Communication-Efficient Private Protocols for Longest Common Subsequence
We design communication efficient two-party and multi-party protocols for the longest common subsequence (LCS) and related problems. Our protocols achieve privacy with 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 Yaos garbled circuit protocol) and, as such, is interesting as a contribution to the theory of communication efficiency for secure two-party and multiparty applications.
Multi-Party Indirect Indexing and Applications
We develop a new multi-party generalization of Naor-Nissim indirect indexing, making it possible for many participants to simulate a RAM machine with only poly-logarithmic blow-up. Our most efficient instantiation (built from length-flexible additively homomorphic public key encryption) improves the communication complexity of secure multi-party computation for a number of problems in the literature. Underlying our approach is a new multi-party variant of oblivious transfer which may be of independent interest.
Improved Efficiency for Private Stable Matching
At Financial Crypto 2006, Golle presented a novel framework for the privacy preserving computation of a stable matching (stable marriage). We show that the communication complexity of Golle's main protocol is substantially greater than what was claimed in that paper, in part due to surprising pathological behavior of Golle's variant of the Gale-Shapley stable matching algorithm. We also develop new protocols in Golle's basic framework with greatly reduced communication complexity.