Some Efficient Algorithms for the Final Exponentiation of η_T Pairing

Abstract

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 η_T pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the η_T pairing in the extension field F_3⁶ⁿ. Indeed, we propose some efficient algorithms using the torus T₂(F_3³ⁿ) that can efficiently compute an inversion and a powering by 3ⁿ+1. Consequently, the total processing cost of computing the η_T pairing can be reduced by 16% for n=97.