Recently, the interest about the Tate pairing over binary fields has decreased due to the existence of efficient attacks to the discrete logarithm problem in the subgroups of such fields. We show that the choice of fields of large size to make these attacks infeasible does not lead to a degradation of the computation performance of the pairing. We describe and evaluate by simulation an implementation of the Tate pairing that allows to achieve good timing results, comparable with those reported in the literature but with a higher level of security