International Association
for Cryptologic Research

We obtain the first two-round two-party computation protocol, in the plain model, that is secure against passive adversaries who can adaptively corrupt all parties where the communication complexity is proportional to the square of the RAM complexity of the function up to polylogarithmic factors assuming the existence of non-committing encryption.

Zero-knowledge proofs allow a prover to convince a verifier of a statement without revealing anything besides its validity. A major bottleneck in scaling sub-linear zero-knowledge proofs is the high space requirement of the prover, even for NP relations that can be verified in a small space. In this work, we ask whether there exist complexity-preserving (i.e. overhead w.r.t time and space are minimal) succinct zero-knowledge arguments of knowledge with minimal assumptions while making only black-box access to the underlying primitives. We essentially resolve this question up to polylogarithmic factors. Namely, for every NP relation that can be verified in time T and space S, we construct a public-coin zero-knowledge argument system that is black-box based on collision-resistant hash-functions (CRH) where the prover runs in time $\O(T)$ and space $\O(S)$, the verifier runs in time $\O(T/S+S)$ and space $\O(\kappa)$ and the communication is $\O(T/S)$, where $\kappa$ is the statistical security parameter. Using the Fiat-Shamir heuristic, our construction yields the first complexity-preserving ZK-SNARK based on CRH (via a black-box construction). Furthermore, we give evidence that reducing the proof length below $\O(T/S)$ will be hard using existing techniques by arguing the space-complexity of constant-distance error correcting codes.