<p><b>Abstract</b>—This paper presents a new parallel multiplier for the Galois field <tmath>$GF(2^m)$</tmath> whose elements are represented using the optimal normal basis of type II. The proposed multiplier requires <tmath>$1.5(m^2-m)$</tmath> XOR gates, as compared to <tmath>$2(m^2-m)$</tmath> XOR gates required by the Massey-Omura multiplier. The time complexities of the proposed and the Massey-Omura multipliers are similar.</p>