We describe a new method to perform the modular exponentiation operation, i.e., the computation of c = me mod n, where c, m, e and n are large integers. The new method uses the discrete Fourier transform over a finite ring, and relies on new techniques to perform multiplication and reduction operations. The method yields efficient and highly parallel architectures for hardware realizations of publickey cryptosystems requiring the modular exponentiation as the core computation, such as the RSA and Diffie-Hellman algorithms.