Modular Construction a Lattices from Cyclotomic Fields and their Applications in Information Security
Bibliographic record
Abstract
We present an overview of recent advances in the area of information security using algebraic number fields. This overview indicates the importance of modular lattices in information security and in recently proposed methods for obtaining modular lattices using algebraic number fields. Obtaining Construction A unimodular lattices using cyclotomic number fields of prime orders have been addressed in the literature. Recently, a new lattice invariant called secrecy gain has been defined and it has been shown that it characterizes the confusion at the eavesdropper when using lattices in the Gaussian wiretap channels. There is a symmetry point, called weak secrecy gain, in the secrecy function of modular lattices. It is conjectured that the weak secrecy gain is the secrecy gain. It is known that d-modular lattices with high level d are more likely to have a large length for the shortest nonzero vector, which results in a higher weak secrecy gain. In search of such lattices, we prove that there is no modular lattices built using Construction A over cyclotomic fields of prime power order pn, with n > 1. We also present a new framework based on Construction A lattices and cyclotomic number fields that gives a family of p-modular lattices with p ≡ 1 (mod 4).
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".