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Double-Basis Multiplicative Inversion Over GF(2m)
September 1998 (vol. 47 no. 9)
pp. 960-970

Abstract—Inversion over Galois fields is much more difficult than the corresponding multiplication. In this article, efficient computation of inverses in GF(2m) is considered by solving a set of linear equations over the ground field GF(2). The proposed algorithm uses two separate bases for the representation of its input and output elements and has low computational complexity. The algorithm is also suitable for hardware implementation using VLSI technologies.

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Index Terms:
Computer arithmetic, Euclid's algorithm, Galois (or finite) fields, multiplicative inverses, canonical (or polynomial) basis and triangular basis.
M. Anwarul Hasan, "Double-Basis Multiplicative Inversion Over GF(2m)," IEEE Transactions on Computers, vol. 47, no. 9, pp. 960-970, Sept. 1998, doi:10.1109/12.713315
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