Information-Theoretic 2-Round MPC without Round Collapsing: Adaptive Security, and More.

We present simpler and improved constructions of 2-round protocols for secure multi-party computation (MPC) in the semi-honest setting. Our main results are new information-theoretically secure protocols for arithmetic NC1 in two settings: (i) the plain model tolerating up to t < n/2 corruptions; and (ii) in the OLE-correlation model tolerating any number of corruptions. Our protocols achieve adaptive security and require only black-box access to the underlying field, whereas previous results only achieve static security and require non-black-box field access. Moreover, both results extend to polynomial-size circuits with computational and adaptive security, while relying on black-box access to a pseudorandom generator. In the OLE correlation model, the extended protocols for circuits tolerate up to n - 1 corruptions. Along the way, we introduce a conceptually novel framework for 2-round MPC that does not rely on the round collapsing framework underlying all of the recent advances in 2-round MPC.