Perfect Zero Knowledge: New Upperbounds and Relativized Separations

Peter Dixon, Sutanu Gayen, Aduri Pavan, N. V. Vinodchandran

Abstract: 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.