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

54 Citations (Scopus)

Abstract

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages178-191
Number of pages14
Volume5209 LNCS
DOIs
Publication statusPublished - 2008
Event2nd International Conference on Pairing-Based Cryptography, Pairing 2008 - Egham, United Kingdom
Duration: Sep 1 2008Sep 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)03029743
ISSN (Electronic)16113349

Other

Other2nd International Conference on Pairing-Based Cryptography, Pairing 2008
CountryUnited Kingdom
CityEgham
Period9/1/089/3/08

Fingerprint

Pairing
Integer
Polynomials
Tate Pairing
Lower bound
Euler Function
Elliptic Curves
Iteration
Curve
Polynomial

Keywords

  • Ate pairing
  • Miller's algorithm

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Nogami, Y., Akane, M., Sakemi, Y., Kato, H., & Morikawa, Y. (2008). Integer variable x-based ate pairing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5209 LNCS, pp. 178-191). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5209 LNCS). https://doi.org/10.1007/978-3-540-85538-5_13

Integer variable x-based ate pairing. / Nogami, Yasuyuki; Akane, Masataka; Sakemi, Yumi; Kato, Hidehiro; Morikawa, Yoshitaka.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5209 LNCS 2008. p. 178-191 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5209 LNCS).

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

Nogami, Y, Akane, M, Sakemi, Y, Kato, H & Morikawa, Y 2008, Integer variable x-based ate pairing. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 5209 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5209 LNCS, pp. 178-191, 2nd International Conference on Pairing-Based Cryptography, Pairing 2008, Egham, United Kingdom, 9/1/08. https://doi.org/10.1007/978-3-540-85538-5_13
Nogami Y, Akane M, Sakemi Y, Kato H, Morikawa Y. Integer variable x-based ate pairing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5209 LNCS. 2008. p. 178-191. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-85538-5_13
Nogami, Yasuyuki ; Akane, Masataka ; Sakemi, Yumi ; Kato, Hidehiro ; Morikawa, Yoshitaka. / Integer variable x-based ate pairing. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5209 LNCS 2008. pp. 178-191 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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