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Distributed-Prover Interactive Proofs

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Theory of Cryptography (TCC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14369))

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Abstract

Interactive proof systems enable a verifier with limited resources to decide an intractable language (or compute a hard function) by communicating with a powerful but untrusted prover. Such systems guarantee soundness: the prover can only convince the verifier of true statements. This is a central notion in computer science with far-reaching implications. One key drawback of the classical model is that the data on which the prover operates must be held by a single machine.

In this work, we initiate the study of distributed-prover interactive proofs (dpIPs): an untrusted cluster of machines, acting as a distributed prover, interacts with a single verifier. The machines in the cluster jointly store and operate on a massive data-set that no single machine can store. The goal is for the machines in the cluster to convince the verifier of the validity of some statement about its data-set. We formalize the communication and space constraints via the massively parallel computation (MPC) model, a widely accepted analytical framework capturing the computational power of massive data-centers.

Our main result is a compiler that generically augments any verification algorithm in the MPC model with a (computational) soundness guarantee. Concretely, for any language L for which there is an MPC algorithm verifying whether \(x \in L\), we design a new MPC protocol capable of convincing a verifier of the validity of \(x \in L\) and where if \(x\not \in L\), the verifier rejects with overwhelming probability. The new protocol requires only slightly more rounds, i.e., a \(\textsf{poly}(\log N)\) blowup, and a slightly bigger memory per machine, i.e., \(\textsf{poly}(\lambda )\) blowup, where N is the total size of the dataset and \(\lambda \) is a security parameter independent of N.

En route, we introduce distributed-prover interactive oracle proofs (dpIOPs), a natural adaptation of the (by now classical) IOP model to the distributed prover setting. We design a dpIOP for verification algorithms in the MPC model and then translate them to “plain model” dpIPs via an adaptation of existing polynomial commitment schemes into the distributed prover setting.

P. Soni—Work was done partially when the author was visiting Carnegie Mellon University.

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Acknowledgements

Rex Fernando, Elaine Shi, and Pratik Soni were sponsored by the Algorand Centres of Excellence (ACE) Programme, the Defense Advanced Research Projects Agency under award number HR001120C0086, the Office of Naval Research under award number N000142212064, and the National Science Foundation under award numbers 2128519 and 2044679. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. Ilan Komargodski is the incumbent of the Harry & Abe Sherman Senior Lectureship at the School of Computer Science and Engineering at the Hebrew University, supported in part by an Alon Young Faculty Fellowship, by a grant from the Israel Science Foundation (ISF Grant No. 1774/20), and by a grant from the US-Israel Binational Science Foundation and the US National Science Foundation (BSF-NSF Grant No. 2020643).

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Authors and Affiliations

  1. UIUC, Champaign, IL, USA

    Sourav Das

  2. Carnegie Mellon University, Pittsburgh, PA, USA

    Rex Fernando & Elaine Shi

  3. Hebrew University of Jerusalem, Jerusalem, Israel

    Ilan Komargodski

  4. NTT Research, Sunnyvale, CA, USA

    Ilan Komargodski

  5. University of Utah, Salt Lake City, UT, USA

    Pratik Soni

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  1. Sourav Das
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  2. Rex Fernando
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  3. Ilan Komargodski
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Correspondence to Sourav Das .

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  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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Das, S., Fernando, R., Komargodski, I., Shi, E., Soni, P. (2023). Distributed-Prover Interactive Proofs. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14369. Springer, Cham. https://doi.org/10.1007/978-3-031-48615-9_4

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