Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18

Md Al Amin Khandaker, Yasuyuki Nogami, Hwajeong Seo, Sylvain Duquesne

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

Abstract

Efficiency of the next generation pairing based security protocols rely not only on the faster pairing calculation but also on efficient scalar multiplication on higher degree rational points. In this paper we proposed a scalar multiplication technique in the context of Ate based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curves with embedding degree k = 18 at the 192-bit security level. From the systematically obtained characteristics p, order r and Frobenious trace t of KSS curve, which is given by certain integer z also known as mother parameter, we exploit the relation #E(F p) = p+1−t mod r by applying Frobenius mapping with rational point to enhance the scalar multiplication. In addition we proposed z-adic representation of scalar s. In combination of Frobenious mapping with multi-scalar multiplication technique we efficiently calculate scalar multiplication by s. Our proposed method can achieve 3 times or more than 3 times faster scalar multiplication compared to binary scalar multiplication, sliding-window and non-adjacent form method.

Original languageEnglish
Title of host publicationInformation Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers
PublisherSpringer Verlag
Pages221-232
Number of pages12
Volume10144 LNCS
ISBN (Print)9783319565484
DOIs
Publication statusPublished - 2017
Event17th International Workshop on Information Security Applications, WISA 2016 - Jeju Island, Korea, Republic of
Duration: Aug 25 2016Aug 25 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10144 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th International Workshop on Information Security Applications, WISA 2016
CountryKorea, Republic of
City Jeju Island
Period8/25/168/25/16

Fingerprint

Scalar multiplication
Pairing
Curve
Rational Points
Security Protocols
Sliding Window
Frobenius
Trace
Scalar
Binary
Calculate
Integer

Keywords

  • Frobenius mapping
  • KSS curve
  • Scalar multiplication

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Khandaker, M. A. A., Nogami, Y., Seo, H., & Duquesne, S. (2017). Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18. In Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers (Vol. 10144 LNCS, pp. 221-232). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10144 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-56549-1_19

Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18. / Khandaker, Md Al Amin; Nogami, Yasuyuki; Seo, Hwajeong; Duquesne, Sylvain.

Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers. Vol. 10144 LNCS Springer Verlag, 2017. p. 221-232 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10144 LNCS).

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

Khandaker, MAA, Nogami, Y, Seo, H & Duquesne, S 2017, Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18. in Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers. vol. 10144 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10144 LNCS, Springer Verlag, pp. 221-232, 17th International Workshop on Information Security Applications, WISA 2016, Jeju Island, Korea, Republic of, 8/25/16. https://doi.org/10.1007/978-3-319-56549-1_19
Khandaker MAA, Nogami Y, Seo H, Duquesne S. Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18. In Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers. Vol. 10144 LNCS. Springer Verlag. 2017. p. 221-232. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-56549-1_19
Khandaker, Md Al Amin ; Nogami, Yasuyuki ; Seo, Hwajeong ; Duquesne, Sylvain. / Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18. Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers. Vol. 10144 LNCS Springer Verlag, 2017. pp. 221-232 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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