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Streaming Zero-Knowledge Proofs

Authors Graham Cormode , Marcel Dall'Agnol , Tom Gur , Chris Hickey

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Author Details

Graham Cormode
  • University of Warwick, UK
Marcel Dall'Agnol
  • Princeton University, NJ, USA
Tom Gur
  • University of Cambridge, UK
Chris Hickey
  • University of Manchester, UK

Funding

  • Cormode, Graham: The work of Graham Cormode and Chris Hickey was supported by European Research Council grant ERC-2014-CoG 647557.
  • Gur, Tom: Tom Gur is supported by UKRI Future Leaders Fellowship MR/S031545/1 and EPSRC New Horizons Grant EP/X018180/1.

Acknowledgements

We thank Aditya Prakash for the proof of Claim 30, as well as Justin Thaler and Nick Spooner for fruitful discussions and careful reading of an earlier version of this manuscript.

Cite AsGet BibTex

Graham Cormode, Marcel Dall'Agnol, Tom Gur, and Chris Hickey. Streaming Zero-Knowledge Proofs. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 2:1-2:66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CCC.2024.2

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 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Interactive proof systems
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Zero-knowledge proofs
  • streaming algorithms
  • computational complexity

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