Area and time efficient AB2 multipliers based on cellular automata

Finite field operations have been widely used in the data communication security applications. This paper proposes two AB² multipliers based on the cellular automata over finite field. They deploy the mixture advantages in the perspective of both in area and time complexity by applying the property of irreducible all one polynomial as a modulus. First, an AB² multiplier is proposed with a new algorithm. Then, another algorithm and its architecture for AB² multiplication are derived to reduce the complex wiring in the first architecture. They can be used as a basic architecture for the public key cryptosystems in IEEE P1363.