An optimized finite-field multiplier is proposed for encryption and error correction devices. It is based on a modified Linear Feedback Shift Register (LFSR) which has lower power consumption and smaller area than prior LFSR-based finite-field multipliers. The proposed finite field multiplier for GF(2n) multiplies two n-bit polynomials using polynomial basis to produce $z(x)=a(x)^*b(x)$ mod p(x), where p(x) is a irreducible polynomial for the Galois Field. The LFSR based on a serial multiplication structure has less complex circuits than array structures and hybrid structures. It is efficient to use the LFSR structure for systems with limited area and power consumption. The prior finite-field multipliers need 3${cdot}$m flip-flops for multiplication of m-bit polynomials. Consequently, they need 6${cdot}$m latches because one flip-flop consists of two latches. The proposed finite-field multiplier requires only 4${cdot}$m latches for m-bit multiplication, which results in 1/3 smaller area than the prior finite-field multipliers. As a result, it can be used effectively in encryption and error correction devices with low-power consumption and small area.