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

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.

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