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2001 Fiscal Year Final Research Report Summary

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
Project Period (FY) 1999 – 2001
Keywordscryptography / information security / hyperelliptic curve / public-key encryption / algorithm / cryptanalysis / elliptic curve / fast computation
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.

  • Research Products

    (10 results)

All Other

All Publications (10 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 2003-09-17  

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