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On the Communication Complexity of Secure Multi-Party Computation With Aborts

James Bartusek, Thiago Bergamaschi, Seri Khoury, Saachi Mutreja, Orr Paradise

TL;DR

This work studies the communication complexity of MPC with abort and devise nearly-optimal communication efficient protocols in this model, and proves trade-offs between the number of honest parties h, the communication complexity, and the locality of the protocols.

Abstract

A central goal of cryptography is Secure Multi-party Computation (MPC), where $n$ parties desire to compute a function of their joint inputs without letting any party learn about the inputs of its peers. Unfortunately, it is well-known that MPC guaranteeing output delivery to every party is infeasible when a majority of the parties are malicious. In fact, parties operating over a point-to-point network (i.e. without access to a broadcast channel) cannot even reach an agreement on the output when more than one third of the parties are malicious (Lamport, Shostak, and Pease, JACM 1980). Motivated by this infeasibility in the point-to-point model, Goldwasser and Lindell (J. Cryptol 2005) introduced a definition of MPC that does not require agreement, referred to as MPC with selective abort. Under this definition, any party may abort the protocol if they detect malicious behavior. They showed that MPC with selective abort is feasible for any number of malicious parties by implementing a broadcast functionality with abort. While the model of MPC with abort has attracted much attention over the years, little is known about its communication complexity over point-to-point networks. In this work, we study the communication complexity of MPC with abort and devise nearly-optimal communication efficient protocols in this model. Namely, we prove trade-offs between the number of honest parties $h$, the communication complexity, and the locality of the protocols. Here, locality is a bound on the number of peers with which each party must communicate.

On the Communication Complexity of Secure Multi-Party Computation With Aborts

TL;DR

This work studies the communication complexity of MPC with abort and devise nearly-optimal communication efficient protocols in this model, and proves trade-offs between the number of honest parties h, the communication complexity, and the locality of the protocols.

Abstract

A central goal of cryptography is Secure Multi-party Computation (MPC), where parties desire to compute a function of their joint inputs without letting any party learn about the inputs of its peers. Unfortunately, it is well-known that MPC guaranteeing output delivery to every party is infeasible when a majority of the parties are malicious. In fact, parties operating over a point-to-point network (i.e. without access to a broadcast channel) cannot even reach an agreement on the output when more than one third of the parties are malicious (Lamport, Shostak, and Pease, JACM 1980). Motivated by this infeasibility in the point-to-point model, Goldwasser and Lindell (J. Cryptol 2005) introduced a definition of MPC that does not require agreement, referred to as MPC with selective abort. Under this definition, any party may abort the protocol if they detect malicious behavior. They showed that MPC with selective abort is feasible for any number of malicious parties by implementing a broadcast functionality with abort. While the model of MPC with abort has attracted much attention over the years, little is known about its communication complexity over point-to-point networks. In this work, we study the communication complexity of MPC with abort and devise nearly-optimal communication efficient protocols in this model. Namely, we prove trade-offs between the number of honest parties , the communication complexity, and the locality of the protocols. Here, locality is a bound on the number of peers with which each party must communicate.
Paper Structure (31 sections, 11 theorems, 7 equations, 8 algorithms)

This paper contains 31 sections, 11 theorems, 7 equations, 8 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Prior work
  4. Organization
  5. Technical overview
  6. The case of h<n
  7. Protocols with optimal communication complexity
  8. Protocols with locality
  9. Preliminaries
  10. Model, basic definitions, and assumptions
  11. The network
  12. The adversary
  13. Communication complexity
  14. The security parameter $\lambda$
  15. Succinct equality testing
  16. ...and 16 more sections

Key Result

Theorem 1

There exists a protocol for MPC with abort against static malicious adversaries using $\Tilde{O}(n^2/h)$ bits of communication, where $n$ is the number of parties of which at least $h$ are honest.

Theorems & Definitions (41)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Lemma 5
  • Definition 6: Secure protocols
  • Remark 7
  • Remark 8
  • Theorem 9
  • proof : Proof sketch
  • ...and 31 more