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Factorization of polynomials over finite fields in subexponential time under GRH

  • Sergei Evdokimov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 877)

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 (nlog 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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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Sergei Evdokimov
    • 1
  1. 1.St. Petersburg Institute for Informatics and Automation of the Academy of Sciences of RussiaSaint-PetersburgRussia

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