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Title:
Best Possible Information-Theoretic MPC
Authors: Shai Halevi, Yuval Ishai, Eyal Kushilevitz, Tal Rabin
Abstract:We reconsider the security guarantee that can be achieved by general protocols for secure multiparty computation in the most basic of settings: information-theoretic security against a semi-honest adversary. Since the 1980s, we have elegant solutions to this problem that offer full security, as long as the adversary controls a minority of the parties, but fail completely when that threshold is crossed. In this work, we revisit this problem, questioning the optimality of the standard notion of security. We put forward a new notion of information-theoretic security which is strictly stronger than the standard one, and which we argue to be ``best possible.‘’ Our new notion still requires full security against dishonest minority in the usual sense, but also requires a meaningful notion of information-theoretic security against dishonest majority. We present protocols for useful classes of functions that satisfy this new notion of security. Our protocols have the unique feature of combining the efficiency benefits of protocols for an honest majority and (most of) the security benefits of protocols for dishonest majority. We further extend some of the solutions to the malicious setting.
ePrint: https://eprint.iacr.org/2018/913
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