Truthful spectrum auctions have been extensively studied in recent years. Truthfulness makes bidders bid their true valuations, simplifying greatly the analysis of auctions. However, revealing ones true valuation causes severe privacy disclosure to the auctioneer and other bidders. To make things worse, previous work on secure spectrum auctions does not provide adequate security. In this paper, based on TRUST, we propose PS-TRUST, a provably secure solution for truthful double spectrum auctions. Besides maintaining the properties of truthfulness and special spectrum reuse of TRUST, PS-TRUST achieves provable security against semi-honest adversaries in the sense of cryptography. Specifically, PS-TRUST reveals nothing about the bids to anyone in the auction, except the auction result. To the best of our knowledge, PS-TRUST is the first provably secure solution for spectrum auctions. Furthermore, experimental results show that the computation and communication overhead of PS-TRUST is modest, and its practical applications are feasible.