Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority

TL;DR

This paper introduces protocols for secure multiparty quantum computation that tolerate up to nearly half of the players cheating, improving the trust threshold compared to previous quantum protocols, and matching classical impossibility bounds.

Contribution

It presents the first quantum protocols that tolerate a strict honest majority of less than half, using approximate quantum error-correcting codes and novel authentication schemes.

Findings

Protocols tolerate up to (n-1)/2 cheaters

Threshold is proven to be tight, matching classical bounds

Introduces new authentication and error-correcting techniques

Abstract

Secret sharing and multiparty computation (also called "secure function evaluation") are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the sole assumption that some number of them will follow the protocol honestly. This paper investigates how much trust is necessary -- that is, how many players must remain honest -- in order for distributed quantum computations to be possible. We present a verifiable quantum secret sharing (VQSS) protocol, and a general secure multiparty quantum computation (MPQC) protocol, which can tolerate any (n-1)/2 (rounded down) cheaters among n players. Previous protocols for these tasks tolerated (n-1)/4 (rounded down) and (n-1)/6 (rounded down) cheaters, respectively. The threshold we achieve is tight - even in the classical case, ``fair'' multiparty computation is not possible if any set of n/2 players can cheat. Our protocols rely on approximate quantum error-correcting codes, which can tolerate a larger fraction of errors than traditional, exact codes. We introduce new families of authentication schemes and approximate codes tailored to the needs of our protocols, as well as new state purification techniques along the lines of those used in fault-tolerant quantum circuits.