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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 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 pomerance.pdf.
- 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".
- Lenstra_elliptic_curve_factorization wikiPageRevisionID "605371923".
- Lenstra_elliptic_curve_factorization hasPhotoCollection Lenstra_elliptic_curve_factorization.
- Lenstra_elliptic_curve_factorization subject Category:Finite_fields.
- Lenstra_elliptic_curve_factorization subject Category:Integer_factorization_algorithms.
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- 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 "Algoritme van Lenstra".
- Lenstra_elliptic_curve_factorization label "Factorisation de Lenstra par les courbes elliptiques".
- Lenstra_elliptic_curve_factorization label "Factorización de curva elíptica de Lenstra".
- Lenstra_elliptic_curve_factorization label "Lenstra elliptic curve factorization".
- Lenstra_elliptic_curve_factorization label "Факторизация с помощью эллиптических кривых".
- Lenstra_elliptic_curve_factorization label "تعميل 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 Q2662711.
- Lenstra_elliptic_curve_factorization sameAs Q2662711.
- Lenstra_elliptic_curve_factorization sameAs Lenstra_elliptic_curve_factorization.
- Lenstra_elliptic_curve_factorization wasDerivedFrom Lenstra_elliptic_curve_factorization?oldid=605371923.
- Lenstra_elliptic_curve_factorization isPrimaryTopicOf Lenstra_elliptic_curve_factorization.