Hashing is not the answer to all the problem. I mean we can't prove they are good, we can only try. And by definition they cannot be perfect since the set of possible inputs is way bigger than the output. You didn't mention security levels in your article. To have the security level we have today (2^80) we need hash functions of size at least 240 bits so 256 is good. But since no one can accurately guess the speed up we will get with quantum computers in classical computing settings, this margin is thin. It is safe to assume that we would need SHA3-384. source: Grover BHT hash function
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