Efficient software implementation of the final exponentiation for pairing

Pairing-based cryptography has got a lot of attention the last years, since the proposition of the tripartite key exchange. The best type of pairing is optimal ate pairing over Barreto-Naehrig curves which are based on two steps: Miller Loop and final exponentiation. Most of the researches were done for the Miller Loop. In this paper, we present the different methods for computing the hard part of the final exponentiation of optimal ate pairings based on a hard mathematical study. Using a comparative study based on the temporary number and memory resources, we will choose the best method to be then implemented in Matlab Software. Thus, the best one is Devigili et al. method presenting a reduced complexity and required number of registers.