Perfect Zero Knowledge: New Upperbounds and Relativized Separations

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 distribution testing problems: computational problems over high-dimensional distributions represented by succinct Boolean circuits. A relatively less-investigated complexity class \(\mathrm{ SBP}\) emerged as significant in this study. The main results we establish are:Results (1) and (3) imply an oracle separating \(\mathrm{ PZK}\) from \(\mathrm{ NIPZK}\). Our results refine the landscape of perfect zero-knowledge classes in relation to traditional complexity classes.