Infrastructures for secure multiparty computation

Abstract

We study the problem of implementing an infrastructure for secure multiparty computation (MPC). The goal of our infrastructure is to enable reliable communication, secure computation and fair computation in a network. The desiderata for an infrastructure include reusability, transferability and fault-tolerance. It is not hard to see that the above criteria are fulfilled for infrastructures that we use in daily life, for e.g., the infrastructure for online communication (e-mail, instant messaging, etc.) consisting of transatlantic undersea cables, routers, wireless access points, etc. We consider which cryptographic primitives would be good building blocks for a secure computation infrastructure. The first, reliable communication. We study the problem of almost-everywhere reliable message transmission.

The goal is to design low-degree networks which allow a large fraction of honest nodes to communicate reliably even while linearly many nodes can experience byzantine corruptions and deviate arbitrarily from the assigned protocol. We consider both the worst-case and randomized corruption scheduling models. In the worst-case model, we achieve a log-degree network with a polylogarithmic work complexity protocol improving over the state-of-the-art results that required a polylogarithmic-degree network and had a linear work complexity. In the randomized model, we improve upon the state of the art protocols, both in work-efficiency and in resilience. Next, we propose an infrastructure for secure computation, which would consist of OT channels between some pairs of parties in the network.

We devise information theoretically secure protocols that allow additional pairs of parties to establish secure OT correlations using the help of other parties in the network in the presence of a dishonest majority. Our main technical contribution is an upper bound that matches known lower bounds regarding the number of OT channels necessary and sufficient for MPC. In particular, we characterize which n-party OT graphs G allow t-secure computation of OT correlations between all pairs of parties, showing that this is possible if and only if the complement of G does not contain the complete bipartite graph Kn-t,n-t as a subgraph. Finally, we study the problem of building an infrastructure for fair secure computation, where we guarantee that if any party receives the output of the secure computation, then all honest parties do as well.

Toward this goal, we introduce a new 2-party primitive FSyX ("synchronizable fair exchange") and show that it is complete for realizing any n-party functionality with fairness in a setting where all n parties are pairwise connected by independent instances of FSyX. Additionally, a pair of parties may reuse a single instance of FSyX in any number of multiparty protocols (possibly involving different sets of parties).