[Resource Topic] 2006/431: Some Efficient Algorithms for the Final Exponentiation of $\eta_T$ Pairing

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Some Efficient Algorithms for the Final Exponentiation of \eta_T Pairing

Authors: Masaaki Shirase, Tsuyoshi Takagi, Eiji Okamoto


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 {\mathbb F}_{3^{6n}}. Indeed, we propose some efficient algorithms using the torus T_2({\mathbb F}_{3^{3n}}) 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 17% for n=97.

ePrint: https://eprint.iacr.org/2006/431

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