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 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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 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".