Normal basis inversion in some finite fields

In this paper, a high efficiency algorithm for the inversion operation in some finite fields is presented. The algorithm is based on the normal basis representation, in which only multipliers constitute the complexity of the inverter. For finite fields of the form GF(2^k↑2+1), the fast algorithm utilizes only 2(k-1) multipliers. In comparison to the conventional binary method, which requires k²-1 multipliers, the new algorithm reduces the number of multipliers of the inverter dramatically and thus more suitable for hardware implementations