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Mosc. Math. J., 2002, Volume 2, Number 4, Pages 693–715 (Mi mmj69)  

This article is cited in 2 scientific papers (total in 2 papers)

Good and bad uses of elliptic curves in cryptography

N. I. Koblitz

University of Washington

Abstract: In the first part of this article I describe the construction of cryptosystems using elliptic curves, discuss the Elliptic Curve Discrete Logarithm Problem (upon which the security of all elliptic curve cryptosystems rests), and survey the different types of elliptic curves that can be chosen for cryptographic applications. In the second part I describe three unsuccessful approaches to breaking various cryptosystems by means of liftings to global elliptic curves. I explain how the failure of these attacks is caused by fundamental properties of the global curves.

Key words and phrases: Public key cryptography, elliptic curve cryptography, discrete logarithm, digital signature, global elliptic curve, index calculus, canonical height, torsion group, uniform boundedness.

DOI: https://doi.org/10.17323/1609-4514-2002-2-4-693-715

Full text: http://www.ams.org/.../abst2-4-2002.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 14G50, 11G05, 94A60; Secondary 11T71, 14H52
Received: February 22, 2002
Language:

Citation: N. I. Koblitz, “Good and bad uses of elliptic curves in cryptography”, Mosc. Math. J., 2:4 (2002), 693–715

Citation in format AMSBIB
\Bibitem{Kob02}
\by N.~I.~Koblitz
\paper Good and bad uses of elliptic curves in cryptography
\jour Mosc. Math.~J.
\yr 2002
\vol 2
\issue 4
\pages 693--715
\mathnet{http://mi.mathnet.ru/mmj69}
\crossref{https://doi.org/10.17323/1609-4514-2002-2-4-693-715}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1986087}
\zmath{https://zbmath.org/?q=an:1063.11051}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208593600004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Freeman D., Scott M., Teske E., “A Taxonomy of Pairing-Friendly Elliptic Curves”, Journal of Cryptology, 23:2 (2010), 224–280  crossref  mathscinet  zmath  isi
    2. Luo Zh., Feng E., Zhang J., “Computing Singular Points of Projective Plane Algebraic Curves By Homotopy Continuation Methods”, Discrete Dyn. Nat. Soc., 2014, 230847  crossref  mathscinet  isi  elib
  • Moscow Mathematical Journal
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