article

A new hardware architecture for operations In GF (2^m)

Authors:

Chang Han Kim,

Sangho Oh,

Jongin LimAuthors Info & Claims

IEEE Transactions on Computers, Volume 51, Issue 1

Page 92

Published: 01 January 2002 Publication History

Abstract

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 [8] and present a new bit-parallel multiplier [2] which is as efficient as the modified Massey-Omura multiplier the type I optimal normal basis.

References

[1]

M.A. Hasan, M.Z. Wang, and V.K. Bhargava, "Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fields GF(2"')," IEEE Trans. Computers, vol. 41, no, 8, pp. 962-971, Aug. 1992.

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[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.

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[3]

T. Itoh and S. Tsujii, "Structure of Parallel Multipliers for a Class of Finite Fields GF(2")," Information and Computation, vol. 83, pp. 21-40, 1989.

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B.S. Kaliski Jr. and Y.L. Yin, "Storage-Efficient Finite Field Basis Conversion," contribution to IEEE Standard P1363, 1998.

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C.K. Koc and B. Sunar, "Low-Complexity Bit-Parallel Canonical and Normal Basis Multiplier for a Class of Finite Fields," IEEE Trans. Computers, vol. 47, no. 3, pp. 353-356, Mar. 1998.

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R. LidI and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed. Cambridge, U.K.: Cambridge Univ. Press, 1994

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Applications of Finite Fields, A.}. Menezes, S. Kluwer Academic, 1993

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[8]

S.H. Oh, C.H. Kim, and J.l. Lam, "Non-Conventional Basis of Finite Field,' Preproceedings Symp. Applied Computing (SAC '99), pp. 109-119, 1999.

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[9]

C.C. Wang, T.K. Truong, H.M. Shao, L.J. Deutsch, J.K. Omura, and I.S. Reed, "VLSI Architecture for Computing Multiplications and lovers in GF(2"')," IEEE Trans. Computers, vol. 34, no. 8, pp. 709-717, Aug. 1985.

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[10]

IEEE P1363, Standard Specifications for Public Key Cryptography, Annex A,1998.

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Index Terms

A new hardware architecture for operations In GF (2^m)
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

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cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 51, Issue 1

January 2002

96 pages

ISSN:0018-9340

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IEEE Computer Society

United States

Publication History

Published: 01 January 2002

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