I would very much like to see the proof regarding the necessity of the Laws of Thermodynamics to be broken in order to brute force a 256-bit key. Is there any link of such proof? I'm a bit concerned about the use of energy to do the calculations.
So yeah, something major will have to be broken, or some break-through in computing. The algo will get broken or aliens have this computer that can crack it.
Then of course, they have to be specifically targeting your one address. Is it a legacy address, is it segwit wrapped or native segwit, has it been spent from ... the number to brute force through all that is so astronomically large that even with any technology available today it would take millions of years.
Anything above a couple of decades is practically impossible. Anything that will take longer than a couple of years and it's much more easier to do the $5 wrench attack.
If they want to be covert about it, they would bug everything you have, install cameras everywhere (or access them), invade everything you do. If you created something like a darknet market called The Silk Road, then you are one such target worth some attention. Unless you are James Bond or Ethan Hunt or Jason Bourne, they will find you.
But then, if you're someone like any one of us here, who are complete nobodies in the grand scale of things, and everyone here had a boating accident or something, or we already got rekt ... what's the point, we are worthless to even talk about, no one is going after your paper wallets or cold storage.
If you have any attachments at all, they can use that too. You may not be willing to die for your bitcoins, but will you be willing to let someone else you love suffer for it?
For perspective:
According to estimates, in the middle of 2019 there were 46.8 million people worldwide whose assets exceeded one million USD, of which nearly 40% lived in the United States. The total net worth of all millionaires stood at US$158,261 billion.
Much easier to extort, kidnap, threaten, steal, mug, whatever ... one of them for the money.
On a similar topic, passwords randomly generated longer than 16 or 20 characters will take longer than your lifetime to crack through conventional methods. Much easier to wait for you right before you go inside your bank or ATM machine.
If you are protecting something behind 12 or 24 words ... I'm sure there is math there to show you that no one is going to guess it unless they are very lucky, got struck by lightning every day, or already won the mega millions super powerball lottery equivalent a few times over.
if an attacker knows that you are using a seven-word Diceware passphrase, and they pick seven random words from the Diceware word list to guess, there is a one in 1,719,070,799,748,422,591,028,658,176 chance that they’ll pick your passphrase each try.
At one trillion guesses per second — per Edward Snowden’s January 2013 warning — it would take an average of 27 million years to guess this passphrase.