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A New Hardware Architecture for Operations in GF(2m)
January 2002 (vol. 51 no. 1)
pp. 90-92

The efficient computation of the arithmetic operations in finite fields is closely related to the particular ways in which the field elements are presented. The common field representations are a polynomial basis representation and a normal basis representation. In this paper, we introduce a nonconventional basis present a new bit-parallel multiplier which is as efficient as the modified Massey-Omura multiplier the type I optimal normal basis.

[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] B.S. Kaliski Jr. and Y.L. Yin, “Storage-Efficient Finite Field Basis Conversion,” contribution to IEEE Standard P1363, 1998.
[5] Ç.K. Koç and B. Sunar, Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields IEEE Trans. Computers, vol. 47, no. 3, pp. 353-356, Mar. 1998.
[6] R. Lidl and H. Niederreiter,An Introduction to Finite Fields and Their Applications.Cambridge: Cambridge Univ. Press, 1986.
[7] Applications of Finite Fields, A.J. Menezes, ed. Kluwer Academic, 1993.
[8] S.H. Oh, C.H. Kim, and J.I. Lim, “Non-Conventional Basis of Finite Field,” Preproceedings Symp. Applied Computing (SAC '99), pp. 109-119, 1999.
[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.
[10] IEEE P1363, Standard Specifications for Public Key Cryptography, Annex A, 1998.

Index Terms:
Finite fields, nonconventional basis, elliptic curve, public-key cryptosystems.
Chang Han Kim, Sangho Oh, Jongin Lim, "A New Hardware Architecture for Operations in GF(2m)," IEEE Transactions on Computers, vol. 51, no. 1, pp. 90-92, Jan. 2002, doi:10.1109/12.980019
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