Polynomial-time Attack on Output Perturbation Sanitizers for Real-valued Databases
Bibliographic record
Abstract
We review the attack given by Dinur and Nissim [6] on the output perturbation sanitizer, and generalize it to a setting that includes, as particular cases, databases with values in {0,1}---with the metric considered in [6]---and databases with real values, with other appropriate metrics (hence the binary case is not included in the real case). Previous works [12, 14] on the binary case gave results more efficient than ours. Those results could be used to extend the binary case to the real-valued case, hence implying our results. The contributions of this paper are: to make the implication explicit, and to give an alternative general proof. We state a property about the function dist that measures the error of the attacker's approximation of the database, which is satisfied in our cases of interest, and is sufficiently strong to prove the impossibility results regarding the privacy provided by the output-perturbation sanitizer, in both the real and binary cases. In this general context we establish an inequality (an upper bound to the probability of adversary's failure) that relates all the parameters of the problem---the size of the database, the relative error of the adversary, the number of queries made by the adversary (which determines its time complexity), its probability of failure, and the perturbation of the sanitizer---making explicit the trade-offs among them. From this inequality we deduce that for binary and real valued databases, the adversary described in [6] can defeat perturbation o(n1/2) with time complexity determined by o(n log n) number of queries (instead of O(n log2 n) as in [6]).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".