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In this paper, we study the round complexity of concurrently secure multi-party computation (MPC) with super-polynomial simulation (SPS) in the plain model. In the plain model, there are known explicit attacks that show that concurrently secure MPC with polynomial simulation is impossible to achieve; SPS security is the most widely studied model for concurrently secure MPC in the plain model. We obtain the following results:

• Three-round concurrent MPC with SPS security against Byzantine adversaries, assuming sub-exponentially secure DDH and LWE.
• Two-round concurrent MPC with SPS security against Byzantine adversaries for input-less randomized functionalities, assuming sub-exponentially secure indistinguishability obfuscation and DDH. In particular, this class includes sampling functionalities that allow parties to jointly sample a …