Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves
► Two distinct efficient endomorphisms are discovered to coexist on some GLS elliptic curves. ► 3-dimensional GLV method for fast point multiplication is generalized to these curves. ► Implementation of 3-dimensional GLV method on these curves is 10 percent more efficient than that of 2-dimensinal G...
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| creator | Zhou, Zhenghua Hu, Zhi Xu, Maozhi Song, Wangan |
| description | ► Two distinct efficient endomorphisms are discovered to coexist on some GLS elliptic curves. ► 3-dimensional GLV method for fast point multiplication is generalized to these curves. ► Implementation of 3-dimensional GLV method on these curves is 10 percent more efficient than that of 2-dimensinal GLV method.
We discover that two distinct efficient endomorphisms can both exist on some Galbraith–Lin–Scott (GLS) elliptic curves Galbraith et al. (2009)
[4]. By using them we generalize the Gallant–Lambert–Vanstone (GLV) method Gallant et al. (2001)
[5] for faster point multiplication on these curves to dimension 3, and give some implementation result which shows that our 3-dimensional GLV (3GLV) method runs in 0.897 the time of 2-dimensional GLV (2GLV) method as Galbraith et al. did in Galbraith et al. (2009)
[4] for the point multiplication on these curves. |
| doi_str_mv | 10.1016/j.ipl.2010.08.014 |
| format | Article |
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We discover that two distinct efficient endomorphisms can both exist on some Galbraith–Lin–Scott (GLS) elliptic curves Galbraith et al. (2009)
[4]. By using them we generalize the Gallant–Lambert–Vanstone (GLV) method Gallant et al. (2001)
[5] for faster point multiplication on these curves to dimension 3, and give some implementation result which shows that our 3-dimensional GLV (3GLV) method runs in 0.897 the time of 2-dimensional GLV (2GLV) method as Galbraith et al. did in Galbraith et al. (2009)
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We discover that two distinct efficient endomorphisms can both exist on some Galbraith–Lin–Scott (GLS) elliptic curves Galbraith et al. (2009)
[4]. By using them we generalize the Gallant–Lambert–Vanstone (GLV) method Gallant et al. (2001)
[5] for faster point multiplication on these curves to dimension 3, and give some implementation result which shows that our 3-dimensional GLV (3GLV) method runs in 0.897 the time of 2-dimensional GLV (2GLV) method as Galbraith et al. did in Galbraith et al. (2009)
[4] for the point multiplication on these curves.</description><subject>Algebra</subject><subject>Algebraic geometry</subject><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Cryptography</subject><subject>Dimensional analysis</subject><subject>Elliptic curve</subject><subject>Exact sciences and technology</subject><subject>GLV method</subject><subject>Lattice basis</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Miscellaneous</subject><subject>Multiplication</subject><subject>Number theory</subject><subject>Point multiplication algorithm</subject><subject>Sciences and techniques of general use</subject><subject>Studies</subject><subject>Theoretical computing</subject><issn>0020-0190</issn><issn>1872-6119</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kMFqFTEUhoMoeG19AHdBEFdzezLJZDK4klKrcKGL2i4NmeQEc5mZjEmm4Nubyy0uXAiBcOD7z598hLxjsGfA5NVxH9Zp30KdQe2BiRdkx1TfNpKx4SXZAbTQABvgNXmT8xEApOD9jvy48T7YgEuhvHFhxiWHuJiJ3h4e6YzlZ3TUx0S9yQUTXWOo5LxNpdYFa0qFaT05zlgj9xSnKawlWGq39IT5krzyZsr49vm-IA9fbr5ff20Od7ffrj8fGsuVLA03ncTRst71PQCXo0BsUQyqjrztRj8qBeCMFZ2VrgPHDDg18m6QqLxDfkE-nveuKf7aMBc9h2zrY8yCcctaiUEI1UlZyff_kMe4pfrjrPuuE0wBhwqxM2RTzDmh12sKs0m_NQN98q2PugrQJ98alK6-a-bD82KTrZl8MosN-W-w5RxqQVu5T2cOq4-ngEnnk3-LLiS0RbsY_tPyB53olNs</recordid><startdate>20101031</startdate><enddate>20101031</enddate><creator>Zhou, Zhenghua</creator><creator>Hu, Zhi</creator><creator>Xu, Maozhi</creator><creator>Song, Wangan</creator><general>Elsevier B.V</general><general>Elsevier</general><general>Elsevier Sequoia S.A</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20101031</creationdate><title>Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves</title><author>Zhou, Zhenghua ; Hu, Zhi ; Xu, Maozhi ; Song, Wangan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c386t-3a56ebc17d770036b4ee2e498770325bfb8800dac45c6d50d1a0d8b3596e8fde3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algebra</topic><topic>Algebraic geometry</topic><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Cryptography</topic><topic>Dimensional analysis</topic><topic>Elliptic curve</topic><topic>Exact sciences and technology</topic><topic>GLV method</topic><topic>Lattice basis</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Miscellaneous</topic><topic>Multiplication</topic><topic>Number theory</topic><topic>Point multiplication algorithm</topic><topic>Sciences and techniques of general use</topic><topic>Studies</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhou, Zhenghua</creatorcontrib><creatorcontrib>Hu, Zhi</creatorcontrib><creatorcontrib>Xu, Maozhi</creatorcontrib><creatorcontrib>Song, Wangan</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Information processing letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhou, Zhenghua</au><au>Hu, Zhi</au><au>Xu, Maozhi</au><au>Song, Wangan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves</atitle><jtitle>Information processing letters</jtitle><date>2010-10-31</date><risdate>2010</risdate><volume>110</volume><issue>22</issue><spage>1003</spage><epage>1006</epage><pages>1003-1006</pages><issn>0020-0190</issn><eissn>1872-6119</eissn><coden>IFPLAT</coden><abstract>► Two distinct efficient endomorphisms are discovered to coexist on some GLS elliptic curves. ► 3-dimensional GLV method for fast point multiplication is generalized to these curves. ► Implementation of 3-dimensional GLV method on these curves is 10 percent more efficient than that of 2-dimensinal GLV method.
We discover that two distinct efficient endomorphisms can both exist on some Galbraith–Lin–Scott (GLS) elliptic curves Galbraith et al. (2009)
[4]. By using them we generalize the Gallant–Lambert–Vanstone (GLV) method Gallant et al. (2001)
[5] for faster point multiplication on these curves to dimension 3, and give some implementation result which shows that our 3-dimensional GLV (3GLV) method runs in 0.897 the time of 2-dimensional GLV (2GLV) method as Galbraith et al. did in Galbraith et al. (2009)
[4] for the point multiplication on these curves.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.ipl.2010.08.014</doi><tpages>4</tpages></addata></record> |
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| subjects | Algebra Algebraic geometry Algorithmics. Computability. Computer arithmetics Applied sciences Computer science control theory systems Cryptography Dimensional analysis Elliptic curve Exact sciences and technology GLV method Lattice basis Mathematical analysis Mathematics Miscellaneous Multiplication Number theory Point multiplication algorithm Sciences and techniques of general use Studies Theoretical computing |
| title | Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves |
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