We consider the problem of round-optimal unbounded MPC: in the first round, parties publish a message that depends only on their input. In the second round, any subset of parties can jointly and securely compute any function $f$ over their inputs in a single round of broadcast. We do not impose any a-priori bound on the number of parties nor on the size of the functions that can be computed.
Our main result is a semi-malicious two-round protocol for unbounded MPC in the plain model from the hardness of the standard learning with errors (LWE) problem. Prior work in the same setting assumes the hardness of problems over bilinear maps. Thus, our protocol is the first example of unbounded MPC that is post-quantum secure.
The central ingredient of our protocol is a new scheme of attribute-based secure function evaluation (AB-SFE) with public decryption. Our construction combines techniques from the realm of homomorphic commitments with delegation of lattice basis. We believe that such a scheme may find further applications in the future.
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