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- Pollards_p_xe2x88x92_1_algorithm abstract "Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning that it is only suitable for integers with specific types of factors; it is the simplest example of an algebraic-group factorisation algorithm.The factors it finds are ones for which the number preceding the factor, p − 1, is powersmooth; the essential observation is that, by working in the multiplicative group modulo a composite number N, we are also working in the multiplicative groups modulo all of N's factors.The existence of this algorithm leads to the concept of safe primes, being primes for which p − 1 is two times a Sophie Germain prime q and thus minimally smooth. These primes are sometimes construed as "safe for cryptographic purposes", but they might be unsafe — in current recommendations for cryptographic strong primes (e.g. ANSI X9.31), it is necessary but not sufficient that p − 1 has at least one large prime factor. Most sufficiently large primes are strong; if a prime used for cryptographic purposes turns out to be non-strong, it is much more likely to be through malice than through an accident of random number generation. This terminology is considered obsolete by the cryptography industry.[1]".
- Pollards_p_xe2x88x92_1_algorithm wikiPageExternalLink maths-factoring-pollard.
- Pollards_p_xe2x88x92_1_algorithm wikiPageExternalLink ecm.
- Pollards_p_xe2x88x92_1_algorithm wikiPageExternalLink node.asp?id=2217.
- Pollards_p_xe2x88x92_1_algorithm wikiPageID "578753".
- Pollards_p_xe2x88x92_1_algorithm wikiPageLength "8135".
- Pollards_p_xe2x88x92_1_algorithm wikiPageOutDegree "26".
- Pollards_p_xe2x88x92_1_algorithm wikiPageRevisionID "680284655".
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink ANSI_X9.31.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Algebraic-group_factorisation_algorithm.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Algorithm.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Category:Integer_factorization_algorithms.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Dixons_identity.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Dixons_theorem.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Elliptic_curve_method.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Fermats_little_theorem.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Great_Internet_Mersenne_Prime_Search.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Greatest_common_divisor.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Integer.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Integer_factorization.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink John_Pollard_(mathematician).
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Lenstra_elliptic_curve_factorization.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink MPrime.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Modular_arithmetic.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Natural_logarithm.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Necessary_but_not_sufficient.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Necessity_and_sufficiency.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Number_theory.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Obsolescence.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Obsolete.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Prime95.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Random_number_generation.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Safe_prime.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Smooth_number.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Sophie_Germain_prime.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Strong_prime.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLink Williams_p_+_1_algorithm.
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLinkText "''p'' − 1 algorithm".
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLinkText "''p'' − 1".
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLinkText "Pollard's ''p'' − 1 algorithm".
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLinkText "Pollard's ''p'' − 1 algorithm".
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLinkText "Pollard's ''p'' − 1 algorithm".
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLinkText "Pollard's ''p'' − 1 algorithm".
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLinkText "Pollard's p − 1 algorithm".
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLinkText "Pollard's p − 1 algorithm".
- Pollards_p_xe2x88x92_1_algorithm wikiPageWikiLinkText "−1 methods".
- Pollards_p_xe2x88x92_1_algorithm hasPhotoCollection Pollards_p_xe2x88x92_1_algorithm.
- Pollards_p_xe2x88x92_1_algorithm wikiPageUsesTemplate Template:=.
- Pollards_p_xe2x88x92_1_algorithm wikiPageUsesTemplate Template:Cite_journal.
- Pollards_p_xe2x88x92_1_algorithm wikiPageUsesTemplate Template:Number_theoretic_algorithms.
- Pollards_p_xe2x88x92_1_algorithm subject Category:Integer_factorization_algorithms.
- Pollards_p_xe2x88x92_1_algorithm comment "Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974.".
- Pollards_p_xe2x88x92_1_algorithm label "Pollard's p − 1 algorithm".
- Pollards_p_xe2x88x92_1_algorithm sameAs Pollard-p-1-Methode.
- Pollards_p_xe2x88x92_1_algorithm sameAs Algoritmo_p_−_1_de_Pollard.
- Pollards_p_xe2x88x92_1_algorithm sameAs الگوریتم_پی-۱_پولارد.
- Pollards_p_xe2x88x92_1_algorithm sameAs Algorithme_p-1_de_Pollard.
- Pollards_p_xe2x88x92_1_algorithm sameAs Pollards_p-1-methode.
- Pollards_p_xe2x88x92_1_algorithm sameAs m.02rzqd.
- Pollards_p_xe2x88x92_1_algorithm sameAs P-1_метод_Полларда.
- Pollards_p_xe2x88x92_1_algorithm sameAs ขั้นตอนวิธีพีลบหนึ่งของพอลลาร์ด.
- Pollards_p_xe2x88x92_1_algorithm sameAs Q1937853.
- Pollards_p_xe2x88x92_1_algorithm sameAs Q1937853.
- Pollards_p_xe2x88x92_1_algorithm wasDerivedFrom Pollards_p_xe2x88x92_1_algorithmoldid=680284655.
- Pollards_p_xe2x88x92_1_algorithm isPrimaryTopicOf Pollards_p_xe2x88x92_1_algorithm.