Interactive hashing and reductions between Oblivious Transfer variants
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Bibliographic record
Abstract
Interactive Hashing has featured as an essential ingredient in protocols realizing a large variety of cryptographic tasks. We present a study of this important cryptographic tool in the information theoretic context. We start by presenting a security definition which is independent of any particular setting or application. We then show that a standard implementation of Interactive Hashing satisfies all the conditions of our definition. Our proof of security improves upon previous ones in several ways. Despite its generality, it is considerably simpler. Moreover, it establishes a tighter upper bound on the cheating probability of a dishonest sender. Specifically, we prove that if the fraction of good strings for a dishonest sender is f, then the probability that both outputs will be good is no larger than 15.6805· f. This upper bound is valid for any f and is tight up to a small constant since a sender acting honestly would get two good outputs with probability very close to f. We illustrate the potential of Interactive Hashing as a cryptographic primitive by demonstrating efficient reductions of String Oblivious Transfer with string length k to Bit Oblivious Transfer and several weaker variants. Our reductions incorporate tests based on Interactive Hashing that allow the sender to verify the receiver's adherence to the protocol without compromising the latter's privacy. This allows a much more efficient use of the available entropy without any appreciable impact on security. As a result, for Bit OT and most of its variants n = (1 + epsilon) k executions suffice, improving efficiency by a factor of two or more compared to the most efficient reductions that do not use Interactive Hashing. As it is theoretically impossible to achieve an expansion factor n/k smaller than 1, our reductions are in fact asymptotically optimal. They are also more general since they place no restrictions on the types of 2-universal hash families used for Privacy Amplification. Lastly, we present a direct reduction of String OT to Rabin OT which uses similar methods to achieve an expansion factor of 2 + epsilon which is again asymptotically optimal.
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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 | 0.002 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.004 |
| 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