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H. Brunner, A. Curiger, M. Hofstetter, "On Computing Multiplicative Inverses in GF(2/sup m/)," IEEE Transactions on Computers, vol. 42, no. 8, pp. 10101015, August, 1993.  
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@article{ 10.1109/12.238496, author = {H. Brunner and A. Curiger and M. Hofstetter}, title = {On Computing Multiplicative Inverses in GF(2/sup m/)}, journal ={IEEE Transactions on Computers}, volume = {42}, number = {8}, issn = {00189340}, year = {1993}, pages = {10101015}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.238496}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  On Computing Multiplicative Inverses in GF(2/sup m/) IS  8 SN  00189340 SP1010 EP1015 EPD  10101015 A1  H. Brunner, A1  A. Curiger, A1  M. Hofstetter, PY  1993 KW  computing multiplicative inverses; modular standard basis inversion; Galois fields; Euclid's algorithm; greatest common divisor; polynomials; asymptotic complexity; computation time; area requirement; ATcomplexity; digital arithmetic. VL  42 JA  IEEE Transactions on Computers ER   
The design of a modular standard basis inversion for Galois fields GF(2/sup m/) based on Euclid's algorithm for computing the greatest common divisor of two polynomials is presented. The asymptotic complexity is linear with m both in computation time and area requirement, thus resulting in an ATcomplexity of O(m/sup 2/). This is a significant improvement over the best previous proposal which achieves ATcomplexity of only O(m/sup 3/).
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