Paper 2020/1527

Zero-Knowledge IOPs with Linear-Time Prover and Polylogarithmic-Time Verifier

Abstract

Interactive oracle proofs (IOPs) are a multi-round generalization of probabilistically checkable proofs that play a fundamental role in the construction of efficient cryptographic proofs. We present an IOP that simultaneously achieves the properties of zero knowledge, linear-time proving, and polylogarithmic-time verification. We construct a zero-knowledge IOP where, for the satisfiability of an $$-gate arithmetic circuit over any field of size $$, the prover uses $$ field operations and the verifier uses $$ field operations (with proof length $$ and query complexity $$). Polylogarithmic verification is achieved in the holographic setting for every circuit (the verifier has oracle access to a linear-time-computable encoding of the circuit whose satisfiability is being proved). Our result implies progress on a basic goal in the area of efficient zero knowledge. Via a known transformation, we obtain a zero knowledge argument system where the prover runs in linear time and the verifier runs in polylogarithmic time; the construction is plausibly post-quantum and only makes a black-box use of lightweight cryptography (collision-resistant hash functions).