Scaling security of elliptic curves with fast pairing using efficient endomorphisms

Katsuyuki Takashima*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


Cryptosystems using pairing computation on elliptic curves have various applications including ID-based encryption ([9], [29], [30] etc.). Scott [33] proposed a scaling method of security by a change of the embedding degree k. On the other hand, he also presented an efficient pairing computation method on an ordinary (non-supersingular) elliptic curve over a large prime field <Fopf>p ([34]). In this paper, we present an implementation method of the pairing computation with both of the security scaling in [33] and the efficiency in [34]. First, we will investigate the mathematical nature of the set of the paremeter r (the order of cyclic group used) so as to support many k's. Then, based on it, we will suggest some modification to the algorithm of Scott in [34] to achieve flexible scalability of security level.

Original languageEnglish
Pages (from-to)152-158
Number of pages7
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - 2007 Jan
Externally publishedYes


  • Elliptic curve cryptography
  • ID-based cryptography
  • Pairing

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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