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What Do Random Polynomials over Finite Fields Look Like?

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Finite Fields and Applications (Fq 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

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Abstract

In this paper, we survey old and new results about random univariate polynomials over a finite field \(\mathbb{F}_q\). We are interested in three aspects: (1) the decomposition of a random polynomial in terms of its irreducible factors, (2) the usage of random polynomials in algorithms, and (3) the average-case analysis of algorithms that use polynomials over finite fields.

The author was funded by NSERC grant number 238757.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6, Canada

    Daniel Panario

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  1. Daniel Panario
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Editors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, 16802, PA, USA

    Gary L. Mullen

  2. University Paul Sabatier, AAECC/IRIT, 118 route de Narbonne, 31300, Toulouse cedex, France

    Alain Poli

  3. Sabancı University - FENS, Orhanli - Tuzla, 34956, Istanbul, Turkey

    Henning Stichtenoth

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Panario, D. (2004). What Do Random Polynomials over Finite Fields Look Like?. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_8

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

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