PATS: Let Parties Have a Say in Threshold Group Key Sharing
Why this work is in the frame
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Bibliographic record
Abstract
We present a password‐authenticated (2, 3)‐threshold group key share (PATS) mechanism. Although PATS resembles threshold secret sharing schemes, it has a different structure. The innovative perspective of the PATS mechanism that makes a difference from the standard secret‐sharing schemes is that it involves parties in the generation of the shares. PATS allows parties to communicate securely to establish their shares over insecure channels. Parties (shareholders) construct a secret (key) using shares obtained at the end of the protocol. PATS takes advantage of zero‐knowledge proofs compared to well‐known threshold key exchange schemes and will tolerate the existence of semi‐trusted parties. We present two variants of PATS, centralized and distributed, and then generalize PATS to ( t , n )‐threshold scheme. PATS supports the distributed operation and optionally facilitates group key verification by a trusted third party, which may also partake in group key sharing. In this paper, we present PATS, which employs finite fields and elliptic curves, along with its security and complexity analyses.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.006 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it