Dakshita Khurana

James Bartusek, Andrea Coladangelo, Dakshita Khurana et al.

We prove that quantum-hard one-way functions imply simulation-secure quantum oblivious transfer (QOT), which is known to suffice for secure computation of arbitrary quantum functionalities. Furthermore, our construction only makes black-box use of the quantum-hard one-way function. Our primary technical contribution is a construction of extractable and equivocal quantum bit commitments based on the black-box use of quantum-hard one-way functions in the standard model. Instantiating the Crépeau-Kilian (FOCS 1988) framework with these commitments yields simulation-secure QOT.

James Bartusek, Andrea Coladangelo, Dakshita Khurana et al.

We construct the first constant-round protocols for secure quantum computation in the two-party (2PQC) and multi-party (MPQC) settings with security against malicious adversaries. Our protocols are in the common random string (CRS) model. - Assuming two-message oblivious transfer (OT), we obtain (i) three-message 2PQC, and (ii) five-round MPQC with only three rounds of online (input-dependent) communication; such OT is known from quantum-hard Learning with Errors (QLWE). - Assuming sub-exponential hardness of QLWE, we obtain (i) three-round 2PQC with two online rounds and (ii) four-round MPQC with two online rounds. - When only one (out of two) parties receives output, we achieve minimal interaction (two messages) from two-message OT; classically, such protocols are known as non-interactive secure computation (NISC), and our result constitutes the first maliciously-secure quantum NISC. Additionally assuming reusable malicious designated-verifier NIZK arguments for NP (MDV-NIZKs), we give the first MDV-NIZK for QMA that only requires one copy of the quantum witness. Finally, we perform a preliminary investigation into two-round secure quantum computation where each party must obtain output. On the negative side, we identify a broad class of simulation strategies that suffice for classical two-round secure computation that are unlikely to work in the quantum setting. Next, as a proof-of-concept, we show that two-round secure quantum computation exists with respect to a quantum oracle.

Amit Agarwal, James Bartusek, Vipul Goyal et al.

We initiate the study of multi-party computation for classical functionalities (in the plain model) with security against malicious polynomial-time quantum adversaries. We observe that existing techniques readily give a polynomial-round protocol, but our main result is a construction of *constant-round* post-quantum multi-party computation. We assume mildly super-polynomial quantum hardness of learning with errors (LWE), and polynomial quantum hardness of an LWE-based circular security assumption. Along the way, we develop the following cryptographic primitives that may be of independent interest: 1. A spooky encryption scheme for relations computable by quantum circuits, from the quantum hardness of an LWE-based circular security assumption. This yields the first quantum multi-key fully-homomorphic encryption scheme with classical keys. 2. Constant-round zero-knowledge secure against multiple parallel quantum verifiers from spooky encryption for relations computable by quantum circuits. To enable this, we develop a new straight-line non-black-box simulation technique against *parallel* verifiers that does not clone the adversary's state. This forms the heart of our technical contribution and may also be relevant to the classical setting. 3. A constant-round post-quantum non-malleable commitment scheme, from the mildly super-polynomial quantum hardness of LWE.