Genetic programming for improved cryptanalysis of elliptic curve cryptosystems
Bibliographic record
Abstract
Public-key cryptography is a fundamental component of modern electronic communication that can be constructed with many different mathematical processes. Presently, cryptosystems based on elliptic curves are becoming popular due to strong cryptographic strength per small key size. At the heart of these schemes is the intractability of the elliptic curve discrete logarithm problem (ECDLP). Pollard's Rho algorithm is a well known method for solving the ECDLP and thereby breaking ciphers based on elliptic curves. It has the same time complexity as other known methods but is advantageous due to smaller memory requirements. This paper considers how to speed up the Rho process by modifying a key component: the iterating function, which is the part of the algorithm responsible for determining what point is considered next when looking for a collision. It is replaced with an alternative that is found through an evolutionary process. This alternative consistently and significantly decreases the number of iterations required by Pollard's Rho Algorithm to successfully find a solution to the ECDLP.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".