Perfect Zero Knowledge: New Upperbounds and Relativized Separations

Peter Dixon; Sutanu Gayen; A.  Pavan; N.  V.  Vinodchandran

Paper 2020/768

Perfect Zero Knowledge: New Upperbounds and Relativized Separations

Peter Dixon, Sutanu Gayen, A. Pavan, and 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 SBP emerged as significant in this study. The main results we establish are: 1. A unconditional inclusion that NIPZK is in 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. These results refine the landscape of perfect zero-knowledge classes in relation to traditional complexity classes.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: non-interactive zero knowledge perfect zero knowledge complexity classes distribution testing SBP
Contact author(s): vinod @ cse unl edu
pavan @ cs iastate edu
History: 2020-06-24: received
Short URL: https://ia.cr/2020/768
License: CC BY

BibTeX

@misc{cryptoeprint:2020/768,
      author = {Peter Dixon and Sutanu Gayen and A.  Pavan and N.  V.  Vinodchandran},
      title = {Perfect Zero Knowledge: New Upperbounds and Relativized Separations},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/768},
      year = {2020},
      url = {https://eprint.iacr.org/2020/768}
}