On the suitable curves for elliptic and hyperelliptic curve cryptography

• Project/Area Number: 20500018
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Osaka 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: ¥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.

Research Products

• [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 on Fundamentals of Electronics, Communications and Computer Sciences E93.A No.6 Pages: 1132-1139
  • NAID: 10026864775
  • 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 on Fundamentals of Electronics, Communications and Computer Sciences Volume: E-93A, no.6 Pages: 1132-1139
  • NAID: 10026864775
  • 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
  • Peer Reviewed
• [Journal Article] Pairing-friendly Hyperelliptic Curves of Type y^2 = x^5 + c (2009)
  • Author(s): A.Comuta, M.Kawazoe, T. Takahashi
  • Journal Title: Proceedings of the 2009 Symposium on Cryptography and Information Security 3C4-3
• [Journal Article] Pairing-friendly Hyperelliptic Curves of Type y^2 = x^9 + cx (2009)
  • Author(s): A.Comuta, M.Kawazoe, T. Takahashi, I.Yoshizawa
  • Journal Title: Proceedings of the 2009 Symposium on Cryptography and Information Security 3C4-4
• [Journal Article] Constructing New Differential Path and Algebraic Cryptanalysis for Full-SHA-1 (2009)
  • Author(s): M.Sugita, M.Kawazoe, H.Imai
  • Journal Title: 信学技報, 109-271 Pages: 1-8
  • NAID: 110007504883
• [Journal Article] Pairing-friendly hyperelliptic curves with ordinary Jacobians of type y^2=x^5 +ax (2008)
  • Author(s): M.Kawazoe, T. Takahashi
  • Journal Title: Springer Lecture Notes in Computer Science 5209 "Pairing 2008" Pages: 164-177
  • Peer Reviewed
• [Journal Article] Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y^2= x^ 5+ ax (2008)
  • Author(s): M. Kawazoe, T. Takahashi
  • Journal Title: Lecture Notes in Computer Science 5209 Pages: 164-177
  • Peer Reviewed
• [Presentation] Jacobian varieties over finite fields and their applications (2011)
  • 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
• [Presentation] Jacobian varieties over finite fields and their applications (2010)
  • 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
• [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
• [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
• [Presentation] Pairing-friendly hyperelli pt ic curves of type $y^2=x^9+cx (2009)
  • Author(s): 小牟田綾, 川添充, 高橋哲也, 吉潭勇武
  • Organizer: 2009暗号と情報セキュリティシンポジウム(SCIS2009)
  • Place of Presentation: 大津プリンスホテル
  • Year and Date: 2009-01-22
• [Presentation] Pairing-friendly Hyperelliptic Curves of Type y^2 = x^5 + c (2009)
  • Author(s): A.Comuta, M.Kawazoe, T. Takahashi
  • Organizer: Symposium on Cryp tography and Information Security
• [Presentation] Pairing-friendly Hyperelliptic Curves of Type y^2 = x^9 + cx (2009)
  • Author(s): A.Comuta, M.Kawazoe, T. Takahashi, I.Yoshizawa
  • Organizer: Symposium on Cryptography and Information Security
• [Presentation] Pairing-friendly hyperelliptic curveswith ordinary Jacobians of type$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