Factorization of solvable polynomials over finite fields and the generalized Riemann hypothesis Article

DOI :
10.1007/BF01104107

Cite this article as: Evdokimov, S.A. J Math Sci (1992) 59: 842. doi:10.1007/BF01104107
Abstract This article presents an algorithm that, assuming the generalized Riemann hypothesis, factors a polynomial f mod p, where f ∃Z [X] is solvable overQ , into irreducible (over the fieldF _{p} m) factors in time polynomial in m, log p, and the length of notation of f. The following problems are also solved in time polynomial in m, n, and log p: 1) construction of the fieldF _{p} m, 2) construction of all isomorphisms between two realizations ofF _{p} ^{m} , and 3) computation of the roots of degree n inF _{p} _{m} .

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Mathematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 176, pp. 104–117, 1989.

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© Plenum Publishing Corporation 1992

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