> There is no reason to believe that an NP-complete problem solver can factorize integers in polynomial time. You're misunderstanding the relationship between

> There is no reason to believe that an NP-complete problem solver can factorize integers in polynomial time. You're misunderstanding the relationship between NP and NP-complete. Integer factorization is in NP, which by definition means that anything that can solve NP-complete problems efficiently can also solve factorization. The question that's currently unresolved is whether factorization is easier than NP-complete, not harder.