Perfect Zero-Knowledge PCPs for #P

arXiv:2403.11941v1 Announce Type: cross
Abstract: We construct perfect zero-knowledge probabilistically checkable proofs (PZK-PCPs) for every language in #P. This is the first construction of a PZK-PCP for any language outside BPP. Furthermore, unlike previous constructions of (statistical) zero-knowledge PCPs, our construction simultaneously achieves non-adaptivity and zero knowledge against arbitrary (adaptive) polynomial-time malicious verifiers.
Our construction consists of a novel masked sumcheck PCP, which uses the combinatorial nullstellensatz to obtain antisymmetric structure within the hypercube and randomness outside of it. To …

arxiv construction cs.cc cs.cr cs.ds knowledge language malicious non perfect zero knowledge