Integer variable x-based ate pairing

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

doi:10.1007/978-3-540-85538-5_13

Integer variable x-based ate pairing

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

61 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 language	English
Title of host publication	Pairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings
Pages	178-191
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-540-85538-5_13
Publication status	Published - 2008
Event	2nd International Conference on Pairing-Based Cryptography, Pairing 2008 - Egham, United Kingdom Duration: Sept 1 2008 → Sept 3 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5209 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	2nd International Conference on Pairing-Based Cryptography, Pairing 2008
Country/Territory	United Kingdom
City	Egham
Period	9/1/08 → 9/3/08

Keywords

Ate pairing
Miller's algorithm

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-540-85538-5_13

Cite this

Nogami, Y., Akane, M., Sakemi, Y., Kato, H., & Morikawa, Y. (2008). Integer variable x-based ate pairing. In Pairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings (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 et al.
Pairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings. 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 proceeding › Conference contribution

Nogami, Y, Akane, M, Sakemi, Y, Kato, H & Morikawa, Y 2008, Integer variable x-based ate pairing. in Pairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings. 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

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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].",

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AU - Akane, Masataka

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AU - Kato, Hidehiro

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AB - 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].

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Integer variable x-based ate pairing

Abstract

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Keywords

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