Bibliographic record
Abstract
We present a new 4-move special honest-verifier zero-knowledge proof of knowledge system for proving that a vector of Pedersen commitments opens to a so-called "one-hot'' vector (i.e., to a vector from the standard orthonormal basis) from Zpn. The need for such proofs arises in the contexts of symmetric private information retrieval (SPIR), end-to-end verifiable voting (E2E), and privacy-preserving data aggregation and analytics, among others. The key insight underlying the new protocol is a simple observation regarding the paucity of roots of polynomials of bounded degree over a finite field. The new protocol is fast and yields succinct proofs: For vectors of length n, the prover evaluates Θ(Θlgn) group operations plus Θ(n) field operations and sends just Θ(Θlgn) group and field elements, while the verifier evaluates one n-base multiexponentiation plus Θ(łlgn) additional group operations and sends just 2(λ+lgn) bits to obtain a soundness error less than 2-λ. (A 5-move variant of the protocol reduces prover upload to just λlgn bits for the same soundness error.) We have implemented both our new protocol and its closest competitors from the literature; in accordance with our analytic results, experiments confirm that the new protocols handily outperform existing protocols for all but the shortest of vectors (roughly, for vectors with more than 16-32 elements).
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".