I recall reading in college about a nascent research area regarding cryptographic techniques for secure computing, relating to zero-knowledge proofs, but I am having trouble remembering the exact term.
In particular, you could imagine a theoretical untrusted computer that you could send encrypted data and an encrypted computer program, and that computer could execute the program on the data without being able to learn anything about the data or the program, and it will produce an encrypted output that it also cannot learn anything about. Further, once the output was received, you could verify the output is the result of the computation in a way that is computationally easier than the computation itself.
Obviously, such a general-purpose protocol is highly unlikely to be feasible, but I imagine various subsets are certainly possible, and I was looking for research on such techniques.
One such area of interest is Trusted Computing, which allows some hardware-level assurances, especially if we relax requirements on the system having access to the data and program; but that is not leading me to any cryptographic models for proofs of accurate computation.
Similarly, problems in NP satisfy some of these requirements, since verification of a solution is in P. So I would expect that certain cryptographic techniques could be use for such problems to make assertions about data security in some cases.
Ultimately, I am looking for keywords relating to this type of research.