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All the currently existing homomorphic e-voting schemes are based on additive homomorphism. In this paper a new e-voting scheme based on multiplicative homomorphism is proposed. In the tallying phase, a decryption is performed to recover the product of the votes, instead of the sum of them (as in the additive homomorphic e-voting schemes). Then, the product is factorized to recover the votes. The new e-voting scheme is more efficient than the additive homomorphic e-voting schemes and more efficient than other voting schemes when the number of candidates is small. Strong vote privacy and public verifiability are obtained in the new e-voting scheme.