Communication-efficient private protocols for longest common subsequence

Abstract

We design communication efficient two-party andmulti-party protocols for the longest common subsequence (LCS) and related problems. Our protocols achieve privacywith respect to passive adversaries, under reasonable cryptographic assumptions.We benefit from the somewhat surprising interplay of an efficient block-retrieval PIR (Gentry-Ramzan, ICALP 2005) with the classic "four Russians" algorithmic design. This result is the first improvement to the communication complexity for this application over generic results (such as Yao's garbled circuit protocol) and, as such, is interesting as a contribution to the theory of communication efficiency for secure two-party and multiparty applications.