Estimating Incidental Collection in Foreign Intelligence Surveillance: Large-Scale Multiparty Private Set Intersection with Union and Sum


Anunay Kulshrestha and Jonathan Mayer, Princeton University


Section 702 of the Foreign Intelligence Surveillance Act authorizes U.S. intelligence agencies to intercept communications content without obtaining a warrant. While Section 702 requires targeting foreigners abroad for intelligence purposes, agencies "incidentally" collect communications to or from Americans and can search that data for purposes beyond intelligence gathering. For over a decade, members of Congress and civil society organizations have called on the U.S. Intelligence Community (IC) to estimate the scale of incidental collection. Senior intelligence officials have acknowledged the value of quantitative transparency for incidental collection, but the IC has not identified a satisfactory estimation method that respects individual privacy, protects intelligence sources and methods, and imposes minimal burden on IC resources.

In this work, we propose a novel approach to estimating incidental collection using secure multiparty computation (MPC). The IC possesses records about the parties to intercepted communications, and communications services possess country-level location for users. By combining these datasets with MPC, it is possible to generate an automated aggregate estimate of incidental collection that maintains confidentiality for intercepted communications and user locations.

We formalize our proposal as a new variant of private set intersection, which we term multiparty private set intersection with union and sum (MPSIU-Sum). We then design and evaluate an efficient MPSIU-Sum protocol, based on elliptic curve cryptography and partially homomorphic encryption. Our protocol performs well at the large scale necessary for estimating incidental collection in Section 702 surveillance.

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@inproceedings {281322,
author = {Anunay Kulshrestha and Jonathan Mayer},
title = {Estimating Incidental Collection in Foreign Intelligence Surveillance: {Large-Scale} Multiparty Private Set Intersection with Union and Sum},
booktitle = {31st USENIX Security Symposium (USENIX Security 22)},
year = {2022},
isbn = {978-1-939133-31-1},
address = {Boston, MA},
pages = {1705--1722},
url = {},
publisher = {USENIX Association},
month = aug,

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