The first company that can crack the full operational cycle of homomorphic crypto will get a license to print money. As long as they don't squander the first-mover advantage, it will take quite a long time for the eventual second-mover to take over.
It's not just doing the computations in an untrusted cloud environment, although that's a big promise. I would say that an even bigger part will be the eventual ability to run computations on multi-party data sets. If you can provide a provably secure zero-knowledge service that still manages to compute results from multiple sources of opaque data, you will have every single financial institution and insurance giant banging on your door.
It's not just doing the computations in an untrusted cloud environment, although that's a big promise. I would say that an even bigger part will be the eventual ability to run computations on multi-party data sets. If you can provide a provably secure zero-knowledge service that still manages to compute results from multiple sources of opaque data, you will have every single financial institution and insurance giant banging on your door.