Issue No. 08 - August (1993 vol. 42)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.238496
<p> 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 AT-complexity of O(m/sup 2/). This is a significant improvement over the best previous proposal which achieves AT-complexity of only O(m/sup 3/).</p>
computing multiplicative inverses; modular standard basis inversion; Galois fields; Euclid's algorithm; greatest common divisor; polynomials; asymptotic complexity; computation time; area requirement; AT-complexity; digital arithmetic.
A. Curiger, H. Brunner and M. Hofstetter, "On Computing Multiplicative Inverses in GF(2/sup m/)," in IEEE Transactions on Computers, vol. 42, no. , pp. 1010-1015, 1993.