Lets assume we know the private key k lies within a limited range:
k ∈ [-1000, +1000] mod N
...
Thats 1 bit of information recovered via curve symmetry and limited search space.
Thats useful:
In biased brute-force attacks
This only works when you're trying to find the private key of a known public key. For address puzzles, you can't shift the search interval. And for public key puzzles, brute-force is not used because exponentially faster algorithms exist (and some already take advantage of the curve symmetry).
That's a solid and worthy response agreed.
However, curve symmetry alone reduces the search space by at least 2×, even before taking into account the full stack of optimized algorithms.
As for determining whether a point is the interpreted negative (i.e., reflection) on the curve,
is there a faster method than direct computation for checking it?
AI-generated
23%
Human-written
77%
One of the big reasons sane people don't post here (or retire) is that it's a waste of time to fight against idiocracy (which is exactly where society is heading if everything people are able to do is 2 things: ask AI about shit they're too dumb to learn, and ask AI whether something was written by AI). This is getting too boredom to hear every 2 sentences that "all your posts are AI based". I guess people will eventually lose their brains all together because of that shit. Fuck education and everything related to it.
Listen, AI is just a tool. Knowledge by itself is nothing more than raw text fileslike school textbooks in plain TXT format without any meaningful connections or context. Without properly aligning and interpreting that knowledge, you wont build a neural network capable of solving tasks smoothly or respectfully.
Basically, having a tool that handles complex tasks doesnt automatically make you dumb for using it. On the contraryyou level up to a higher plane of abstraction, shifting away from the technical grind to managing meaning. You dont just push buttonsyou create and interpret concepts, letting the tool handle the messy technical parts.
Looking at the bigger picturethe world built on debts and deficits will always grow exponentially into chaos, spawning endless conflicts and crises. But within that chaos lies the chance to see deeper and build something truly your own, outside the dumb consumer cycle and idiocracy.
So AI isnt the end of intellectual evolutionits the start of a new layer you have to learn to read and use. The key is not to become a script in someone elses system, but to stay the architect of your own abstractions.
