Towards the positive results, we first introduce the notion of Oblivious Quantum Function Evaluation (OQFE). An OQFE is a two-party quantum cryptographic primitive with one fully classical party (Alice) whose input is (a classical description of a) quantum unitary, $U$, and a quantum party (Bob) whose input is a quantum state, $\psi$. In particular, Alice receives the classical output corresponding to the measurement of $U (\psi)$ while Bob receives no output. At the same time, the functionality guarantees that Bob remains oblivious to Alice's input $U$, while Alice learns nothing about $\psi$ more than what can be learned from the output of the computation. We present two concrete constructions, one secure against semi-honest parties and the other secure against malicious parties. Due to the no-go result mentioned above, we consider what is arguably the best possible notion obtainable in our model with respect to malicious adversaries: one-sided simulation security. This notion protects the input of one party (the quantum Bob) in the standard simulation-based sense, and protects the privacy of the other party's input (the classical Alice). We realize our protocol relying on the assumption of quantum secure injective homomorphic trapdoor one-way functions, which in turn rely on the learning with errors problem. As a result, we put forward a first, simple and modular construction of secure one-sided quantum two-party computation and quantum oblivious transfer over classical networks.
Category / Keywords: cryptographic protocols / Secure Quantum Two-party Computation, Proofs of Quantum Knowledge, Simulation-based Security Date: received 15 Oct 2020 Contact author: atul mantri91 at gmail com,micheleciampi1990@gmail com,ekashefi@gmail com,a d cojocaru@sms ed ac uk Available format(s): PDF | BibTeX Citation Version: 20201016:064829 (All versions of this report) Short URL: ia.cr/2020/1286