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On the suitable curves for elliptic and hyperelliptic curve cryptography

Research Project

Project/Area Number 20500018
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionOsaka Prefecture University

Principal Investigator

TAKAHASHI Tetusya  Osaka Prefecture University, 総合教育研究機構, 教授 (20212011)

Co-Investigator(Kenkyū-buntansha) KAWAZOE Mitsuru  大阪府立大学, 総合教育研究機構, 准教授 (10295735)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords楕円曲線暗号 / 超楕円曲線暗号 / ペアリング暗号 / 楕円曲線暗 / 超楕円曲線亜
Research Abstract

We construct many paring-friendly genus 2 hyperelliptic curves of the form y^2=x^5+ ax, y^2=x^5+a and genus 4 hyperelliptic curves of the form y^2=x^9+ax by using the closed point counting formula of the Jacobian of these hyperelliptic curves.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (16 results)

All 2011 2010 2009 2008

All Journal Article (8 results) (of which Peer Reviewed: 5 results) Presentation (8 results)

  • [Journal Article] Construction of Pairing-Friendly Hyperelliptic Curves Based on the Closed Formulae of the Order of the Jacobian Group2010

    • Author(s)
      A.Comuta, M.Kawazoe, T. Takahashi, I.Yoshizawa
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E93.A No.6

      Pages: 1132-1139

    • NAID

      10026864775

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Construction of Pairing-Friendly Hyperelliptic Curves Based on the Closed Formulae of the Order of the Jacobian Group2010

    • Author(s)
      A.Comuta, M.Kawazoe, T.Takahashi, I.Yoshizawa
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E-93A, no.6 Pages: 1132-1139

    • NAID

      10026864775

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Construction of pairing-friendly hyperelliptic curves based on the closed formulae of the order of the Jacobian group,2010

    • Author(s)
      A.Comuta, M.Kawazoe, T.Takahashi, I.Yoshizawa
    • Journal Title

      IEICE Transactions E93-A

      Pages: 1132-1139

    • NAID

      10026864775

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pairing-friendly Hyperelliptic Curves of Type y^2 = x^5 + c2009

    • Author(s)
      A.Comuta, M.Kawazoe, T. Takahashi
    • Journal Title

      Proceedings of the 2009 Symposium on Cryptography and Information Security 3C4-3

    • Related Report
      2010 Final Research Report
  • [Journal Article] Pairing-friendly Hyperelliptic Curves of Type y^2 = x^9 + cx2009

    • Author(s)
      A.Comuta, M.Kawazoe, T. Takahashi, I.Yoshizawa
    • Journal Title

      Proceedings of the 2009 Symposium on Cryptography and Information Security 3C4-4

    • Related Report
      2010 Final Research Report
  • [Journal Article] Constructing New Differential Path and Algebraic Cryptanalysis for Full-SHA-12009

    • Author(s)
      M.Sugita, M.Kawazoe, H.Imai
    • Journal Title

      信学技報, 109-271

      Pages: 1-8

    • NAID

      110007504883

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Pairing-friendly hyperelliptic curves with ordinary Jacobians of type y^2=x^5 +ax2008

    • Author(s)
      M.Kawazoe, T. Takahashi
    • Journal Title

      Springer Lecture Notes in Computer Science 5209 "Pairing 2008"

      Pages: 164-177

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y^2= x^ 5+ ax2008

    • Author(s)
      M. Kawazoe, T. Takahashi
    • Journal Title

      Lecture Notes in Computer Science 5209

      Pages: 164-177

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Jacobian varieties over finite fields and their applications2011

    • Author(s)
      川添充
    • Organizer
      代数幾何学研究集会-ファノ多様体と正標数上の話題を中心として
    • Place of Presentation
      九州大学伊都キャパス
    • Year and Date
      2011-02-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Jacobian varieties over finite fields and their applications2010

    • Author(s)
      川添充
    • Organizer
      「非可換代数幾何学の大域的問題とその周辺」高知小研究集会
    • Place of Presentation
      高知大学理学部
    • Year and Date
      2010-12-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Constructing New Differential Paths and Implementing Algebraic Cryptanalysis for Full-SHA-1,2010

    • Author(s)
      M.Sugita, M.Kawazoe, H.Imai
    • Organizer
      2010暗号と情報セキュリティシンポジウム(SCIS2010)
    • Place of Presentation
      サンポートホール高松
    • Year and Date
      2010-01-20
    • Related Report
      2009 Annual Research Report
  • [Presentation] Pairing-friendly hyperelliptic curves of type $y^2=x^5+c$2009

    • Author(s)
      小牟田綾, 川添充, 高橋哲也
    • Organizer
      2009暗号と情報セキュリティシンポジウム(SCIS2009)
    • Place of Presentation
      大津プリンスホテル
    • Year and Date
      2009-01-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] Pairing-friendly hyperelli pt ic curves of type $y^2=x^9+cx2009

    • Author(s)
      小牟田綾, 川添充, 高橋哲也, 吉潭勇武
    • Organizer
      2009暗号と情報セキュリティシンポジウム(SCIS2009)
    • Place of Presentation
      大津プリンスホテル
    • Year and Date
      2009-01-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] Pairing-friendly Hyperelliptic Curves of Type y^2 = x^5 + c2009

    • Author(s)
      A.Comuta, M.Kawazoe, T. Takahashi
    • Organizer
      Symposium on Cryp tography and Information Security
    • Related Report
      2010 Final Research Report
  • [Presentation] Pairing-friendly Hyperelliptic Curves of Type y^2 = x^9 + cx2009

    • Author(s)
      A.Comuta, M.Kawazoe, T. Takahashi, I.Yoshizawa
    • Organizer
      Symposium on Cryptography and Information Security
    • Related Report
      2010 Final Research Report
  • [Presentation] Pairing-friendly hyperelliptic curveswith ordinary Jacobians of type$y^2=x^5+ax$2008

    • Author(s)
      M,Kawazoe, T.Takahashi
    • Organizer
      Pairing 2008
    • Place of Presentation
      Royal Holloway, University of London, Egham, UK.
    • Year and Date
      2008-09-02
    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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