Streaming Zero-Knowledge Proofs

TL;DR

This paper introduces zero-knowledge proofs for streaming algorithms, enabling verification of large data computations with minimal space and communication, using novel protocols based on sumcheck and polynomial evaluation.

Contribution

It defines zero-knowledge in streaming settings and constructs efficient protocols for key streaming problems, expanding the scope of streaming interactive proofs.

Findings

Zero-knowledge SIPs for index, point, and range queries.

Protocols have polylogarithmic verifier space complexity.

Efficient non-interactive setup with near-linear randomness.

Abstract

Streaming interactive proofs (SIPs) enable a space-bounded algorithm with one-pass access to a massive stream of data to verify a computation that requires large space, by communicating with a powerful but untrusted prover. This work initiates the study of zero-knowledge proofs for data streams. We define the notion of zero-knowledge in the streaming setting and construct zero-knowledge SIPs for the two main algorithmic building blocks in the streaming interactive proofs literature: the sumcheck and polynomial evaluation protocols. To the best of our knowledge all known streaming interactive proofs are based on either of these tools, and indeed, this allows us to obtain zero-knowledge SIPs for central streaming problems such as index, point and range queries, median, frequency moments, and inner product. Our protocols are efficient in terms of time and space, as well as communication: the verifier algorithm's space complexity is $\mathrm{polylog}(n)$ and, after a non-interactive setup that uses a random string of near-linear length, the remaining parameters are $n^{o(1)}$. En route, we develop an algorithmic toolkit for designing zero-knowledge data stream protocols, consisting of an algebraic streaming commitment protocol and a temporal commitment protocol.Our analyses rely on delicate algebraic and information-theoretic arguments and reductions from average-case communication complexity.