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Exclusion Basis Systems (EBS) is a combinatorial optimization methodology for key management of group communication. The EBS approach proves to be very scalable for large networks and enables great flexibility in network management. But it is highly vulnerable to collusion attacks. In this paper, a novel secure group management scheme based on EBS and attribute encryption is proposed. Our proposed scheme provides group forward/backward secrecy, and it is resilience to colluding attacks. Moreover, compared to some previous approaches, performance evaluation shows that our scheme is more efficient in communication (O(m) for single leave), storage (O(k) for each group member), and computation (O(k) for each group member), where k and m are the number of the attributes that each member holds or not. As k and m could be relatively small even in large-scale systems, so as to our new scheme works well in large-scale applications.