BREAKING AND REPAIRING AN APPROXIMATE MESSAGE AUTHENTICATION SCHEME
Bibliographic record
Abstract
Traditional hash functions are designed to protect against even the slightest modification of a message. Thus, one bit changed in a message would result in a totally different message digest when a hash function is applied. This feature is not suitable for applications whose message spaces admit a certain fuzziness, such as multimedia communications or biometric authentication applications. In these applications, approximate hash functions must be designed so that the distance between messages are proportionally reflected in the distance between message digests. Most of the previous designs of approximate hash functions employ traditional hash functions. In an ingenious approximate message authentication scheme for an N-ary alphabet recently proposed by Ge, Arce and Crescenzo, the approximate hash functions are based on the majority selection function. This scheme is suitable for N-ary messages with arbitrary alphabet size N. In this paper, we show a hidden property of the majority selection function, which allows us to successfully break this scheme. We show that an adversary, by observing just one message and digest pair, without any knowledge of the secret information, can generate N - 1 new valid message and digest pairs. In order to resist the attack, we propose some modifications to the original design. The corrected scheme is as efficient as the original scheme and it is secure against the attack. By a new combinatorial approach, we calculate explicitly the security parameters of the corrected scheme.
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".