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Complexity class of integer factorization

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Is integer factorization confirmed to be an NP-complete problem? If not, then if one could transform IF into an equivalent problem which is already proved to be NP-complete, would it mean that IF is itself NP-complete as well? Would such a thing have any practical meaning?

Asked By : plktrautman
Answered By : Yuval Filmus

Integer factorization (or rather, an appropriate decision version) is not known to be NP-complete. In fact, it is conjectured not to be NP-complete. However, any reasonable decision version of integer factorization is in NP, and so reducible to any NP-complete problem (by definition). There are specialized algorithms for integer factorization which are better than, say, reducing integer factorization to SAT and then using a SAT solver.

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