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Security is one of the most important issues in the grid. Several processes generated by a user need to communicate securely. The existing architectures do not provide support for secure group communication in grid. Grid applications differ in various parameters such as life time, arrival rate, departure rate, staying period, and tolerance times for join and leave. These parameters are critical for optimizing performance and meeting the security requirements of the application. Existing grid security architectures do not harness knowledge of these parameters. In this paper, we propose an extended grid security infrastructure (EGSI) to support secure group communication in grid. We also present an authentication and access control scheme at virtual organization level.