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On computing multiplicative inverses in GF(2m)

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3 Author(s)
Brunner, H. ; Integrated Syst. Lab., ETH, Zurich, Switzerland ; Curiger, A. ; Hofstetter, M.

The design of a modular standard basis inversion for Galois fields GF(2m) 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( m2). This is a significant improvement over the best previous proposal which achieves AT-complexity of only O (m3)

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Computers, IEEE Transactions on  (Volume:42 ,  Issue: 8 )