A Comparative Implementation of GLV Technique on KSS-16 Curve

Md Al Amin Khandaker, Yuki Nanjo, Takuya Kusaka, Yasuyuki Nogami

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

Abstract

Pairing-based protocols are getting popular in many cryptographic applications. Pairing algorithms involve computations on elements in all three pairing groups, G 1 , G 2 and G 3 ; however, most protocols usually require additional scalar multiplication and exponentiation in any of these three groups. The Gallant-Lambert-Vanstone (GLV) method is an elegant technique to accelerate the scalar multiplication which can reduce the number of elliptic curve doubling by using Straus-Shamir simultaneous multi-scalar multiplication technique. However, efficiently computable endomorphisms are required to apply GLV for the elliptic curves. This paper shows the GLV technique by deriving efficiently computable endomorphism for Kachisa-Schaefer-Scott (KSS) curve defined over degree 16 extension field. In addition, the authors show explicit formulas to compute the GLV method together with Straus-Shamir simultaneous multi-scalar multiplication technique for 2, 4 and 8 dimensions in G 2 group. The comparative implementation shows that dimension 4 gives faster computational time than dimension 8 and 2.

Original languageEnglish
Title of host publicationProceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages106-112
Number of pages7
ISBN (Electronic)9781538691823
DOIs
Publication statusPublished - Dec 27 2018
Event6th International Symposium on Computing and Networking, CANDAR 2018 - Takayama, Japan
Duration: Nov 27 2018Nov 30 2018

Publication series

NameProceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018

Conference

Conference6th International Symposium on Computing and Networking, CANDAR 2018
CountryJapan
CityTakayama
Period11/27/1811/30/18

Keywords

  • GLV method
  • KSS-16 curve
  • pairing-based cryptography
  • scalar multiplication

ASJC Scopus subject areas

  • Hardware and Architecture
  • Computer Networks and Communications
  • Software
  • Safety, Risk, Reliability and Quality

Cite this

Khandaker, M. A. A., Nanjo, Y., Kusaka, T., & Nogami, Y. (2018). A Comparative Implementation of GLV Technique on KSS-16 Curve. In Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018 (pp. 106-112). [8594750] (Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CANDAR.2018.00021