They would presumably pay for the computations on the network (by paying gas). The output would be still encrypted with the FHE public key and can be signed. Having the clear text is the same as having the private key. How would someone cheat? I’ll admit I’m no crypto nerd but I’m not sure how you would cheat.
They'd pay themselves for computation on the network? You can't see a game theoretical problem with this?
If simply encrencrypting the output is less work than running the computation on the ciphertext input, they'll do that and publish the encrypted output as proof. This would mean alliners would up bid for the computation because they know that if their computation becomes the limiting factor in block creation they can beat everyone else to it.
There's also the problem of benefitting from mining. Mining has to only be useful in that it is used to construct blocks, if it is useful for any other purpose whatsoever, whoever benefits from that purpose has an opportunity to mine at lower marginal cost than other miners.
2. calculate the solution based on the cleartext and encrypt it
3. wait a while--just enough time so that it's plausible that you found the solution based on the cyphertext
4. submit encrypted solution
5. get your bounty back: $$
6. get the reward for having found the solution: $
7. now you have $$$, and everybody else who worked harder than you did has nothing
A $ based on a system that is that easy to cheat isn't going to be worth very much. Personally I think bitcoin is kind of dumb because from a compete-for-rewards perspective the only thing it has going for it is that it's difficult to cheat in this way.
Better would be if we solved the game theoretic issues here so that nobody has an incentive to cheat and the compete-for-rewards work was actually beneficial to society, but so far as I know that doesn't yet exist.
There's BOINC (like folding@home but more generic), coupled with gridcoin (which rewards people in crypto for having "volunteered" their compute for use in BOINC). But it only works because there's a centralized authority in charge of which jobs get submitted to BOIC, and that authority cares more about scientific computing than they care about making money.
