Secure group communication model poses the challenge of key management to enforce the access control among the users of the group. Secure group key management schemes should be designed such that there is less rekeying and storage cost involved to manage the group keys. We propose a centralized, scalable, share-based secure group key management scheme employing a new approach on the basis of the polynomial interpolation technique. We prove the security of the scheme. We design a multilayer share-based key management scheme to manage the keys in the multilayer communication model. A new aggregate tree structure is proposed to manage the keys in the multilayer communication model. We analyze and evaluate the performance of the designed schemes in detail for storage and rekeying cost. We show that the proposed share-based group key management scheme and the multilayer key management schemes are efficient in terms of storage and rekeying cost in comparison with two schemes based on threshold secret-sharing method available in the literature. Copyright © 2012 John Wiley & Sons, Ltd.