The reason for referencing the sun is that it is a massive fusion power plant on a scale which nothing humans have ever done even comes close.  Do I realistically think someone would turn the sun into a power plant (dyson sphere) for a giant private key breaking machine? No; but if the sun doesn't have enough energy than nothing in our solar system has enough energy.

The largest nuclear power plants are on the order of 1 GW (10^9 watts).  The sun is on the order of 10^26 watts.  Thus it has the output of 10 quadrillion 1GW nuclear power plants. Even the relatively tiny amount of solar energy which strikes the earth is more than 100x the total energy usage of the human race (in all forms).

If a theoretical "solution" requires more than what is available from our star, given our knowledge of physics, it can't be accomplished.  At least not until humans can travel to other larger sources of power (stars).