Reduced-Latency Algorithm for Finite Field Inversion in GF(2m)

Abstract: In this letter, we propose a novel reduced-latency finite field inversion algorithm for binary extension fields GF(2m) using normal basis representation. A similar approach to that in Itoh-Tsujii inversion algorithm is used, however, the latency is significantly reduced for the time required to perform the necessary multiplications for inversion, which is a function of the binary length of the extension degree of the concerned field. The latency of our proposed finite field inversion algorithm is always comparable to the best case scenario in Itoh-Tsujii inversion algorithm for any given extension degree , or equivalently, for any given GF(2m).

Keywords: Finite field inversion, Fermat's little theorem, normal basis representation, binary extension fields GF(2m).