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Some Efficient Algorithms for the Final Exponentiation of $\eta_T$ Pairing
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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 $\eta_T$ 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. |
BibTeX
@misc{eprint-2006-21922, title={Some Efficient Algorithms for the Final Exponentiation of $\eta_T$ Pairing}, booktitle={IACR Eprint archive}, keywords={public-key cryptography / Tate pairing, $\eta_T$ pairing, final exponentiation, torus}, url={http://eprint.iacr.org/2006/431}, note={ shirase@fun.ac.jp 13472 received 20 Nov 2006}, author={Masaaki Shirase and Tsuyoshi Takagi and Eiji Okamoto}, year=2006 }