TY - GEN

T1 - Interactive proofs for social graphs

AU - Katzir, Liran

AU - Shikhelman, Clara

AU - Yogev, Eylon

N1 - Publisher Copyright:
© International Association for Cryptologic Research 2020.

PY - 2020

Y1 - 2020

N2 - We consider interactive proofs for social graphs, where the verifier has only oracle access to the graph and can query for the ith 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 · τmix· Δ) queries to the graph, where τmix 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.

AB - We consider interactive proofs for social graphs, where the verifier has only oracle access to the graph and can query for the ith 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 · τmix· Δ) queries to the graph, where τmix 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.

KW - Interactive proofs

KW - Social graphs

KW - Succinct arguments

UR - http://www.scopus.com/inward/record.url?scp=85089720590&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-56877-1_20

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

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AN - SCOPUS:85089720590

SN - 9783030568764

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 574

EP - 601

BT - Advances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings

A2 - Micciancio, Daniele

A2 - Ristenpart, Thomas

PB - Springer

T2 - 40th Annual International Cryptology Conference, CRYPTO 2020

Y2 - 17 August 2020 through 21 August 2020

ER -