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On Computing Multiplicative Inverses in GF(2/sup m/)
August 1993 (vol. 42 no. 8)
pp. 1010-1015

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/).

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Index Terms:
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.
H. Brunner, A. Curiger, M. Hofstetter, "On Computing Multiplicative Inverses in GF(2/sup m/)," IEEE Transactions on Computers, vol. 42, no. 8, pp. 1010-1015, Aug. 1993, doi:10.1109/12.238496
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