You are confusing different things. You are talking about hash algorithms, whereas the OP is about encryption algorithms. And it is not proper terminology to re

You are confusing different things. You are talking about hash algorithms, whereas the OP is about encryption algorithms. And it is not proper terminology to refer to hashes as "keys". What you are trying to convey, is that hash algorithms need to generate hash sizes of 512 bits if they want to make collision generation as hard as bruteforcing a 256-bit symmetric encryption key. This is true. But please use proper terminology.