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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.

[1] M.A. Hasan, M. Wang, and V.K. Bhargava, Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fields$GF(2^m)$ IEEE Trans. Computers, vol. 41, no. 8, pp. 962-971, Aug. 1992.
[2] M.A. Hasan, M.Z. Wang, and V.K. Bhargava, “A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields,” IEEE Trans. Computers, vol. 42, no. 10, pp. 1278-1280, Oct. 1993.
[3] T. Itoh and S. Tsujii, “Structure of Parallel Multipliers for a Class of Finite Fields$GF(2^m)$,” Information and Computation, vol. 83, pp. 21-40, 1989.
[4] R. Lidl and H. Niederreiter,An Introduction to Finite Fields and Their Applications.Cambridge: Cambridge Univ. Press, 1986.
[5] E.D. Mastrovito,"VLSI Design for Multiplication over Finite Fields," LNCS-357, Proc. AAECC-6, pp. 297-309,Rome, July 1988, Springer-Verlag.
[6] Applications of Finite Fields, A.J. Menezes, ed. Boston: Kluwer Academic, 1993.
[7] J. Omura and J. Massey, "Computational Method and Apparatus for Finite Field Arithmetic," U.S. Patent Number 4,587,627, May 1986.
[8] C. Paar, "Efficient VLSI Architectures for Bit Parallel Computation in Galois Fields," PhD thesis, Universität GH Essen, VDI Verlag, 1994.
[9] C.C. Wang,T.K. Truong,H.M. Shao,L.J. Deutsch,J.K. Omura, and I.S. Reed,"VLSI Architectures for Computing Multiplications and Inverses inGF(2m)," IEEE Trans. Computers, vol. 34, no. 8, pp. 709-716, Aug. 1985.

Index Terms:
Finite fields, multiplication, normal basis, canonical basis, all-one-polynomial.
Citation:
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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