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What are the two "closest" known Keccak256 (not SHA-3 256) hashes in terms of the Hamming distance between the pair of hashes?

EDIT: This was marked as opinion based, so to clarify, when I asked this question, I was hoping that people responding would provide two hashes that had a close Hamming distance, as well as the data hashed to generate those hashes. I hope that removes any ambiguity that could result in this being seen as opinion-based.

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closed as primarily opinion-based by e-sushi Apr 26 '18 at 10:16

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ XOR distance? That's known as Hamming distance! I don't know all calculated keccak256 hashes - nobody does. The output of a hash is randomized, so even if there was a search I don't know how it would apply to anything. Do note that the birthday thingy applies though and that the position of the bits doesn't matter, so finding many identical / non-identical bits will be easier than finding e.g. a hash that starts with a fixed prefix of a certain length. $\endgroup$ – Maarten Bodewes Apr 25 '18 at 20:07
  • $\begingroup$ Thanks for telling me what the correct term was! I know that no one knows all hashes, I guess I was just looking in terms of a "record" sense; two closest ones known to anyone. I'm trying to make an implementation of Kademlia based off of keccak256 instead of SHA1, so I was curious about minimal Hamming Distances. $\endgroup$ – Lev Knoblock Apr 25 '18 at 20:52
  • $\begingroup$ Have you seen this page about the XY problem? Generally the output of (symmetric) hash functions should be indistinguishable from random. The hash would be terribly broken if this isn't the case. With your comment I really have two questions: why not SHA-3 and why are you afraid that the Hamming distance is of influence on your protocol? Are you afraid of collisions of a downsized hash output? $\endgroup$ – Maarten Bodewes Apr 25 '18 at 20:56
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    $\begingroup$ I'm not afraid of any issues with the Hamming Distance, and I avoided SHA-3 simply because I'm building a cryptocurrency based off of Ethereum, which uses Keccak. I'm asking this question solely based off of curiosity; I'm trying to sort nodes into k-buckets as per Kademlia, and I was wondering about the likelihood of any nodes getting into one of the low-distance k-buckets. $\endgroup$ – Lev Knoblock Apr 25 '18 at 21:02
  • $\begingroup$ Does this question and answers possibly answer your question? Searching is easier if you know the terms :) $\endgroup$ – Maarten Bodewes Apr 25 '18 at 21:09