Galois groups and factoring polynomials over finite fields

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

Let p be a prime and F be a polynomial with integer coefficients. Suppose that the discriminant of F is not divisible by p, and denote by m the degree of the splitting field of F over Q and by L the maximal size of the coefficients of F. Then, assuming the generalized Riemann hypothesis (GRH), it is shown that the irreducible factors of F modulo p can be found in (deterministic) time polynomial in deg F, m, log p, and L. As an application, it is shown that it is possible under GRH to solve certain equations of the form nP = R, where R is a given and P is an unknown point of an elliptic curve defined over GF(p) in polynomial time (n is counted in unary). An elliptic analog of results obtained recently about factoring polynomials with the help of smooth multiplicative subgroups of finite fields is proved.

Original languageEnglish
Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
PublisherPubl by IEEE
Pages99-104
Number of pages6
ISBN (Print)0818619821
Publication statusPublished - Nov 1989
Event30th Annual Symposium on Foundations of Computer Science - Research Triangle Park, NC, USA
Duration: Oct 30 1989Nov 1 1989

Other

Other30th Annual Symposium on Foundations of Computer Science
CityResearch Triangle Park, NC, USA
Period10/30/8911/1/89

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Polynomials

ASJC Scopus subject areas

  • Hardware and Architecture

Cite this

Rónyai, L. (1989). Galois groups and factoring polynomials over finite fields. In Annual Symposium on Foundations of Computer Science (Proceedings) (pp. 99-104). Publ by IEEE.

Galois groups and factoring polynomials over finite fields. / Rónyai, L.

Annual Symposium on Foundations of Computer Science (Proceedings). Publ by IEEE, 1989. p. 99-104.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Rónyai, L 1989, Galois groups and factoring polynomials over finite fields. in Annual Symposium on Foundations of Computer Science (Proceedings). Publ by IEEE, pp. 99-104, 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, USA, 10/30/89.
Rónyai L. Galois groups and factoring polynomials over finite fields. In Annual Symposium on Foundations of Computer Science (Proceedings). Publ by IEEE. 1989. p. 99-104
Rónyai, L. / Galois groups and factoring polynomials over finite fields. Annual Symposium on Foundations of Computer Science (Proceedings). Publ by IEEE, 1989. pp. 99-104
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