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Kryptografie verständlich pp 273–295Cite as

Kryptosysteme mit elliptischen Kurven

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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.

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Notes

  1. 1.

    Man beachte, dass elliptische Kurven nicht Ellipsen sind. Der Name stammt daher, dass elliptische Kurven bei der Bestimmung der Bogenlänge von Ellipsen eine Rolle spielen.

  2. 2.

    Man beachte, dass die Bezeichnung der Gruppenoperation als Addition rein willkürlich ist. Man hätte sie ebenso gut Multiplikation nennen können.

  3. 3.

    Man beachte, dass das Zeichen \(+\) für die Gruppenoperation willkürlich gewählt wurde. Bei Wahl einer multiplikativen Notation hätte das ECDLP die Form \(P^{d}=T\), was konsistent mit der Darstellung des DLP über endlichen Körpern \(\mathbb{Z}_{p}^{*}\) wäre.

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Author information

Authors and Affiliations

  1. Computer Security, Hochschule Hamm-Lippstadt, Hamm, Nordrhein-Westfalen, Deutschland

    Jan Pelzl

  2. Horst Görtz Institut für IT-Sicherheit, Ruhr-Universität Bochum, Bochum, Deutschland

    Christof Paar

Authors
  1. Jan Pelzl
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  2. Christof Paar
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Correspondence to Jan Pelzl .

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Pelzl, J., Paar, C. (2016). Kryptosysteme mit elliptischen Kurven. In: Kryptografie verständlich. eXamen.press. Springer Vieweg, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49297-0_9

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  • DOI: https://doi.org/10.1007/978-3-662-49297-0_9

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  • Publisher Name: Springer Vieweg, Berlin, Heidelberg

  • Print ISBN: 978-3-662-49296-3

  • Online ISBN: 978-3-662-49297-0

  • eBook Packages: Computer Science and Engineering (German Language)

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