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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Factorization of multivariate polynomials over finite fields

Authors: J. von zur Gathen and E. Kaltofen
Journal: Math. Comp. 45 (1985), 251-261
MSC: Primary 12E05; Secondary 11Y16, 68Q40
MathSciNet review: 790658
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Abstract: We present a probabilistic algorithm that finds the irreducible factors of a bivariate polynomial with coefficients from a finite field in time polynomial in the input size, i.e., in the degree of the polynomial and log (cardinality of field). The algorithm generalizes to multivariate polynomials and has polynomial running time for densely encoded inputs. A deterministic version of the algorithm is also discussed, whose running time is polynomial in the degree of the input polynomial and the size of the field.

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Keywords: Polynomial factorization, multivariate polynomials, finite fields, probabilistic algorithms
Article copyright: © Copyright 1985 American Mathematical Society