In this work we consider the following question: What is the cost of security for multi-party protocols? Specifically, given an insecure protocol where parties exchange (in the worst case) Γ bits in N rounds, is it possible to design a secure protocol with communication complexity close to Γ and N rounds? We systematically study this problem in a variety of settings and we propose solutions based on the intractability of different cryptographic problems. For the case of two parties we design an interaction-preserving compiler where the number of bits exchanged in the secure protocol approaches Γ and the number of rounds is exactly N, assuming the hardness of standard problems over lattices. For the more general multi-party case, we obtain the same result assuming either (i) an additional round of interaction or (ii) the existence of extractable witness encryption and succinct non-interactive arguments of knowledge. As a contribution of independent interest, we construct the first multi-key fully homomorphic encryption scheme with message-to-ciphertext ratio (i.e., rate) of 1 - o(1), assuming the hardness of the learning with errors (LWE) problem. We view our work as a support for the claim that, as far as interaction and communication are concerned, one does not need to pay a significant price for security in multi-party protocols.
@InProceedings{dottling_et_al:LIPIcs.ITCS.2022.57, author = {D\"{o}ttling, Nico and Goyal, Vipul and Malavolta, Giulio and Raizes, Justin}, title = {{Interaction-Preserving Compilers for Secure Computation}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {57:1--57:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-217-4}, ISSN = {1868-8969}, year = {2022}, volume = {215}, editor = {Braverman, Mark}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.57}, URN = {urn:nbn:de:0030-drops-156534}, doi = {10.4230/LIPIcs.ITCS.2022.57}, annote = {Keywords: Multiparty Computation, Communication Complexity, Fully Homomorphic Encryption} }
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