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We present a practical system for conducting sealed-bid auctions that preserves the secrecy of the bids while providing for verifiable correctness and trustworthiness of the auction. The auctioneer must accept all bids submitted and follow the published rules of the auction. No party receives any useful information about bids before the auction closes and no bidder is able to change or repudiate her bid. Our solution uses Paillier's homomorphic encryption scheme [25] for zero knowledge proofs of correctness. Only minimal cryptographic technology is required of bidders; instead of employing complex interactive protocols or multi-party computation, the single auctioneer computes optimal auction results and publishes proofs of the results' correctness. Any party can check these proofs of correctness via publicly verifiable computations on encrypted bids. The system is illustrated through application to first-price, uniform-price and second-price auctions, including multi-item auctions. Our empirical results demonstrate the practicality of our method: auctions with hundreds of bidders are within reach of a single PC, while a modest distributed computing network can accommodate auctions with thousands of bids.