On Round Optimal Statistical Zero Knowledge Arguments.

We construct the first three message statistical zero knowledge arguments for all of NP, matching the known lower bound. We do so based on keyless multi-collision resistant hash functions and the Learning with Errors assumption-the same assumptions used to obtain round optimal computational zero knowledge. The main component in our construction is a statistically witness indistinguishable argument of knowledge based on a new notion of statistically hiding commitments with subset opening.