Post-Quantum Multi-Party Computation

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 postquantum 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:

• 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 fullyhomomorphic encryption scheme with classical keys.

• 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.

• A constant-round post-quantum non-malleable commitment scheme, from the mildly super-polynomial quantum hardness of LWE.