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Encyclopedia of Cryptography and Security pp 186Cite as

Elliptic Curve Cryptography

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Elliptic curve cryptographic schemes were proposed independently in 1985 by Neal Koblitz [3] and Victor Miller [5]. 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. 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 problem in the multiplicative group of a finite field, or with the integer factoring problem, there is no subexponential-timealgorithm known for the ECDLP. Consequently, significantly smaller parameters can be selected for elliptic curve schemes than for ordinary discrete loga-rithm schemes or for RSA, and achieve the same level of security. Smaller parameters can poten-tially result in significant...

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References

  1. Blake, I., G. Seroussi, and N. Smart (1999). Elliptic Curves in Cryptography. Cambridge University Press.

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  2. Hankerson, D., A. Menezes, and S. Vanstone (2003). Guide to Elliptic Curve Cryptography. Springer-Verlag, Berlin.

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  3. Koblitz, N. (1987). “Elliptic curve cryptosystems.” Mathematics of Computation, 48, 203–209.

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  4. Menezes, A. (1993). Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, Boston, MA.

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  5. Miller, V. (1986). “Use of elliptic curves in cryptography.” Advances in Cryptology—CRYPTO'85, Lecture Notes in Computer Science, vol. 218, ed. H.C. Williams. Springer-Verlag, Berlin, 417–426.

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Authors
  1. Darrel Hankerson
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  2. Alfred Menezes
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Editor information

Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

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© 2005 International Federation for Information Processing

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Hankerson, D., Menezes, A. (2005). Elliptic Curve Cryptography. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_131

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