Lattice Reduction by Random Sampling and Birthday Methods
We present a novel practical algorithm that given a lattice basis b1, ..., bn finds in O(n2( k/6 )k/4) average time a shorter vector than b1 provided that b1 is ( k/6 )n/(2k) times longer than the length of the shortest, nonzero lattice vector. We assume that the given basis b1, ..., bn has an ortho...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buchkapitel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 156 |
|---|---|
| container_issue | |
| container_start_page | 145 |
| container_title | |
| container_volume | 2607 |
| creator | Schnorr, Claus Peter |
| description | We present a novel practical algorithm that given a lattice basis b1, ..., bn finds in O(n2( k/6 )k/4) average time a shorter vector than b1 provided that b1 is ( k/6 )n/(2k) times longer than the length of the shortest, nonzero lattice vector. We assume that the given basis b1, ..., bn has an orthogonal basis that is typical for worst case lattice bases. The new reduction method samples short lattice vectors in high dimensional sublattices, it advances in sporadic big jumps. It decreases the approximation factor achievable in a given time by known methods to less than its fourth-th root. We further speed up the new method by the simple and the general birthday method. |
| doi_str_mv | 10.1007/3-540-36494-3_14 |
| format | Book Chapter |
| fullrecord | <record><control><sourceid>proquest_pasca</sourceid><recordid>TN_cdi_pascalfrancis_primary_14724974</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>EBC3071509_19_160</sourcerecordid><originalsourceid>FETCH-LOGICAL-j334t-f8c0598891be2a8d42c8bc690fa7b23c8e8cfc3a6725aace3b9ba9518fbf5c9f3</originalsourceid><addsrcrecordid>eNotkMtPwzAMxsNTjLE7x144Fpw4aZMjTLykISQe58hNU9axtaMJh_33ZBuSJcv250_2j7FLDtccoLzBXEnIsZBG5mi5PGDnmDq7Bh6yES84zxGlOdoPAAqBcMxGgCByU0o8ZSODShgopDpjkxAWSQQoCq3KETMzirF1Pnvz9a-Lbd9l1SZ7o67uV9k7rdbLtvvKUpndtUOc17TJXnyc93W4YCcNLYOf_Ocx-3y4_5g-5bPXx-fp7SxfpLNi3mgHymhteOUF6VoKpytXGGiorAQ67bVrHFJRCkXkPFamIqO4bqpGOdPgmF3tfdcUHC2bgTrXBrse2hUNm4SkFHL755hd73UhjbovP9iq77-D5WC3JC3ahMfuwNktybSA_8ZD__PrQ7R-u-F8Fwdaujmtox-CRSi5AmN5igLwD4LfcNM</addsrcrecordid><sourcetype>Index Database</sourcetype><iscdi>true</iscdi><recordtype>book_chapter</recordtype><pqid>EBC3071509_19_160</pqid></control><display><type>book_chapter</type><title>Lattice Reduction by Random Sampling and Birthday Methods</title><source>Springer Books</source><creator>Schnorr, Claus Peter</creator><contributor>Alt, Helmut ; Habib, Michel</contributor><creatorcontrib>Schnorr, Claus Peter ; Alt, Helmut ; Habib, Michel</creatorcontrib><description>We present a novel practical algorithm that given a lattice basis b1, ..., bn finds in O(n2( k/6 )k/4) average time a shorter vector than b1 provided that b1 is ( k/6 )n/(2k) times longer than the length of the shortest, nonzero lattice vector. We assume that the given basis b1, ..., bn has an orthogonal basis that is typical for worst case lattice bases. The new reduction method samples short lattice vectors in high dimensional sublattices, it advances in sporadic big jumps. It decreases the approximation factor achievable in a given time by known methods to less than its fourth-th root. We further speed up the new method by the simple and the general birthday method.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 3540006230</identifier><identifier>ISBN: 9783540006237</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 3540364943</identifier><identifier>EISBN: 9783540364948</identifier><identifier>DOI: 10.1007/3-540-36494-3_14</identifier><identifier>OCLC: 935290645</identifier><identifier>LCCallNum: QA75.5-76.95</identifier><language>eng</language><publisher>Germany: Springer Berlin / Heidelberg</publisher><subject>Algorithmics. Computability. Computer arithmetics ; Applied sciences ; Computer science; control theory; systems ; Exact sciences and technology ; Geometric Series ; Lattice Basis ; Lattice Reduction ; Lattice Vector ; Sample Algorithm ; Theoretical computing</subject><ispartof>Lecture notes in computer science, 2003, Vol.2607, p.145-156</ispartof><rights>Springer-Verlag Berlin Heidelberg 2003</rights><rights>2003 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttps://ebookcentral.proquest.com/covers/3071509-l.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/3-540-36494-3_14$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/3-540-36494-3_14$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,775,776,780,785,786,789,4036,4037,27902,38232,41418,42487</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14724974$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Alt, Helmut</contributor><contributor>Habib, Michel</contributor><creatorcontrib>Schnorr, Claus Peter</creatorcontrib><title>Lattice Reduction by Random Sampling and Birthday Methods</title><title>Lecture notes in computer science</title><description>We present a novel practical algorithm that given a lattice basis b1, ..., bn finds in O(n2( k/6 )k/4) average time a shorter vector than b1 provided that b1 is ( k/6 )n/(2k) times longer than the length of the shortest, nonzero lattice vector. We assume that the given basis b1, ..., bn has an orthogonal basis that is typical for worst case lattice bases. The new reduction method samples short lattice vectors in high dimensional sublattices, it advances in sporadic big jumps. It decreases the approximation factor achievable in a given time by known methods to less than its fourth-th root. We further speed up the new method by the simple and the general birthday method.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Geometric Series</subject><subject>Lattice Basis</subject><subject>Lattice Reduction</subject><subject>Lattice Vector</subject><subject>Sample Algorithm</subject><subject>Theoretical computing</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>3540006230</isbn><isbn>9783540006237</isbn><isbn>3540364943</isbn><isbn>9783540364948</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2003</creationdate><recordtype>book_chapter</recordtype><recordid>eNotkMtPwzAMxsNTjLE7x144Fpw4aZMjTLykISQe58hNU9axtaMJh_33ZBuSJcv250_2j7FLDtccoLzBXEnIsZBG5mi5PGDnmDq7Bh6yES84zxGlOdoPAAqBcMxGgCByU0o8ZSODShgopDpjkxAWSQQoCq3KETMzirF1Pnvz9a-Lbd9l1SZ7o67uV9k7rdbLtvvKUpndtUOc17TJXnyc93W4YCcNLYOf_Ocx-3y4_5g-5bPXx-fp7SxfpLNi3mgHymhteOUF6VoKpytXGGiorAQ67bVrHFJRCkXkPFamIqO4bqpGOdPgmF3tfdcUHC2bgTrXBrse2hUNm4SkFHL755hd73UhjbovP9iq77-D5WC3JC3ahMfuwNktybSA_8ZD__PrQ7R-u-F8Fwdaujmtox-CRSi5AmN5igLwD4LfcNM</recordid><startdate>2003</startdate><enddate>2003</enddate><creator>Schnorr, Claus Peter</creator><general>Springer Berlin / Heidelberg</general><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>FFUUA</scope><scope>IQODW</scope></search><sort><creationdate>2003</creationdate><title>Lattice Reduction by Random Sampling and Birthday Methods</title><author>Schnorr, Claus Peter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-j334t-f8c0598891be2a8d42c8bc690fa7b23c8e8cfc3a6725aace3b9ba9518fbf5c9f3</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2003</creationdate><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Geometric Series</topic><topic>Lattice Basis</topic><topic>Lattice Reduction</topic><topic>Lattice Vector</topic><topic>Sample Algorithm</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schnorr, Claus Peter</creatorcontrib><collection>ProQuest Ebook Central - Book Chapters - Demo use only</collection><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schnorr, Claus Peter</au><au>Alt, Helmut</au><au>Habib, Michel</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Lattice Reduction by Random Sampling and Birthday Methods</atitle><btitle>Lecture notes in computer science</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2003</date><risdate>2003</risdate><volume>2607</volume><spage>145</spage><epage>156</epage><pages>145-156</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>3540006230</isbn><isbn>9783540006237</isbn><eisbn>3540364943</eisbn><eisbn>9783540364948</eisbn><abstract>We present a novel practical algorithm that given a lattice basis b1, ..., bn finds in O(n2( k/6 )k/4) average time a shorter vector than b1 provided that b1 is ( k/6 )n/(2k) times longer than the length of the shortest, nonzero lattice vector. We assume that the given basis b1, ..., bn has an orthogonal basis that is typical for worst case lattice bases. The new reduction method samples short lattice vectors in high dimensional sublattices, it advances in sporadic big jumps. It decreases the approximation factor achievable in a given time by known methods to less than its fourth-th root. We further speed up the new method by the simple and the general birthday method.</abstract><cop>Germany</cop><pub>Springer Berlin / Heidelberg</pub><doi>10.1007/3-540-36494-3_14</doi><oclcid>935290645</oclcid><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Lecture notes in computer science, 2003, Vol.2607, p.145-156 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_14724974 |
| source | Springer Books |
| subjects | Algorithmics. Computability. Computer arithmetics Applied sciences Computer science control theory systems Exact sciences and technology Geometric Series Lattice Basis Lattice Reduction Lattice Vector Sample Algorithm Theoretical computing |
| title | Lattice Reduction by Random Sampling and Birthday Methods |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-06T09%3A59%3A53IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_pasca&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=bookitem&rft.atitle=Lattice%20Reduction%20by%20Random%20Sampling%20and%20Birthday%20Methods&rft.btitle=Lecture%20notes%20in%20computer%20science&rft.au=Schnorr,%20Claus%20Peter&rft.date=2003&rft.volume=2607&rft.spage=145&rft.epage=156&rft.pages=145-156&rft.issn=0302-9743&rft.eissn=1611-3349&rft.isbn=3540006230&rft.isbn_list=9783540006237&rft_id=info:doi/10.1007/3-540-36494-3_14&rft_dat=%3Cproquest_pasca%3EEBC3071509_19_160%3C/proquest_pasca%3E%3Curl%3E%3C/url%3E&rft.eisbn=3540364943&rft.eisbn_list=9783540364948&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=EBC3071509_19_160&rft_id=info:pmid/&rfr_iscdi=true |