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 1 2016

Fingerprint

Cryptography
Field programmable gate arrays (FPGA)
Torsional stress
Hardware

Keywords

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

ASJC Scopus subject areas

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

Cite this

FPGA implementation of various elliptic curve pairings over odd characteristic field with non supersingular curves. / Nogami, Yasuyuki; Kagotani, Hiroto; Iokibe, Kengo; Miyatake, Hiroyuki; Narita, Takashi.

In: IEICE Transactions on Information and Systems, Vol. E99D, No. 4, 01.04.2016, p. 805-815.

Research output: Contribution to journalArticle

@article{44ee411a74944295a6ab4fc7af66a390,
title = "FPGA implementation of various elliptic curve pairings over odd characteristic field with non supersingular curves",
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.",
keywords = "Elliptic curve cryptography, FPGA implementation, Odd characteristic, Pairing-based cryptography",
author = "Yasuyuki Nogami and Hiroto Kagotani and Kengo Iokibe and Hiroyuki Miyatake and Takashi Narita",
year = "2016",
month = "4",
day = "1",
doi = "10.1587/transinf.2015ICP0018",
language = "English",
volume = "E99D",
pages = "805--815",
journal = "IEICE Transactions on Information and Systems",
issn = "0916-8532",
publisher = "Maruzen Co., Ltd/Maruzen Kabushikikaisha",
number = "4",

}

TY - JOUR

T1 - FPGA implementation of various elliptic curve pairings over odd characteristic field with non supersingular curves

AU - Nogami, Yasuyuki

AU - Kagotani, Hiroto

AU - Iokibe, Kengo

AU - Miyatake, Hiroyuki

AU - Narita, Takashi

PY - 2016/4/1

Y1 - 2016/4/1

N2 - 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.

AB - 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.

KW - Elliptic curve cryptography

KW - FPGA implementation

KW - Odd characteristic

KW - Pairing-based cryptography

UR - http://www.scopus.com/inward/record.url?scp=84962821839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962821839&partnerID=8YFLogxK

U2 - 10.1587/transinf.2015ICP0018

DO - 10.1587/transinf.2015ICP0018

M3 - Article

AN - SCOPUS:84962821839

VL - E99D

SP - 805

EP - 815

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

SN - 0916-8532

IS - 4

ER -