I am currently saving hashed passwords for my website. Passwords are salted and then hashed using SHA3-512. I understand the security level of SHA3-512, as it is for all Keccak algorithms, is half the capacity (as it is explained here) , so 512 bits in this case.
My question is, how does re-hashing the resulting hash n times affect the security? Is there a way to effectively compute that? In the scenario of someone stealing the database, what difference would it make having the password hashed, say, 500 times vs just once?
I have seen a similar discussion about entropy after re-hashing here, but they don't address security.