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The recent focus on auction field has been to multiple item auctions where bidders are not restricted to buying only one item of the merchandize. In this paper, we concentrate on the use of the multi-item auction and propose a novel PRDA auction protocol to solve problems of bid privacy in multi-item auction. A verifiable technique of shared key chain is used to find the winners without revealing the losing bids and unnecessary information. Through analysis, our new scheme is robust against cheating bidders.