Practical applications of homomorphic encryption algorithms?

Question

It appears there there were interesting things going on in cryptography: the first homomorphic encryption scheme appeared recently (explanation, HT). Roughly sp

Answer 1

The problem with the existing homomorphic encryption algorithm is that you can only execute a polylogarithmic (NC1) circuit with it, which rules out almost anything interesting algorithmically.

Plus it doesn't seem that the complexity of encoding is in any way lower than the complexity of executing the polylogarithmic circuit yourself, so you haven't picked up any free work at first blush, unless you do something particularly tricky with it.