Statistical Security in Two-Party Computation Revisited

We present a new framework for building round-optimal one-sided statistically se- cure two party computation (2PC) protocols in the plain model. We demonstrate that a relatively weak notion of oblivious transfer (OT), namely a three round elementary oblivious transfer eOT with statistical receiver privacy, along with a non-interactive commitment scheme suffices to build a one-sided statistically secure two party computation protocol with black-box simulation. Our framework enables the first instantiations of round-optimal one-sided statistically secure 2PC protocols from the CDH assumption and certain families of isogeny-based assumptions.

As part of our compiler, we introduce the following new one-sided statistically secure primitives in the pre-processing model that might also be of independent interest:

1. Three round statistically sender private random-OT where only the last OT mes- sage depends on the receiver’s choice bit and the sender receives random outputs generated by the protocol.
2. Four round delayed-input statistically sender private conditional disclosure of secrets where the first two rounds of the protocol are independent of the inputs of the parties.

The above primitives are directly constructed from eOT and hence we obtain their instantiations from the same set of assumptions as our 2PC.