This paper presents two new algorithms and their architectures for $AB^2 $ multiplication over $GF(2^m)$.First, a new architecture with a new algorithm is designed based on LFSR (Linear Feedback Shift Register) architecture. Furthermore, modified $AB^2 $ multiplier is derived from the multiplier. The multipliers and the structure use AOP (All One Polynomial) as a modulus, which hat the properties of ail coefficients with 1. Simulation results thews that proposed architecture has lower hardware complexity than previous architectures. They could be. Therefore it is useful for implementing the exponential ion architecture, which is the tore operation In public-key cryptosystems.