This paper revisits Paillier's trapdoor one-way function, focusing on the computational problem underlying its one-wayness. A new computational problem called the one-more Paillier inversion problem is formulated. It is a natural extension of Paillier inversion problem to the setting where adversaries have access to an inversion oracle and a challenge oracle. The relation between the one-more Paillier inversion problem and the one-more RSA problem introduced by Bellare, et al. It is shown that the one-more Paillier inversion problem is hard if and only if the one-more RSA problem is hard. Based on this, a new identification scheme is proposed. It is shown that the assumed hardness of the one-more Paillier inversion problem leads to a proof that the proposed identification scheme achieves security against concurrent impersonation attack.