[Resource Topic] 2020/768: Perfect Zero Knowledge: New Upperbounds and Relativized Separations

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Title:
Perfect Zero Knowledge: New Upperbounds and Relativized Separations

Authors: Peter Dixon, Sutanu Gayen, A. 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 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.

ePrint: https://eprint.iacr.org/2020/768

Talk: https://www.youtube.com/watch?v=cjTBVRtJIVg

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