If I understand this right, this would mean now you could do all the calculations on your data on a cloud based solution without disclosing the data or results,

If I understand this right, this would mean now you could do all the calculations on your data on a cloud based solution without disclosing the data or results, a huge breakthrough for securing sensitive data on the cloud. Or another example, you could run a Google search and Google would return the results without knowing the results or what you initially searched for. This kind of reminds me of the tor network. On the other side, it would make it impossible to know if your cloud system was infected with spyware because you could never prove what it would be doing. But on the other hand, that could actually be a solution to a larger problem, which would solve the problem of pirated software by limiting crackers the ability to decipher the registration-code algorithm of a software product.