A new method, homomorphic e-auction based on multiplicative homomorphic encryption algorithm like ElGamal encryption is proposed in this paper. Its advantage is obvious and useful in practice: efficient distributed private key generation and thus efficient trust sharing. A long existing problem in homomorphic e-auction, inefficiency of bid validity check, is solved in the new multiplicative homomorphic e-auction scheme in this paper, which employs efficient bid re-formatting to enforce bid validity. Another contribution of the new multiplicative homomorphic e-auction scheme is that it is the first e-auction scheme to provide formal and comprehensive security analysis to achieve formally provable security (especially privacy).