An efficient residue group multiplication for the η T pairing over

Yuta Sasaki; Satsuki Nishina; Masaaki Shirase; Tsuyoshi Takagi

doi:10.1007/978-3-642-05445-7_23

An efficient residue group multiplication for the η _T pairing over

Yuta Sasaki, Satsuki Nishina, Masaaki Shirase, Tsuyoshi Takagi

Laboratory of Mathematical Design for Advanced Cryptography

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Selected Areas in Cryptography - 16th Annual International Workshop, SAC 2009, Revised Selected Papers
Pages	364-375
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-05445-7_23
Publication status	Published - 2009
Event	16th Annual International Workshop on Selected Areas in Cryptography, SAC 2009 - Calgary, AB, Canada Duration: Aug 13 2009 → Aug 14 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5867 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	16th Annual International Workshop on Selected Areas in Cryptography, SAC 2009
Country/Territory	Canada
City	Calgary, AB
Period	8/13/09 → 8/14/09

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-05445-7_23

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

An efficient residue group multiplication for the η _T pairing over. / Sasaki, Yuta; Nishina, Satsuki; Shirase, Masaaki et al.

Selected Areas in Cryptography - 16th Annual International Workshop, SAC 2009, Revised Selected Papers. 2009. p. 364-375 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5867 LNCS).

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

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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5867 LNCS, pp. 364-375, 16th Annual International Workshop on Selected Areas in Cryptography, SAC 2009, Calgary, AB, Canada, 8/13/09. https://doi.org/10.1007/978-3-642-05445-7_23

Sasaki Y, Nishina S, Shirase M, Takagi T. 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. 2009. p. 364-375. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-05445-7_23

Sasaki, Yuta ; Nishina, Satsuki ; Shirase, Masaaki et al. / An efficient residue group multiplication for the η _T pairing over. Selected Areas in Cryptography - 16th Annual International Workshop, SAC 2009, Revised Selected Papers. 2009. pp. 364-375 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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