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2009 Fiscal Year Final Research Report

On security of pairing based elliptic curve cryptosystems in view of number theory

Research Project

  • PDF
Project/Area Number 18340005
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Institute of Technology

Principal Investigator

SATOH Takakazu  Tokyo Institute of Technology, 大学院・理工学研究科, 准教授 (70215797)

Co-Investigator(Renkei-kenkyūsha) KUROKAWA Nobushige  東京工業大学, 大学院・理工学研究科, 教授 (70114866)
KAWACHI Takeshi  東京工業大学, 大学院・理工学研究科, 助教 (30323778)
TAGUCHI Yuichiro  九州大学, 数理学研究院, 准教授 (90231399)
Project Period (FY) 2006 – 2009
Keywordsペアリング / 楕円曲線暗号 / 離散対数問題
Research Abstract

A pairing inversion formula is considered to be a possible pairing based elliptic curve cryptography specific cryptanalysis. In this research, we gave explicit formulae for the Weil pairing inversion. The result is a dense rational formula and therefore pairing based cryptosystems are not vulnerable to evaluation of the explicit formula. We also constructed pairing friendly hyperelliptic curves from certain pairing non-friendly elliptic curves.

  • Research Products

    (31 results)

All 2010 2009 2008 2007 2006

All Journal Article (12 results) (of which Peer Reviewed: 12 results) Presentation (19 results)

  • [Journal Article] Flat modules and Gr¨obner bases over truncated discrete valuation rings2010

    • Author(s)
      T. Hiranouchi, Y. Taguchi
    • Journal Title

      Interdisciplinary Information Sciences 16

      Pages: 33-37

    • Peer Reviewed
  • [Journal Article] Generating Genus Two Hyperelliptic Curves over Large Characteristic Finite Fields2009

    • Author(s)
      T. Satoh
    • Journal Title

      Advances in Cryptology-Eurocrypt 2009, Lect. Notes in Comput. Sci. 5479

      Pages: 536-553

    • Peer Reviewed
  • [Journal Article] Automorphy of the principal Eisenstein series of weight 1: an application of the double sine function2009

    • Author(s)
      N. Kurokawa
    • Journal Title

      Kodai Math. J. 32

      Pages: 391-403

    • Peer Reviewed
  • [Journal Article] A multivariable Euler product of Igusa type and its applications2009

    • Author(s)
      N. Kurokawa, H. Ochiai
    • Journal Title

      J. Number Theory 129

      Pages: 1919-1930

    • Peer Reviewed
  • [Journal Article] More discriminants with the Brezing-Weng method, Progress in cryptology-INDOCRYPT 20082008

    • Author(s)
      G. Bisson, T. Satoh
    • Journal Title

      Lect. Notes in Comput. Sci. 5365

      Pages: 389-399

    • Peer Reviewed
  • [Journal Article] Euclid prime sequences over unique factorization domains2008

    • Author(s)
      N. Kurokawa, T. Satoh
    • Journal Title

      17

      Pages: 145-152

    • Peer Reviewed
  • [Journal Article] Closed formulae for the Weil pairing inversion2008

    • Author(s)
      T. Satoh
    • Journal Title

      Finite fields and their appl. 14

      Pages: 743-765

    • Peer Reviewed
  • [Journal Article] Limit values of Eisenstein series and multiple cotangent functions2008

    • Author(s)
      N. Kurokawa
    • Journal Title

      J. Number Theory 128

      Pages: 1775-1783

    • Peer Reviewed
  • [Journal Article] Multiple Eisenstein series and multiple cotangent functions2008

    • Author(s)
      S. Koyama, N. Kurokawa
    • Journal Title

      J. Number Theory 128

      Pages: 1769-1774

    • Peer Reviewed
  • [Journal Article] Extensions of truncated discrete valuation rings2008

    • Author(s)
      T. Hiranouchi, Y. Taguchi
    • Journal Title

      Pure and Applied Mathematics Quarterly 4

      Pages: 1205-1214

    • Peer Reviewed
  • [Journal Article] On the finiteness and non-existence of certain mod 2 Galois representations of quadratic fields2008

    • Author(s)
      H. Moon, Y. Taguchi
    • Journal Title

      Kyungpook Math. J. 48

      Pages: 323-330

    • Peer Reviewed
  • [Journal Article] The nonexistence of certain mod 2 Galois representations of some small quadratic fields2008

    • Author(s)
      H. Moon, Y. Taguchi
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci. 84

      Pages: 63-67

    • Peer Reviewed
  • [Presentation] Explicit formulae for certain primitive varieties associated to elliptic curves2009

    • Author(s)
      T. Satoh
    • Organizer
      2009 KMS-AMS joint meeting
    • Place of Presentation
      Seoul
    • Year and Date
      2009-12-19
  • [Presentation] Absolute zeta functions, absolute Riemann hypothesis and absolute Casimir energies2009

    • Author(s)
      N. Kurokawa
    • Organizer
      Casimir force, Casimir operators and Riemann hypothesis
    • Place of Presentation
      Fukuoka, Japan
    • Year and Date
      2009-11-13
  • [Presentation] Generating genus two hyperelliptic curves over large characteristic finite fields2009

    • Author(s)
      T. Satoh
    • Organizer
      13th Workshop on elliptic curve cryptography
    • Place of Presentation
      Calgary, Canada
    • Year and Date
      2009-08-26
  • [Presentation] Simple but not absolutely simple Jacobians in cryptography2009

    • Author(s)
      T. Satoh
    • Organizer
      1st PRIMA congress
    • Place of Presentation
      Sydney, Australia
    • Year and Date
      2009-07-08
  • [Presentation] Extensions of truncated discrete valuation rings, Modular Forms and Function Field Arithmetic2009

    • Author(s)
      Y. Taguchi
    • Organizer
      a conference in honor of Jing Yu's 60th birthday
    • Place of Presentation
      National Taiwan University, Taiwan
    • Year and Date
      2009-05-20
  • [Presentation] Generating genus two hyperelliptic curves over large characteristic finite fields2009

    • Author(s)
      T. Satoh
    • Organizer
      Eurocrypt 2009
    • Place of Presentation
      Cologne, Germany
    • Year and Date
      2009-04-30
  • [Presentation] Absolute modular forms2009

    • Author(s)
      N. Kurokawa
    • Organizer
      Non commutative geometry and geometry over the field with one element
    • Place of Presentation
      Baltimore, U.S.A.
    • Year and Date
      2009-03-26
  • [Presentation] Zeta functions over F12009

    • Author(s)
      N. Kurokawa
    • Organizer
      ibid
    • Place of Presentation
      Baltimore, U.S.A.
    • Year and Date
      2009-03-24
  • [Presentation] 超楕円暗号に適したある種の種数2の超楕円曲線の生成法2009

    • Author(s)
      佐藤孝和
    • Organizer
      2009暗号と情報セキュリティーシンポジウム
    • Place of Presentation
      大津
    • Year and Date
      2009-01-23
  • [Presentation] Extensions of truncated discrete valuation rings (joint work with Toshiro Hiranouchi) Pan Asian Number Theory Conference2009

    • Author(s)
      Y. Taguchi
    • Place of Presentation
      Pohang, Korea
    • Year and Date
      2009-01-10
  • [Presentation] Groebner bases over truncated discrete valuation rings2009

    • Author(s)
      Y. Taguchi
    • Organizer
      1st POSTECH-Kyushu U. Joint Workshop
    • Place of Presentation
      Pohang, Korea.
    • Year and Date
      2009-01-06
  • [Presentation] 頂切離散付値環のガロア理論(平之内俊郎氏との共同研究)2008

    • Author(s)
      田口雄一郎
    • Organizer
      ガロア理論とその周辺
    • Place of Presentation
      徳島、日本
    • Year and Date
      2008-09-10
  • [Presentation] Inversion Problems on the Weil pairing2008

    • Author(s)
      T. Satoh
    • Organizer
      Intensive Lectures in Mathmatical Problems in cryptography
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      2008-01-28
  • [Presentation] The non-existence of certain mod 2 Galois representations of some small quadratic fields2008

    • Author(s)
      Y. Taguchi
    • Organizer
      East Asia Number Theory Conference
    • Place of Presentation
      Daejeon, Korea.
    • Year and Date
      2008-01-21
  • [Presentation] On Pairing Inversion Problems2007

    • Author(s)
      T. Satoh
    • Organizer
      Pairing conference
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2007-07-04
  • [Presentation] Moduli of Galois representations and their applications2007

    • Author(s)
      Y. Taguchi
    • Organizer
      Padic method and its applications in arithmetic geometry 2007
    • Place of Presentation
      Tokyo, Japan.
    • Year and Date
      2007-06-12
  • [Presentation] Problems on q-Specht modules2007

    • Author(s)
      Y. Taguchi
    • Organizer
      he 19th PNU-POSTECH Algebraic Combinatorics Seminar
    • Place of Presentation
      Pohang, Korea.
    • Year and Date
      2007-06-02
  • [Presentation] On Euclid prime sequences (joint work with Nobushige Kurokawa)2006

    • Author(s)
      T. Satoh
    • Organizer
      Workshop on computational challenges arising in algorithmic number theory and cryptography
    • Place of Presentation
      Canada, Toronto
    • Year and Date
      2006-11-03
  • [Presentation] On extensions of truncated discrete valuation rings2006

    • Author(s)
      Y. Taguchi
    • Organizer
      joint work with T. Hiranouchi
    • Place of Presentation
      Number Theory Seminar, Seoul, Korea.
    • Year and Date
      2006-09-27

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Published: 2011-06-18   Modified: 2016-04-21  

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