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<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>
Finite fields, multiplication, normal basis, canonical basis, all-one-polynomial.
B. Sunar, Ç.k. Koç, "Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields", IEEE Transactions on Computers, vol. 47, no. , pp. 353-356, March 1998, doi:10.1109/12.660172
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