Shift register synthesis for multiplicative inversion over GF(2m)

Galois or finite fields have applications in cryptography and coding theory. For example, both encoding and decoding of Reed-Solomon codes require computations in the field over which the code is defined. Among the different arithmetic operations in finite fields, multiplicative inversion (hereafter called simply inversion) has been identified as the most complicated operation. Recently, several approaches have been made to compute the inverse efficiently. The approaches which have been given considerable attention in the literature are based on either Euclid´s algorithm, or Fermat´s theorem, or solution of a set of linear equations. The latter approach is used in our present work to compute inverses