Statistical WI (and more) in Two Messages Yael Tauman Kalai MSR Cambridge, USA. yael@microsoft.com Dakshita Khurana UCLA, USA. dakshita@cs.ucla.edu Amit Sahai UCLA, USA. sahai@cs.ucla.edu Abstract Two-message witness indistinguishable protocols were first constructed by Dwork and Naor (FOCS 2000). They have since proven extremely useful in the design of several cryptographic primitives. However, so far no two-message arguments for NP provided statistical privacy against malicious verifiers. In this paper, we construct the first: ◦ Two-message statistical witness indistinguishable (SWI) arguments for NP. ◦ Two-message statistical zero-knowledge arguments for NP with super-polynomial simula- tion (Statistical SPS-ZK). ◦ Two-message statistical distributional weak zero-knowledge (SwZK) arguments for NP, where the instance is sampled by the prover in the second round. These protocols are based on quasi-polynomial hardness of two-message oblivious transfer (OT) with game-based security against PPT senders and unbounded receivers, which in turn can be based on quasi-polynomial hardness of DDH or QR or N th residuosity. We also demonstrate simple applications of these arguments to constructing more secure forms of oblivious transfer. Along the way, we show that the Kalai and Raz (Crypto 09) transform compressing interac- tive proofs to two-message arguments can be generalized to compress certain types of interactive arguments. We introduce and construct a new technical tool, which is a variant of extractable two-message statistically hiding commitments, building on the recent work of Khurana and Sahai (FOCS 17). These techniques may be of independent interest.