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M. Elia, M. Leone, "On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)," IEEE Transactions on Computers, vol. 51, no. 3, pp. 346351, March, 2002.  
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@article{ 10.1109/12.990131, author = {M. Elia and M. Leone}, title = {On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)}, journal ={IEEE Transactions on Computers}, volume = {51}, number = {3}, issn = {00189340}, year = {2002}, pages = {346351}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.990131}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/) IS  3 SN  00189340 SP346 EP351 EPD  346351 A1  M. Elia, A1  M. Leone, PY  2002 KW  finite fields KW  parallel multiplier KW  optimal normal basis VL  51 JA  IEEE Transactions on Computers ER   
A lower bound to the number of AND gates used in parallel multipliers for
[1] A.V. Aho, J.E. Hopcroft, and J.D. Ullman, The Design and Analysis of Computer Algorithms. Reading, Mass.: AddisonWesley, 1975.
[2] L.E. Dickson, Linear Groups with an Exposition of the Galois Field Theory. New York: Dover, 1958.
[3] A.J. Menezes, I. Blake, X. Gao, R. Mullin, S. Vanstone, and T. Yaghoobian, Applications of Finite Fields. Boston: Kluwer Academic, 1993.
[4] R. Lidl and H. Niederreiter, Finite Fields. Reading, Mass.: AddisonWesley, 1983.
[5] I.E. Shparlinski, Computational and Algorithmic Problems in Finite Fields. Boston: Kluwer Academic, 1992.
[6] S. Winograd, Arithmetic Complexity of Computation. Philadelphia: SIAM, 1980.
[7] G. Drolet, “A New Representation of Elements of Finite Fields$\big. {\rm GF}(2^m)\bigr.$Yielding Small Complexity Arithmetic Circuits,” IEEE Trans. Computers, vol. 47, no. 9, pp. 938946, Sept. 1998.
[8] J. Hastad, “Tensor Rank Is NPComplete,” J. Algorithms, vol. 11, no. 4, pp. 644654, 1990.
[9] Ç.K. Koç and B. Sunar, LowComplexity BitParallel Canonical and Normal Basis Multipliers for a Class of Finite Fields IEEE Trans. Computers, vol. 47, no. 3, pp. 353356, Mar. 1998.
[10] B. Sunar and Ç.K. Koç, Mastrovito Multiplier for All Trinomials IEEE Trans. Computers, vol. 48, no. 5, pp. 522527, May 1999.
[11] J. Omura and J. Massey, “Computational Method and Apparatus for Finite Field Arithmetic,” US Patent Number 4,587,627, May 1986.
[12] 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. 962971, Aug. 1992.
[13] M.A. Hasan, M.Z. Wang, and V.K. Bhargava, “A Modified MasseyOmura Parallel Multiplier for a Class of Finite Fields,” IEEE Trans. Computers, vol. 42, no. 10, pp. 12781280, Oct. 1993.
[14] M.A. Hasan, DoubleBasis Multiplicative Inversion over${\rm GF}(2^m)$ IEEE Trans.n Computers, vol. 47, no. 9, pp. 960970, Sept. 1998.
[15] T. Itoh and S. Tsujii, “Structure of Parallel Multipliers for a Class of Finite Fields$GF(2^m)$,” Information and Computation, vol. 83, pp. 2140, 1989.
[16] C. Paar, “A New Architecture for a Parallel Finite Field Multiplier with Low Complexity Based on Composite Fields,” IEEE Trans. Computers, vol. 45, no. 7, pp. 846861, July 1996.
[17] E.D. Mastrovito, “VLSI Architectures for Computation in Galois Fields,” PhD thesis, Dept. of Electrical Eng., Linköping Univ., Sweden, 1991.
[18] A. ReyhaniMasoleh and M.A. Hasan, “A Reduced Redundancy MasseyOmura Parallel Multiplier over$GF(2^m)$,” Proc. 20th Biennal Symp. Comm., May 2000.
[19] B. Sunar and Ç.K. Koç, An Efficient Optimal Normal Basis Type II Multiplier IEEE Trans. Computers, vol. 50, no. 1, pp. 8387, Jan. 2001.
[20] M. Elia, M. Leone, and C. Visentin, “Low Complexity BitParallel Multipliers for$GF(2^m)$with Generator Polynomial$x^m+x^k+1$,” Electronics Letters, vol. 35, no. 7, pp. 551552, Apr. 1999.