Journal of Applied Science and Engineering

Published by Tamkang University Press


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Che-Wun Chiou This email address is being protected from spambots. You need JavaScript enabled to view it.1 , Fu-Hua Chou1 , Su-Frang Shu1 and Jim-Min Lin2

1Department of Electronic Engineering, Ching Yun University, Chung-Li, Taiwan 320, R.O.C.
2Department of Information Engineering and Computer Science, Feng Chia University, Taichung, Taiwan 407, R.O.C.


Received: January 13, 2005
Accepted: June 1, 2005
Publication Date: December 1, 2005

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The natural fault-tolerant properties and regular structure of the Lee-Lu-Lee’s array multiplier over GF(2m) fields make it very attractive for VLSI implementation. However, the Lee-Lu-Lee’s array multiplier is time-consuming while comparing with other existing array multipliers. To overcome this problem, we will present a pipeline algorithm for such array multipliers with multiple speeds as comparing with the Lee-Lu-Lee’s array multiplier.

Keywords: Finite Fields Arithmetic, Modular Arithmetic, Public-Key Cryptosystem, Array Multiplier, Elliptic Curve Cryptosystem, Pipeline Processing


  1. [1] MacWilliams, P. J. and Sloane, N. J. A., “The Theory of Error-Correcting Codes,” Amsterdam, NorthHolland (1978).
  2. [2] Peterson, W. W. and Weldon, Jr. E. J., “ErrorCorrecting Codes”. 2nd ed. Cambridge, MA, MIT Press (1972).
  3. [3] Berlekamp, E. R., “Algebraic Coding Theory,” New York, McGraw-Hill (1968).
  4. [4] Lidl, R. and Niederreiter, H., “Introduction to Finite Fields and Their Applications,” New York, Cambridge Univ. Press (1994).
  5. [5] “Application of Finite Fields”, Menezes, A. J., Boston, Kluwer Academic (1993).
  6. [6] Yeh, C. S., Reed, S. and Truong, T. K., “Systolic Multipliers for Finite Fields GF(2m),” IEEE Trans. Computers, Vol. 33, pp. 357360 (1984).
  7. [7] Massey, J. L. and Omura, J. K., “Computational Method and Apparatus for Finite Field Arithmetic,” U.S. Patent Number 4,587,627, May (1986).
  8. [8] Itoh, T. and Tsujii, S., “Structure of Parallel Multipliers for a Class of Fields GF(2m),” Information and Computation, Vol. 83, pp. 2140 (1989).
  9. [9] Hasan, M. A., Wang, M. and Bhargava, V. K., “Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fields GF(2m),” IEEE Trans. Computers, Vol. 41, pp. 962971 (1992).
  10. [10] Wu, H., Hasan, M. A. and Blake, I. F., “New Low-complexity Bit-parallel Finite Field Multipliers Using Weakly Dual Bases,” IEEE Trans. Computers, Vol. 47, pp. 1223-1234 (1998).
  11. [11] Wu, H. and Hasan, M. A., “Low-complexity Bitparallel Multipliers for a Class of Finite Fields,” IEEE Trans. Computers, Vol. 47, pp. 883887 (1998).
  12. [12] Lee, C.-Y., Lu, E.-H. and Lee, J.-Y., “Bit-parallel Systolic Multipliers for GF(2m) Fields Defined by Allone and Equally Spaced Polynomials,” IEEE Trans. Computers, Vol. 50, pp. 385393 (2001).
  13. [13] Sunar, B. and Koç, C. K., “Mastrovito Multiplier for All Trinomials,” IEEE Trans Computers, Vol. 48, pp. 522527 (1999).
  14. [14] Wu, H., Hasan, M. A. and Blake, I. F., “On Complexity of Bit-parallel Finite Field Multiplier,” Proc. Canadian Workshop Information Theory’97 (1997).
  15. [15] Wu, H., “Bit-parallel Finite Field Multiplier and Square using Polynomial Basis,” IEEE Trans. Computers, Vol. 51, pp. 750758 (2002).
  16. [16] Chiou, C. W., “Concurrent Error Detection in Array Multipliers for GF(2m) Fields,” IEE Electronics Letters, Vol. 38, pp. 688689 (2002).



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