MétaCan
Menu
Back to cohort
Record W1985265065 · doi:10.1090/s0025-5718-00-01213-8

On random walks for Pollard’s rho method

2000· article· en· W1985265065 on OpenAlexaff
Edlyn Teske

Bibliographic record

VenueMathematics of Computation · 2000
Typearticle
Languageen
FieldComputer Science
TopicChaos-based Image/Signal Encryption
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsMathematicsRandom walkDiscrete mathematicsCalculus (dental)Statistical physicsCombinatoricsStatistics

Abstract

fetched live from OpenAlex

We consider Pollard’s rho method for discrete logarithm computation. Usually, in the analysis of its running time the assumption is made that a random walk in the underlying group is simulated. We show that this assumption does not hold for the walk originally suggested by Pollard: its performance is worse than in the random case. We study alternative walks that can be efficiently applied to compute discrete logarithms. We introduce a class of walks that lead to the same performance as expected in the random case. We show that this holds for arbitrarily large prime group orders, thus making Pollard’s rho method for prime group orders about 20 20% faster than before.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.004
metaresearch head score (Gemma)0.020
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.009
Threshold uncertainty score0.029

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0040.020
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0020.002
Science and technology studies0.0010.002
Scholarly communication0.0020.004
Open science0.0010.003
Research integrity0.0020.002
Insufficient payload (model declined to judge)0.0090.004

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.

Opus teacher head0.016
GPT teacher head0.303
Teacher spread0.287 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations116
Published2000
Admission routes1
Has abstractyes

Explore more

Same venueMathematics of ComputationSame topicChaos-based Image/Signal EncryptionFrench-language works237,207