Perfect Zero-Knowledge PCPs for #P
June 2024
Pages 1724 - 1730
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 nullstellen- satz to obtain antisymmetric structure within the hypercube and randomness outside of it. To prove zero knowledge, we introduce the notion of locally simulatable encodings: randomised encodings in which every local view of the encoding can be efficiently sampled given a local view of the message. We show that the code arising from the sumcheck protocol (the Reed–Muller code augmented with subcube sums) admits a locally simulatable encoding. This reduces the algebraic problem of simulating our masked sumcheck to a combinatorial property of antisymmetric functions.
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Index Terms
- Perfect Zero-Knowledge PCPs for #P
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June 2024
2049 pages
ISBN:9798400703836
DOI:10.1145/3618260
- General Chairs:
- Bojan Mohar,
- Igor Shinkar,
- Program Chair:
- Ryan O'Donnell
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This work is licensed under a Creative Commons Attribution International 4.0 License.
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Published: 11 June 2024
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