Integer variable x-based ate pairing

Yasuyuki Nogami, Masataka Akane, Yumi Sakemi, Hidehiro Kato, Yoshitaka Morikawa

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

61 Citations (Scopus)


In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log2 r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log 2r] to[log2(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ". For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log2X].

Original languageEnglish
Title of host publicationPairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings
Number of pages14
Publication statusPublished - 2008
Event2nd International Conference on Pairing-Based Cryptography, Pairing 2008 - Egham, United Kingdom
Duration: Sept 1 2008Sept 3 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5209 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other2nd International Conference on Pairing-Based Cryptography, Pairing 2008
Country/TerritoryUnited Kingdom


  • Ate pairing
  • Miller's algorithm

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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