Study of Extended Euclidean and Itoh-Tsujii Algorithms in GF(2m) using polynomial bases

Abstract

Finite field arithmetic is important for the field of information security. The inversion operation consumes most of the time and resources among all finite field arithmetic operations. In this report, two main classes of algorithms for inversion are studied. The first class of inverters is Extended Euclidean based inverters. Extended Euclidean Algorithm is an extension of Euclidean algorithm that computes the greatest common divisor. The other class of inverters is based on Fermat's little theorem. This class of inverters is also called multiplicative based inverters, because, in these algorithms, the inversion is performed by a sequence of multiplication and squaring. This report represents a literature review of inversion algorithm and implements a multiplicative based inverter and an Extended Euclidean based inverter in MATLAB. The experimental results show that inverters based on Extended Euclidean Algorithm are more efficient than inverters based on Fermat's little theorem.