Round Efficient Secure Multiparty Quantum Computation with Identifiable Abort

A recent result by Dulek et al. (EUROCRYPT 2020) showed a secure protocol for computing any quantum circuit even without the presence of an honest majority. Their protocol, however, is susceptible to a "denial of service" attack and allows even a single corrupted party to force an abort. We propose the first quantum protocol that admits security-with-identifiable-abort, which allows the honest parties to agree on the identity of a corrupted party in case of an abort. Additionally, our protocol is the first to have the property that the number of rounds where quantum communication is required is independent of the circuit complexity. Furthermore, if there exists a post-quantum secure classical protocol whose round complexity is independent of the circuit complexity, then our protocol has this property as well. Our protocol is secure under the assumption that classical quantum-resistant fully homomorphic encryption schemes with decryption circuit of logarithmic depth exist. Interestingly, our construction also admits a reduction from quantum fair secure computation to classical fair secure computation.