Search for: All records

We investigate the complexity of problems that admit perfect zero-knowledge interactive protocols and establish new unconditional upper bounds and oracle separation results. We establish our results by investigating certain {\em distribution testing problems}: computational problems over high-dimensional distributions represented by succinct Boolean circuits. A relatively less-investigated complexity class $$\SBP$$ emerged as significant in this study. The main results we establish are: 1. A unconditional inclusion that NIPZK is a subset of CoSBP. 2. Construction of a relativized world in which there is a distribution testing problem that lies in NIPZK but not in SBP, thus giving a relativized separation of NIPZK (and hence PZK) from SBP. 3. Construction of a relativized world in which there is a distribution testing problem that lies in PZK but not in CoSBP, thus giving a relativized separation of PZK from CoSBP.. Results (1) and (3) imply an oracle separating PZK from NIPZK. Our results refine the landscape of perfect zero-knowledge classes in relation to traditional complexity classes.