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M. Anwarul Hasan, "DoubleBasis Multiplicative Inversion Over GF(2m)," IEEE Transactions on Computers, vol. 47, no. 9, pp. 960970, September, 1998.  
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@article{ 10.1109/12.713315, author = {M. Anwarul Hasan}, title = {DoubleBasis Multiplicative Inversion Over GF(2m)}, journal ={IEEE Transactions on Computers}, volume = {47}, number = {9}, issn = {00189340}, year = {1998}, pages = {960970}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.713315}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  DoubleBasis Multiplicative Inversion Over GF(2m) IS  9 SN  00189340 SP960 EP970 EPD  960970 A1  M. Anwarul Hasan, PY  1998 KW  Computer arithmetic KW  Euclid's algorithm KW  Galois (or finite) fields KW  multiplicative inverses KW  canonical (or polynomial) basis and triangular basis. VL  47 JA  IEEE Transactions on Computers ER   
Abstract—Inversion over Galois fields is much more difficult than the corresponding multiplication. In this article, efficient computation of inverses in GF(2
[1] M.A. Hasan, "DoubleBasis Inversion in GF(2m)," Proc. 1995 Canadian Conf. Electrical and Computer Eng., pp. 229232, 1995.
[2] W. Diffie and M.E. Hellman, New Directions in Cryptography IEEE Trans. Information Theory, vol. 22, pp. 644654, 1976.
[3] G.B. Agnew, R.C. Mullin, and S.A. Vanstone, An Implementation of Elliptic Curve Cryptosystems over$F_{2^{155}}$ IEEE J. Selected Areas in Comm., vol. 11, no. 5, pp. 804813, June 1993.
[4] M.A. Hasan, V.K. Bhargava, and T. LeNgoc, "Algorithms and Architectures for the Design of a VLSI ReedSolomon Codec," ReedSolomon Codes and Their Applications, S.B. Wicker and V.K. Bhargava, eds., chapter 4, pp. 60107. IEEE Press, June 1994.
[5] 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. 709716, Aug. 1985.
[6] K. Araki, I. Fujita, and M. Morisue, "Fast Inverter Over Finite Field Based on Euclid's Algorithm," Trans. Inst. Electronics, Information, and Comm. Engineers, vol. E72, pp. 1,2301,234, Nov. 1989.
[7] M.A. Hasan and V.K. Bhargava,"BitSerial Systolic Divider and Multiplier for Finite FieldsGF(2m)," IEEE Trans. Computers, vol. 41, no. 8, pp. 972980, Aug. 1992.
[8] M.A. Hasan and V.K. Bhargava,"Division and BitSerial Multiplication overGF(qm)," IEE Proc. E., vol. 139, pp. 230236, May 1992.
[9] C. Paar, Some Remarks on Efficient Inversion in Finite Fields Proc. 1995 Int'l Symp. Information Theory, 1995.
[10] E.R. Berlekamp,"BitSerial ReedSolomon Encoders," IEEE Trans. Information Theory, vol. 28, pp. 869874, Nov. 1982.
[11] M. Morii,M. Kasahara, and D.L. Whiting,"Efficient BitSerial Multiplication and the DiscreteTime WienerHopft Equation over Finite Fields," IEEE Trans. Information Theory, vol. 35, pp. 1,1771,183, Nov. 1989.
[12] M. Wang and I.F. Blake,"BitSerial Multiplication in Finite Fields," SIAM J. Discrete Maths., vol. 3, pp. 140148, Feb. 1990.
[13] M.A. Hasan and V.K. Bhargava, "Architecture for a Low Complexity RateAdaptive ReedSolomon Encoder," IEEE Trans. Computers, vol. 44, no. 7, pp. 938942, July 1995.
[14] Y. Sugiyama, "An Algorithm for Solving Discrete Time WienerHopf Equations Based on Euclid's Algorithm," IEEE Trans. Information Theory, vol. 32, pp. 394409, May 1986.
[15] R.P. Brent and H.T. Kung, "Systolic VLSI Arrays for Polynomial GCD Computation," IEEE Trans. Computers, vol. 33, no. 8, pp. 731736, Aug. 1984.
[16] H. Brunner, A. Curiger, and M. Hofstetter, On Computing Multiplicative Inverses in${\rm GF}(2^m)$ IEEE Trans. Computers, vol. 42, no. 8, pp. 10101015, Aug. 1993.
[17] S.T.J. Fenn, M. Benaissa, and D. Taylor, $GF(2^m)$Multiplication and Division over the Dual Basis IEEE Trans. Computers, vol. 45, no. 3, pp. 319327, Mar. 1996.
[18] M.A. Hasan, "DivisionandAccumulation over GF(2m)," IEEE Trans. Computers, vol. 46, no. 6, pp. 705708, June 1997.
[19] R E. Ziemer and R.L. Peterson, Digital Communications and Spread Spectrum Systems.New York: Macmillan, 1985.