Some Efficient Algorithms for the Final Exponentiation of η_T Pairing Masaaki Shirase

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 #T pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the #T pairing in the extension field F 3 6n . Indeed, we propose some efficient algorithms using the torus T2 (F 3 3n) that can efficiently compute an inversion and a powering by 3 +1. Consequently, the total processing cost of computing the #T pairing can be reduced by 17% for n = 97