Diffie-Hellman key exchange on the Heisenberg group
Bibliographic record
Abstract
This paper introduces Hadamard-type t-Fibonacci-Lehmer (HTFL) sequences, a new hybrid construction combining Lehmer and Fibonacci recurrences. We establish their fundamental properties, including simple periodicity, and extend the definition to finite groups, with a detailed study of the Heisenberg group. Building on these results, we propose two Diffie–Hellman-style key exchange protocols based on upper-triangular unipotent matrices parameterized by HTFL sequence terms. Our work thus connects sequence theory, group theory, and cryptography in a novel way. While the algebraic framework and periodicity analysis are rigorous, we present the cryptographic constructions primarily as a conceptual foundation. We also discuss potential security considerations and outline directions for strengthening these schemes under formal hardness assumptions. This study demonstrates that HTFL sequences provide a fertile ground for both combinatorial investigations and future cryptographic applications.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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 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".