Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation

Author Kunal Talwar

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Kunal Talwar
  • Apple, Cupertino, CA, USA


We would like to thank Ulfar Erlingsson for many helpful discussions, and the anonymous referees for their feedback.

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Kunal Talwar. Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Computing the noisy sum of real-valued vectors is an important primitive in differentially private learning and statistics. In private federated learning applications, these vectors are held by client devices, leading to a distributed summation problem. Standard Secure Multiparty Computation protocols for this problem are susceptible to poisoning attacks, where a client may have a large influence on the sum, without being detected. In this work, we propose a poisoning-robust private summation protocol in the multiple-server setting, recently studied in PRIO [Henry Corrigan-Gibbs and Dan Boneh, 2017]. We present a protocol for vector summation that verifies that the Euclidean norm of each contribution is approximately bounded. We show that by relaxing the security constraint in SMC to a differential privacy like guarantee, one can improve over PRIO in terms of communication requirements as well as the client-side computation. Unlike SMC algorithms that inevitably cast integers to elements of a large finite field, our algorithms work over integers/reals, which may allow for additional efficiencies.

Subject Classification

ACM Subject Classification
  • Security and privacy → Privacy-preserving protocols
  • Zero Knowledge
  • Secure Summation
  • Differential Privacy


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