A Brief Survey of Two Recent Polynomial Commitment Schemes from Lattices
Bibliographic record
Abstract
A polynomial commitment scheme (PCS) enables a prover to commit to a polynomial and later prove the correctness of its evaluation without revealing the polynomial. Although discrete logarithm-based PCSs offer succinct proofs, they are not quantum-safe. Lattice-based PCSs provide post-quantum security and additive homomorphism, making them suitable for applications such as zero-knowledge proofs and secure multiparty computation. In this article, we review two recent lattice-based PCSs, Greyhound and HyperWolf, both relying on the Module-SIS assumption but differing in target polynomial classes and proof techniques. In particular, Greyhound achieves a smaller proof size O(log log N) through folding and LaBRADOR proofs, while HyperWolf supports univariate and multilinear polynomials with lower verifier cost O(log N) using hypercube evaluation.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.000 |
| 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 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".