The present invention relates to a finite field multiplier used for implementing an encrypting algorithm circuit, thereby minimizing power consumption and circuit area in implementing the finite field multiplier with a LFSR (Linear Feedback Shift Register) structure. The Finite field multiplier of the present invention is an operator performing a modular operation on the multiplication result of two data represented on a polynomial basis in a Galois Field into an irreducible polynomial. The LFSR structure is a serial finite field multiplication structure, and has a merit over an array structure and a hybrid structure in application to systems that are limited in size and power due to its simplicity of circuits and also its capability of being implemented in a small size.