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Bid validity proof and verification is an efficiency bottleneck and privacy drawback in homomorphic e-auction. The existing bid validity proof technique is inefficient and only achieves honest-verifier zero knowledge (ZK). In this study, an efficient proof and verification technique is proposed to guarantee bid validity in homomorphic e-auction. The new proof technique is mainly based on hash function operations and only needs a very small number of costly public key cryptographic operations. Moreover, it can handle untrusted verifiers and achieve perfect ZK. As a result, efficiency and privacy of homomorphic e-auction applications are significantly improved. To the best of authors' knowledge, it proof technique is the first to handle untrusted verifiers in e-auction applications.