Signature analyzers are widely used for compressing test responses. Off-line determination of signatures (for both good circuit and faulty circuits) is a compute-intensive process that involves cycle-by-cycle simulation of the signature analyzer. In this paper, we investigate techniques for speeding up the simulation of multi-input signature registers (MISRs). We first analyze a speedup technique that processes each input independently by table lookups, and show its shortcomings. We then propose a speedup technique that converts the MISR into an equivalent single input circuit. We also present the results of a simulation study that show that this technique achieves a good speedup.