Adaptively Secure MPC with Sublinear Communication Complexity

Ran Cohen, Abhi Shelat, Daniel Wichs

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

Abstract

A central challenge in the study of MPC is to balance between security guarantees, hardness assumptions, and resources required for the protocol. In this work, we study the cost of tolerating adaptive corruptions in MPC protocols under various corruption thresholds. In the strongest setting, we consider adaptive corruptions of an arbitrary number of parties (potentially all) and achieve the following results: A two-round secure function evaluation (SFE) protocol in the CRS model, assuming LWE and indistinguishability obfuscation (iO). The communication, the CRS size, and the online-computation are sublinear in the size of the function. The iO assumption can be replaced by secure erasures. Previous results required either the communication or the CRS size to be polynomial in the function size.Under the same assumptions, we construct a “Bob-optimized” 2PC (where Alice talks first, Bob second, and Alice learns the output). That is, the communication complexity and total computation of Bob are sublinear in the function size and in Alice’s input size. We prove impossibility of “Alice-optimized” protocols.Assuming LWE, we bootstrap adaptively secure NIZK arguments to achieve proof size sublinear in the circuit size of the NP-relation. On a technical level, our results are based on laconic function evaluation (LFE) (Quach, Wee, and Wichs, FOCS’18) and shed light on an interesting duality between LFE and FHE. Next, we analyze adaptive corruptions of all-but-one of the parties and show a two-round SFE protocol in the threshold PKI model (where keys of a threshold FHE scheme are pre-shared among the parties) with communication complexity sublinear in the circuit size, assuming LWE and NIZK. Finally, we consider the honest-majority setting, and show a two-round SFE protocol with guaranteed output delivery under the same constraints.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2019 - 39th Annual International Cryptology Conference, Proceedings
EditorsAlexandra Boldyreva, Daniele Micciancio
PublisherSpringer Verlag
Pages30-60
Number of pages31
ISBN (Print)9783030269500
DOIs
StatePublished - 2019
Externally publishedYes
Event39th Annual International Cryptology Conference, CRYPTO 2019 - Santa Barbara, United States
Duration: 18 Aug 201922 Aug 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11693 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference39th Annual International Cryptology Conference, CRYPTO 2019
Country/TerritoryUnited States
CitySanta Barbara
Period18/08/1922/08/19

Bibliographical note

Publisher Copyright:
© 2019, International Association for Cryptologic Research.

Funding

R. Cohen—Research supported by the Northeastern University Cybersecurity and Privacy Institute Post-doctoral fellowship, NSF grant TWC-1664445, NSF grant 1422965, and by the NSF MACS project. A. Shelat—Research supported by NSF grant TWC-1664445 and a Google Faculty fellowship. D. Wichs—Research supported by NSF grants CNS-1314722, CNS-1413964, CNS-1750795 and the Alfred P. Sloan Research Fellowship.

FundersFunder number
National Science Foundation1422965, TWC-1664445
Alfred P. Sloan Foundation
GoogleCNS-1750795, CNS-1413964, CNS-1314722
Northeastern University

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