Factoring numbers in 0 (log n) arithmetic steps:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge, Mass.
Massachusetts Inst. of Technology, Lab. for Computer Science
1977
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| Schlagwörter: | |
| Abstract: | A non-trivial factor of a composite number n can be found by performing arithmetic steps in a number proportional to the number of bits in n, and thus there are extremely short straight-line factoring programs. However, this theoretical result does not imply that natural numbers can be factored in polynomial time in the Turing-Machine model of complexity, since the numbers operated on can be as big as 2 to the power c n-squared, thus requiring exponentially many bit operations. |
| Umfang: | 13 S. |
Internformat
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| 520 | 3 | |a A non-trivial factor of a composite number n can be found by performing arithmetic steps in a number proportional to the number of bits in n, and thus there are extremely short straight-line factoring programs. However, this theoretical result does not imply that natural numbers can be factored in polynomial time in the Turing-Machine model of complexity, since the numbers operated on can be as big as 2 to the power c n-squared, thus requiring exponentially many bit operations. | |
| 650 | 7 | |a Algorithms |2 dtict | |
| 650 | 7 | |a Arithmetic |2 dtict | |
| 650 | 7 | |a Decomposition |2 dtict | |
| 650 | 7 | |a Functions(mathematics) |2 dtict | |
| 650 | 7 | |a Logarithm functions |2 dtict | |
| 650 | 7 | |a Mathematical analysis |2 dtict | |
| 650 | 7 | |a Polynomials |2 dtict | |
| 650 | 7 | |a Theoretical Mathematics |2 scgdst | |
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Datensatz im Suchindex
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| author | Šāmîr, ʿAdî |
| author_facet | Šāmîr, ʿAdî |
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| id | DE-604.BV021882355 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T12:44:03Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015097711 |
| oclc_num | 227477504 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | 13 S. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Massachusetts Inst. of Technology, Lab. for Computer Science |
| record_format | marc |
| spelling | Šāmîr, ʿAdî Verfasser aut Factoring numbers in 0 (log n) arithmetic steps Adi Shamir Cambridge, Mass. Massachusetts Inst. of Technology, Lab. for Computer Science 1977 13 S. txt rdacontent n rdamedia nc rdacarrier A non-trivial factor of a composite number n can be found by performing arithmetic steps in a number proportional to the number of bits in n, and thus there are extremely short straight-line factoring programs. However, this theoretical result does not imply that natural numbers can be factored in polynomial time in the Turing-Machine model of complexity, since the numbers operated on can be as big as 2 to the power c n-squared, thus requiring exponentially many bit operations. Algorithms dtict Arithmetic dtict Decomposition dtict Functions(mathematics) dtict Logarithm functions dtict Mathematical analysis dtict Polynomials dtict Theoretical Mathematics scgdst Faktor Algebra (DE-588)4234581-9 gnd rswk-swf Primzahl (DE-588)4047263-2 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Algorithmus (DE-588)4001183-5 s DE-604 Primzahl (DE-588)4047263-2 s Faktor Algebra (DE-588)4234581-9 s |
| spellingShingle | Šāmîr, ʿAdî Factoring numbers in 0 (log n) arithmetic steps Algorithms dtict Arithmetic dtict Decomposition dtict Functions(mathematics) dtict Logarithm functions dtict Mathematical analysis dtict Polynomials dtict Theoretical Mathematics scgdst Faktor Algebra (DE-588)4234581-9 gnd Primzahl (DE-588)4047263-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4234581-9 (DE-588)4047263-2 (DE-588)4001183-5 |
| title | Factoring numbers in 0 (log n) arithmetic steps |
| title_auth | Factoring numbers in 0 (log n) arithmetic steps |
| title_exact_search | Factoring numbers in 0 (log n) arithmetic steps |
| title_full | Factoring numbers in 0 (log n) arithmetic steps Adi Shamir |
| title_fullStr | Factoring numbers in 0 (log n) arithmetic steps Adi Shamir |
| title_full_unstemmed | Factoring numbers in 0 (log n) arithmetic steps Adi Shamir |
| title_short | Factoring numbers in 0 (log n) arithmetic steps |
| title_sort | factoring numbers in 0 log n arithmetic steps |
| topic | Algorithms dtict Arithmetic dtict Decomposition dtict Functions(mathematics) dtict Logarithm functions dtict Mathematical analysis dtict Polynomials dtict Theoretical Mathematics scgdst Faktor Algebra (DE-588)4234581-9 gnd Primzahl (DE-588)4047263-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Algorithms Arithmetic Decomposition Functions(mathematics) Logarithm functions Mathematical analysis Polynomials Theoretical Mathematics Faktor Algebra Primzahl Algorithmus |
| work_keys_str_mv | AT samirʿadi factoringnumbersin0lognarithmeticsteps |