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In this paper, we present a new exponentiation architecture and multiplier/ squarer which are the basic operations for exponentiation on GF(2m). 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(2m) 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.

Fast Exponentiaion over GF(2m) Based on Cellular Automata