An efficient solution to the socialist millionaires' problem
Bibliographic record
Abstract
We present a two-round protocol to solve the socialist millionaire problem based on the homomorphic property of the Goldwasser-Micali (GM) cryptosystem. We require the proposed protocol to be secure against active and passive attacks. However, homomorphic encryption schemes are malleable by design [14][1]. To tackle this problem we apply an authenticated encryption scheme, called Encrypt-then-MAC, to our protocol [3]. We analyze the security of the proposed protocol, and we show that an active adversary, who has access to the ciphertext on the communication channel and the decryption oracle, cannot forge another ciphertext which leads him to guess the plaintext (IND-CCA2 security). Moreover, the active adversary cannot modify the ciphertext which leads to a desired modification of the plaintext to affect the outcome of the protocol (NM-CCA2 security). Note that our solution can be applied to other problems which are solvable with an exclusive- or homomorphic property.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".