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Perfect Zero Knowledge: New Upperbounds and Relativized Separations
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| 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 SBP emerged as significant in this study. The main results we establish are: (1) A unconditional inclusion that $\NIPZK \subseteq \CoSBP$. (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. |
Video from TCC 2020
BibTeX
@article{tcc-2020-30643,
title={Perfect Zero Knowledge: New Upperbounds and Relativized Separations},
booktitle={Theory of Cryptography},
publisher={Springer},
author={Peter Dixon and Sutanu Gayen and A. Pavan and N. V. Vinodchandran},
year=2020
}