Some efficient algorithms for the final exponentiation of ηT pairing

Recently Tate pairing and its variations are attracted in cryptography. Their operations consist of a main iteration loop and a final exponentiation. The final exponentiation is necessary for generating a unique value of the bilinear pairing in the extension fields. The speed of the main loop has become fast by the recent improvements, e.g., the Duursma-Lee algorithm and eta(T) pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the eta(T) pairing in the extension field F-36n. Indeed, we propose some efficient algorithms using the torus T-2(F-33n) that can efficiently compute an inversion and a powering by 3(n) + 1. Consequently, the total processing cost of computing the eta(T) pairing can be reduced by 16% for n = 97.