Some promising recent schemes for XML access control employ encryption for implementing security policies on published data, avoiding data duplication. In this paper we study one such scheme, due to Miklau and Suciu. That scheme was introduced with some intuitive explanations and goals, but without precise definitions and guarantees for the use of cryptography (specifically, symmetric encryption and secret sharing). We bridge this gap in the present work. We analyze the scheme in the context of the rigorous models of modern cryptography. We obtain formal results in simple, symbolic terms close to the vocabulary of Miklau and Suciu. We also obtain more detailed computational results that establish security against probabilistic polynomial-time adversaries. Our approach, which relates these two layers of the analysis, continues a recent thrust in security research and may be applicable to a broad class of systems that rely on cryptographic data protection.