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One important problem for public broadcast Location-Based Services (LBS) is to enforce access control on a large number of subscribers. In such a system a user typically subscribes to a LBS for a time interval (a, b) and a spatial region (xbl, ybl, xir, ytr) according to a 3-dimensional spatial-temporal authorization model. In this paper, we argue that current approaches to access control using group key management protocols are not scalable. Our proposal STauth minimizes the number of keys which needs to be distributed and is thus scalable to a much higher number of subscribers and the dimensionality of the authorization model. We analytically and experimentally demonstrate the performance and scalability benefits of our approach against other group key management protocols.