Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Integer_factorization> ?p ?o }
- Integer_factorization abstract "In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called prime factorization.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. However, it has not been proven that no efficient algorithm exists. 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 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.
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- Integer_factorization wikiPageRevisionID "682261203".
- Integer_factorization wikiPageWikiLink AKS_primality_test.
- Integer_factorization wikiPageWikiLink Adleman–Pomerance–Rumely_primality_test.
- Integer_factorization wikiPageWikiLink Advanced_Micro_Devices.
- Integer_factorization wikiPageWikiLink Algebraic-group_factorisation_algorithm.
- Integer_factorization wikiPageWikiLink Algebraic-group_factorisation_algorithms.
- Integer_factorization wikiPageWikiLink Algebraic_number_theory.
- Integer_factorization wikiPageWikiLink Algorithm.
- Integer_factorization wikiPageWikiLink BQP.
- Integer_factorization wikiPageWikiLink Big_O_notation.
- Integer_factorization wikiPageWikiLink Binary_search.
- Integer_factorization wikiPageWikiLink Binary_search_algorithm.
- Integer_factorization wikiPageWikiLink Bit.
- Integer_factorization wikiPageWikiLink Canonical_representation_of_a_positive_integer.
- Integer_factorization wikiPageWikiLink Carl_Pomerance.
- Integer_factorization wikiPageWikiLink Category:Computational_hardness_assumptions.
- Integer_factorization wikiPageWikiLink Category:Integer_factorization_algorithms.
- Integer_factorization wikiPageWikiLink Category:Unsolved_problems_in_computer_science.
- Integer_factorization wikiPageWikiLink Co-NP.
- Integer_factorization wikiPageWikiLink Co-NP-complete.
- Integer_factorization wikiPageWikiLink Complexity_class.
- Integer_factorization wikiPageWikiLink Composite_number.
- Integer_factorization wikiPageWikiLink Computational_complexity_theory.
- Integer_factorization wikiPageWikiLink Computer_science.
- Integer_factorization wikiPageWikiLink Congruence_of_squares.
- Integer_factorization wikiPageWikiLink Continued_fraction_factorization.
- Integer_factorization wikiPageWikiLink Cryptography.
- Integer_factorization wikiPageWikiLink Decision_problem.
- Integer_factorization wikiPageWikiLink Discriminant.
- Integer_factorization wikiPageWikiLink Discriminant_of_a_quadratic_form.
- Integer_factorization wikiPageWikiLink Dixons_algorithm.
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- Integer_factorization wikiPageWikiLink Donald_Knuth.
- Integer_factorization wikiPageWikiLink Elliptic_curve.
- Integer_factorization wikiPageWikiLink Elliptic_curve_method.
- Integer_factorization wikiPageWikiLink Empty_product.
- Integer_factorization wikiPageWikiLink Eulers_factorization_method.
- Integer_factorization wikiPageWikiLink FNP_(complexity).
- Integer_factorization wikiPageWikiLink FP_(complexity).
- Integer_factorization wikiPageWikiLink Factorization.
- Integer_factorization wikiPageWikiLink Fast_Fourier_transform.
- Integer_factorization wikiPageWikiLink Fermats_factorization_method.
- Integer_factorization wikiPageWikiLink Function_problem.
- Integer_factorization wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Integer_factorization wikiPageWikiLink General_number_field_sieve.
- Integer_factorization wikiPageWikiLink Generalized_Riemann_hypothesis.
- Integer_factorization wikiPageWikiLink Generating_set_of_a_group.
- Integer_factorization wikiPageWikiLink Greatest_common_divisor.
- Integer_factorization wikiPageWikiLink Group_(mathematics).
- Integer_factorization wikiPageWikiLink Ideal_class_group.
- Integer_factorization wikiPageWikiLink Kronecker_symbol.
- Integer_factorization wikiPageWikiLink L-notation.
- Integer_factorization wikiPageWikiLink Lenstra_elliptic_curve_factorization.
- Integer_factorization wikiPageWikiLink Manindra_Agrawal.
- Integer_factorization wikiPageWikiLink Mathematics.
- Integer_factorization wikiPageWikiLink Maurice_Kraitchik.
- Integer_factorization wikiPageWikiLink Multiplicative_partition.
- Integer_factorization wikiPageWikiLink NP-complete.
- Integer_factorization wikiPageWikiLink NP-completeness.
- Integer_factorization wikiPageWikiLink NP-intermediate.
- Integer_factorization wikiPageWikiLink NP_(complexity).
- Integer_factorization wikiPageWikiLink Number_theory.
- Integer_factorization wikiPageWikiLink Opteron.
- Integer_factorization wikiPageWikiLink P_(complexity).
- Integer_factorization wikiPageWikiLink Partition_(number_theory).
- Integer_factorization wikiPageWikiLink Peter_Shor.
- Integer_factorization wikiPageWikiLink Pollards_p_xe2x88x92_1_algorithm.
- Integer_factorization wikiPageWikiLink Pollards_rho_algorithm.
- Integer_factorization wikiPageWikiLink Polynomial_time.
- Integer_factorization wikiPageWikiLink Primality_test.
- Integer_factorization wikiPageWikiLink Prime_factor.
- Integer_factorization wikiPageWikiLink Prime_number.
- Integer_factorization wikiPageWikiLink Probabilistic_algorithm.
- Integer_factorization wikiPageWikiLink Public-key.
- Integer_factorization wikiPageWikiLink Public-key_cryptography.
- Integer_factorization wikiPageWikiLink Quadratic_form.
- Integer_factorization wikiPageWikiLink Quadratic_sieve.
- Integer_factorization wikiPageWikiLink Quantum_computer.
- Integer_factorization wikiPageWikiLink Quantum_computing.
- Integer_factorization wikiPageWikiLink RSA-768.
- Integer_factorization wikiPageWikiLink RSA_(algorithm).
- Integer_factorization wikiPageWikiLink RSA_(cryptosystem).
- Integer_factorization wikiPageWikiLink RSA_number.
- Integer_factorization wikiPageWikiLink RSA_numbers.
- Integer_factorization wikiPageWikiLink RSA_problem.
- Integer_factorization wikiPageWikiLink Randomized_algorithm.
- Integer_factorization wikiPageWikiLink Rational_sieve.
- Integer_factorization wikiPageWikiLink Richard_Crandall.
- Integer_factorization wikiPageWikiLink Semiprime.