This paper proposes two new multipliers based on cellular automata over finite field. Finite fields arithmetic operations have been widely used in the areas of data communication and network security applications. First, a multiplier with generalized irreducible polynomial is implemented with MSB-first fashion. Then, new algorithm and architecture are proposed to reduce the size of the first multiplier. The algorithm and architecture uses the property of irreducible all one polynomial as a modulus. Since the proposed architectures have regularity, modularity and concurrency, they are suitable for VLSI implementation and could be used in 1C cards because they have particularly simple architecture. They can be used as a basic architecture for the public-key cryptosystems.
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