Cryptography and Class Groups

• Surveys
  • A Survey on IQ Cryptography (Buchmann, Hamsdy, 2000)
• Class group papers
  • Computing Discrete Logarithms in Quadratic Fields (Jacobson, 2000)
  • Security of Crytosystems Based on Class Groups of Imaginary Quadratic Orders (S. Hamdy, B. Möller, Asiacrypt 2000)
  • Towards practical non-interactive public-key cryptosystems using non-maximal imaginary quadratic orders (D. Hühnlein, M. Jacobson and D. Weber, 2001)
  • A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption (Huehnlein, Jacobson, Paulus, Takagi, 1998)
• Cryptography in groups of unknown order: papers
  • Public Key Cryptography With A Group Of Unknown Order (Richard Brent, 2000)
  • An Integer Commitment Scheme based on Groups with Hidden Order (Ivan Damgard and Eiichiro Fujisaki, Asiacrypt 2002 (eprint 2001/064))
  • Generic Lower Bounds for Root Extraction and Signature Schemes in General Groups (Ivan Damgard and Maciej Koprowski, Eurocrypt 2001, eprint 2002/013)
  • A Signature Scheme Based on the Intractability of Computing Roots (I. Biehl, J. Buchmann, S. Hamdy, A. Meyer, DCC 2002)
  • A Variant of the Cramer-Shoup Cryptosystem for Groups with Unknwon Order (Stefan Lucks, eprint 2002/052)
• Other destructive/constructive uses of class groups
  • A New Distributed Primality Test for Shared RSA Keys using Quadratic Fields (Ingrid Biehl, Takagi, ACISP 2002)
• Class group algorithms
  • On Class Group Computations Using the Number Field Sieve (M.L. Bauer, S. Hamdy, Asiacrypt 2003)
• Theses
  • Über die Sicherheit und Effizienz kryptographischer Verfahren mit Klassengruppen imaginär-quadratischer Zahlkörper (Safuat Hamdy, Darmstadt, 2002)
• People and Groups
  • The Number Field Cryptography Project (Darmstadt)
    • Johannes Buchmann (Darmstadt)
    • Bodo Möller (Darmstadt)
    • Tsuyoshi Takagi (Darmstadt)
  • Safuat Hamdy (Calgary)
  • Michael J. Jacobson, Jr. (Calgary)
  • Sachar Paulus (Secude)
  • Renate Scheidler (Calgary)
  • Hugh C. Williams (Calgary)
• Paper collections, TRs, ...
  • Darmstadt Technical Reports
• Software
  • A library for arithmetic in class groups of imaginary quadratic orders (Safuat Hamdy)

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Cryptology Pointers by Helger Lipmaa
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(C) Helger Lipmaa 1997-2009.