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Elliptic Curves over Finite Fields: Number Theoretic and Cryptographic Aspects

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Advances in Applied Mathematics, Modeling, and Computational Science

Part of the book series: Fields Institute Communications ((FIC,volume 66))

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Abstract

We present a collection of several natural questions about elliptic curves, mostly over finite fields, that have led to some interesting number theoretic questions and whose solutions require rather involved techniques from various area of number theory. Some of these questions are of intrinsic value for the theory of elliptic curves; they stem from their application to cryptography.

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  1. Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

    Igor E. Shparlinski

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  1. , Department of Mathematics, Wilfrid Laurier University, University Avenue West 75, Waterloo, N2L 3C5, Ontario, Canada

    Roderick Melnik

  2. , Dept. of Physics and Computer Science, Wilfrid Laurier University, University Avenue West 75, Waterloo, N2L 3C5, Canada

    Ilias S. Kotsireas

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Shparlinski, I.E. (2013). Elliptic Curves over Finite Fields: Number Theoretic and Cryptographic Aspects. In: Melnik, R., Kotsireas, I. (eds) Advances in Applied Mathematics, Modeling, and Computational Science. Fields Institute Communications, vol 66. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5389-5_4

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