Let’s clarify something I’ve observed from those prefix supporters:
Prefix-based approaches aren’t about breaking SHA-256 or any hashing algorithm—they’re about optimizing search efficiency within a small keyspace.
Those statements are equivalent.
Strategies like Kangaroo and BSGS don’t contradict SHA-256 either, yet they’re widely used to reduce computational load. Prefix approaches follow a similar mindset—not to break cryptography, but to shave off time and cycles where possible.
They're used in a totally different context, which has nothing to do with any hashes.
Prefix approach mindset is
trying to break crypto while claiming it doesn't break crypto. Interesting mindset! Do you realize that it has zero importance whether the search is done on some subrange or on the full 256-bit range? There's nothing to take advantage of.
I don't support the idea of prefixes, since I haven't seen any software that represents an improvement, but to say that if a probabilistic search works on an insecure bit, it means that cryptography is broken is like smoking a joint the size of a cucumber.
Even managing to work out a single bit, or having a single bit bias (force it to not be 50% a 0 or 1 long-term), somehow, in a hash function or on an ECC,
would definitely mean that said crypto was broken. Just ask any cryptographer.