Cryptography isn't perfect; someone could always guess your private key. But that doesn't make it useless, since you're hoping that it's just sufficiently improbable that nobody in their right mind will even try doing it.
> Cryptography isn't perfect; someone could always guess your private key.
For the accepted standards, even the smartest people working in this area have not yet found a method to find the private key sufficiently fast (at least such a method has not been published). So to the best of our current knowledge, those methods are at least very near to the perfection that is possible with our current technology.
> Cryptography isn't perfect; someone could always guess your private key.
Cryptography is a branch of mathematics, and cryptographic systems can be formally proved to have certain properties, such as being unable to derive the private key from the content of the encrypted message. That the private key can be guessed is a trivial observation, and a bad argument for dismissing formal proofs. ASLR is a hack on a hack that does not tell you anything about the formal properties of the system.
> Cryptography is a branch of mathematics, and cryptographic systems can be formally proved to have certain properties, such as being unable to derive the private key from the content of the encrypted message.
A small correction: All those proofs (if they exist) are relative to complexity-theoretical conjectures that are (ideally) widely believed to be true, but open. The only system that I am aware of where an "absolute" security proof exists is OTP, but this is hardly suitable to use in practice.
For the accepted standards, even the smartest people working in this area have not yet found a method to find the private key sufficiently fast (at least such a method has not been published). So to the best of our current knowledge, those methods are at least very near to the perfection that is possible with our current technology.