An Algorithm for Inversion in GF(2^m) Suitable for Implementation Using a Polynomial Multiply Instruction on GF(2)

An algorithm for inversion in GF(2^m) suitable for implementation using a polynomial multiply instruction on GF(2) is proposed. It is based on the extended Euclid´s algorithm. In the algorithm, operations corresponding to several contiguous iterations of the VLSI algorithm proposed by Brunner et al. is represented as a matrix. They are calculated at once through the matrix efficiently by means of a polynomial multiply instruction on GF(2). For example, in the case where the word size of a processor and m are 32 and 571, respectively, the algorithm calculates inversion with about the half number of instructions of the conventional algorithm on the average.