On the suitable curves for elliptic and hyperelliptic curve cryptography

2010 Fiscal Year Final Research Report

• 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
• Keywords: 楕円曲線暗号 / 超楕円曲線暗号 / ペアリング暗号

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
  • 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] 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
• [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
  • Year and Date: 20090000
• [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
  • Year and Date: 20090000
• [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