Short zero-knowledge PCPs

Determine whether there exist zero-knowledge probabilistically checkable proofs for NP with O(1) query complexity and quasi-linear proof length, that is, proof length \tilde{O}(n).

Background

The paper proves a zero-knowledge PCP theorem matching the constant-query feature of the classical PCP theorem, but does not optimize proof length. In the classical (non-zero-knowledge) setting, decades of work have reduced PCP proof length to quasilinear, with the current state of the art based on Reed–Solomon arithmetization and combinatorial gap amplification.

The authors ask whether analogous quasilinear-length constructions can be achieved in the zero-knowledge setting. They note their techniques rely on Reed–Muller arithmetization and the sumcheck protocol, so new ideas may be required to reach quasilinear length with zero-knowledge guarantees.