A comparative study of twist property in KSS curves of embedding degree 16 and 18 from the implementation perspective

Md Al Amin Khandaker, Taehwan Park, Yasuyuki Nogami, Howon Kim

Research output: Contribution to journalArticle

Abstract

Implementation of faster pairing calculation is the basis of efficient pairing-based cryptographic protocol implementation. Generally, pairing is a costly operation carried out over the extension field of degree k ≥ 12. But the twist property of the pairing friendly curve allows us to calculate pairing over the sub-field twisted curve, where the extension degree becomes k/d and twist degree d = 2, 3, 4, 6. The calculation cost is reduced substantially by twisting but it makes the discrete logarithm problem easier if the curve parameters are not carefully chosen. Therefore, this paper considers the most recent parameters setting presented by Barbulescu and Duquesne [1] for pairing-based cryptography; that are secure enough for 128- bit security level; to explicitly show the quartic twist (d = 6) and sextic twist (d = 4) mapping between the isomorphic rational point groups for KSS (Kachisa-Schaefer-Scott) curve of embedding degree k = 16 and k = 18, receptively. This paper also evaluates the performance enhancement of the obtained twisted mapping by comparing the elliptic curve scalar multiplications.

Original languageEnglish
Pages (from-to)97-103
Number of pages7
JournalJournal of Information and Communication Convergence Engineering
Volume15
Issue number2
DOIs
Publication statusPublished - Jun 1 2017

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Point groups
Cryptography
Costs

Keywords

  • Isomorphic mapping
  • KSS curve
  • Pairing-based cryptography
  • Quartic twist
  • Sextic twist

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Media Technology
  • Electrical and Electronic Engineering

Cite this

A comparative study of twist property in KSS curves of embedding degree 16 and 18 from the implementation perspective. / Khandaker, Md Al Amin; Park, Taehwan; Nogami, Yasuyuki; Kim, Howon.

In: Journal of Information and Communication Convergence Engineering, Vol. 15, No. 2, 01.06.2017, p. 97-103.

Research output: Contribution to journalArticle

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