On an Almost-Universal Hash Function Family with Applications to Authentication and Secrecy Codes
Bibliographic record
Abstract
Universal hashing, discovered by Carter and Wegman in 1979, has many important applications in computer science. MMH[Formula: see text], which was shown to be [Formula: see text]-universal by Halevi and Krawczyk in 1997, is a well-known universal hash function family. We introduce a variant of MMH[Formula: see text], that we call GRDH, where we use an arbitrary integer [Formula: see text] instead of prime [Formula: see text] and let the keys [Formula: see text] satisfy the conditions [Formula: see text] ([Formula: see text]), where [Formula: see text] are given positive divisors of [Formula: see text]. Then via connecting the universal hashing problem to the number of solutions of restricted linear congruences, we prove that the family GRDH is an [Formula: see text]-almost-[Formula: see text]-universal family of hash functions for some [Formula: see text] if and only if [Formula: see text] is odd and [Formula: see text] [Formula: see text]. Furthermore, if these conditions are satisfied then GRDH is [Formula: see text]-almost-[Formula: see text]-universal, where [Formula: see text] is the smallest prime divisor of [Formula: see text]. Finally, as an application of our results, we propose an authentication code with secrecy scheme which strongly generalizes the scheme studied by Alomair et al. [J. Math. Cryptol. 4 (2010) 121–148], and [J.UCS 15 (2009) 2937–2956].
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.001 | 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".