Accountable Private Set Cardinality for Distributed Measurement
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We introduce cryptographic protocols for securely and efficiently computing the cardinality of set union and set intersection. Our private set-cardinality protocols ( PSC ) are designed for the setting in which a large set of parties in a distributed system makes observations, and a small set of parties with more resources and higher reliability aggregates the observations. PSC allows for secure and useful statistics gathering in privacy-preserving distributed systems. For example, it allows operators of anonymity networks such as Tor to securely answer the questions: How many unique users are using the network? and How many hidden services are being accessed? We prove the correctness and security of PSC in the Universal Composability framework against an active adversary that compromises all but one of the aggregating parties. Although successful output cannot be guaranteed in this setting, PSC either succeeds or terminates with an abort, and we furthermore make the adversary accountable for causing an abort by blaming at least one malicious party. We also show that PSC prevents adaptive corruption of the data parties from revealing past observations, which prevents them from being victims of targeted compromise, and we ensure safe measurements by making outputs differentially private. We present a proof-of-concept implementation of PSC and use it to demonstrate that PSC operates with low computational overhead and reasonable bandwidth. It can count tens of thousands of unique observations from tens to hundreds of data-collecting parties while completing within hours. PSC is thus suitable for daily measurements in a distributed system.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it