A study on Secure and Efficient Multivariate Public Key Cryptosystems

• Project/Area Number: 20700016
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Fundamental theory of informatics
• Research Institution: Osaka University of Economics and Law
• Principal Investigator: IWAMI Maki 大阪経済法科大学, 教養部, 准教授 (00422197)
• Project Period (FY): 2008 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥5,067,699 (Direct Cost: ¥3,898,230、Indirect Cost: ¥1,169,469); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥907,699 (Direct Cost: ¥698,230、Indirect Cost: ¥209,469); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 計算代数 / セキュリティ / 多変数 / 公開鍵暗号 / 数式処理 / 暗号 / アルゴリズム / 計算機代数 / 因数分解

Research Abstract

To construct secure and efficient multivariate public key cryptosystems (MPKC), this research has focused attention on the interactions between MPKC and Computer Algebra which cause the improvement of their algorithms and various types of MPKC. To suggest algorithm to attack, we have researched leading-edge study by interdisciplinary approach, investigating the possibility of application of computer algebra techniques, modified them to fit and verified the effectiveness by experiments.

Research Products

• [Journal Article] Computer Algebra Techniques in the Development of Public-Key Cryptosystems using Multivariate Polynomials (2013)
  • Author(s): Maki IWAMI
  • Journal Title: 大阪経済法科大学論集 Volume: Vol.105
  • NAID: 40020612844
• [Journal Article] Computer Algebra Techniques in the Development of Public-Key Cryptosystems using Multivariate Polynomials (2013)
  • Author(s): Maki Iwami
  • Journal Title: 大阪経済法科大学論集 Volume: 105
  • NAID: 40020612844
• [Journal Article] An improvement of Voloch's rational point attack on improved algebraic surface cryptosystem (2011)
  • Author(s): Maki IWAMI
  • Journal Title: 京都大学数理解析研究所講究録(RIMS Kokyuroku) Volume: Vol.1759 Pages: 105-114
  • URL: http://hdl.handle.net/2433/171329
• [Journal Article] Series solution and Cryptography (2009)
  • Author(s): Maki IWAMI
  • Journal Title: 数式処理(Bulletin of the Japan Society for Symbolic and Algebraic Computation) Volume: Vol.16, No.2 Pages: 127-130
  • NAID: 10026791983
  • URL: http://ci.nii.ac.jp/naid/10026791983
• [Journal Article] Applying expansion techniques of multivariate expansion base method and extended Hensel construction to cryptography (2009)
  • Author(s): Maki IWAMI
  • Journal Title: Abstracts of Papers Presented to the American Mathematical Society Volume: Vol.30, No.1 Pages: 152-153
  • Peer Reviewed
• [Journal Article] Series solution and Cryptography (2009)
  • Author(s): Maki IWAMI
  • Journal Title: 数式処理(Bulletin of the Japan Society for Symbolic and Algebraic Computation) Vol.16, No.2 Pages: 127-130
  • NAID: 10026791983
• [Journal Article] Applying expansion techniques of multivariate expansion base method and extended Hensel construction to cryptography (2009)
  • Author(s): Maki IWAMI
  • Journal Title: Abstracts of Papers Presented to the American Mathematical Society Vol.30, No.1, Issue 155 Pages: 152-153
  • Peer Reviewed
• [Journal Article] Series solution and Cryptography (2009)
  • Author(s): Maki Iwami
  • Journal Title: 数式処理(Journal of the Japan Society for Symbolic and Algebraic Computation) Vol.16, No.2 Pages: 127-130
  • NAID: 10026791983
• [Journal Article] 脆弱性のない代数曲面公開鍵暗号にむけて(Towards designing the invulnerable algebraic surface public-key cryptosystem) (2009)
  • Author(s): Maki Iwami
  • Journal Title: 京都大学数理解析研究所講究録(RIMS Kokyuroku) 1652 Pages: 162-172
• [Journal Article] Applying oxpansion techniques of multivariate expansion base method and extended Honsel construction to cryptography (2009)
  • Author(s): Maki Iwami
  • Journal Title: Abstracts of Papers Prosented to the Amorican Mathematical Society Vol.30, No.1, Issue 155 Pages: 152-153
  • Peer Reviewed
• [Journal Article] Breaking the Improved Akiyama-GotoAlgebraic Surface Public-keyCryptosystem (2008)
  • Author(s): Maki IWAMI
  • Journal Title: 数式処理(Journal of the Japan Society for Symbolic and Algebraic Computation) Volume: Vol.15, No.2 Pages: 124-127
  • URL: http://ci.nii.ac.jp/naid/10023902615
• [Journal Article] An Attack on Improved Algebraic Surface Public-key Cryptosystem (2008)
  • Author(s): Maki IWAMI
  • Journal Title: ACM Communications in Computer Algebra (Poster Abstracts ECCAD 2008) Volume: Vol.42, No.2 Pages: 71-74
• [Journal Article] Breaking the Improved Akiyama-Goto Algebraic Surface Public-key Cryptosystem (2008)
  • Author(s): Maki IWAMI
  • Journal Title: 数式処理(Journal of the Japan Society for Symbolic and Algebraic Computation) Vol.15, No.2 Pages: 124-127
  • NAID: 10023902615
• [Journal Article] An Attack on Improved Algebraic Surface Public-key Cryptosystem (2008)
  • Author(s): Maki IWAMI
  • Journal Title: ACM Communications in Computer Algebra (Poster Abstracts ECCAD 2008) Issue 164, Vol.42, No.2 Pages: 71-74
• [Journal Article] An Attack on Improved Algebraic Surface Public-key Cryptosystem (2008)
  • Author(s): Maki Iwami
  • Journal Title: ACM Communications in Computer Algebra (Poster Abstracts ECCAD 2008) Issue 164, Vol.42, No.2 Pages: 71-74
• [Journal Article] Breaking the Improved Akiyama-Goto Algebraic Surface Public-key Cryptosystem (2008)
  • Author(s): Maki Iwami
  • Journal Title: Bullotin of the Japan Society for Symbolic and Algebraic Computation Vol.15, No.2 Pages: 124-127
  • NAID: 10023902615
• [Journal Article] An improvement of Voloch's rational point attack on improved algebraic surface cryptosystem
  • Author(s): Maki IWAMI
  • Journal Title: 京都大学数理解析研究所講究録(RIMS Kokyuroku) 印刷中
• [Presentation] Computer Algebra Techniques in the Development of Public-Key Cryptosystems using Multivariate Polynomials (2013)
  • Author(s): Maki IWAMI
  • Organizer: Application of Fundamental Mathematics to Computer Science from Algebraic Perspective (大阪経済法科大学科学研究費採択課題合同研究会)
  • Place of Presentation: Osaka University of Economics and Law, Japan
  • Year and Date: 2013-03-29
• [Presentation] Computer Algebra Techniques in the Development of Public-Key Cryptosystems using Multivariate Polynomials (2013)
  • Author(s): 岩見真希
  • Organizer: Application of Fundamental Mathematics to Computer Science from Algebraic Perspective (大阪経済法科大学科学研究費採択課題合同研究会)
  • Place of Presentation: 大阪経済法科大学
• [Presentation] An improvement of Voloch's rational point attack on improved algebraicsurface cryptosystem (2010)
  • Author(s): Maki IWAMI
  • Organizer: RIMS Workshop on Developments in Computer Algebra Research
  • Place of Presentation: Research Institute for Mathematical Sciences, Kyoto University, Japan
  • Year and Date: 2010-07-09
• [Presentation] An improvement of Voloch's rational point attack on improved algebraic surface cryptosystem, RIMS Workshop on Developments in Computer Algebra Research (2010)
  • Author(s): Maki IWAMI
  • Organizer: Research Institute for Mathematical Sciences
  • Place of Presentation: Kyoto University, Kyoto, Japan
  • Year and Date: 2010-07-09
• [Presentation] Computer Algebra and Cryotography (2009)
  • Author(s): Maki IWAMI
  • Organizer: 稚内北星学園大学数学・数理科学談話会
  • Place of Presentation: Wakkanai Hokusei Gakuen University, Japan
  • Year and Date: 2009-09-04
• [Presentation] Computer Algebra and Cryotography (2009)
  • Author(s): Maki IWAMI
  • Organizer: 稚内北星学園大学 数学・数理科学談話会
  • Place of Presentation: Wakkanai Hokusei Gakuen University, Japan
  • Year and Date: 2009-09-04
• [Presentation] Computer Algebra and Cryotography (2009)
  • Author(s): Maki Iwami
  • Organizer: 稚内北星学園大学 数学・数理科学談話会
  • Place of Presentation: Wakkanai Hokusei Gakuen University
  • Year and Date: 2009-09-04
• [Presentation] Towards applications of computer algebra for attacking cryptosystems (2009)
  • Author(s): Maki IWAMI
  • Organizer: Combinatorics Summer school 2009
  • Place of Presentation: Wakkanai Hokusei Gakuen University, Japan
  • Year and Date: 2009-09-01
• [Presentation] Towards applications of computer algebra for attacking cryptosystems (2009)
  • Author(s): Maki Iwami
  • Organizer: Combinatorics Summer school 2009
  • Place of Presentation: Wakkanai Hokusei Gakuen University
  • Year and Date: 2009-09-01
• [Presentation] Series solution and Cryptography (2009)
  • Author(s): Maki IWAMI
  • Organizer: 18th Jssac meeting
  • Place of Presentation: Ryukoku University, Japan
  • Year and Date: 2009-06-12
• [Presentation] Series solution and Cryptography (2009)
  • Author(s): Maki Iwami
  • Organizer: 第18回 数式処理学会大会(18th Jssac meeting)
  • Place of Presentation: Ryukoku University, Japan
  • Year and Date: 2009-06-12
• [Presentation] Applying expansion techniques of multivariate expansion base method and extended Hensel construction to cryptography (2009)
  • Author(s): Maki IWAMI
  • Organizer: Joint Mathematics Meetings 2009, Meeting #1046
  • Place of Presentation: Washington, DC, U.S.A.
  • Year and Date: 2009-01-08
• [Presentation] Applying expansion techniques of multivariate expansion base method and extended Hensel construction to cryptography (2009)
  • Author(s): Maki Iwami
  • Organizer: Joint Mathematics Meetings 2009, Meeting #1046
  • Place of Presentation: Marriott Wardman Park, U.S.A.
  • Year and Date: 2009-01-08
• [Presentation] Surface Parametirizaion and Cryptography (poster presentation) (2009)
  • Author(s): Maki IWAMI
  • Organizer: The 11th International Workshop on Computer Algebra in Scientific Computing
  • Place of Presentation: Kobe University, Japan
• [Presentation] Surface Parametirizaion and Cryptography(poster presentation) (2009)
  • Author(s): Maki Iwami
  • Organizer: The 11th International Workshop on Computer Algebra in Scientific Computing
  • Place of Presentation: Kobe University, Japan
• [Presentation] Breaking the Improved Akiyama-Goto Algebraic Surface Public-key (2008)
  • Author(s): Maki IWAMI
  • Organizer: Cryptosystem 17th Jssac meeting
  • Place of Presentation: Josai University, Japan
  • Year and Date: 2008-06-07
• [Presentation] Breaking the Improved Akiyama-Goto Algebraic Surface Public-key Cryptosystem (2008)
  • Author(s): Maki IWAMI
  • Organizer: 17th Jssac meeting
  • Place of Presentation: Josai University, Japan
  • Year and Date: 2008-06-07
• [Presentation] Breaking the Improved Akiyama-Goto Algebraic Surface Public-key Cryptosystem (2008)
  • Author(s): Maki Iwami
  • Organizer: 第17回日本数式処理学会大会
  • Place of Presentation: 城西大学
  • Year and Date: 2008-06-07
• [Presentation] An Attack on Improved AlgebraicSurface Public-key Cryptosystem (2008)
  • Author(s): Maki IWAMI
  • Organizer: ECCAD (East Coast Computer AlgebraDay) 2008 (poster presentation)
  • Place of Presentation: Shepherd University, U.S.A.
  • Year and Date: 2008-05-10
• [Presentation] An Attack on Improved Algebraic Surface Public-key Cryptosystem (2008)
  • Author(s): Maki IWAMI
  • Organizer: ECCAD (East Coast Computer Algebra Day) 2008 (poster presentation)
  • Place of Presentation: Shepherd University, U.S.A.
  • Year and Date: 2008-05-10
• [Presentation] An Attack on Improved Algebraic Surface Public-key Cryptosystem (2008)
  • Author(s): Maki Iwami
  • Organizer: ECCAD (East Coast Computer Algebra Day) 2008
  • Place of Presentation: Shepherd. University,U.S.A.
  • Year and Date: 2008-05-10
• [Presentation] Breaking the Akiyama-Goto Algebraic Surface Public-key Cryptosystem and a Short Introduction to Multivariate Analytic Factorization, Symbolic Computation Seminar (2008)
  • Author(s): Maki IWAMI
  • Organizer: North Carolina State University, Mathematics Department
  • Place of Presentation: North Carolina State University, U.S.A.
  • Year and Date: 2008-05-07
• [Presentation] Breaking the Akiyama-Goto Algebraic Surface Public-key Cryptosystem and a Short Introduction to Multivariate Analytic Factorization (2008)
  • Author(s): Maki Iwami
  • Organizer: Symbolic Computation Seminar, North Carolina State University. Mathematics Department
  • Place of Presentation: North Carolina State University, U.S.A.
  • Year and Date: 2008-05-07
• [Remarks]
  • URL: http://researchmap.jp/read0104915/