As noted above already, there is a unique mapping between every possible private key and every possible public key, so yes, technically it is 100% possible to "derive" the private key of any (valid) public key, since the mapping is bijective. This uniqueness property is even a basic requirement in order for Bitcoin to actually be able to prove actual ownership.

Even better, unlike hashing, it's not even a brute-force problem to reverse the initial bijective (which was: pub from private). It's simply the discrete log problem, which has known optimal algorithms (and it's still an open question whether it's even that difficult to solve anyway), That's why Bitcoin's security is not even close to 256 bits. It's more around 124 bits or so, given the endomorphism property of the curve, and Pollard's rho algorithm.

So, possible? 100% guaranteed. Feasible? It depends on how much compute power you throw at it, and whatever other details you have (like, a range subset, known bits, etc).

As noted above already, there is a unique mapping between every possible private key and every possible public key, so yes, technically it is 100% possible to "derive" the private key of any (valid) public key, since the mapping is bijective.

Even better, unlike hashing, it's not even a brute-force problem to reverse the initial bijective (which was: pub from private). It's simply the discrete log problem, which has known optimal algorithms (and it's still an open question whether it's even that difficult to solve anyway), That's why Bitcoin's security is not even close to 256 bits. It's more around 124 bits or so, given the endomorphism property of the curve, and Pollard's rho algorithm.

So, possible? 100% guaranteed. Feasible? It depends on how much compute power you throw at it, and whatever other details you have (like, a range subset, known bits, etc).