Ask HN: Can FHE solve the PoW energy problem?

Hi there,<p>I had an interesting idea on how to perform useful compute with proof of work. We could wrap a problem using Homomorphic Encryption techniques. Each node gets a different problem to solve. If the solution matches a certain pattern, they can write the next block (similar to already existing methods).<p>The key difference is that the research institution interested in submitting a job would pay a fee, and that fee is split among all miners that worked in solving the puzzle - creating a second, STEADY source of revenue to GPU miners!<p>This would put a massive number of GPUs out there into service of science, while increasing the revenue of miners. Efficiency would improve overtime as FHE algorithms evolve. ASIC miners would be very welcome.<p>Please criticize.