Scheme of extending elliptic curve method to three phases
Elliptic curve method for integer factorization (ECM) is one of the most popular integer factorization algorithms,and it was firstly proposed by Lenstra in 1985.The original ECM contained just first phase.Since its invention,researches about the algorithm and implementation emerged up,among which th...
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| Format: | Article |
| Language: | English |
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POSTS&TELECOM PRESS Co., LTD
2018-12-01
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| Series: | 网络与信息安全学报 |
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| Online Access: | http://www.cjnis.com.cn/thesisDetails#10.11959/j.issn.2096-109x.2018101 |
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| _version_ | 1841530094818951168 |
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| author | Guiwen LUO |
| author_facet | Guiwen LUO |
| author_sort | Guiwen LUO |
| collection | DOAJ |
| description | Elliptic curve method for integer factorization (ECM) is one of the most popular integer factorization algorithms,and it was firstly proposed by Lenstra in 1985.The original ECM contained just first phase.Since its invention,researches about the algorithm and implementation emerged up,among which the most important improvement is the extension to two phases proposed by Brent and Montgomery.This improvement tremendously strengthened ECM's capacity and efficiency.Elliptic curve method was extended to three phases.Extension method is kind of like “mixing together” the first phase and second phase.Compared to the best current two phases ECM,the new algorithm shows 2 advantages.First,under the same factorization parameters,the proposed algorithm improves the probability of finding out prime factor at the expense of negligible increasement of time.Second,when searching the same prime factor,the proposed algorithm can utilize smaller “smoothness parameters”. |
| format | Article |
| id | doaj-art-e51e5c84bb7b426f99af3df7ea757931 |
| institution | Kabale University |
| issn | 2096-109X |
| language | English |
| publishDate | 2018-12-01 |
| publisher | POSTS&TELECOM PRESS Co., LTD |
| record_format | Article |
| series | 网络与信息安全学报 |
| spelling | doaj-art-e51e5c84bb7b426f99af3df7ea7579312025-01-15T03:13:15ZengPOSTS&TELECOM PRESS Co., LTD网络与信息安全学报2096-109X2018-12-014626659555093Scheme of extending elliptic curve method to three phasesGuiwen LUOElliptic curve method for integer factorization (ECM) is one of the most popular integer factorization algorithms,and it was firstly proposed by Lenstra in 1985.The original ECM contained just first phase.Since its invention,researches about the algorithm and implementation emerged up,among which the most important improvement is the extension to two phases proposed by Brent and Montgomery.This improvement tremendously strengthened ECM's capacity and efficiency.Elliptic curve method was extended to three phases.Extension method is kind of like “mixing together” the first phase and second phase.Compared to the best current two phases ECM,the new algorithm shows 2 advantages.First,under the same factorization parameters,the proposed algorithm improves the probability of finding out prime factor at the expense of negligible increasement of time.Second,when searching the same prime factor,the proposed algorithm can utilize smaller “smoothness parameters”.http://www.cjnis.com.cn/thesisDetails#10.11959/j.issn.2096-109x.2018101integer factorizationfast factorizationelliptic curve methodsmoothness parameter |
| spellingShingle | Guiwen LUO Scheme of extending elliptic curve method to three phases 网络与信息安全学报 integer factorization fast factorization elliptic curve method smoothness parameter |
| title | Scheme of extending elliptic curve method to three phases |
| title_full | Scheme of extending elliptic curve method to three phases |
| title_fullStr | Scheme of extending elliptic curve method to three phases |
| title_full_unstemmed | Scheme of extending elliptic curve method to three phases |
| title_short | Scheme of extending elliptic curve method to three phases |
| title_sort | scheme of extending elliptic curve method to three phases |
| topic | integer factorization fast factorization elliptic curve method smoothness parameter |
| url | http://www.cjnis.com.cn/thesisDetails#10.11959/j.issn.2096-109x.2018101 |
| work_keys_str_mv | AT guiwenluo schemeofextendingellipticcurvemethodtothreephases |