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GROUP STRUCTURE OF ELLIPTIC CURVES OVER FINITE FIELDS AND APPLICATIONS

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Book cover Topics in Geometry, Coding Theory and Cryptography

Part of the book series: Algebra and Applications ((AA,volume 6))

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Abstract

Let E be an elliptic curve defined over Fq, the finite field of q elements. It is known that the set of F q-rational points of E has a structure of an abelian group. This fact, since the works of Koblitz [68] and Miller [98], underlies all known applications of elliptic curves to cryptography, see [3, 15, 16, 50, 73] and references therein. We give a survey of recent results about the structure of this group as well as techniques used.

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Authors
  1. Ram Murty
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  2. Igor Shparlinski
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Editors and Affiliations

  1. Instituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil

    Arnaldo Garcia

  2. University of Duisburg-Essen, Germany and Sabanci University, Istanbul, Turkey

    Henning Stichtenoth

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© 2006 Springer

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Murty, R., Shparlinski, I. (2006). GROUP STRUCTURE OF ELLIPTIC CURVES OVER FINITE FIELDS AND APPLICATIONS. In: Garcia, A., Stichtenoth, H. (eds) Topics in Geometry, Coding Theory and Cryptography. Algebra and Applications, vol 6. Springer, Dordrecht . https://doi.org/10.1007/1-4020-5334-4_5

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