Updated on 2022/05/26

写真a

 
ADACHI, Norio
 
Affiliation
Faculty of Science and Engineering
Job title
Professor Emeritus

Education

  •  
    -
    1970

    Tokyo Institute of Technology  

  •  
    -
    1970

    Tokyo Institute of Technology   Graduate School, Division of Natural Science  

  •  
    -
    1965

    Waseda University   School of Science and Engineering  

  •  
    -
    1965

    Waseda University   Faculty of Science and Engineering  

Degree

  • 理学博士

  • Tokyo Institute of Technology   (BLANK)

Research Experience

  • 1979
    -
     

    - 早稲田大学理工学部教授

  • 1974
    -
    1979

    Waseda University   School of Science and Engineering

  • 1972
    -
    1974

    Waseda University   School of Science and Engineering

  • 1970
    -
    1972

    助手(学習院大学)

Professional Memberships

  •  
     
     

    日本科学基礎論学会

  •  
     
     

    日本科学史学会

  •  
     
     

    日本数学会

 

Research Interests

  • 数学/数理哲学

  • mathematics/philosophy of mathematics

Books and Other Publications

  • 無限の果てに何があるか

    光文社知恵の森文庫  2002

  • 数 一体系と歴史

    朝倉書店  2002

  • 無限のパラドクス

    講談社  2000

  • 類体論講義

    日本評論社  1998

  • ガロア理論講義

    日本評論社  1996

  • フェルマーの大定理ー整数論の源流( 第3版)

    日本評論社  1996

  • フェルマーの大定理が解けた!

    講談社  1995

  • √2の不思議

    光文社カッパサイエンス  1994

  • 歴史から見た代数学

    放送大学教育振興会  1991

  • フェルマーを読む

    日本評論社  1986

  • 類体論へ至る道

    日本評論社  1979

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Misc

  • Solutions to security problems of Rivest and Shamir's PayWord scheme

    N Adachi, S Aoki, Y Komano, K Ohta

    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES   E88A ( 1 ) 195 - 202  2005.01

     View Summary

    The PayWord Scheme, invented by Rivest and Shamir, is an efficient micropayment scheme utilizing a hash function. We point out that the scheme has the following problem: a malicious customer can damage the bank by purchasing in excess of the customer's credit which the bank has guaranteed by issuing a certificate. Generally, there are two positions of the bank with regard to the certificate. Position 1: the bank takes full responsibility for the certificate and compensates all payments created by the customer's purchases; and Position 2: the bank does not redeem payments exceeding a limit set for the customer and shares the loss with the shop if trouble occurs. In the PayWord Scheme, the bank can reduce its risk by adopting Position 2 rather than Position 1. However, this paper points out that the bank can damage the shop in Position 2 by impersonating an imaginary customer and making the shop share the loss with the bank. We propose a micropayment scheme (countermeasure) that overcomes these problems.

    DOI CiNii

  • Elliptic Curves : From Fermat to Weil

    N.ADACHI

    Historia Scientiarum   9/1,27  1999

  • Elliptic Curves: From Fermat to Weil

    N.ADACHI

    Historia Scientiarum   Vol.9 ( 1 ) 1 - 23  1999

  • Elliptic Curves : From Fermat to Weil

    N.ADACHI

    Historia Scientiarum   9/1,27  1999

  • The Dawn of Mathematical Philosophy

    N.ADACHI

    Historia Scientiarum   Vol.5 ( 1 ) 1 - 23  1995

  • The Dawn of Mathematical Philosophy

    N.ADACHI

    Historia Scientiarum/The History of Science Society of Japan   96;5  1995

  • AN APPLICATION OF FREY IDEA TO EXPONENTIAL DIOPHANTINE EQUATIONS

    N ADACHI

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   70 ( 8 ) 261 - 263  1994.10

  • The diophantine equation formula present connected with fermat’s last theorem

    Norio Adachi

    Tokyo Journal of Mathematics   11 ( 1 ) 85 - 94  1988

    DOI

  • A VALUATIONAL INTERPRETATION OF KUMMER-THEORY OF IDEAL NUMBERS

    N ADACHI

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   61 ( 7 ) 235 - 238  1985

  • Generalization of Kummer's Criterion for Divisibility of Class Numbers

    N.ADACHI

    Journal of Number Theory   5 ( 4 ) 253 - 265  1973

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Works

  • 楕円曲線暗号

    2001
    -
     

  • Elliptic Cryptography

    2001
    -
     

Research Projects

  • 時間概念の発展史

  • 類体論の応用

  • ニュートンの『Principia(プリンキピア)』研究

  • 無限と時間の概念の発展史

  • Application of Class Field Theory

  • Study of Newton's Principia

  • Development of the concepts of infinity and time

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Specific Research

  • 数理科学の基礎研究

    1997   小松 啓一, 橋本 喜一朗, 尾崎 学, 加川 貴章

     View Summary

    代数的整数論分野 Greenberg予想に関しては、総実代数体の相対p-拡大に於いて基礎体のλp=μp=0が拡大体に“遺伝”するための必要条件を与えた。そして具体的に与えられた素数pに対して、λp=μp=0となる総実代数体のパラメータ付きの無限族を発見した。また、虚数乗法論の代数的整数論への応用に関しては、虚二次体のある種のアーベル拡大体上のZp-拡大が正規p整数基底を持つことを楕円曲線に対する虚数乗法論(志村理論)を用いて示すことに成功した。保型関数論分野 ある種のQ上のアーベル多様体に対してこの問題を解決し、その応用として代数体上のQ-curveと呼ばれる楕円曲線や、種数2の代数曲線で、ヤコビ多様体が四元数乗法をもつもの(QM-curve)について、谷山・志村予想を証明した。さらに、この結果を用いて1パラメータ付きのモジュラーQ-curveの無限族の具体的な構成も行なった。楕円曲線論分野 本年度は、24個の実二次体に対し、その上で至るところgood reduction を持つ楕円曲線の非存在を示し、8個の実二次体に対しては、その上で至る所good reduction を持つ楕円曲線を全て決定した。決定された8個の実二次体にはQ(√37)が含まれるが、その決定の過程で、4x4-37y2=-1(x, y∈Z)を解く必要が生じたが、それを含むより一般的な問題も解決した。研究成果の発表M. Ozaki, On the cyclotomic unit group and the ideal class group of a real abelian number field, Journal of Number Theory, vol. 64, 1997, pp. 211-222.M. Ozaki, On the cyclotomic unit group and the ideal class group of a real abelian number field II, Journal of Number Theory, vol. 64, 1997, pp.223-232.M. Ozaki, Kummer's lemma for Zp-extensions over totally real number fields, Acta Arith., vol. 81, 1997, pp.37-44.M. Ozaki, The class group of Zp-extensions over totally real number fields, TÔ hoku Math. Journal, vol. 49, 1997, pp.431-435.M. Ozaki, On the cyclotomic unit group and the p-ideal class group, Tokyo Journal of Math., vol. 20, 1997, pp. 475-480.T. Fukuda, K. Komatsu, M. Ozaki and H. Taya, On Iwasawa λp-invariants of relative real cyclic extensions of degree p, Tokyo Jounal of Math., vol. 20, 1997, pp. 475-480M. Ozaki and H. Taya, On the Iwasaki λ2-invariant of certain families of real quadratic fields, Manuscripta Math., vol. 94, 1997, pp. 437-444.M. Kida and T. Kagawa, Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields, J. Number Theory, vol. 66, 1997, pp.201-210.T. Kagawa, Determination of elliptic curves with everywhere good reduction over Q(√37), Acta Arith., vol. 83, 1998, pp. 253-269.T. Hibino and N. Murabayashi, Modular equations of hyperelliptic X0(N) and an application, Acta Arith., vol. 82, 1997, pp.279-291.T. Hibino and A. Umegaki, Families of elliptic Q-curves defined over number fields with large degrees, Proc. Japan Acad., vol. 74, Ser. A, No 1, 1998, pp. 20-24.G. Yamamoto, On the vanishing of Iwasawa in variants of certain (p, p)-extensions of Q, Proc. Japan Acad., vol. 73, Ser. A, No 3, 1997, pp. 45-47.T. Ito, A construction of normal bases over the Hilbert p-class field of imaginary quadratic field, Proc. Japan Acad., vol. 74, Ser. A, No 1, 1998, pp.25-28.K. Hashimoto, Q-curve of degree 5 and jacobian surfaces of GL2-type, 理工総研Technical Report No. 97-8.K. Hashimoto and Ko. Miyake, Inverse Galois Problem for Dihedral Groups, 理工総研 Technical Report No. 98-4.