> who end up being left with the impression that graph isomorphism and factorization are NP-hard, because (a) they hear those problems are hard, and (b) they're told the polynomials are the easy problems, and (c) the only non-polynomial algorithms they've ever seen are exponential-time.
In a decent textbook on computational complexity theory, you can read that a problem is NP-hard if for every problem in NP there exists a polynomial-time reduction to it. Nobody claims that such a reduction exists, e.g. for integer factorization and graph isomorphism.
In a decent textbook on computational complexity theory, you can read that a problem is NP-hard if for every problem in NP there exists a polynomial-time reduction to it. Nobody claims that such a reduction exists, e.g. for integer factorization and graph isomorphism.