Interactive proofs for social graphs

Liran Katzir; Clara Shikhelman; Eylon Yogev

doi:10.1007/978-3-030-56877-1_20

Interactive proofs for social graphs

Liran Katzir, Clara Shikhelman, Eylon Yogev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We consider interactive proofs for social graphs, where the verifier has only oracle access to the graph and can query for the i^th neighbor of a vertex v, given i and v. In this model, we construct a doubly-efficient public-coin two-message interactive protocol for estimating the size of the graph to within a multiplicative factor ε >0. The verifier performs O(1/ε² · τ_mix· Δ) queries to the graph, where τ_mix is the mixing time of the graph and Δ is the average degree of the graph. The prover runs in quasi-linear time in the number of nodes in the graph. Furthermore, we develop a framework for computing the quantiles of essentially any (reasonable) function f of vertices/edges of the graph. Using this framework, we can estimate many health measures of social graphs such as the clustering coefficients and the average degree, where the verifier performs only a small number of queries to the graph. Using the Fiat-Shamir paradigm, we are able to transform the above protocols to a non-interactive argument in the random oracle model. The result is that social media companies (e.g., Facebook, Twitter, etc.) can publish, once and for all, a short proof for the size or health of their social network. This proof can be publicly verified by any single user using a small number of queries to the graph.

Original language	English
Title of host publication	Advances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings
Editors	Daniele Micciancio, Thomas Ristenpart
Publisher	Springer
Pages	574-601
Number of pages	28
ISBN (Print)	9783030568764
DOIs	https://doi.org/10.1007/978-3-030-56877-1_20
State	Published - 2020
Externally published	Yes
Event	40th Annual International Cryptology Conference, CRYPTO 2020 - Santa Barbara, United States Duration: 17 Aug 2020 → 21 Aug 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12172 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	40th Annual International Cryptology Conference, CRYPTO 2020
Country/Territory	United States
City	Santa Barbara
Period	17/08/20 → 21/08/20

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2020.

Funding

This work was done (in part) while the second and third authors were visiting the Simons Institute for the Theory of Computing. Eylon Yogev is funded by the ISF grants 484/18, 1789/19, Len Blavatnik and the Blavatnik Foundation, and The Blavatnik Interdisciplinary Cyber Research Center at Tel Aviv University. Acknowledgments. This work was done (in part) while the second and third authors were visiting the Simons Institute for the Theory of Computing. Eylon Yogev is funded by the ISF grants 484/18, 1789/19, Len Blavatnik and the Blavatnik Foundation, and The Blavatnik Interdisciplinary Cyber Research Center at Tel Aviv University.

Funders	Funder number
Blavatnik Foundation
Blavatnik Family Foundation
Israel Science Foundation	1789/19, 484/18
Tel Aviv University

Keywords

Interactive proofs
Social graphs
Succinct arguments

Access to Document

10.1007/978-3-030-56877-1_20

Cite this

Katzir, L., Shikhelman, C., & Yogev, E. (2020). Interactive proofs for social graphs. In D. Micciancio, & T. Ristenpart (Eds.), Advances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings (pp. 574-601). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12172 LNCS). Springer. https://doi.org/10.1007/978-3-030-56877-1_20

Katzir, Liran ; Shikhelman, Clara ; Yogev, Eylon. / Interactive proofs for social graphs. Advances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings. editor / Daniele Micciancio ; Thomas Ristenpart. Springer, 2020. pp. 574-601 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Katzir, L, Shikhelman, C & Yogev, E 2020, Interactive proofs for social graphs. in D Micciancio & T Ristenpart (eds), Advances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12172 LNCS, Springer, pp. 574-601, 40th Annual International Cryptology Conference, CRYPTO 2020, Santa Barbara, United States, 17/08/20. https://doi.org/10.1007/978-3-030-56877-1_20

Interactive proofs for social graphs. / Katzir, Liran; Shikhelman, Clara; Yogev, Eylon.
Advances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings. ed. / Daniele Micciancio; Thomas Ristenpart. Springer, 2020. p. 574-601 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12172 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Katzir L, Shikhelman C, Yogev E. Interactive proofs for social graphs. In Micciancio D, Ristenpart T, editors, Advances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings. Springer. 2020. p. 574-601. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-56877-1_20

Interactive proofs for social graphs

Abstract

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Keywords

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