A private lookup protocol with low online complexity for secure multiparty computation

Abstract

We present a secure multiparty computation (SMC) protocol for obliviously reading an element of an array, achieving constant online communication complexity. While the total complexity of the protocol is linear in the size of the array, the bulk of it is pushed into the offline precomputation phase, which is independent of the array and the index of the element. Although private lookup is less general than oblivious RAM (ORAM), it allows us to give new and/or more efficient SMC protocols for a number of important computational tasks. In this paper, we present protocols for executing deterministic finite automata (DFA), and for finding shortest distances in sparse graphs. All our protocols are given in the arithmetic black box model, which allows them to be freely composed and used in larger applications.