In an exponentiation device, a relatively large table is generated outside of a coprocessor so as to enable high-speed exponentiation to be performed using the small window method. The selection of data from the table and transfer of data to the coprocessor are conducted in parallel with a multiple-length arithmetic operation performed in the coprocessor. So as to avoid bottlenecks occurring in the data transfer between a CPU and the coprocessor, two data banks are provided in the coprocessor for storing the data to be used in the arithmetic operation. By providing two banks in the coprocessor, it is possible to use one for transferring data while data stored in the other is being used in the arithmetic operation. When the operation using the stored data has been completed, the banks are switched, and the arithmetic operation is then repeated using the newly transferred data while at the same time conducting data transfer in readiness for the following operation.