To renew group key is necessary to ensure secrecy of multicast contents. However how to distribute updated key to all legitimate members efficiently is a hard problem in opening research. All existing works have complexity of O(clogn) in batch re-keying, where c is total additions/evictions. The Minimum Exact Cover Problem of Group Key Distribution is presented and studied, which can reduce the complexity down to O(1). Efficiency analysis and simulation test show that the achievement ca...