Quote from: kTimesG on Today at 11:24:07 AM

It is so funny how some people think that because two points look alike then its a hot zone worth to investigate, while some others think the complete opposite. And they're both right: you can indeed argue that you can get closer to a solution little by little (see genetic algorithms), and you can also argue that statistically the solution should be as far away as possible from any other similar solution.

It's a very good example of why they are both actually wrong, and the winner here is simple, his name is Random and it seems no one wants to accept its definition or his highly entropic personality. Random is very hated and bullied, and no one believes him or takes him for granted, because he has a really big problem: every time you look at him, there are high chances he may look completely different. Or maybe not. Or maybe just a little? But random has a girlfriend: Prime. Prime understands him and the two share a lot of common ground, but they have a secret relationship.

The curve equation and parameters are completely and intentionally devised and chosen in such a way to ruin all of these assumptions, hopes, and "I know better"s. No, there is no magic pattern, formula, neural network, simplification, reduction, statistical analysis anomalies, or other similar BS. There is no pattern in either decimal, hex, binary, ASCII art, Photoshop horoscope, or any other visual mapping from bits to representation that you can ever think of.

Also if one does not have a clue about what hex numbers mean, they should really not waste time on discovering fundamental knowledge (for themselves only) while trying to break something called Elliptic Curve Cryptography. Now, this doesn't mean they are stupid, it just means that someone may be able to understand black holes equations, but it doesn't mean they should ever touch programming.

It’s clear you have a strong understanding of elliptic curve cryptography, and your points about randomness and the intentional design of ECC are well taken. I completely agree that the parameters of the curve were chosen to defy patterns, and my attempt to find hot zones or meaningful clustering was based on flawed assumptions.

I think there’s still value in experimenting, I am a layman in cryptography after all, even when the outcome is almost certainly failure. I went into this knowing that without GPU acceleration or distributed systems, my chances of finding the key were practically zero. But for me, this was less about cracking ECC and more about learning and challenging myself.

Even though the process didn’t lead to a solution, it gave me a deeper appreciation for the strength of ECC and how robust these systems are. I recognize now that randomness really is the "winner" here, and any clustering I thought I saw was more a product of my own misinterpretation than a meaningful signal.

I share this not to "reinvent the wheel" or to claim expertise, but because I found the process rewarding and hope others might learn from my mistakes or even just my curiosity. While I’ll be stepping away from this puzzle, I’ve gained a lot from the experience, and for me, that’s what matters most.