Amortized Sublinear Secure Multi Party Computation

We study the problem of secure two-party and multi-party computation in a setting where some of the participating parties hold very large inputs. Such settings increasingly appear when participants wish to securely query a database server, a typical situation in cloud related applications. Classic results in secure computation require work that grows linearly with the size of the input, while insecure versions of the same computation might require access to only a small number of database entries. We present new secure MPC protocols that, in an amortized analysis, have only polylogarithmic overhead when compared with the work done in an insecure computation of the functionality. Our first protocol is generically constructed from any Oblivious RAM scheme and any secure computation protocol. The second protocol is optimized for secure two-party computation, and is based directly on basic cryptographic primitives.