Bibliographic record
Abstract
The difficulty of factoring large integers into primes is the basis for cryptosystems such as RSA. Due to the widespread popularity of RSA, there have been many proposed attacks on the factorization problem such as side-channel attacks where some bits of the prime factors are available. When enough bits of the prime factors are known, two methods that are effective at solving the factorization problem are satisfiability (SAT) solvers and Coppersmith’s method. The SAT approach reduces the factorization problem to a Boolean satisfiability problem, while Coppersmith’s approach uses lattice basis reduction. Both methods have their advantages, but they also have their limitations: Coppersmith’s method does not apply when the known bit positions are randomized, while SAT-based methods can take advantage of known bits in arbitrary locations, but have no knowledge of the algebraic structure exploited by Coppersmith’s method. In this paper we describe a new hybrid SAT and computer algebra approach to efficiently solve random leaked-bit factorization problems. Specifically, Coppersmith’s method is invoked by a SAT solver to determine whether a partial bit assignment can be extended to a complete assignment. Our hybrid implementation solves random leaked-bit factorization problems significantly faster than either a pure SAT or pure computer algebra approach.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".