Round and Communication Balanced Protocols for Oblivious Evaluation of Finite State Machines

Abstract

We propose protocols for obliviously evaluating finite-state machines, i.e., the evaluation is shared between the provider of the finite-state machine and the provider of the input string in such a manner that neither party learns the other's input, and the states being visited are hidden from both. For alphabet size |Σ|, number of states |Q|, and input length n, previous solutions have either required a number of rounds linear in n or communication Ω(n|Σ||Q| log |Q|). Our solutions require 2 rounds with communication O(n(|Σ|+|Q| log |Q|)). We present two different solutions to this problem, a two-party one and a setting with an untrusted but non-colluding helper.