Lower Bounds for Zero-knowledge on the Internet

TL;DR

This paper demonstrates that zero-knowledge proofs with four rounds or more cannot be maintained in asynchronous, multi-proof environments, highlighting fundamental limitations in realistic communication settings.

Contribution

It establishes that many existing zero-knowledge protocols lose their zero-knowledge property in asynchronous, multi-proof environments, especially for protocols with four or more rounds.

Findings

Zero-knowledge is not preserved in asynchronous settings for many protocols.

Four-round zero-knowledge proofs are not black-box simulatable asynchronously.

The result applies to a broad class of protocols for non-trivial languages.

Abstract

We consider zero knowledge interactive proofs in a richer, more realistic communication environment. In this setting, one may simultaneously engage in many interactive proofs, and these proofs may take place in an asynchronous fashion. It is known that zero-knowledge is not necessarily preserved in such an environment; we show that for a large class of protocols, it cannot be preserved. Any 4 round (computational) zero-knowledge interactive proof (or argument) for a non-trivial language L is not black-box simulatable in the asynchronous setting.