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ACM Symposium on Theory of Computing (STOC)

On achieving the "best of both worlds" in secure multiparty computation

Jonathan I. Katz

Published Jun 11, 2007• 75 citations
Publisher

Abstract

Two settings are typically considered for secure multipartycomputation, depending on whether or not a majority of the partiesare assumed to be honest. Protocols designed under this assumptionprovide "full security" (and, in particular, guarantee outputdelivery and fairness) when this assumption is correct; however, if half or more of the parties are dishonest then security iscompletely compromised. On the other hand, protocols toleratingarbitrarily-many faults do not provide fairness or guaranteed output delivery even if only a single party is dishonest. It isnatural to wonder whether it is possible to achieve the "best ofboth worlds" : namely, a single protocol that simultaneouslyachieves the best possible security in both the above settings. Ishai, et al. (Crypto 2006) recently addressed this question, andruled out constant-round protocols of this type.

DOI
10.1145/1250790.1250793

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Two settings are typically considered for secure multipartycomputation, depending on whether or not a majority of the partiesare assumed to be honest. Protocols designed under this assumptionprovide "full security" (and, in particular, guarantee outputdelivery and fairness) when this assumption is correct; however, if half or more of the parties are dishonest then security iscompletely compromised. On the other hand, protocols toleratingarbitrarily-many faults do not provide fairness or guaranteed output delivery even if only a single party is dishonest. It isnatural to wonder whether it is possible to achieve the "best ofboth worlds" : namely, a single protocol that simultaneouslyachieves the best possible security in both the above settings. Ishai, et al. (Crypto 2006) recently addressed this question, andruled out constant-round protocols of this type.
Two settings are traditionally considered for secure multiparty computation, depending on whether or not a majority of the parties are assumed to be honest. Protocols designed under this assumption provide “full security ” (and, in particular, guarantee output delivery and fairness) when this assumption holds; unfortunately, these protocols are completely insecure if this assumption is violated. On the other hand, protocols tolerating an arbitrary number of corruptions do not guarantee fairness or output delivery even if only a single party is dishonest. It is natural to wonder whether it is possible to achieve the “best of both worlds”: namely, a single protocol that simultaneously achieves the best possible security in both the above settings. Here, we rule out this possibility (at least for general functionalities) but show some positive results regarding what can be achieved.
Two settings are traditionally considered for secure multiparty computation, depending on whether or not a majority of the parties are assumed to be honest. Existing protocols that assume an honest majority provide “full security” (and, in particular, guarantee output delivery and fairness) when this assumption holds, but are completely insecure if this assumption is violated. On the other hand, known protocols tolerating an arbitrary number of corruptions do not guarantee fairness or output delivery even if only a single party is dishonest. It is natural to wonder whether it is possible to achieve the “best of both worlds”: namely, a single protocol that simultaneously achieves the best possible security in both the above settings. Here, we rule out this possibility (at least for general functionalities) and show some positive results regarding what can be achieved.
The notion of Best-of-Both-Worlds introduced in the work of Ishai et al. (CRYPTO 2006) investigated whether an MPC protocol can simultaneously provide two incomparable security guarantees: guaranteed output delivery against an honest majority and security with abort against a dishonest majority and provided tight upper and lower bounds in the presence of computationally bounded, i.e., PPT adversaries. Another line of works starting from the work of Chaum (CRYPTO 1989) considered protocols that simultaneously achieved security against an unbounded adversary corrupting a minority of the parties and security against arbitrary corruption by a PPT adversary. In this work, we generalize previous work to investigate a fundamental challenge of designing an MPC in a multiverse where security is specified with respect to (1) GOD, (2) fairness, (3) security w.r.t. unbounded adversaries, and (4) security with abort. The work of Lucas et al. (PODC 2010) resolved this question when considering threshold adversaries; however, the case of general adversary structures remains open. Our main result completely characterizes when a protocol can simultaneously achieve all properties. Namely, given adversary structures ZGOD,Zfair,ZS\mathcal{Z}_{\textsf{GOD}}, \mathcal{Z}_{\textsf{fair}},\mathcal{Z}_{\textsf{S}}ZGOD​,Zfair​,ZS​ and ZC\mathcal{Z}_{\textsf{C}}ZC​ , we provide tight upper and lower bounds for when an MPC protocol can provide GOD, fairness, and security with abort respectively for unbounded and PPT adversaries w.r.t. these adversary structures.
In the setting of secure multiparty computation, a set of parties wish to compute a joint function of their private inputs. The computation should preserve security properties such as privacy, correctness, independence of inputs, fairness and guaranteed output delivery. In the case of no honest majority, fairness and guaranteed output delivery cannot always be obtained. Thus, protocols for secure multiparty computation are typically of two disparate types: protocols that assume an honest majority (and achieve all properties including fairness and guaranteed output delivery), and protocols that do not assume an honest majority (and achieve all properties except for fairness and guaranteed output delivery). In addition, in the two-party case, fairness and guaranteed output delivery are equivalent. As a result, the properties of fairness (which means that if corrupted parties receive output then so do the honest parties) and guaranteed output delivery (which means that corrupted parties cannot prevent the honest parties from receiving output in any case) have typically been considered to be the same. In this paper, we initiate a study of the relation between fairness and guaranteed output delivery in secure multiparty computation. We show that in the multiparty setting these proper-ties are distinct and proceed to study under what conditions fairness implies guaranteed output delivery (the opposite direction always holds). We also show the existence of non-trivial func-tions for which complete fairness is achievable (without an honest majority) but guaranteed output delivery is not, and the existence of non-trivial functions for which complete fairness and guaranteed output delivery are achievable. Our study sheds light on the role of broadcast in fairness and guaranteed output delivery, and shows that these properties should sometimes be considered separately.