Deterministic distinct-degree factorization of polynomials over finite fields

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Abstract

A deterministic polynomial time algorithm is presented for finding the distinct-degree factorization of multivariate polynomials over finite fields. As a consequence, one can count the number of irreducible factors of polynomials over finite fields in deterministic polynomial time, thus resolving a theoretical open problem of Kaltofen from 1987.

Keywords

Multivariate polynomial
Deterministic algorithm
Distinct-degree factorization

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This research was done while the authors were members at the Mathematical Sciences Research Institute in Berkeley, CA, USA.

1

A.G.B. Lauder is a Royal Society University Research Fellow.