Statistical Zaps and New Oblivious Transfer Protocols.

We study the problem of achieving statistical privacy in interactive proof systems and oblivious transfer - two of the most well studied two-party protocols - when limited rounds of interaction are available. - Statistical Zaps: We give the first construction of statistical Zaps, namely, two-round statistical witness-indistinguishable (WI) protocols with a public-coin verifier. Our construction achieves computational soundness based on the quasi-polynomial hardness of learning with errors assumption. - Three-Round Statistical Receiver-Private Oblivious Transfer: We give the first construction of a three-round oblivious transfer (OT) protocol - in the plain model - that achieves statistical privacy for receivers and computational privacy for senders against malicious adversaries, based on polynomial-time assumptions. The round-complexity of our protocol is optimal. We obtain our first result by devising a public-coin approach to compress sigma protocols, without relying on trusted setup. To obtain our second result, we devise a general framework via a new notion of statistical hash commitments that may be of independent interest.