How strong is Monero cryptography against such an attack?
This image says that all the energy of the sun would not be enough to try all the Bitcoin private keys (256-bit keys).
The elliptic curve that Monero uses works with 255-bit private keys, and trying all of them would not be feasible either.
One weakness that Bitcoin and Monero both share are from quantum computing. With quantum computing, significantly less energy would be required to crack private keys.
Therefore Monero is (essentially) equally secure, withstanding that quantum computation is not available.