Quote from: Bram24732 on Today at 02:44:47 PM

Quote from: deep_seek on Today at 02:32:26 PM

No one can definitively prove that there's no connection between the prefix and the private key—just like you can't conclusively prove that there is any relation.

So in my opinion, it would be better to pause this debate until either side can bring stronger evidence. Right now, it's just unnecessarily stretching the thread without any productive outcome.

All 3 steps in the algorithm are designed so that there is no connection. It’s part of the basic properties of a hash function and of an elliptic curve. Having a connection means there is a different flaw in all 3. So unless people come up with a proof of each of those flaws, then there is no link. Not the other way around.

Agree on not talking about it anymore, given how something so obvious is hard to understand for some.

Everyone knows about the three irreversible processes involved in address generation from a private key. But what's truly interesting is what @mcdouglasx pointed out:

Quote from: mcdouglasx on Today at 02:33:28 PM

The prefix theory for searching matches in Bitcoin is a mathematically unexplored topic; it has only been investigated for the purpose of vanity addresses.

I completely agree — no one has really explored this area deeply. That’s likely because of the overwhelming complexity, which discourages many due to the sheer scale of the mathematical research required. But if someone dares to explore any possibilities or probabilities hidden in this mountainous domain, it should be encouraged — not criticized or dismissed.

Rather than demotivating or distracting someone with endless arguments, it's more constructive to support those who want to dive deeper into new ideas. I respect both of your perspectives, and I’m just suggesting that instead of engaging in debates that might humiliate or discourage others, we focus on fresh approaches. That doesn’t mean every crypto rookie gets a free pass to drop “hot takes” with no homework Grin

this isn’t Twitter, it’s math!

Fresh approach For example - Kangaroo & BSGS now Prefix-based strategies seem to be another tool of that nature - not a breakthrough, but possibly a way to refine brute-force efforts when dealing with the small key ranges like 69, 71, 72 Bits & so on..