Quote from: pooya87 on Today at 05:43:35 AM

Quote from: j2002ba2 on October 03, 2020, 12:05:54 PM

About 90 years ago Kurt Gödel found out, that one cannot make such "impossible" statements.

that's true and there may be something done in the future but my comment was mainly about "reversing" a hash. meaning finding message by having the hash which is simply impossible and will always be impossible because of the way hash algorithms are defined. i always like to use this example, imagine you have a very simple formula x+y=z and you know the result (z) is 10. it doesn't matter how much computing power, or what kind of crazy mathematics algorithm you use, you can never reverse x+y=10 to find x and y. there is just no way. what you can do is finding different x and y that can give same result which is the same as finding collision but not being able to reverse it.

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SHA256 "solved" means cheap mining, leaving ASIC farms in the dust. One could easily mine 300 coins/day without being noticed, no need to announce anything to the big world.

that's not how bitcoin works. there is this thing called difficulty which would adjust and prevent blocks from being found too fast. on top of that if there were any kind of progress in breaking SHA256 most of the internet would be at a much bigger danger. meanwhile bitcoin simply could switch to another mining algorithm.

There are two things here: reversing hash to "a message", and reversing a hash to "the message". Depending on "the message", it is way more impossible than just "a message".

Mining is "a message" one, and can be viewed as finding small number of bits (currently less than 80), which produce corresponding zero bits in the output of a complex single hash function (changing with each new block, selected transactions, etc.).

So, we could view that hash as 80-bit input 80-bit output one.

Given a good hashing function, the probability of being able to get the desired output is 1/2 (for equal number of input and output bits).

Let's look at a hypothetical O(2^n/2) algorithm.

While everyone else would be doing 2⁸⁰ work, the smart algo would be doing only 2⁴⁰.

Such algorithm would be complex, so it would take certain fixed time to get the result, let's say 300 seconds (5 min).

Getting 33% of the hashrate means adding 50% more hashrate than the current one. Adding hashrate should be incremental, with increase about 0.2% per day. This amounts to 250 days til reaching the desired 1/3 of the total.

Reversing p2pkh is way more complex - if we view transformation from private key to public key as a hash function, then we have a sequence of 3 hash funcs., the first one being the most complex, but aslo the lousiest.

With the n/2 hypothetical algo, we get complexity 2⁸⁰ of both operations and memory requirements, which is way beyond what's available now.

But it looks like possible in the future. One day, when a memory cell is of size 9x9x9 nm, a cube with size only 1 meter would contain 2⁸⁰ bits.

The algorithm is hypothetical, and we might never know if anybody found it.

But such memory, and corresponding computers are achievable with todays technology. It's only matter of time, and desire to get rid of the current chip-based stuff.