In this study, we present an efficient finite field arithmetic architecture based on systolic array for multiplication which is a core algorithm for division and exponentiation operations. In order to obtain dedicated area-efficient circuits, we adopt Montgomery multiplication algorithm and systolic array. First of all we induce an efficient arithmetic algorithm from typical Montgomery multiplication using an effective factor, then we design an efficient semi-systolic array based multiplication architecture which is highly suitable for pipelined operations. The proposed multiplier saves at least 40% area complexity as compared to the corresponding existing structures.