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Secure and reliable group communication is an active area of research. Its popularity is fuelled by the growing importance of group-oriented and collaborative applications. The central research challenge is secure and efficient group key management. The present paper is based on the Scalable and Secure Multicast Group Key Management using Boolean Function Simplification technique along with the most popular absolute encoder output type code named Gray Code. The main issue in secure group communication is group dynamics and key management. A scalable secure group communication model ensures that whenever there is a membership change, a new group key is computed and distributed to the group members with minimal computation and communication cost. This paper explores the use of batching of group membership changes to reduce the frequency, and hence the cost, of key re-distribution operations. It focuses explicitly on the issue of snowballing member removal and presents a protocol that minimizes the number of messages required to distribute new keys to the remaining group members. Handling member removal(leave) is more complex than member join event in any secure group communication model. Our snowballing member removal uses the reflected binary code called Gray Code and outperforms all other schemes known to us in terms of message complexity. Most importantly, our technique is superior in minimizing the number of rekeying messages when multiple members leave the session in the same round.