FPGA implementation of various elliptic curve pairings over odd characteristic field with non supersingular curves

Yasuyuki Nogami, Hiroto Kagotani, Kengo Iokibe, Hiroyuki Miyatake, Takashi Narita

Research output: Contribution to journalArticle

Abstract

Pairing-based cryptography has realized a lot of innovative cryptographic applications such as attribute-based cryptography and semi homomorphic encryption. Pairing is a bilinear map constructed on a torsion group structure that is defined on a special class of elliptic curves, namely pairing-friendly curve. Pairing-friendly curves are roughly classified into supersingular and non supersingular curves. In these years, non supersingular pairing-friendly curves have been focused on from a security reason. Although non supersingular pairing-friendly curves have an ability to bridge various security levels with various parameter settings, most of software and hardware implementations tightly restrict them to achieve calculation efficiencies and avoid implementation difficulties. This paper shows an FPGA implementation that supports various parameter settings of pairings on non supersingular pairing-friendly curves for which Montgomery reduction, cyclic vector multiplication algorithm, projective coordinates, and Tate pairing have been combinatorially applied. Then, some experimental results with resource usages are shown.

Original languageEnglish
Pages (from-to)805-815
Number of pages11
JournalIEICE Transactions on Information and Systems
VolumeE99D
Issue number4
DOIs
Publication statusPublished - Apr 2016

Keywords

  • Elliptic curve cryptography
  • FPGA implementation
  • Odd characteristic
  • Pairing-based cryptography

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence

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