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1998 Fiscal Year Final Research Report Summary

Research on secure cryptosystems based on elliptic curves

Research Project

Project/Area Number 09650424
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 情報通信工学
Research InstitutionCHUO UNIVERSITY

Principal Investigator

CHAO Jinhu  Factulty of Science and Engineering Chuo University Professor, 理工学部, 教授 (60227345)

Co-Investigator(Kenkyū-buntansha) MOMOSE Fumiyuki  Factulty of Science and Engineering Chuo University Professor, 理工学部, 教授 (80182187)
TSUJII Shigeo  Factulty of Science and Engineering Chuo University Professor, 理工学部, 教授 (50020350)
Project Period (FY) 1997 – 1998
KeywordsInformation security / Cryptosystems / Public key cryptosystems / Elliptic cryptosystems / Discrete logarithm problem / Finite fields
Research Abstract

Elliptic curves over finite fields have been used in recent public key clyptosysterns and authentication. The discrete logarithm problems over the elliptic curves can resist all known subexponential attacks which then can implement cryptographic schemes in higher speed and less key sizes while retain the same security comparing with traditional cryptographic functions. In this research, we propose efficient algorithms to construct secure elliptic arid hyperelliptic cryptosysterns.
The point-counting algorithms to construct explicitly secure elliptic curves for cryptosystems can find secure curves over finite fields from randomly selected elliptic curves, but are quite time consuming especially when one wishes to choose different curves for different users or periodically change curves over finite fields in the same cryptosystem, Elliptic curves over number fields with CM can be used to design non-isogenous elliptic cryptosystems over finite fields efficiently. The existing algorithm to build such CM curves, costing exponential time of computations OMICRON(2^<5h/2>h^<21/4>) where h is the class number of the endomorphism ring of the CM curve. Thus it carl only be used to construct CM elliptic curves with small class numbers.
We propose polynomial time algorithms in h to build CM elliptic curves over number fields : by lifting the ring class equations from small finite fields thus constructing CM curves. Its complexity is shown as in a polynomial time in h, i.e., . OMICRON(h^7). Furthermore, these algorithms are also extented to hyperelliptic cryptosystems, for which no efficient algorithm is known until now for construction of secure hyperelliptic curves. We propose efficient algorithms to construct secure discrete logarithm problems over hyperelliptic curves based on Weil elements. The lifting approach to build CM curves is also generalized to Jacobian varieties of algebraic curves of higher genera.

  • Research Products

    (34 results)

All Other

All Publications (34 results)

  • [Publications] J.Chao, N.Matsuda, S.Tsujii: "Efficient construction of secure hyperelliptic discrete logarithm problems" Springer, LNCS, Information and Communication Seculity. 1334. 292-301 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J.Chao, O.Nakamura, K.Sobataka, S.Tsujii: "Construction of secure elliptic cryptosystems using CM feste and Liftings" Springer, LNCS, Advances in Cryptology-ASIACRTPTO'98. 1514. 95-109 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 佐藤, 松田, 趙, 辻井: "素体上における大種数超楕円曲線の構成方法の考察" 電子情報通信学会1997年暗号と情報セキュリティシンポジウム. 12C. 1-8 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 松尾, 趙, 辻井: "拡大体上のアーベル多様体に基づく暗号系の構成法" 電子情報通信学会1997年暗号と情報セキュリティシンポジウム. 12D. 1-8 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 中村, 松田, 趙, 辻井: "CMP-ベル多様体に基づく暗号系に関する考察" 電子情報通信学会1997年暗号と情報セキュリティシンポジウム. 12E. 1-9 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 黒谷, 趙, 辻井: "アーベル多様体上の離散対数問題に基づく暗号系の安全性に関する考察" 電子情報通信学会1997年暗号と情報セキュリティシンポジウム. 12F. 1-6 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 佐藤, 松田, 趙, 辻井: "素体上における大種数超楕円曲線の構成方法の考察" 電子情報通信学会 信学技報 ISEC研究会. 96-80. 165-170 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 中村, 松田, 趙, 辻井: "CMを有するアーベル多様体を用いた暗号系に関する考察" 電子情報通信学会 信学技報 ISEC研究会. 96-81. 171-176 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 松尾, 趙, 辻井: "拡大体上のアーベル多様体に基づく暗号系の構成法" 電子情報通信学会 信学技報 ISEC研究会. 97-30. 9-18 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 川白, 中村, 趙, 百瀬, 辻井: "RMファミリを用いた安全な超楕円曲線の効率的な構成法" 電子情報通信学会1998年暗号と情報セュリティシンポジウム. 4、1、A. 1-8 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 側高, 中村, 趙, 百瀬, 辻井: "CMテストとLiftingによる安全な楕円曲線の構成法に関する考察" 電子情報通信学会1998年暗号と情報セキュリティシンポジウム. 4、1、B. 1-7 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 側高, 中村, 趙, 辻井: "CMテストとリフティングによる安全な楕円暗号系の構成法に関する考察" 電子情報通信学会 信学技報 ISEC研究会. 97-71. 35-42 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 川白, 中村, 趙, 百瀬, 辻井: "RMファミリを用いた安全な超楕円曲線の効率的な構成法" 電子情報通信学会 信学技報 ISEC研究会. 97-72. 43-49 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Nakamizo, K.Sobataka, J.Chao, S, Tsujii: "Construction of elliptic cryptosystems using super sirgular liftings" Proceedings of SCIS'99. W3-1-1. 1-4 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Hosoya, K.Sobataka, J.Chao, S.Tsujii: "Construction of elliptic cryptosystems using ordinary liftings" Proceedings of SCIS'99. W3-1-2. 1-4 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Matsuo, J.Chao, S.Tsujii: "On lifting of CM hyperelliptic curves" Proceedings of SCIS'99. W3-1-4. 1-5 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K. Kamio, H.Kawasiro, J.Chao, S. Tsujii: "A fast algorithm of model lifting fa CM hyperelliptic carves" Proceedings of SCIS'99. W3-1-6. 1-4 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J.Chao, N.Matsuda, S.Tsujii: ""Efficient construction of se-cure hyperelliptic discrete logarithm problems"" Y.Han, T.Okamoto, S.Qing (Eds.) Information and Communication Secu-rity, LNCS,1334, Springer, pp.292-301, Beijing, China, November. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J.Chao, O.Nakamura, K.Sobataka, S.Tsujii: ""Construction of secure elliptic cryptosystems using CM tests and liftings"" K.Ohta, D.Pei (Eds.) Advances in Cryptology-ASIACRYPTO'98, LNCS,1514, Springer, pp.95-109, Beijing, China, October. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J.Sato, N.Matsuda, J.Chao, S.Tsujii: "Efficient construc-tion of secure hyperelliptic discrete logarithm problems of large genera" Proceedings of SCIS'97. 12C. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Matsuo, J.Chao, S.Tsujii: "Design of cryptosystems based on abelian varieties over extension fields" Proceedings of SCIS'97. 12D. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] O.Nakamura, N.Matsuda, J.Chao, S.Tsujii: ""Cryptosys-tems based on CM abelian variety"" Proceedings of SCIS'97. 12E. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kurotani, J.Chao, S.Tsujii: "A Consideration on secu-rity of cryptosystems based on discrete logarithm problems over abelian varieties" Proceedings of SCIS'97. 12F. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J.Sato, N.Matsuda, J.Chao, S.Tsujii: "Efficient construc-tion of secure hyperelliptic discrete logarithm problems of large genera" IEICE,Tech.Rep. ISEC96-80. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] O.Nakamura, N.Matsuda, J.Chao, S.Tsujii: "Cryptosys-tems based on CM abelian variety" IEICE,Tech.Rep.ISEC96-81. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Matsuo, J.Chao, S.Tsujii: "Design of cryptosystems based on abelian varieties over extension fields" IEICE,Tech.Rep. ISEC97-30. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kawasiro, O.Nakamura, J.Chao, F.Momose, S.Tsujii: "Construction of CM hyperelliptic curves using RM familiy/" Proceedings of SCIS'98. 4.1.A. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Sobataka, O.Nakamura, J.Chao, F.Momose, S.Tsujii: "Construction of elliptic curves using CM tests and lift-ing" Proceedings of SCIS'98. 4.1.B. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Sobataka, O.Nakamura, J.Chao, S.Tsujii: "Construction of secure elliptic cryptosystems using CM tests and Lifting" IEICE,Tech.Rep.ISEC98-71. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kawasiro, O.Nakamura, J.Chao, F.Momose, S.Tsujii: "Construction of CM hyperelliptic curves using RM familiy" IEICE,Tech.Rep.ISEC98-72. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Nakamizo, K.Sobataka, J.Chao, S.Tsujii: "Construction of elliptic cryptosystems using supersingular lifting" Proceedings of SCIS'99. W3-1-1. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Momose, K.Sobataka, J.Chao, S.Tsujii: "Construction of elliptic cryptosystems using ordinary lifting" Proceedings of SCIS'99. W3-1-2. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Matsuo, J.Chao, S.Tsujii: "On lifting of CM hypere llip-tic curves" Proceedings of SCIS'99. W3-1-4. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kamio, H.Kawasiro, J.Chao, S.Tsujii: "A fast algorism of model lifting for CM hyperelliptic curves" Proceedings of SCIS'99. W3-1-6. (1999)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1999-12-08  

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