Kryptosysteme mit elliptischen Kurven

Chapter
Part of the eXamen.press book series (EXAMEN)

Zusammenfassung

In diesem Kapitel erlernen Sie
  • die Vor- und Nachteile von ECC im Vergleich zu RSA und Diskreter-Logarithmus-Verfahren,

  • was eine elliptische Kurve ist und wie man auf ihr Berechnungen ausführt,

  • wie DLP über elliptischen Kurven konstruiert werden können,

  • Beispiele für Protokolle mit elliptischen Kurven,

  • Einschätzungen zum Sicherheitsniveau von ECC.

Literatur

  1. 1.
    ANSI X9.6g2-1999, The Elliptic Curve Digital Signature Algorithm (ECDSA). Technical report (American Bankers Association, 1999) Google Scholar
  2. 2.
    ANSI X9.62-2001, Elliptic Curve Key Agreement and Key Transport Protocols. Technical report (American Bankers Association, 2001) Google Scholar
  3. 3.
    Daniel J. Bernstein, Tanja Lange, SafeCurves: choosing safe curves for elliptic-curve cryptography, http://safecurves.cr.yp.to. Zugegriffen am 1. April 2016
  4. 4.
    I. Blake, G. Seroussi, N. Smart, J. W. S. Cassels, Advances in Elliptic Curve Cryptography. London Mathematical Society Lecture Note Series (Cambridge University Press, New York, NY, USA, 2005) CrossRefMATHGoogle Scholar
  5. 5.
    Ian F. Blake, G. Seroussi, N. P. Smart, Elliptic Curves in Cryptography (Cambridge University Press, New York, NY, USA, 1999) CrossRefMATHGoogle Scholar
  6. 6.
    Dan Boneh, Matthew Franklin, Identity-based encryption from the Weil pairing. SIAM J. Comput. 32(3), 586–615 (2003) MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Bundesamt für Sicherheit in der Informationstechnik (BSI), http://www.bsi.de/english/publications/bsi_standards/index.htm. Zugegriffen am 1. April 2016
  8. 8.
    H. Cohen, G. Frey, R. Avanzi, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Discrete Mathematics and Its Applications (Chapman and Hall/CRC, 2005) CrossRefMATHGoogle Scholar
  9. 9.
    D. R. Hankerson, A. J. Menezes, S. A. Vanstone, Guide to Elliptic Curve Cryptography (Springer, 2004) MATHGoogle Scholar
  10. 10.
    Ann Hibner Koblitz, Neal Koblitz, Alfred Menezes, Elliptic curve cryptography: The serpentine course of a paradigm shift. Cryptology ePrint Archive, Report 2008/390 (2008), http://eprint.iacr.org/cgi-bin/cite.pl?entry=2008/390. Zugegriffen am 1. April 2016
  11. 11.
    Neal Koblitz, Introduction to Elliptic Curves and Modular Forms (Springer, 1993) CrossRefMATHGoogle Scholar
  12. 12.
    Neal Koblitz, Alfred Menezes, Scott Vanstone, The state of elliptic curve cryptography. Des. Codes Cryptography 19(2–3):173–193 (2000) MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Julio López, Ricardo Dahab, Fast multiplication on elliptic curves over gf(2m) without precomputation, in Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems, CHES ’99 (Springer, London, UK, 1999), S. 316–327 CrossRefGoogle Scholar
  14. 14.
    M. Lochter, J. Merkle, Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation (RFC5639) (2010), http://www.ietf.org/rfc/rfc5639.txt. Zugegriffen am 1. April 2016
  15. 15.
    Peter L. Montgomery, Speeding the pollard and elliptic curve methods of factorization. Mathematics of Computation 48(177), 243–264 (1987) MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    National Institute of Standards and Technology (NIST), Digital Signature Standards (DSS), FIPS186-3. Technical report, Federal Information Processing Standards Publication (FIPS) (2009), http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf. Zugegriffen am 1. April 2016
  17. 17.
    NSA Suite B Cryptography, http://www.nsa.gov/ia/programs/suiteb_cryptography/index.shtml. Zugegriffen am 1. April 2016
  18. 18.
    J. H. Silverman, The Arithmetic of Elliptic Curves (Springer, 1986) CrossRefMATHGoogle Scholar
  19. 19.
    J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves (Springer, 1994) CrossRefMATHGoogle Scholar
  20. 20.
    Jerome A. Solinas, Efficient arithmetic on Koblitz curves. Designs, Codes and Cryptography 19(2–3), 195–249 (2000) MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Annual Workshop on Elliptic Curve Cryptography, ECC, http://cacr.math.uwaterloo.ca/conferences/. Zugegriffen am 1. April 2016
  22. 22.
    Thomas Wollinger, Jan Pelzl, Christof Paar, Cantor versus Harley: Optimization and analysis of explicit formulae for hyperelliptic curve cryptosystems. IEEE Transactions on Computers 54(7), 861–872 (2005) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Computer SecurityHochschule Hamm-LippstadtHammDeutschland
  2. 2.Horst Görtz Institut für IT-SicherheitRuhr-Universität BochumBochumDeutschland

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