Cellular automata based signature analyzers are becoming very popular for compressing test responses in built-in self-test applications. Off-line determination of signatures (both good circuit signature and faulty circuit signatures) is a compute-intensive process that involves cycle-by-cycle simulation of the signature analyzer. In this paper, we investigate a technique for speeding up the simulation of cellular automata-based multi-input signature registers (C-MISRs). First, we describe a technique for converting a C-MISR into an equivalent single input circuit. We then present an algorithm for parallelizing the simulation of these single input circuits.