What Security can we Achieve in 4-Rounds?

In this paper we study the question of what security is achievable for stand-alone two-party computation in four-rounds. Our starting point point is the Katz-Ostrovsky lower bound [KO04] which determines that the exact round complexity of achieving a secure two-party computation protocol is five. To get around this lower bound we consider two relaxations of the standard simulation-based security definition, where each relaxation implies a different security guarantee. Specifically, we analyze our protocols in the presence of malicious non-aborting adversaries (for which we obtain full security) and malicious aborting adversaries (for which we obtain 1/p-security, which implies that the simulation fails with probability at most 1/p + negl). We further prove that our security guarantee is tight with respect to the party that obtains the input first.