An efficient residue group multiplication for the η T pairing over

Yuta Sasaki, Satsuki Nishina, Masaaki Shirase, Tsuyoshi Takagi

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

1 Citation (Scopus)

Abstract

When we implement the η T pairing, which is one of the fastest pairings, we need multiplications in a base field and in a group G. We have previously regarded elements in G as those in to implement the η T pairing. Gorla et al. proposed a multiplication algorithm in that takes 5 multiplications in , namely 15 multiplications in . This algorithm then reaches the theoretical lower bound of the number of multiplications. On the other hand, we may also regard elements in G as those in the residue group in which βa is equivalent to a for and . This paper proposes an algorithm for computing a multiplication in the residue group. Its cost is asymptotically 12 multiplications in as m → ∞, which reaches beyond the lower bound the algorithm of Gorla et al. reaches. The proposed algorithm is especially effective when multiplication in the finite field is implemented using a basic method such as shift-and-add.

Original languageEnglish
Title of host publicationSelected Areas in Cryptography - 16th Annual International Workshop, SAC 2009, Revised Selected Papers
Pages364-375
Number of pages12
DOIs
Publication statusPublished - Dec 1 2009
Event16th Annual International Workshop on Selected Areas in Cryptography, SAC 2009 - Calgary, AB, Canada
Duration: Aug 13 2009Aug 14 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5867 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other16th Annual International Workshop on Selected Areas in Cryptography, SAC 2009
CountryCanada
CityCalgary, AB
Period8/13/098/14/09

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sasaki, Y., Nishina, S., Shirase, M., & Takagi, T. (2009). An efficient residue group multiplication for the η T pairing over. In Selected Areas in Cryptography - 16th Annual International Workshop, SAC 2009, Revised Selected Papers (pp. 364-375). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5867 LNCS). https://doi.org/10.1007/978-3-642-05445-7_23