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Factorization of polynomials over finite fields in subexponential time under GRH

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Algorithmic Number Theory (ANTS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 877))

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Abstract

We show assuming the Generalized Riemann Hypothethis that the factorization of a one-variable polynomial of degree n over an explicitly given finite field of cardinality q can be done in deterministic time (n log n log q)O(1). Since we need the hypothesis only to take roots in finite fields in polynomial time, the result can also be formulated in the following way: a polynomial equation over a finite field can be solved “by radicals” in subexponential time.

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Authors and Affiliations

  1. St. Petersburg Institute for Informatics and Automation of the Academy of Sciences of Russia, the 14th liniya 39, 199178, Saint-Petersburg, Russia

    Sergei Evdokimov

Authors
  1. Sergei Evdokimov
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Leonard M. Adleman Ming-Deh Huang

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© 1994 Springer-Verlag Berlin Heidelberg

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Evdokimov, S. (1994). Factorization of polynomials over finite fields in subexponential time under GRH. In: Adleman, L.M., Huang, MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58691-1_58

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  • DOI: https://doi.org/10.1007/3-540-58691-1_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58691-3

  • Online ISBN: 978-3-540-49044-9

  • eBook Packages: Springer Book Archive

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