General computation on encrypted data was discovered by a graduate student at Stanford named Craig Gentry. He now works for IBM, and has been pretty active in

General computation on encrypted data was discovered by a graduate student at Stanford named Craig Gentry. He now works for IBM, and has been pretty active in that field, along with a handful of other experts. It's very slow, sure, but over the past 4 years speeds have increased to the point where it is reasonable to start talking about practical applications. It is also worth pointing out that systems supported restricted classes of functions preceded Gentry's work. If you are willing to limit yourself to NC1 functions (i.e. those that can be represented as boolean circuits with depth that is the logarithm of the input size), you can use oblivious transfer or the SYY construction (cannot recall their names off the top of my head). If you only need products in certain groups, you can use ElGamal. If you only need an XOR, you can use the Goldwasser-Micali system. Also, there are garbled circuits, which date back to the 1980s. That is a somewhat different notion of computing on encrypted data, since it requires messages to be sent every time the computation is performed. Garbled circuits are substantially faster than FHE right now, although that may change due to FHE's low communication overhead and the rate at which FHE speeds have been improving. Also in this category are multiparty protocols that use arithmetic circuits, which have seen at least one major real-world use: http://fc09.ifca.ai/papers/15_Secure_MPC_goes_live.pdf http://fc09.ifca.ai/papers/15_Secure_MPC_goes_live.pdf