Key chain, as an effective tool to achieve strong bid privacy non-interactively, was employed by Watanabe and Imai in an auction scheme. But in their scheme bid privacy cannot be achieved unconditionally and losing bidders must trust bidders with higher bids for privacy of their bids. Moreover, their scheme is not effcient. In this paper the key chain in the shceme by Watanabe and Imai is optimised to achieve unconditional bid privacy. In the new scheme, every losing bidder can control privacy of their own bids while no trust is needed. Computational cost of this scheme is optimised by avoiding the costly verifiable encryption technique in their scheme.