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https://eprint.iacr.org/2019/078 is a good overview of the statistical properties of SHA hashes.

Basically after ~10 rounds the output is always indistinguishable from randomness which means hamming distance is what you'd expect (about half the bits differ) between the hashes of any two bitstreams.



CRC does better than random vs burst errors. And vs random errors is indistinguishable from any other methodology.

If you are only worried about random errors, might as well use chksum.




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