This paper presents the first scalable, efficient, and reliable privacy-preserving fingerprint authentication based on minutiae representation. Our method is provably secure by leveraging the Yao's classic Garbled Circuit (GC) protocol. While the concept of using GC for secure fingerprint matching has been suggested earlier, to the best of our knowledge, no prior reliable method or implementation applicable to real fingerprint data has been available. Our technique achieves both accuracy and practicability by customizing a widely adopted minutiae-based fingerprint matching algorithm, Bozorth matcher, as our core authentication engine. We modify the Bozorth matcher and identify certain sensitive parts of this algorithm. For these critical parts, we create a sequential circuit description which can be efficiently synthesized and customized to GC using the TinyGarble framework. We show evaluations of our modified matching algorithm on a standard fingerprint database FVC2002 DB2 to demonstrate its reliability. The implementation of privacy-preserving fingerprint authentication using Synopsis Design Compiler on a commercial Intel processor shows the efficiency and scalability of the proposed methodologies.