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Biometric systems, while offering convenient authentication, often fall short in providing rigorous security assurances. A primary reason is the ad-hoc design of protocols and components, which hinders the establishment of comprehensive security proofs. This paper introduces a formal framework for constructing secure and privacy-preserving biometric systems. By leveraging the principles of universal composability, we enable the modular analysis and verification of individual system components. This approach allows us to derive strong security and privacy properties for the entire system, grounded in well-defined computational assumptions.