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.
CITATION STYLE
Evdokimov, S. (1994). Factorization of polynomials over finite fields in subexponential time under GRH. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 877 LNCS, pp. 209–219). Springer Verlag. https://doi.org/10.1007/3-540-58691-1_58
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