Some Efficient Algorithms for the Final Exponentiation of $\eta_T$ Pairing

Masaaki Shirase; Tsuyoshi Takagi; Eiji Okamoto

Paper 2006/431

Some Efficient Algorithms for the Final Exponentiation of $\eta_T$ Pairing

Masaaki Shirase, Tsuyoshi Takagi, and Eiji Okamoto

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Tate pairing $\eta_T$ pairing final exponentiation torus
Contact author(s): shirase @ fun ac jp
History: 2006-11-21: received
Short URL: https://ia.cr/2006/431
License: CC BY

BibTeX

@misc{cryptoeprint:2006/431,
      author = {Masaaki Shirase and Tsuyoshi Takagi and Eiji Okamoto},
      title = {Some Efficient Algorithms for the Final Exponentiation of $\e{ta_T}$ Pairing},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/431},
      year = {2006},
      url = {https://eprint.iacr.org/2006/431}
}