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- Lenstra_elliptic_curve_factorization abstract "The Lenstra elliptic curve factorization or the elliptic curve factorization method (ECM) is a fast, sub-exponential running time algorithm for integer factorization which employs elliptic curves. For general purpose factoring, ECM is the third-fastest known factoring method. The second fastest is the multiple polynomial quadratic sieve and the fastest is the general number field sieve. The Lenstra elliptic curve factorization is named after Hendrik Lenstra.Practically speaking, ECM is considered a special purpose factoring algorithm as it is most suitable for finding small factors. Currently, it is still the best algorithm for divisors not greatly exceeding 20 to 25 digits (64 to 83 bits or so), as its running time is dominated by the size of the smallest factor p rather than by the size of the number n to be factored. Frequently, ECM is used to remove small factors from a very large integer with many factors; if the remaining integer is still composite, then it has only large factors and is factored using general purpose techniques. The largest factor found using ECM so far has 83 digits and was discovered on 7 September 2013 by R. Propper. Increasing the number of curves tested improves the chances of finding a factor, but they are not linear with the increase in the number of digits.".
- Lenstra_elliptic_curve_factorization wikiPageExternalLink pomerance.pdf.
- Lenstra_elliptic_curve_factorization wikiPageExternalLink ECM.HTM.
- Lenstra_elliptic_curve_factorization wikiPageExternalLink large-integers-factorization.
- Lenstra_elliptic_curve_factorization wikiPageExternalLink ecm.gforge.inria.fr.
- Lenstra_elliptic_curve_factorization wikiPageExternalLink 016.
- Lenstra_elliptic_curve_factorization wikiPageExternalLink 016,.
- Lenstra_elliptic_curve_factorization wikiPageExternalLink ecmnet.html.
- Lenstra_elliptic_curve_factorization wikiPageExternalLink yoyo.
- Lenstra_elliptic_curve_factorization wikiPageExternalLink pyecm.
- Lenstra_elliptic_curve_factorization wikiPageID "154212".
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- Lenstra_elliptic_curve_factorization wikiPageRevisionID "660540652".
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Annals_of_Mathematics.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Big_O_notation.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Binary_digit.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Bit.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Canfield–Erdős–Pomerance_theorem.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Category:Finite_fields.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Category:Integer_factorization_algorithms.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Computer.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Coprime_integers.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Decimal.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Divisor.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink EXPTIME.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Edwards_curve.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Elliptic_curve.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Euclidean_algorithm.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Exponential_running_time.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Extended_Euclidean_algorithm.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Factorial.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Fermats_little_theorem.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Finite_field.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink General_number_field_sieve.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink General_purpose_computer.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Greatest_common_divisor.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Group_(mathematics).
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Hasses_theorem_on_elliptic_curves.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Hendrik_Lenstra.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Heuristic.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Hyperelliptic_curve.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Integer_factorization.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink L-notation.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Lagranges_theorem_(group_theory).
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Linear.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Linearity.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Mathematics_of_Computation.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Modular_arithmetic.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Modular_inverse.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Modular_multiplicative_inverse.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Montgomery_curve.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Multiplicative_group.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Notices_of_the_American_Mathematical_Society.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink PDF.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Point_(geometry).
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Pollards_p_xe2x88x92_1_algorithm.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Portable_Document_Format.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Projective_space.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Quadratic_sieve.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Relatively_prime.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Smooth_number.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Strong_prime.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink Torsion_group.
- Lenstra_elliptic_curve_factorization wikiPageWikiLink UBASIC.
- Lenstra_elliptic_curve_factorization wikiPageWikiLinkText "ECM".
- Lenstra_elliptic_curve_factorization wikiPageWikiLinkText "ECMNET".
- Lenstra_elliptic_curve_factorization wikiPageWikiLinkText "Elliptic Curve Method".
- Lenstra_elliptic_curve_factorization wikiPageWikiLinkText "Lenstra elliptic curve factorization".
- Lenstra_elliptic_curve_factorization wikiPageWikiLinkText "ecm".
- Lenstra_elliptic_curve_factorization wikiPageWikiLinkText "elliptic curve method".
- Lenstra_elliptic_curve_factorization wikiPageWikiLinkText "elliptic curves in factorization".
- Lenstra_elliptic_curve_factorization hasPhotoCollection Lenstra_elliptic_curve_factorization.
- Lenstra_elliptic_curve_factorization wikiPageUsesTemplate Template:As_of.
- Lenstra_elliptic_curve_factorization wikiPageUsesTemplate Template:Cite_book.
- Lenstra_elliptic_curve_factorization wikiPageUsesTemplate Template:Cite_journal.
- Lenstra_elliptic_curve_factorization wikiPageUsesTemplate Template:Cite_paper.
- Lenstra_elliptic_curve_factorization wikiPageUsesTemplate Template:Harvtxt.
- Lenstra_elliptic_curve_factorization wikiPageUsesTemplate Template:Number_theoretic_algorithms.
- Lenstra_elliptic_curve_factorization wikiPageUsesTemplate Template:Reflist.
- Lenstra_elliptic_curve_factorization subject Category:Finite_fields.
- Lenstra_elliptic_curve_factorization subject Category:Integer_factorization_algorithms.
- Lenstra_elliptic_curve_factorization type Article.
- Lenstra_elliptic_curve_factorization type Algorithm.
- Lenstra_elliptic_curve_factorization type Article.
- Lenstra_elliptic_curve_factorization type Field.
- Lenstra_elliptic_curve_factorization comment "The Lenstra elliptic curve factorization or the elliptic curve factorization method (ECM) is a fast, sub-exponential running time algorithm for integer factorization which employs elliptic curves. For general purpose factoring, ECM is the third-fastest known factoring method. The second fastest is the multiple polynomial quadratic sieve and the fastest is the general number field sieve.".
- Lenstra_elliptic_curve_factorization label "Lenstra elliptic curve factorization".
- Lenstra_elliptic_curve_factorization sameAs تحليل_عدد_صحيح_باستعمال_منحنى_لنسترا_الإهليلجي.
- Lenstra_elliptic_curve_factorization sameAs Factorización_de_curva_elíptica_de_Lenstra.
- Lenstra_elliptic_curve_factorization sameAs Factorisation_de_Lenstra_par_les_courbes_elliptiques.
- Lenstra_elliptic_curve_factorization sameAs Algoritme_van_Lenstra.
- Lenstra_elliptic_curve_factorization sameAs m.0144hm.
- Lenstra_elliptic_curve_factorization sameAs Факторизация_с_помощью_эллиптических_кривых.
- Lenstra_elliptic_curve_factorization sameAs Q2662711.
- Lenstra_elliptic_curve_factorization sameAs Q2662711.
- Lenstra_elliptic_curve_factorization wasDerivedFrom Lenstra_elliptic_curve_factorization?oldid=660540652.
- Lenstra_elliptic_curve_factorization isPrimaryTopicOf Lenstra_elliptic_curve_factorization.