Energy requirements to brute force SHA-256

[DannyHamilton]

In other words, if we ever manage to build a supercomputer with the unbelievable power and efficiency to brute force SHA-256 within a human's lifetime, we'd turn that computer into the equivalent of a supernova as soon as we turned it on.

Hmm.  What's the necessary energy density to form a black hole?

M = E / C²

Is it possible that an earth sized computer with enough energy packed into that earth sized space to "brute force SHA-256 within a human's lifetime" might collapse into a black hole, meaning that even if it could find a key, there'd be no way to get that information out of the computer?

[1715393610]

1715393610

[qwk]

Is it possible that an earth sized computer with enough energy packed into that earth sized space to "brute force SHA-256 within a human's lifetime" might collapse into a black hole, meaning that even if it could find a key, there'd be no way to get that information out of the computer?

My intuition instantly said "no", way too little energy.
But to make sure, I did a rough, back-of-the-envelope calculation.

2^256 * 1.56×10^-32 joules ~ 1.8 × 10^45 J
e=mc^2 converts that to 20,027,701,008,965,131,779,133,619,367,264g, or give or take 3,350 earths!

Now, that may seem a lot, but the Schwarzschild radius of an object with that mass is less than 30m.
Since we're packing that in a sphere much larger than 30m, it's not a black hole.

Again, I could be off by orders of magnitude and we'd still get nowhere close to a block hole.
So, our only hope for a black hole earth still rests with the LHC.