Equality Operators for Constant-weight Codewords with Applications in (Keyword) PIR
Bibliographic record
Abstract
Homomorphic encryption allows computation to be performed on data while in encrypted form. However, the computational overhead of a circuit that is run using homomorphic encryption depends on the number of multiplications and multiplicative depth. For example, equality checks which are a common step in many tasks, have a multiplicative depth that depends on the bit-length of the numbers. In this work, we propose constant-weight equality operators, which compare constant-weight codewords using a circuit that has a multiplicative depth that depends solely on the Hamming weight of the constant-weight code, not the size of the operands. \n \nPrivate Information Retrieval (PIR) is one task where equality operations are a solution. In a PIR protocol, a user wishes to query a database without revealing which element is queried to the server. In this thesis, we also detail an architecture for PIR which was previously assumed to be impractical. At the heart of this architecture is the constant-weight equality operator. \n \nOur experiments show how constant-weight equality operators outperform existing equality operators and can be used for practical purposes. We also conduct experiments to show the practicality of PIR using our approach and our results show how constant-weight PIR outperforms existing work in aspects of scale such as large domain sizes and large responses.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".