Multiparty computation (MPC) among n parties can tolerate up to t < n/2 active corruptions in a synchronous communication setting; however, in an asynchronous communication setting, the resiliency bound decreases to only t < n/3 active corruptions. We improve the resiliency bound for asynchronous MPC (AMPC) to match synchronous MPC using non-equivocation. Non-equivocation is a message authentication mechanism to restrict a corrupted sender from mak-ing conflicting statements to different (honest) parties. It can be implemented using an increment-only counter and a digital signature oracle, realizable with trusted hardware modules readily available in com-modity computers and smartphone devices. A non-equivocation mechanism can also be transferable and allow a receiver to verifiably transfer the authenticated statement to other parties. In this work, using transferable non-equivocation, we present an AMPC protocol tolerating t < n/2 faults. From a practical point of view, our AMPC protocol requires fewer setup assumptions than the previous AMPC protocol with t < n/2 by Beerliová-Trubı́niová, Hirt and Nielsen [PODC 2010]: unlike their AMPC protocol, it does not require any synchronous broadcast round at the beginning of the protocol and avoids the threshold homomorphic encryption setup assumption. Moreover, our AMPC protocol is also efficient and provides a gain of Θ(n) in the communication complexity per multiplication gate, over the AMPC protocol of Beerliová-Trubı́niova ́ et al. In the process, using non-equivocation, we also define the first asynchronous verifiable secret sharing (AVSS) scheme with t < n/2, which is of independent interest to threshold cryptography. 1
We present a secure asynchronous multiparty computation (AMPC) protocol with optimal resilience, involving n = 3t + 1 parties and tolerating a computationally bounded static adversary, capable of corrupting upto t parties. For a security parameter k and for circuits of sufficiently large size, our protocol has an amortized communication complexity of O(cMnk) bits, where cM denotes the number of multiplication gates in the arithmetic circuit, representing the function to be computed. Prior to our work, the most efficient optimally resilient, computationally secure AMPC protocol was due to Hirt et al. (ICALP 2008). The protocol offers an amortized communication complexity of O(cMn2k) bits.
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.
Securemulti-party computation(MPC) is a fundamental problem in secure distributed computing. An MPC protocol allows a set of
nmutually 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 any
ts<n/3parties. On the other hand, perfectly-secureasynchronousMPC protocols can tolerate up to
ta<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 to
ts<n/3corruptions in a synchronous network and up to
ta<n/4corruptions in anasynchronousnetwork. We design such abest-of-both-worldsperfectly-secure MPC protocol, provided
3ts+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 tolerating
t<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 to
tsand
tacorruptions in asynchronousand in anasynchronousnetwork respectively.
In this paper, we present an optimally-resilient, unconditionally-secure asynchronous multi-party computation (AMPC) protocol for n parties, tolerating a computationally unbounded adversary, capable of corrupting up to t < n/3 parties. Our protocol needs a communication of 𝒪(n⁴) field elements per multiplication gate. This is to be compared with previous best AMPC protocol (Patra et al, ICITS 2009) in the same setting, which needs a communication of 𝒪(n⁵) field elements per multiplication gate. To design our protocol, we present a simple and highly efficient asynchronous verifiable secret-sharing (AVSS) protocol, which is of independent interest.