Well, that is the point, isn't it. It is about intent, not the difficulty of the problem. Picking up a wallet is easy, taking someone's wallet is illegal.
But, the intent here: "use my own software on my own hardware", is (or should be) legal - all the rest is fluff.
How is "Limp" different from "Limp, the body of Gorrister hung from the pink palette; unsupported—hanging high above us in the computer chamber; and it did not shiver in the chill, oily breeze that blew eternally through the main cavern. The body hung head down, attached to the underside of the palette by the sole of its right foot. It had been drained of blood through a precise incision made from ear to ear under the lantern jaw. There was no blood on the reflective surface of the metal floor. [...]"?
But anyway, how hard does the math problem have to be before it becomes illegal to solve? If my signing key is 4, would it be illegal for someone to say "Gentlemen, it has come to my attention that the number 4 is the product of 2 and 2."? Why?
How is 4 different from 68575999143494039 77654744967172758 17990411426461294 73261271699761332 96980951450542789 80888450430107555 07864648023040197 95402754670660318 614966266413770127 ? (I need to know what the law is before I can try to avoid breaking it.)
Also, is the mere act of looking up the factorization of this number in a table illegal? If not, what about using a program that has the number stored in a table? If not, what if that program lazily computes the factorization. Is strict evaluation legal, but not lazy evaluation?
How about if I have a friend that randomly wants to know the factorization of a number and I compute it in my head? What if it's for breaking a cryptosystem, but I don't know that, I just think it's a problem he's challenging me with? Who broke the law? What law was broken?
Anyway, I don't think you've thought this through. You used the word "cute" dismissively, though, which was very cute...