Centralized spectrum management is one of the key dynamic spectrum access (DSA) mechanisms proposed to govern the spectrum sharing between government incumbent users (IUs) and commercial secondary users (SUs). In the current centralized DSA designs, the operation data of both government IUs and commercial SUs need to be shared with a central server. However, the operation data of government IUs are often classified information and the SU operation data may also be commercial secrets. The current system design dissatisfies the privacy requirement of both IUs and SUs, since the central server is not necessarily trustworthy for holding such sensitive operation data. To address the privacy issue, this paper presents a privacy-preserving centralized DSA system (P2-SAS), which realizes the complex spectrum allocation process of DSA through efficient secure multi-party computation. In P2-SAS, none of the IU or SU operation data would be exposed to any snooping party, including the central server itself. We formally prove the correctness and privacy-preserving property of P2-SAS and evaluate its scalability and practicality using experiments based on real-world data. Experiment results show that P2-SAS can respond an SU's spectrum request in 6.96 s with communication overhead of less than 4 MB.