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arXiv:2208.06223 · Leibniz international proceedings in informatics

Network Agnostic Perfectly Secure MPC Against General Adversaries

Ananya Appan, Anirudh Chandramouli, Ashish Choudhury

Published Aug 12, 2022• 1 citation
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Abstract

In this work, we study perfectly-secure multi-party computation (MPC) against general (non-threshold) adversaries. Known protocols in a synchronous network are secure against $Q^{(3)}$ adversary structures, while in an asynchronous network, known protocols are secure against $Q^{(4)}$ adversary structures. A natural question is whether there exists a single protocol which remains secure against $Q^{(3)}$ and $Q^{(4)}$ adversary structures in a synchronous and in an asynchronous network respectively, where the parties are not aware of the network type. We design the first such best-of-both-worlds protocol against general adversaries. Our result generalizes the result of Appan, Chandramouli and Choudhury (PODC 2022), which presents a best-of-both-worlds perfectly-secure protocol against threshold adversaries. To design our protocol, we present two important building blocks which are of independent interest. The first building block is a best-of-both-worlds perfectly-secure Byzantine agreement (BA) protocol for $Q^{(3)}$ adversary structures, which remains secure both in a synchronous, as well as an asynchronous network. The second building block is a best-of-both-worlds perfectly-secure verifiable secret-sharing (VSS) protocol, which remains secure against $Q^{(3)}$ and $Q^{(4)}$ adversary structures in a synchronous network and an asynchronous network respectively.

DOI
10.4230/lipics.disc.2023.3

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In this work, we study perfectly-secure multi-party computation (MPC) against general (non-threshold) adversaries. Known protocols in a synchronous network are secure against Q(3)Q^{(3)}Q(3) adversary structures, while in an asynchronous network, known protocols are secure against Q(4)Q^{(4)}Q(4) adversary structures. A natural question is whether there exists a single protocol which remains secure against Q(3)Q^{(3)}Q(3) and Q(4)Q^{(4)}Q(4) adversary structures in a synchronous and in an asynchronous network respectively, where the parties are not aware of the network type. We design the first such best-of-both-worlds protocol against general adversaries. Our result generalizes the result of Appan, Chandramouli and Choudhury (PODC 2022), which presents a best-of-both-worlds perfectly-secure protocol against threshold adversaries. To design our protocol, we present two important building blocks which are of independent interest. The first building block is a best-of-both-worlds perfectly-secure Byzantine agreement (BA) protocol for Q(3)Q^{(3)}Q(3) adversary structures, which remains secure both in a synchronous, as well as an asynchronous network. The second building block is a best-of-both-worlds perfectly-secure verifiable secret-sharing (VSS) protocol, which remains secure against Q(3)Q^{(3)}Q(3) and Q(4)Q^{(4)}Q(4) adversary structures in a synchronous network and an asynchronous network respectively.
In this work, we initiate the study of network-agnostic perfectly-secure multi-party computation (MPC) against general (non-threshold) adversaries, where the corruption capacity of the adversary is specified through an adversary structure, which is a set of potentially corrupt subsets of parties. Known MPC protocols are designed either assuming a synchronous network where every sent message is guaranteed to be delivered within some known time or assuming an asynchronous network where no timing assumptions are made and every sent message is eventually delivered. Perfectly-secure MPC protocols in the synchronous network can be designed as long as the underlying adversary structure satisfies the$ {{\mathcal {Q}}}^{(3)}condition,meaningthattheunionofnothreesubsetsfromtheadversarystructurecoverstheentiresetofparties.Ontheotherhand,perfectly−secureMPCprotocolsintheasynchronousnetworkcanbedesignedonlyagainstcondition, meaning that the union of no three subsets from the adversary structure covers the entire set of parties. On the other hand, perfectly-secure MPC protocols in the asynchronous network can be designed only againstcondition,meaningthattheunionofnothreesubsetsfromtheadversarystructurecoverstheentiresetofparties.Ontheotherhand,perfectly−secureMPCprotocolsintheasynchronousnetworkcanbedesignedonlyagainst {{\mathcal {Q}}}^{(4)}adversarystructures,meaningthattheunionofnofoursubsetsfromtheadversarystructurecoverstheentiresetofparties.AnaturalquestioniswhetherasingleMPCprotocolexists,whichremainssecureevenifthepartiesareunawareofthenetworkconditionsatexecutiontime.Thatis,ifthesynchronyissatisfiedthroughouttheprotocolexecutionthentheprotocolshouldbesecureagainstanyadversary structures, meaning that the union of no four subsets from the adversary structure covers the entire set of parties. A natural question is whether a single MPC protocol exists, which remains secure even if the parties are unaware of the network conditions at execution time. That is, if the synchrony is satisfied throughout the protocol execution then the protocol should be secure against anyadversarystructures,meaningthattheunionofnofoursubsetsfromtheadversarystructurecoverstheentiresetofparties.AnaturalquestioniswhetherasingleMPCprotocolexists,whichremainssecureevenifthepartiesareunawareofthenetworkconditionsatexecutiontime.Thatis,ifthesynchronyissatisfiedthroughouttheprotocolexecutionthentheprotocolshouldbesecureagainstany {{\mathcal {Q}}}^{(3)}adversarystructure.However,evenifanysynchronyassumptionisviolatedduringtheexecution,theprotocolshouldstillbesecureagainstanyadversary structure. However, even if any synchrony assumption is violated during the execution, the protocol should still be secure against anyadversarystructure.However,evenifanysynchronyassumptionisviolatedduringtheexecution,theprotocolshouldstillbesecureagainstany {{\mathcal {Q}}}^{(4)}adversarystructure.Weanswertheabovequestionaffirmatively.Fixanyadversarystructureadversary structure. We answer the above question affirmatively. Fix any adversary structureadversarystructure.Weanswertheabovequestionaffirmatively.Fixanyadversarystructure{\mathcal {Z}}_{s}andandand{\mathcal {Z}}_{a}satisfyingsatisfyingsatisfying {{\mathcal {Q}}}^{(3)}andandand {{\mathcal {Q}}}^{(4)}conditionsrespectively,suchthatconditions respectively, such thatconditionsrespectively,suchthat{\mathcal {Z}}_{a} \subset {\mathcal {Z}} _{s}.Weshowtheexistenceofanetwork−agnosticperfectly−secureMPCprotocoltolerating. We show the existence of a network-agnostic perfectly-secure MPC protocol tolerating.Weshowtheexistenceofanetwork−agnosticperfectly−secureMPCprotocoltolerating{\mathcal {Z}}_{s}andandand{\mathcal {Z}}_{a}insynchronousandasynchronousnetworksrespectivelyaslongasthein synchronous and asynchronous networks respectively as long as theinsynchronousandasynchronousnetworksrespectivelyaslongasthe {{\mathcal {Q}}}^{(3, 1)}conditionissatisfied,meaningthattheunionofnothreesubsetsfromcondition is satisfied, meaning that the union of no three subsets fromconditionissatisfied,meaningthattheunionofnothreesubsetsfrom{\mathcal {Z}}_{s}andonesubsetfromand one subset fromandonesubsetfrom{\mathcal {Z}}_{a}$covers the entire set of parties. Our result generalizes the result of Appan, Chandramouli and Choudhury (IEEE Transactions on IT, 2023), which presents the only known perfectly-secure network-agnostic MPC protocol against threshold adversaries.
Securemulti-party computation(MPC) is a fundamental problem in secure distributed computing. An MPC protocol allows a set ofnnnmutually distrusting parties to carry out any joint computation of their private inputs, without disclosing any additional information about their inputs. MPC withinformation-theoreticsecurity (also calledunconditional security) provides the strongest security guarantees and remains secure even againstcomputationally unboundedadversaries.Perfectly-secureMPC protocols are a class of information-theoretically secure MPC protocols, which provide all the security guarantees in anerror-freefashion. The focus of this work is perfectly-secure MPC. Known protocols are designedassumingeither asynchronousorasynchronouscommunication network. It is well known that perfectly-securesynchronousMPC is possible as long as the adversary can corrupt anyts<n/3t_{s} < n/3ts​<n/3parties. On the other hand, perfectly-secureasynchronousMPC protocols can tolerate up tota<n/4t_{a} < n/4ta​<n/4corrupt parties. A natural question is does there exist asingleMPC protocol for the setting where the parties arenot awareof the exact network type and which can tolerate up tots<n/3t_{s} < n/3ts​<n/3corruptions in a synchronous network and up tota<n/4t_{a} < n/4ta​<n/4corruptions in anasynchronousnetwork. We design such abest-of-both-worldsperfectly-secure MPC protocol, provided3ts+ta<n3t_{s} + t_{a} < n3ts​+ta​<nholds. For designing our protocol, we design two important building blocks which are of independent interest. The first building block is a best-of-both-worldsByzantine agreement(BA) protocol toleratingt<n/3t < n/3t<n/3corruptions which remains securebothin a synchronous as well as asynchronous network. The second building block is a polynomial-based best-of-both-worldsverifiable secret-sharing(VSS) protocol, which can tolerate up totst_{s}ts​andtat_{a}ta​corruptions in asynchronousand in anasynchronousnetwork respectively.
Secure multi-party computation (MPC) is a fundamental problem in secure distributed computing. The optimal resilience for perfectly-secure MPC in synchronous and asynchronous networks is t < n/3 and t < n/4 respectively, where n is the number of parties and t is the number of corruptions. A natural question is whether there exists a protocol tolerating ts < n/3 corruptions in a synchronous network and ta < n/4 corruptions in an asynchronous network. We design such a protocol, if 3ts + ta < n. For our protocol, we present a perfectly-secure Byzantine agreement (BA) protocol, tolerating t < n/3 corruptions in any network and a perfectly-secure verifiable secret-sharing (VSS) protocol, tolerating ts and ta corruptions in a synchronous and an asynchronous network respectively.
Perfectly-secure verifiable secret sharing (VSS) and multi-party computation (MPC) protocols in asynchronous network tolerate only at most one-fourth of corruption, while their counterparts in synchronous network sustain against at most one-third corruption. Moreover property-wise, synchronous protocols provide much stronger guarantees than the asynchronous counterparts. Taking note of the fact that asynchronous network is more realistic on one hand and on the other, synchrony of a network has positive impact on several aspects of distributed protocols including properties and fault-tolerance, we explore the power of hybrid networks that combines best of both the worlds by supporting a few synchronous rounds at the onset of a protocol execution, before turning to asynchronous mode. In hybrid networks, we investigate various feasibility questions pertaining to protocols giving guarantees attainable in synchronous and asynchronous networks. For the asynchronous protocols in hybrid networks, we hope to leverage the initial synchronous rounds to bridge the gap in the fault-tolerance with the synchronous protocols under minimal synchrony assumption. We ask the following fundamental question of both theoretical and practical importance: What is the minimum number of initial synchronous rounds necessary and sufficient in a hybrid network to construct asynchronous perfectly-secure VSS and MPC protocols with the fault-tolerance of synchronous protocols? On the positive note, we show that the answer is one for VSS which is clearly optimal. Notably no broadcast oracle is invoked in the synchronous round of our proposed VSS protocol. On the negative side, we prove that one synchronous round is not enough for MPC, putting MPC on a higher pedestal than VSS in terms of difficulty. For synchronous protocols in hybrid networks, we hope to save on the synchronous rounds leveraging conveniently the available asynchronous phase. We settle the question for VSS in the negative showing that three rounds that are known to be necessary (and sufficient) for VSS in synchronous networks, are also required in hybrid networks. VSS being a special case of MPC, the lower bound holds true for MPC. We match the lower bound with a three-round protocol. Notably, synchronous MPC with cryptographic security is known to be achievable in hybrid networks with one synchronous round.
Verifiable Secret-Sharing(VSS) is a fundamental primitive in secure distributed computing that allows a designated dealer to share a secret amongnparties in the presence of an adversary controlling at mosttof them. We study VSS in the presence ofcomputationally-boundedadversaries. Known VSS protocols tolerate up totstaperfectsecurity (Appan et al. IEEE IT 2023) where the threshold conditions arenotknown to be optimal or withstatistical security(Appan et al. TCC 2023) where the threshold conditions are optimal, but the parties need to performexponentialamount of computation and communication. Using our VSS protocol, we design a secureMulti-Party Computation(MPC) protocol in theplain Public Key Infrastructure (PKI) model, i.e., without assuming an expensive trusted setup. Although our proposed MPC protocol incurs higher communication complexity than state-of-the-art network-agnostic MPC protocols, it motivates alternative directions for designingcomputationally inexpensiveMPC protocols based on a plain PKI setup, which has not been explored in the domain of computationally secure networkagnostic MPC and offers valuable insights into designing it.
In this paper, we design secure multi-party computation (MPC) protocols in the asynchronous communication setting with optimal resilience. Our protocols are secure against a computationally-unbounded malicious adversary, characterized by an adversary structure Z\mathcal{Z}Z, which enumerates all possible subsets of potentially corrupt parties. Our protocols incur a communication of O(∣Z∣2)\mathcal{O}(|\mathcal{Z}|^2)O(∣Z∣2) and O(∣Z∣)\mathcal{O}(|\mathcal{Z}|)O(∣Z∣) bits per multiplication for perfect and statistical security respectively. These are the first protocols with this communication complexity, as such protocols were known only in the synchronous communication setting (Hirt and Tschudi, ASIACRYPT 2013).