So, I get that if we have the x coordinate, we can easily figure out the y coordinate. But is there a way to find x if we’re only given the y coordinate?
Sure but there are three possibilities for the three cube roots, analogous to the two for y given x for the two square roots. it's just highschool algebra.
In general solving cubic modulo of a large prime is believed to be computationally hard as there is no polynomial time algorithm is known for an arbitrary large large prime fields in the case of secp256k1. Therefore Ill say finding x from y could be really difficult even though it can be possible.
It's difficult at all, as two people just beat me to showing.
Don't respond to forum questions using AI-- if someone wants Automated Ignorance the can get it themselves directly without it being laundered through you.
Does anyone know the private key on this one? It is possible to compute the private key on this public keys?
04146d3b65add9f54ccca28533c88e2cbc63f7443e1658783ab41f8ef97c2a10b50000000000000 000000000000000000000000000000000000000000000000001
x1 = 9239253246023934947662416411507919214268280226895293549906036206298523635893
Two y values:.
y1 = 1
y2 = 115792089237316195423570985008687907853269984665640564039457584007908834671662
Bitcoin (BTC):
Compressed: 1PiiawxF6H1GysDYZyPLsPnyGinMWtrg1Q
Uncompressed: 1vzUAMhmjryjSud2ojJ5XtS9YwiwqsdZM
and this.
Public compressed: 030000000000000000000000000000000000000000000000000000000000000002
Result Public uncompressed: 040000000000000000000000000000000000000000000000000000000000000002990418d84d45f 61f60a56728f5a10317bdb3a05bda4425e3aee079f8a847a8d1
x1 = 2
y1= 69211104694897500952317515077652022726490027694212560352756646854116994689233
Bitcoin (BTC):
Compressed: 1No6KkoyLWUxbyZDApmTWhPn9mezV4cZa4
Uncompressed: 1Po5CisZWp5yc6jkDHXT2cSfFSqgym9yHs