Secure Multi-party Quantum Computation with a Dishonest Majority

TL;DR

This paper presents a new secure multi-party quantum computation protocol that tolerates a dishonest majority, extending previous two-party results to any number of players with proven security against collusion.

Contribution

It generalizes existing two-party quantum security protocols to multi-party settings with dishonest majorities, introducing efficient verification and testing methods.

Findings

Protocol secure against up to k-1 colluding adversaries

Quantum round complexity is O(k(d + log n)) for circuits of depth d

Develops classical MPC-based verification and testing protocols

Abstract

The cryptographic task of secure multi-party (classical) computation has received a lot of attention in the last decades. Even in the extreme case where a computation is performed between $k$ mutually distrustful players, and security is required even for the single honest player if all other players are colluding adversaries, secure protocols are known. For quantum computation, on the other hand, protocols allowing arbitrary dishonest majority have only been proven for $k=2$. In this work, we generalize the approach taken by Dupuis, Nielsen and Salvail (CRYPTO 2012) in the two-party setting to devise a secure, efficient protocol for multi-party quantum computation for any number of players $k$, and prove security against up to $k-1$ colluding adversaries. The quantum round complexity of the protocol for computing a quantum circuit of $\{\mathsf{CNOT, T}\}$ depth $d$ is $O(k \cdot (d + \log n))$, where $n$ is the security parameter. To achieve efficiency, we develop a novel public verification protocol for the Clifford authentication code, and a testing protocol for magic-state inputs, both using classical multi-party computation.