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We study the advantages and applicability of stateful and stateless rekeying algorithms to different applications. We analytically compare the storage cost and the rekeying cost (number of unit-size encrypted messages) of LKH and SDR in immediate and batch rekeying scenarios. We implemented the two algorithms and simulated different membership scenarios to compare the rekeying cost. The simulation study shows that LKH performs better in immediate rekeying and small batch rekeying, whereas stateless rekeying performs better as we process membership changes in larger batches. In some cases, stateless rekeying was observed to be as inefficient as encrypting the group key separately for each member of the group. We also report on the effect of member adjacency on rekeying cost. Based on our analysis, we make recommendations in using group key management algorithms for various application scenarios.