A Construction Method of Final Exponentiation for a Specific Cyclotomic Family of Pairing-Friendly Elliptic Curves with Prime Embedding Degrees

Yuki Nanjo, Masaaki Shirase, Yuta Kodera, Takuya Kusaka, Yasuyuki Nogami

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

Abstract

Pairings on elliptic curves which are carried out by the Miller loop and final exponentiation are used for innovative protocols such as ID-based encryption and group signature authentication. As the recent progress of attacks for finite fields in which pairings are defined, the importance of the use of the curves with prime embedding degrees k has been increased. In this manuscript, the authors provide a method for providing efficient final exponentiation algorithms for a specific cyclotomic family of curves with arbitrary prime k of k\equiv 1(\text{mod}\ 6). Applying the proposed method for several curves such as k=7, 13, and 19, it is found that the proposed method gives rise to the same algorithms as the previous state-of-The-Art ones by the lattice-based method.

Original languageEnglish
Title of host publicationProceedings - 2021 9th International Symposium on Computing and Networking, CANDAR 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages148-154
Number of pages7
ISBN (Electronic)9781665442466
DOIs
Publication statusPublished - 2021
Event9th International Symposium on Computing and Networking, CANDAR 2021 - Virtual, Online, Japan
Duration: Nov 23 2021Nov 26 2021

Publication series

NameProceedings - 2021 9th International Symposium on Computing and Networking, CANDAR 2021

Conference

Conference9th International Symposium on Computing and Networking, CANDAR 2021
Country/TerritoryJapan
CityVirtual, Online
Period11/23/2111/26/21

Keywords

  • elliptic curve
  • final exponentiation
  • Pairing-based cryptography

ASJC Scopus subject areas

  • Computer Networks and Communications

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