Double-basis inversion in GF(2m)

In order to provide digital signatures or message authentication, many digital communications systems are becoming increasingly equipped with some form of cryptosystems. Many of these cryptosystems require computation in Galois (finite) fields. The Galois field inversion is much more complicated than the corresponding multiplication. Two algorithms for computation of inverses in GF(2^m) are presented which combine Euclid´s algorithm and the concept of solving a set of equations over the ground field GF(2). The proposed algorithms use two separate bases for the representation of its input and output elements, and have low computational complexity. One of the algorithms is highly suitable for hardware implementation using VLSI technologies