In this paper two different approaches to the design of a reconfigurable Tate pairing hardware accelerator are presented. The first uses macro components based on a large, fixed number of underlying Galois Field arithmetic units in parallel to minimise the computation time. The second is an area efficient approach based on a small, variable number of underlying components. Both architectures are prototyped on an FPGA. Timing results for each architecture with various different design parameters are presented.