Using brute force (i.e. "immense computing capabilities") for properly sized keys is unlikely to ever be practical with classical computers. With quantum computers, many currently deployed key lengths that would be impractical to brute force with classical computers would become vulnerable to attack, but nobody is currently known to have quantum computers of sufficient power. See Wikipedia for basic details[1].
IMO, an intelligence agency would be more likely to invest in other methods (algorithm implementation weaknesses, software bugs, insider access, etc), due to the higher liklihood of sucess.
That said, it's interesting to note that the NSA is moving towards "post-quantum" cryptography[2], under the assumption that suitably powerful quantum computers will be, or have been, built. Whether the NSA already has such suitably powerful quantum computers is anybodys guess.
IMO, an intelligence agency would be more likely to invest in other methods (algorithm implementation weaknesses, software bugs, insider access, etc), due to the higher liklihood of sucess.
That said, it's interesting to note that the NSA is moving towards "post-quantum" cryptography[2], under the assumption that suitably powerful quantum computers will be, or have been, built. Whether the NSA already has such suitably powerful quantum computers is anybodys guess.
[1] https://en.wikipedia.org/wiki/Key_size#Brute_force_attack [2] https://www.nsa.gov/ia/programs/suiteb_cryptography/