Instance-Dependent Commitment Schemes and the Round Complexity of Perfect Zero-Knowledge Proofs.
Bibliographic record
Abstract
Abstract. We study the question whether the number of rounds in public-coin perfect zero-knowledge (PZK) proofs can be collapsed to a constant. Despite extensive research into the round complexity of interactive and zero-knowledge protocols, there is no indication how to address this question. Furthermore, the main tool to tackle this question is instance-dependent commitments, but currently such schemes are only statistically hiding, whereas we need perfectly hiding schemes. We give the first perfectly hiding instance-dependent commitment scheme. This scheme can be con-structed from any problem that has a PZK proof. We then show that obtaining such a scheme that is also constant-round is not only sufficient, but also necessary to collapse the number of rounds in PZK proofs. Hence, we show an equivalence between the tasks of obtaining the commitment, and collapsing the rounds. Our idea also yields an elegant equivalence between zero-knowledge and commitments. In the second part of the paper we construct a non-interactive, perfectly hiding scheme whose binding property holds on all but an exponentially small fraction of the inputs. Informally, this shows that the rounds in public-coin PZK proofs can be collapsed if we can guarantee that the prover is not choosing its randomness from a small set. We formalize this condition using a preamble, which we then apply to some simple cases. An interesting consequence of independent interest is that we use the circuits from the study of NIPZK in the commitment scheme of Naor [39], and this leads to a new perfectly-hiding instance-dependent commitment for NIPZK problems with a small soundness error. Key words: constant-round, perfect zero-knowledge, instance-dependent commitment schemes. 1
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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 | 0.014 | 0.075 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.009 |
| Scholarly communication | 0.007 | 0.026 |
| Open science | 0.006 | 0.007 |
| Research integrity | 0.004 | 0.011 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".