As an effective resource allocation approach, double auctions (DAs) have been extensively studied in electronic commerce. Most previous studies have focused on how to design strategy-proof DA mechanisms, while not much research effort has been done concerning privacy and security issues. However, security, especially privacy issues have become such a public concern that the European governments lay down the law to enforce the privacy guarantees recently. In this paper, to address the privacy issue in electronic auctions, we concentrate on how to design a privacy-preserving mechanism for double auctions by employing Goldwasser-Micali homomorphic encryption and sorting networks. We achieve provable privacy such that the auctions do not reveal any bid information except the auction results, resulting in a strict privacy guarantee. Moreover, to achieve practical system performance, we compare different sorting algorithms, and suggest using the faster ones. Experimental results show that different sorting algorithms may have great effect on the performance of our mechanism, and demonstrate the practicality of our protocol for real-world applications in electronic commerce.