Can We Derive X from Y in Bitcoin?

If we have the y coordinate, can we figure out x? I feel like there must be a way.

No way that's possible. Just doesn't work like that.

Why not? There’s gotta be some formula out there.

There might be but it’s tricky. For every x, there are three possible y values, kinda like how you have two roots in a square root scenario. Just basic algebra.

Can you break down the formula you’re talking about?

Well, solving cubic equations modulo a large prime is tough, especially with secp256k1. No known polynomial-time algorithm exists for this, so finding x from y is a real challenge.

Thanks for the info. I heard somewhere that it’s impossible to derive x from y.

Yeah, it’s not just hard, it’s nearly impossible. Saw some people trying to explain it earlier.

Anyone know if it’s possible to get the private key from these public keys? What do you think about this?

I tried finding x1 = 1 once. Honestly, those points are pretty much a mystery to everyone. Finding them is super tough.