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Perfect Zero Knowledge: New Upperbounds and Relativized Separations

Authors:
Peter Dixon
Sutanu Gayen
A. Pavan
N. V. Vinodchandran
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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⊆\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.
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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
}