Can Statistical Zero Knowledge be made Non-Interactive? or On the Relationship of NISZK

We extend the study of non-interactive statistical zero-knowledge proofs. Our main focus is to compare the class NISZK of problems possessing such non-interactive proofs to the class SZK of problems possessing interactive statistical zero-knowledge proofs. Along these lines, we first show that if statistical zero knowledge is non-trivial then so is non-interactive statistical zero knowledge, where by non-trivial we mean that the class includes problems which are not solvable in probabilistic polynomial-time. (The hypothesis holds under various assumptions, such as the intractability of the Discrete Logarithm Problem.) Furthermore, we show that if NISZK is closed under complement, then in fact SZK = NISZK, i.e. all statistical zeroknowledge proofs can be made non-interactive. The main tools in our analysis are two promise problems that are natural restrictions of promise problems known to be complete for SZK. We show that these restricted problems are in fact complete for NISZK and u..