Factorization of solvable polynomials over finite fields and the generalized Riemann hypothesis Abstract
This article presents an algorithm that, assuming the generalized Riemann hypothesis, factors a polynomial f mod p, where f ∃
Z[X] is solvable over Q, into irreducible (over the field F pm) 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 field F pm, 2) construction of all isomorphisms between two realizations of F p m, and 3) computation of the roots of degree n in F 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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