Traditionally, there are two very costly operations in homomorphic e-auction schemes. First, bid validity check is an efficiency bottleneck for both the bidders and auctioneers, but it is needed to guarantee validity of the bids and correctness of homomorphic bid opening. Second, although the auctioneers can employ binary search to reduce the instances of homomorphic bid opening, every bid opening needs a costly equality test. The two costly operations prevent homomorphic e-auction from being applied to efficiency-sensitive applications. In this paper, three new homomorphic e-auction protocols are proposed to get rid of them in homomorphic e-auction. As a result, efficiency of e-auction is greatly improved. Copyright © 2012 John Wiley & Sons, Ltd.