Universal ηT pairing algorithm over arbitrary extension degree

Masaaki Shirase, Yuto Kawahara, Tsuyoshi Takagi, Eiji Okamoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)


The ηT pairing on supersingular is one of the most efficient algorithms for computing the bilinear pairing [3]. The rfr pairing defined over finite field F3n has embedding degree 6, so that it is particularly efficient for higher security with large extension degree n. Note that the explicit algorithm over F3n in [3] is designed just for n Ξ 1 (mod 12), and it is relatively complicated to construct an explicit algorithm for n ≢ 1 (mod 12). It is better that we can select many n's to implement the r¡T pairing, since n corresponds to security level of the ηT pairing. In this paper we construct an explicit algorithm for computing the ηT pairing with arbitrary extension degree n. However, the algorithm should contain many branch conditions depending on n and the curve parameters, that is undesirable for implementers of the ηT pairing. This paper then proposes the universal ηT pairing (ηT pairing), which satisfies the bilinearity of pairing (compatible with Tate pairing) without any branches in the program, and is as efficient as the original one. Therefore the proposed universal ηT pairing is suitable for the implementation of various extension degrees n with higher security.

Original languageEnglish
Title of host publicationInformation Security Applications - 8th International Workshop, WISA 2007, Revised Selected Papers
PublisherSpringer Verlag
Number of pages15
ISBN (Print)354077534X, 9783540775348
Publication statusPublished - 2007
Externally publishedYes
Event8th International Workshop on Information Security Applications, WISA 2007 - Jeju Island, Korea, Republic of
Duration: Aug 27 2007Aug 29 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4867 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other8th International Workshop on Information Security Applications, WISA 2007
Country/TerritoryKorea, Republic of
CityJeju Island

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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