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Research on public-key cryptosystems from hyperelliptic-curves

Research Project

Project/Area Number 11558033
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section展開研究
Research Field 計算機科学
Research InstitutionKyushu University

Principal Investigator

SAKURAI Kouichi  Kyushu Univ., Dept. Computer Science, Associate Prof., システム情報科学研究院, 助教授 (60264066)

Co-Investigator(Kenkyū-buntansha) ASAHIRO Yuichi  Kyushu Univ., Dept. Computer Science, Assistant, 大学院・システム情報科学研究院, 助手 (40304761)
SUZUKI Masakazu  Kyushu Univ., Dept. Mathematics, Prof., 大学院・数理学研究院, 教授 (20112302)
SHIZUYA Hiroki  TOHOKU Univ., Information Synergy Center, Prof., 情報シナジーセンター, 教授 (50196383)
SAKAI Yasuyuki  Mitsubishi Electronic Co., Information Systems Lab., Research Engineer, 情報総合研究所, 主任研究員
酒井 康之  三菱電機(株), 情報総合研究所, 主任研究員
Project Period (FY) 1999 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥6,200,000 (Direct Cost: ¥6,200,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2000: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1999: ¥2,900,000 (Direct Cost: ¥2,900,000)
Keywordscryptography / information security / hyperelliptic curve / public-key encryption / algorithm / cryptanalysis / elliptic curve / fast computation / モンゴメリー型 / 梗塞演算
Research Abstract

We have designed hyperelliptic curve cryptosystems with considering security and efficiency.
We have implemented our designed hyperelliptic curve cryptosystems both over software and over hardware, and confirm their practical performance.
We consider the performance of hyperelliptic curve cryptosystems over GF(p) vs. over GF(2^n).
We analyze the complexity of the group law of Jacobians and make comparison of their performance between over over GF(p) vs. over GF(2^n). with considering the effectiveness of the word size (32-bit or 64-bit) of the applied CPU (Alpha and Pentium) on the arithmetic on the definition field.
We also develop efficient algorithms for the jacobian of the hyperelliptic curve defined by the equation $y^2 = x^p-x+1$ over a finite field GF(p^n) of odd characteristic p. We first determine the zeta function of the curve which yields the order of the jacobian. And we investigate the Frobenius operator and use it to show that, for field extensions GF(p^n) of degree n prime to p, the jacobian has a cyclic group structure. We furthermore propose a method for faster scalar multiplication in the jacobian by using efficient operators other than the Frobenius that have smaller eigenvalues.

Report

(4 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (26 results)

All Other

All Publications (26 results)

  • [Publications] Yasuyuki SAKAI, Kouichi SAKURAI: "Efficient Scalar Multiplications on Elliptic Curves with Direct Computations of Several Doublings"Ieice Trans.. E84-A. 120-129 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Okeya, K., Sakurai, K.: "Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery-form elliptic curve"Proc. Workshop on Cryptographic Hardware and Embedded Systems 2001 (May 2001, Paris) Springer LNCS (2001).. Vol.2162. 126-141 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Masato YAMAMICHI, Masahiro MAMBO, Hiroki SHIZUYA: "On the Complexity of Constructing an Elliptic Curve of a Given Order"Ieice Trans.. E84-A. 140-145 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Fujimoto, M.Suzuki: "Construction of Affine Plane Curves With One Place at Infinity"Osaka J. Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 櫻井 幸一: "「楕円暗号の現状と課題」 数論アルゴリズムと楕円曲線暗号入門 第6刷付録"シュプリンガー東京. 10 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Yasuyuki SAKAI and Kouichi SAKURAI: "Efficient Scalar Multiplications on Elliptic Curves with Direct Computations of Several Doublings"Ieice Trans.. E84-A. 120-129 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Okeya,K. and Sakurai,K.: "Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery-form elliptic curve"Proc. Workshop on Cryptographic Hard ware and Embedded Systems 2001 (May 2001, Paris) Springer LNCS (2001). Vol. 2162. 126-141 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Masato YAMAMICHI, Masahiro MAMBO and Hiroki SHIZUYA: "On the Complexity of Constructing an Elliptic Curve of a Given Order"Ieice Trans.. E84-A. 140-145 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Fujimoto and M. Suzuki: "Construction of Affine Plane Curves With One Place at Infinity"Osaka J Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] SAKURAI Kouichi: ""The develpoment and issue on elliptic curve cryptosystems" in Appendix of 6th printing at Japanese translation of "a course in number-theory and crypography""Springer-Tokyo. 10 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Yasuyuki SAKAI, Kouichi SAKURAI: "Efficient Scalar Multiplications on Elliptic Curves with Direct Computations of Several Doublings"Ieice Trans.. E84-A・No.1. 120-129 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Okeya, K., Sakurai, K.: "Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery-form elliptic curve"Proc.Workshop on Cryptographic Hardware and Embedded Systems 2001 (May 2001, Paris) Springer LNCS (2001). (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Masato YAMAMICHI, Masahiro MAMBO, Hiroki SHIZUYA: "On the Complexity of Constructing an Elliptic Curve of a Given Order"Ieice Trans.. E84-A・No.1. 140-145 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Fujimoto, M.Suzuki: "Construction of Affine Plane Curves With One Place at Infinity"Osaka J.Math. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] 櫻井 幸一: "「楕円暗号の現状と課題」 数論アルゴリズムと楕円曲線暗号入門 第6刷付録"シュプリンガー東京. (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Okeya,Kurumatani,and Sakurai: "Elliptic Curves with the Montgomery-Form and Their Cryptographic Applications"Proc.International workshop on practice and theory in public-key cryptography. LNCS1751. 238-257 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Sakai and K.Sakurai: "On the Practical Performance of Hyperelliptic Curve Cryptosystems in Software Implementation"IEICE Transactions. E83-A,4. 692-703 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Sakai,Y.,and Sakurai,K.: "Efficient Scalar Multiplications on Elliptic Curves without Repeated Doublings and Their Practical Performance"Proc.Australasian Conference on Information Security and Privacy. LNCS1841. 59-73 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] YAMAMICHI,MAMBO,and SHIZUYA: "On the Complexity of Constructing an Elliptic Curve of a Given Order"IEICE Trans.Fundamentals. E84-A,1. 141-145 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] CHIDA,OHMORI,and SHIZUYA: "A Way of Making Trapdoor One-Way Functions Trapdoor No-Way"IEICE Trans.Fundamentals. E84-A,1. 151-156 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 酒井康行,櫻井幸一: "有限体F_<2^n>上の超楕円曲線暗号のソフトウエア実装"電子情報通信学会論文誌. J82-A,No.8. 1305-1306 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] I. Duursma and K. Sakurai: "Efficient algorithms for the Jacobian variety to hyperelliptic curves y^2=x^p -x +1 over a finite field of odd characteristic p"Coding Theory,Cryptography and related areas,Buchmann et al. edit.(Springer). (印刷中). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Sakai and K. Sakurai: "Over F_p vs.F_<2^n> over and on Pentium vs. Alpha in Software Implementation of Hyperelliptic Curve"PreProc, 1999 International Conference on Information Security and Cryptology December 9-10,1999 Korea University,Seoul,Korea. 67-86 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Tamura and K. Sakurai: "A Hardware-Oriented Algorithm for Computing in Jacobians and Its Implementation for Hyperelliptic Cryptosystems"PreProc. 1999 International Conference on Information Security and Cryptology December9-10,1999 Korea University,Seoul,Korea. 213-227 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 近江貴晴,静谷啓樹,西関隆夫: "離散対数暗号系に付随する言語の複雑さについて"電子情報通信学会論文誌(A). J82-A,No.3. 405-414 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 山道将人,満保雅浩,静谷啓樹: "与えれた位数の楕円曲線を構成する複雑さについて"電子情報通信学会技術研究報告(暗号と情報セキュリティ研究会). ISEC99-59. 51-58 (1999)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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