Constant-Round Asynchronous Multi-Party Computation Based on One-Way Functions

Constant-Round Asynchronous Multi-Party Computation Secure multi-party computation (MPC) allows several mutually distrustful parties to securely compute a joint function of their inputs and exists in two main variants: In *synchronous* MPC parties are connected by a synchronous network with a global clock, and protocols proceed in *rounds* with strong delivery guarantees, whereas *asynchronous* MPC protocols can be deployed even in networks that deliver messages in an arbitrary order and impose arbitrary delays on them. The two models---synchronous and asynchronous---have to a large extent developed in parallel with results on both feasibility and asymptotic efficiency improvements in either track. The most notable gap in this parallel development is with respect to round complexity. In particular, although under standard assumptions on a synchronous communication network (availability of secure channels and broadcast), synchronous MPC protocols with (exact) constant rounds have been constructed, to the best of our knowledge, thus far no constant-round asynchronous MPC protocols are known, with the best protocols requiring a number of rounds that is linear in the multiplicative depth of the arithmetic circuit computing the desired function. In this work we close this gap by providing the first constant-round asynchronous MPC protocol. Our protocol is optimally resilient (i.e., it tolerates up to $t<n/3$ corrupted parties), adaptively secure, and makes black-box use of a pseudo-random function. It works under the standard network assumptions for protocols in the asynchronous MPC setting, namely, a complete network of point-to-point (secure) asynchronous channels with eventual delivery and asynchronous Byzantine agreement (aka consensus). We provide formal definitions of these primitives and a proof of security in the Universal Composability framework

Peer-to-Peer Secure Multi-Party Numerical Computation Facing Malicious Adversaries

We propose an efficient framework for enabling secure multi-party numerical computations in a Peer-to-Peer network. This problem arises in a range of applications such as collaborative filtering, distributed computation of trust and reputation, monitoring and other tasks, where the computing nodes is expected to preserve the privacy of their inputs while performing a joint computation of a certain function. Although there is a rich literature in the field of distributed systems security concerning secure multi-party computation, in practice it is hard to deploy those methods in very large scale Peer-to-Peer networks. In this work, we try to bridge the gap between theoretical algorithms in the security domain, and a practical Peer-to-Peer deployment. We consider two security models. The first is the semi-honest model where peers correctly follow the protocol, but try to reveal private information. We provide three possible schemes for secure multi-party numerical computation for this model and identify a single light-weight scheme which outperforms the others. Using extensive simulation results over real Internet topologies, we demonstrate that our scheme is scalable to very large networks, with up to millions of nodes. The second model we consider is the malicious peers model, where peers can behave arbitrarily, deliberately trying to affect the results of the computation as well as compromising the privacy of other peers. For this model we provide a fourth scheme to defend the execution of the computation against the malicious peers. The proposed scheme has a higher complexity relative to the semi-honest model. Overall, we provide the Peer-to-Peer network designer a set of tools to choose from, based on the desired level of security.Comment: Submitted to Peer-to-Peer Networking and Applications Journal (PPNA) 200

Computing on Anonymous Quantum Network

This paper considers distributed computing on an anonymous quantum network, a network in which no party has a unique identifier and quantum communication and computation are available. It is proved that the leader election problem can exactly (i.e., without error in bounded time) be solved with at most the same complexity up to a constant factor as that of exactly computing symmetric functions (without intermediate measurements for a distributed and superposed input), if the number of parties is given to every party. A corollary of this result is a more efficient quantum leader election algorithm than existing ones: the new quantum algorithm runs in O(n) rounds with bit complexity O(mn^2), on an anonymous quantum network with n parties and m communication links. Another corollary is the first quantum algorithm that exactly computes any computable Boolean function with round complexity O(n) and with smaller bit complexity than that of existing classical algorithms in the worst case over all (computable) Boolean functions and network topologies. More generally, any n-qubit state can be shared with that complexity on an anonymous quantum network with n parties.Comment: 25 page

Resource-Efficient and Robust Distributed Computing

There has been a tremendous growth in the size of distributed systems in the past three decades. Today, distributed systems, such as the Internet, have become so large that they require highly scalable algorithms; algorithms that have asymptotically-small communication, computation, and latency costs with respect to the network size. Moreover, systems with thousands or even millions of parties distributed throughout the world is likely in danger of faults from untrusted parties. In this dissertation, we study scalable and secure distributed algorithms that can tolerate faults from untrusted parties. Throughout this work, we balance two important and often conflicting characteristics of distributed protocols: security and efficiency. Our first result is a protocol that solves the MPC problem in polylogarithmic communication and computation cost and is secure against an adversary than can corrupt a third of the parties. We adapted our synchronous MPC protocol to the asynchronous setting when the fraction of the corrupted parties are less than 1/8. Next, we presented a scalable protocol that solves the secret sharing problem between rational parties in polylogarithmic communication and computation cost. Furthermore, we presented a protocol that can solve the interactive communication problem over a noisy channel when the noise rate in unknown. In this problem, we have focused on the cost of the protocol in the resource-competitive analysis model. Unlike classic models, resource-competitive models consider the cost that the adversary must pay to succeed in corrupting the protocol