Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it
Yes, you can replace any key by other key.
A logical speedup is to ignore the rest of the elements in the range/set, and choose a new range/set, to maximize chances to find another new element.
Then the new set has exactly the same odds to find a match as the set you were about to run when finishing the range.
It feels counter intuitive, I know. If you want to be convinced just run the odds of both cases by taking a range of size 1000 with 5% probability.
Then how do you explain this: if I have some 32 bits mask, and jump keys based on how many bits the mask matched, then I hash less keys overall, but the total matches are, on average, much better finds than if I traverse linearly?.
Or are you saying that this does not happen?
Oh this can clearly happen on a small enough subset because of the huge deviations that may happen.It would not work as well on a bigger scale because everything would even out.
Yeah, seems I hurried a bit. I only averaged the best matches; if all the possible prefix lengths are included, then on average there is only a 1.0000... bits prefix match, long-term.
This is identical to simply not even doing a prefix match at all. Because, on average, a H160 hash has a length of 159 bits. Zero improvement trying to break the hash distribution.
It also doesn't matter whether the hash inputs are random data or produced by EC scalar-mul.
It is just placebo to think that, by "skipping" a number of hashes (no matter in what way you do that) you maximize chances to obtain, in a faster way, some prefix. The same exact thing would happen if the keys are hashed in continuation, or the hashing is done on random inputs. Or if you simply wait it out, drink a coffee, and hash a bit more from where you left off. Or simply ignore the results of a couple of hashes and then go as usual.
Set/range A: keys 1 to N
Set/range B: keys N + 1 to 2N (or some other M to M + size)
After A is scanned (fully or not), we can simply swap keys from B into A (or not), there is no correlation between the way we split the sets, and what the hashing produces. Unless there is a link between the private key and the H160, this is where conspiracy theories begin.