Passive RFID tags have limited rewritable memory for data storage and limited computation power, which pose difficulties to implement security protection on RFID tags. It has been shown that strong security and privacy protections for RFID require utilizing public-key cryptography. Unfortunately, the implementation of public key cryptography is infeasible in low-cost passive tags. With this issue in mind, in this work, we propose a pre-computable signature scheme with a very efficient signature verification algorithm for RFID applications. Our signature scheme is provably secure under the DDH assumption and a variant of q-SDH assumption. With pre-computations, no exponentiation is required in our signature verification. Our research shows that it is feasible for low-cost RFID tags to verify signatures with the basic modular multiplication only (if they have a small amount of writable memory).