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Modern software development and run-time environments, such as Java and the Microsoft .NET Common Language Runtime (CLR), have adopted a declarative form of access control. Permissions are granted to code providers, and during execution, the platform verifies compatibility between the permissions required by a security-sensitive operation and those granted to the executing code. While convenient, configuring the access-control policy of a program is not easy. If a code component is not granted sufficient permissions, authorization failures may occur. Thus, security administrators tend to define overly permissive policies, which violate the Principle of Least Privilege (PLP). A considerable body of research has been devoted to building program-analysis tools for computing the optimal policy for a program. However, Java and the CLR also allow executing code under the authority of a subject (user or service), and no program-analysis solution has addressed the challenges of determining the policy of a program in the presence of subjects. This paper introduces Subject Access Rights Analysis (SARA), a novel analysis algorithm for statically computing the permissions required by subjects at run time. We have applied SARA to 348 libraries in IBM WebSphere Application Server - a commercial enterprise application server written in Java that consists of >2 million lines of code and is required to support the Java permission- and subject-based security model. SARA detected 263 PLP violations, 219 cases of policies with missing permissions, and 29 bugs that led code to be unnecessarily executed under the authority of a subject. SARA corrected all these vulnerabilities automatically, and additionally synthesized fresh policies for all the libraries, with a false-positive rate of 5% and an average running time of 103 seconds per library. SARA also implements mechanisms for mitigating the risk of false negatives due to reflection and native code; according to a thorough result evaluation based on testing, no false negative was detected. SARA enabled IBM WebSphere Application Server to receive the Common Criteria for Information Technology Security Evaluation Assurance Level 4 certification.