Incorrect, the best factoring algorithms are subexponential.
To clarify, subexponential does not mean polynomial, but super-polynomial.
(Interestingly, while factoring a given integer is hard, there is a way to get a random integer within [1..N] and its factorization quickly. See Adam Kalai’s paper Generating Random Factored Numbers, Easily (PDF).
To clarify, subexponential does not mean polynomial, but super-polynomial.
(Interestingly, while factoring a given integer is hard, there is a way to get a random integer within [1..N] and its factorization quickly. See Adam Kalai’s paper Generating Random Factored Numbers, Easily (PDF).
Interesting. I had not seen that paper before. That’s very cute.