Efficient and Generic Methods to Achieve Active Security in Private Information Retrieval and More Advanced Database Search

Motivated by secure database search, we present secure computation protocols for a function $f$ in the client-servers setting, where a client can obtain $f(x)$ on a private input $x$ by communicating with multiple servers each holding $f$. Specifically, we propose generic compilers from passively secure protocols, which only keep security against servers following the protocols, to actively secure protocols, which guarantee privacy and correctness even against malicious servers. Our compilers are applied to protocols computing any class of functions, and are efficient in that the overheads in communication and computational complexity are only polynomial in the number of servers, independent of the complexity of functions. We then apply our compilers to obtain concrete actively secure protocols for various functions including private information retrieval (PIR), bounded-degree multivariate polynomials and constant-depth circuits. For example, our actively secure PIR protocols achieve exponentially better computational complexity in the number of servers than the currently best-known protocols. Furthermore, our protocols for polynomials and constant-depth circuits reduce the required number of servers compared to the previous actively secure protocols. In particular, our protocol instantiated from the sparse Learning Parity with Noise (LPN) assumption is the first actively secure protocol for multivariate polynomials which has the minimum number of servers, without assuming fully homomorphic encryption.