Quasi-Linear Size Zero Knowledge from Linear-Algebraic PCPs

The seminal result that every language having an interactive proof also has a zero-knowledge interactive proof assumes the existence of one-way functions. Ostrovsky and Wigderson (ISTCS 1993) proved that this assumption is necessary: if one-way functions do not exist, then only languages in BPP have zero-knowledge interactive proofs. Ben-Or et al. (STOC 1988) proved that, nevertheless, every language having a multi-prover interactive proof also has a zero-knowledge multi-prover interactive proof, unconditionally. Their work led to, among many other things, a line of work studying zero knowledge without intractability assumptions. In this line of work, Kilian, Petrank, and Tardos (STOC 1997) defined and constructed zero-knowledge probabilistically checkable proofs (PCPs). While PCPs with quasilinear-size proof length, but without zero knowledge, are known, no such result is known for zero knowledge PCPs. In this work, we show how to construct “2-round” PCPs that are zero knowledge...

• Type: Journal
• Year: 2016
• Where: ECCC
• Authors: Eli Ben-Sasson, Alessandro Chiesa, Ariel Gabizon, Madars Virza
• Keywords: ECCC 2016