encryption and decryption. Analyses show that it performs well in small scale multicast. This polynomial expansion based algorithm is then integrated with the Logical Key Hierarchy; while preserving the logarithmic communication cost with the group size, the presented PE-LKH scheme lowers the computation complexity observably, thus is scalable to large dynamic groups.