Some efficient algorithms for the final exponentiation of ηT pairing

Masaaki Shirase, Tsuyoshi Takagi, Eiji Okamoto

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 nt pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the nt pairing in the extension field double-struck F sign;36n. Indeed, we propose some efficient algorithms using the torus T 2(double-struck F sign;33n) that can efficiently compute an inversion and a powering by 3n + 1. Consequently, the total processing cost of computing the nt pairing can be reduced by 16% for n = 97.

Original languageEnglish
Pages (from-to)221-228
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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