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- Integer_factorization abstract "In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer.When the numbers are very large, no efficient, non-quantum integer factorization algorithm is known; an effort by several researchers concluded in 2009, factoring a 232-digit number (RSA-768), utilizing hundreds of machines over a span of two years. The presumed difficulty of this problem is at the heart of widely used algorithms in cryptography such as RSA. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing.Not all numbers of a given length are equally hard to factor. The hardest instances of these problems (for currently known techniques) are semiprimes, the product of two prime numbers. When they are both large, for instance more than two thousand bits long, randomly chosen, and about the same size (but not too close, e.g. to avoid efficient factorization by Fermat's factorization method), even the fastest prime factorization algorithms on the fastest computers can take enough time to make the search impractical; that is, as the number of digits of the primes being factored increases, the number of operations required to perform the factorization on any computer increases drastically.Many cryptographic protocols are based on the difficulty of factoring large composite integers or a related problem—for example, the RSA problem. An algorithm that efficiently factors an arbitrary integer would render RSA-based public-key cryptography insecure.".
- Integer_factorization thumbnail PrimeDecompositionExample.svg?width=300.
- Integer_factorization wikiPageExternalLink factor.exe.
- Integer_factorization wikiPageExternalLink 327036.html.
- Integer_factorization wikiPageExternalLink rsa-640.
- Integer_factorization wikiPageExternalLink msieve.
- Integer_factorization wikiPageExternalLink primality_v6.pdf.
- Integer_factorization wikiPageExternalLink showthread.php?t=3255.
- Integer_factorization wikiPageExternalLink www.shamus.ie.
- Integer_factorization wikiPageID "15491".
- Integer_factorization wikiPageRevisionID "606715620".
- Integer_factorization hasPhotoCollection Integer_factorization.
- Integer_factorization subject Category:Computational_hardness_assumptions.
- Integer_factorization subject Category:Integer_factorization_algorithms.
- Integer_factorization subject Category:Unsolved_problems_in_computer_science.
- Integer_factorization type Abstraction100002137.
- Integer_factorization type Act100030358.
- Integer_factorization type Activity100407535.
- Integer_factorization type Algorithm105847438.
- Integer_factorization type Attribute100024264.
- Integer_factorization type Communication100033020.
- Integer_factorization type ComputationalHardnessAssumptions.
- Integer_factorization type Condition113920835.
- Integer_factorization type Difficulty114408086.
- Integer_factorization type Event100029378.
- Integer_factorization type IntegerFactorizationAlgorithms.
- Integer_factorization type Message106598915.
- Integer_factorization type Postulate106753299.
- Integer_factorization type Premise106753800.
- Integer_factorization type Problem114410605.
- Integer_factorization type Procedure101023820.
- Integer_factorization type Proposition106750804.
- Integer_factorization type PsychologicalFeature100023100.
- Integer_factorization type Rule105846932.
- Integer_factorization type State100024720.
- Integer_factorization type Statement106722453.
- Integer_factorization type UnsolvedProblemsInComputerScience.
- Integer_factorization type YagoPermanentlyLocatedEntity.
- Integer_factorization comment "In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer.When the numbers are very large, no efficient, non-quantum integer factorization algorithm is known; an effort by several researchers concluded in 2009, factoring a 232-digit number (RSA-768), utilizing hundreds of machines over a span of two years.".
- Integer_factorization label "Décomposition en produit de facteurs premiers".
- Integer_factorization label "Factorización de enteros".
- Integer_factorization label "Fatoração de inteiros".
- Integer_factorization label "Integer factorization".
- Integer_factorization label "Ontbinden in priemfactoren".
- Integer_factorization label "Primfaktorzerlegung".
- Integer_factorization label "Факторизация целых чисел".
- Integer_factorization label "تحليل عدد صحيح إلى عوامل".
- Integer_factorization label "整数分解".
- Integer_factorization label "素因数分解".
- Integer_factorization sameAs Prvočíselný_rozklad.
- Integer_factorization sameAs Primfaktorzerlegung.
- Integer_factorization sameAs Factorización_de_enteros.
- Integer_factorization sameAs Décomposition_en_produit_de_facteurs_premiers.
- Integer_factorization sameAs Faktorisasi_prima.
- Integer_factorization sameAs 素因数分解.
- Integer_factorization sameAs 소인수_분해.
- Integer_factorization sameAs Ontbinden_in_priemfactoren.
- Integer_factorization sameAs Fatoração_de_inteiros.
- Integer_factorization sameAs m.03zsm.
- Integer_factorization sameAs Q4846249.
- Integer_factorization sameAs Q4846249.
- Integer_factorization sameAs Integer_factorization.
- Integer_factorization wasDerivedFrom Integer_factorization?oldid=606715620.
- Integer_factorization depiction PrimeDecompositionExample.svg.
- Integer_factorization isPrimaryTopicOf Integer_factorization.
