Factoring integers with large prime variations of the quadratic sieve:
Abstract: "We present the results of many factorization runs with the single and double large prime variations (PMPQS, and PPMPQS, respectively) of the quadratic sieve factorization method on SGI workstations, and on a Cray C90 vectorcomputer. Experiments with 71-, 87-, and 99-digit numbers sho...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1995
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1995,13 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "We present the results of many factorization runs with the single and double large prime variations (PMPQS, and PPMPQS, respectively) of the quadratic sieve factorization method on SGI workstations, and on a Cray C90 vectorcomputer. Experiments with 71-, 87-, and 99-digit numbers show that for our Cray C90 implementations PPMPQS beats PMPQS for numbers of more than 80 digits, and this cross-over point goes down with the amount of available central memory. For PMPQS a known theoretical formula is worked out and tested that helps to predict the total running time on the basis of a short test run. The accuracy of the prediction is within 10% of the actual running time. For PPMPQS such a prediction formula is not known and the determination of an optimal choice of the parameters for a given number would require many full runs with that given number, and the use of an inadmissible amount of CPU-time. In order yet to provide measurements that can help to determine a good choice of the parameters in PPMPQS, we have factored many numbers in the 66 - 88 decimal digits range, where each number was run once with a specific choice of the parameters. In addition, an experimental prediction formula is given that has a restricted scope in the sense that it only applies to numbers of a given size, for a fixed choice of the parameters of PPMPQS. So such a formula may be useful if one wishes to factor many different large numbers of about the same size with PPMPQS." |
| Beschreibung: | 27 S. |
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| 100 | 1 | |a Boender, H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Factoring integers with large prime variations of the quadratic sieve |c H. Boender ; H. J. J. te Riele |
| 264 | 1 | |a Amsterdam |c 1995 | |
| 300 | |a 27 S. | ||
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |v 1995,13 | |
| 520 | 3 | |a Abstract: "We present the results of many factorization runs with the single and double large prime variations (PMPQS, and PPMPQS, respectively) of the quadratic sieve factorization method on SGI workstations, and on a Cray C90 vectorcomputer. Experiments with 71-, 87-, and 99-digit numbers show that for our Cray C90 implementations PPMPQS beats PMPQS for numbers of more than 80 digits, and this cross-over point goes down with the amount of available central memory. For PMPQS a known theoretical formula is worked out and tested that helps to predict the total running time on the basis of a short test run. The accuracy of the prediction is within 10% of the actual running time. For PPMPQS such a prediction formula is not known and the determination of an optimal choice of the parameters for a given number would require many full runs with that given number, and the use of an inadmissible amount of CPU-time. In order yet to provide measurements that can help to determine a good choice of the parameters in PPMPQS, we have factored many numbers in the 66 - 88 decimal digits range, where each number was run once with a specific choice of the parameters. In addition, an experimental prediction formula is given that has a restricted scope in the sense that it only applies to numbers of a given size, for a fixed choice of the parameters of PPMPQS. So such a formula may be useful if one wishes to factor many different large numbers of about the same size with PPMPQS." | |
| 610 | 2 | 4 | |a Supercomputing |
| 650 | 4 | |a Factorization (Mathematics) | |
| 650 | 4 | |a Numbers, Prime | |
| 700 | 1 | |a Riele, Herman H. te |e Verfasser |4 aut | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1995,13 |w (DE-604)BV010177152 |9 1995,13 | |
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Datensatz im Suchindex
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| author | Boender, H. Riele, Herman H. te |
| author_facet | Boender, H. Riele, Herman H. te |
| author_role | aut aut |
| author_sort | Boender, H. |
| author_variant | h b hb h h t r hht hhtr |
| building | Verbundindex |
| bvnumber | BV011062770 |
| ctrlnum | (OCoLC)34740289 (DE-599)BVBBV011062770 |
| format | Book |
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| id | DE-604.BV011062770 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:21Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007408960 |
| oclc_num | 34740289 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 27 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Boender, H. Verfasser aut Factoring integers with large prime variations of the quadratic sieve H. Boender ; H. J. J. te Riele Amsterdam 1995 27 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1995,13 Abstract: "We present the results of many factorization runs with the single and double large prime variations (PMPQS, and PPMPQS, respectively) of the quadratic sieve factorization method on SGI workstations, and on a Cray C90 vectorcomputer. Experiments with 71-, 87-, and 99-digit numbers show that for our Cray C90 implementations PPMPQS beats PMPQS for numbers of more than 80 digits, and this cross-over point goes down with the amount of available central memory. For PMPQS a known theoretical formula is worked out and tested that helps to predict the total running time on the basis of a short test run. The accuracy of the prediction is within 10% of the actual running time. For PPMPQS such a prediction formula is not known and the determination of an optimal choice of the parameters for a given number would require many full runs with that given number, and the use of an inadmissible amount of CPU-time. In order yet to provide measurements that can help to determine a good choice of the parameters in PPMPQS, we have factored many numbers in the 66 - 88 decimal digits range, where each number was run once with a specific choice of the parameters. In addition, an experimental prediction formula is given that has a restricted scope in the sense that it only applies to numbers of a given size, for a fixed choice of the parameters of PPMPQS. So such a formula may be useful if one wishes to factor many different large numbers of about the same size with PPMPQS." Supercomputing Factorization (Mathematics) Numbers, Prime Riele, Herman H. te Verfasser aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1995,13 (DE-604)BV010177152 1995,13 |
| spellingShingle | Boender, H. Riele, Herman H. te Factoring integers with large prime variations of the quadratic sieve Supercomputing Factorization (Mathematics) Numbers, Prime |
| title | Factoring integers with large prime variations of the quadratic sieve |
| title_auth | Factoring integers with large prime variations of the quadratic sieve |
| title_exact_search | Factoring integers with large prime variations of the quadratic sieve |
| title_full | Factoring integers with large prime variations of the quadratic sieve H. Boender ; H. J. J. te Riele |
| title_fullStr | Factoring integers with large prime variations of the quadratic sieve H. Boender ; H. J. J. te Riele |
| title_full_unstemmed | Factoring integers with large prime variations of the quadratic sieve H. Boender ; H. J. J. te Riele |
| title_short | Factoring integers with large prime variations of the quadratic sieve |
| title_sort | factoring integers with large prime variations of the quadratic sieve |
| topic | Supercomputing Factorization (Mathematics) Numbers, Prime |
| topic_facet | Supercomputing Factorization (Mathematics) Numbers, Prime |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT boenderh factoringintegerswithlargeprimevariationsofthequadraticsieve AT rielehermanhte factoringintegerswithlargeprimevariationsofthequadraticsieve |