Novel Way of Generating Random Numbers Using Lucas Sequence and Associated in ATM/Ecommerce for Secured Online Transactions
Bibliographic record
Abstract
This paper proposes novel pseudorandom number generators (PRNGs) based on the Lucas sequence and the SHA3-512 hashing algorithm over the finite field Fp. We introduce one primary algorithm capable of generating random numbers up to 32 digits (256 bits) in length, suitable for highly confidential applications such as international communications, defense activities, and large monetary transactions. Additionally, three associated sub-algorithms produce fixed-length random numbers of 4, 6, and 8 digits (32, 48, and 64 bits, respectively), optimized for ATM and e-commerce transactions. Unlike existing PRNGs that rely on a single seed, our approach utilizes two seeds: a userprovided, context-specific seed, and a server-generated seed derived from the Lucas sequence over the Pell curve. The server-generated seed remains entirely outside user control, enhancing the security of the generated random numbers. The PRNG process involves hashing the sum of solutions to the Pell curve, converting the resulting hexadecimal hash output into binary, and extracting the first half of the 512 bits, which is then mapped to an integer over the field Fq to produce the random number. Statistical analysis using the Kolmogorov-Smirnov test confirms that the generated numbers follow a uniform distribution. Security analysis demonstrates resilience against various attacks, including direct cryptanalytic, input-based, iterative guessing, backtracking, and gap-filling attacks. These results suggest that the proposed PRNGs offer improved security and efficiency for applications in ATM operations and e-commerce.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".