This paper presents the hardware architectures for inversion in GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ), in order to be used in elliptic curve cryptosystems. In this case, the Extended Euclidean Algorithm (EEA) and the Itoh-Tsujii Algorithm (ITA) are implemented. The simulation were carried out using Quartus II v. 9,0 and the design were synthesized on the Stratix III EP3SE50F780C2. The simulation results show a very good performance using small area.