<p><b>Abstract</b>—We present a new low-complexity bit-parallel canonical basis multiplier for the field GF(2<super><it>m</it></super>) generated by an all-one-polynomial. The proposed canonical basis multiplier requires <it>m</it><super>2</super><tmath>$-$</tmath> 1 XOR gates and <it>m</it><super>2</super> AND gates. We also extend this canonical basis multiplier to obtain a new bit-parallel normal basis multiplier.</p>