International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Interactive Proofs for Social Graphs

Eylon Yogev , Tel Aviv University
Liran Katzir , Google Research
Clara Shikhelman , California Institute of Technology
DOI: 10.1007/978-3-030-56877-1_20 (login may be required)
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Presentation: Slides
Conference: CRYPTO 2020
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 $\epsilon>0$. The verifier performs $\widetilde{O}(1/\epsilon^2 \cdot \tau \cdot \Delta)$ queries to the graph, where $\tau$ is the mixing time of the graph and $\Delta$ 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 average of essentially any (reasonable) function $f$ of vertices 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 any social media company (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.
Video from CRYPTO 2020
  title={Interactive Proofs for Social Graphs},
  author={Eylon Yogev and Liran Katzir and Clara Shikhelman},