EC is a spiral curve like spring
try this 3d graph generator:
for i in range(start, end + 1):
# point calculation index i
Px = i * Gx
Py = i * Gy
x.append(Px % p)
y.append(Py % p)
Is mapping modular multiples of G.x and G.y how EC scalar multiplication work? Oh wow, I thought it's about tangents, intersections, and X-axis reflection under an abelian group using the y**2 = f(x) of the curve equation. I may be wrong but you'll get a spiral for any values of Gx, Gy, and P.
Anyway, new guy here stumbling into the puzzle. I'm amazed by few things so far: the level of innovation by some of you, the level of innocent stupidity by others who think they discovered electricity by playing with stones, and finally the level of arrogance. No, there aren't a handful of people who can approach the issue with competence. I can firmly make a few affirmations, I may or may not let you know which ones are correct (if any or all):
1. EC may very well be, by de-facto, broken because no one can prove it's not. Stop making an assumption a belief you try to indulge on others, this is called fake faith or propaganda. 99.99% of all users based on EC crypto-systems have no idea what awaits them very soon.
2. You don't need a quantum computer or waste power on running 100 GPUs to run some dude's flawed implementation. Do you REALLY understand what the code is actually doing? Unfortunately I'm in that category of people who do understand (20+ years of C/C++ coding plus many other languages, and that's because I love it, not because it pays for my life style).
3. EC was studied centuries before semiconductors were discovered and the transistor got invented. There are 500+ years old math problems not yet solved / proven, and very simple ones, much more simple than ECDLP.
That said, let's just say that there is something very obvious hidden in plain sight, when dealing with all modular arithmetics, be it the discrete logarithm, ECDLP or prime factorization problem. Let me just say this: a hash algorithm can always collide. But the real math, like actual good programming, doesn't work without guarantees. Take everything you have at your disposal, modular math is like "losing" information and pretending it can never be retrieved back, and calling it a "discrete problem". I do have some pen and paper results taken out from ideas you will never find in any study, ChatGPT, or school. Are there chances for any of them to break EC? Maybe, maybe not. But if it does, puzzle 66 may be the last of your problems.