--- Log opened Fri Mar 07 00:00:37 2025
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09:41 < Ademan_> I've been ignorant of all of the ZK stuff (to my own detriment) is it possible to construct a reasonably sized ZK proof that the private key to a particular public key has a certain bit prefix? You could create kind of a POW coin that way. Alternatively, that a hash preimage has a particular bit prefix?
09:43 < sipa> a bulletproof can do that in a kilobyte or so
09:44 < sipa> or even just a ring signature, if you care more about simplicity than proof size
09:51 < Ademan_> thanks! I really should start learning about this stuff... I'm aware of both concepts but only barely...
10:10 < sipa> the very simple way: say you have P=xG
10:11 < sipa> and you want to prove that its first 4 bits are 1010
10:13 < sipa> let P' = P - (2**255 + 2**253)G, so the DL of P' starts with 4 zeroes
10:15 < sipa> now pick 252 random values r0, r1, r2, r3, ..., r251, which sum to 0, and corresponding points Qi = riH + (x & 2**i)*G, such that sum Qi = P'
10:15 < sipa> where H is an alternatigr generator of the group
10:16 < sipa> then you know the DL wrt H of either Qi, or Qi-(2**i)*G for each i
10:16 < sipa> so you can produce a ring signature over those two points
10:17 < sipa> and the combination of all of them proves that P is of the form rH + (0..2**252-1)*G
10:18 < sipa> if you additionally produce a (normal) signature with P itself, you prove that the H component is 0
10:33 < Ademan_> wow, thank you!
10:36 < Ademan_> digesting it a bit right now, but that basically makes sense!
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--- Log closed Sat Mar 08 00:00:38 2025