In this paper we propose a new exponentiation architecture in GF(2m). The core of the architecture is a parallel structure for multiplication and squaring, which is based on the state transitions of programmable Cellular Automata (CA). The proposed architecture requires hardware of the order m2 and the time complexity is m. The performance of the design outperformed existing architectures based on Systolic Array and Cellular Automata. The design can thus be effectively applied in public key cryptosystems like ElGamal and Diffie-Hellman Key exchange. The regular, cascadable structure of the Cellular Automata leads to extremely scalable VLSI design.