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

TL;DR

This paper introduces efficient protocols for obliviously evaluating finite-state machines, achieving minimal rounds and communication, with solutions suitable for two-party and helper-assisted settings.

Contribution

It presents two novel protocols that significantly reduce rounds and communication for oblivious finite-state machine evaluation compared to prior methods.

Findings

Two-round protocols with linear communication complexity

Protocols applicable to both two-party and helper-assisted settings

Improved efficiency over previous linear-round solutions

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 $|\Sigma|$, number of states $|Q|$, and input length $n$, previous solutions have either required a number of rounds linear in $n$ or communication $\Omega(n|\Sigma||Q|\log|Q|)$. Our solutions require 2 rounds with communication $O(n(|\Sigma|+|Q|\log|Q|))$. We present two different solutions to this problem, a two-party one and a setting with an untrusted but non-colluding helper.