Cryptology ePrint Archive: Report 2020/768

Perfect Zero Knowledge: New Upperbounds and Relativized Separations

Peter Dixon and Sutanu Gayen and 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.

Category / Keywords: foundations / non-interactive zero knowledge, perfect zero knowledge, complexity classes, distribution testing, SBP

Date: received 22 Jun 2020

Contact author: vinod at cse unl edu,pavan@cs iastate edu

Available format(s): PDF | BibTeX Citation

Version: 20200624:075211 (All versions of this report)

Short URL: ia.cr/2020/768


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