Secure multi-party computation in large networks

Abstract

We describe scalable protocols for solving the secure multi-party computation (MPC) problem among a large number of parties. We consider both the synchronous and the asynchronous communication models. In the synchronous setting, our protocol is secure against a static malicious adversary corrupting less than a 1/3 fraction of the parties. In the asynchronous setting, we allow the adversary to corrupt less than a 1/8 fraction of parties. For any deterministic function that can be computed by an arithmetic circuit with m gates, both of our protocols require each party to send a number of field elements and perform an amount of computation that isÕ(m/n + √ n). We also show that our protocols provide perfect and universally-composable security.To achieve our asynchronous MPC result, we define the threshold counting problem and present a distributed protocol to solve it in the asynchronous setting. This protocol is load balanced, with computation, communication and latency complexity of O(log n), and can also be used for designing other load-balanced applications in the asynchronous communication model. * This is the extended version of the paper published in the • Each party sendsÕ(m/n + √ n) field elements.• Each party performsÕ(m/n + √ n) computations.• The expected running time is O(d polylog(n)).Paper Organization. In Section 2, we discuss related work. In Section 3, we define our notation and discuss the building blocks used in our protocols. We present our MPC protocols in Section 4. In Section 5, we prove the security of our MPC protocols. Section 6 is a self-contained presentation of the threshold counting problem and our solution to this problem. In Section 7, we describe an asynchronous protocol for the quorum building problem. Finally, we conclude in Section 8 and discuss future directions. Related WorkDue to the large body of work, we do not attempt a comprehensive review of the MPC literature here, but rather focus on seminal work and, in particular, schemes that achieve sublinear per-party communication costs. The MPC problem was first described by Yao [Yao82]. He described an algorithm for MPC with two parties in the presence of a semi-honest adversary. Goldreich et al.[GMW87] propose the first MPC protocol that is secure against a malicious adversary. This work along with [CDG88, GHY88] are all based on cryptographic hardness assumptions. These were later followed by several cryptographic improvements [BMR90, GRR98, CFGN96]. In a seminal work, Ben-Or et al.[BGW88] show that every function can be computed with information-theoretic security in the presence of a semi-honest adversary controlling less than half of the parties, and in the presence of a malicious adversary controlling less than a third of the parties. They describe a protocol for securely evaluating an arithmetic circuit that represents the function.This work was later improved in terms of both communication and computation costs in [CCD88, Bea91, GRR98]. Unfortunately, these methods all have poor communication scalability. In particular, ...

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