On computing multiplicative inverses in GF(2/sup m/)

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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