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Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
March 1998 (vol. 47 no. 3)
pp. 353-356

Abstract—We present a new low-complexity bit-parallel canonical basis multiplier for the field GF(2m) generated by an all-one-polynomial. The proposed canonical basis multiplier requires m2$-$ 1 XOR gates and m2 AND gates. We also extend this canonical basis multiplier to obtain a new bit-parallel normal basis multiplier.

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Index Terms:
Finite fields, multiplication, normal basis, canonical basis, all-one-polynomial.
Ç.k. Koç, B. Sunar, "Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields," IEEE Transactions on Computers, vol. 47, no. 3, pp. 353-356, March 1998, doi:10.1109/12.660172
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