The hash-sign-switch paradigm was firstly proposed by Shamir and Tauman with the aim to design an efficient on-line/off-line signature scheme. However, all existing on-line/off-line signature schemes based on Shamir-Taumans paradigm suffer from the key exposure problem of chameleon hashing. That is, if the signer applies the same hash value more than once to obtain two signatures on two different messages,the recipient can obtain a hash collision and use it to recover the signers trapdoor information. Therefore, the signer should pre-compute and store plenty of different chameleon hash values and the corresponding signatures on the hash values in the off-line phase, and send the collision and the signature for a certain hash value in the on-line phase.Hence, the computation and storage cost for the off-line phase and the communication cost for the on-line phase in Shamir-Taumans signature scheme are still a little more overload. In this paper, we first introduce a special double-trapdoor hash family based on the discrete logarithm assumption to solve this problem. We then apply the hash-sign-switch paradigm to propose a much more efficient generic on-line/off-line signature scheme. Additionally, we use a one-time trapdoor/hash key pair for each message signing, which prevents the recipient from recovering the trapdoor information of the signer and computing other collisions.