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Elliptic Curve Cryptography

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Encyclopedia of Cryptography, Security and Privacy

Synonyms

ECC

Definition

Elliptic curve cryptography (ECC) encompasses the design and analysis of public key cryptographic schemes that can be implemented using elliptic curves.

Background

Elliptic curve cryptographic schemes were proposed independently in 1985 by Neal Koblitz (Koblitz, 1987) and Victor Miller (Miller, 1986). They are the elliptic curve analogues of schemes based on the discrete logarithm problem where the underlying group is the group of points on an elliptic curve defined over a finite field (Blake et al., 1999; Hankerson et al., 2004). See Koblitz et al. (2011) for a historical account of the development and commercial acceptance of elliptic curve cryptography.

Theory

The security of all elliptic curve signature schemes, elliptic curve key agreement schemes, and elliptic curve public-key encryption schemes is based on the apparent intractability of the elliptic curve discrete logarithm problem (ECDLP). Unlike the case of the ordinary discrete logarithm problemin...

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References

  • Blake I, Seroussi G, Smart N (1999) Elliptic curves in cryptography. Cambridge University Press, Cambridge

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  • Cohen H, Frey G, Avanzi R, Doche C, Lange T, Nguyen K, Vercauteren F (2005) Handbook of elliptic and hyperelliptic curve cryptography. Chapman & Hall/CRC, Boca Ratonx

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  • Hankerson D, Menezes A, Vanstone S (2004) Guide to elliptic curve cryptography. Springer, New York

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  • Koblitz N (1987) Elliptic curve cryptosystems. Math Comput 48:203–209

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  • Koblitz AH, Koblitz N, Menezes A (2011) Elliptic curve cryptography: the serpentine course of a paradigm shift. J Number Theory 131:781–814

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  • Miller V (1986) Use of elliptic curves in cryptography. In: Advances in cryptology—CRYPTO’85. Lecture notes in computer science, vol 218. Springer, pp 417–426

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Auburn University, Auburn, AL, USA

    Darrel Hankerson

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada

    Alfred Menezes

Authors
  1. Darrel Hankerson
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  2. Alfred Menezes
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Corresponding author

Correspondence to Alfred Menezes .

Editor information

Editors and Affiliations

  1. Center for Secure Information Systems, George Mason University, Fairfax, VA, VA, USA

    Sushil Jajodia

  2. University of Milan, Milan, Italy

    Pierangela Samarati

  3. Google Inc, New York, NY, USA

    Moti Yung

Section Editor information

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada

    Alfred Menezes

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Hankerson, D., Menezes, A. (2021). Elliptic Curve Cryptography. In: Jajodia, S., Samarati, P., Yung, M. (eds) Encyclopedia of Cryptography, Security and Privacy. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27739-9_245-2

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  • DOI: https://doi.org/10.1007/978-3-642-27739-9_245-2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27739-9

  • Online ISBN: 978-3-642-27739-9

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

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