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Abstract. In this paper, we present a new exponentiation architecture and multiplier/squarer which are the basic operations for exponentiation on GF(2 m ). The proposed multiplier/squarer is used as kernal architecture of exponentiation and processes the modular multiplication and squaring at the same time for effective exponentiation on GF(2 m ) using a cellular automata. Proposed architecture can be used efficiently for the design of the modular exponentiation on the finite field in most public key crypto systems such as Diffie-Hellman key exchange, ElGamal, etc. Also, the cellular automata architecture is simple, regular, modular, cascadable and therefore, can be utilized efficiently for the implementation of VLSI.

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