{"id":"https://openalex.org/W2098530776","doi":"https://doi.org/10.1109/fpt.2004.1393277","title":"Reconfigurable hardware implementation of mesh routing in number field sieve factorization","display_name":"Reconfigurable hardware implementation of mesh routing in number field sieve factorization","publication_year":2005,"publication_date":"2005-03-21","ids":{"openalex":"https://openalex.org/W2098530776","doi":"https://doi.org/10.1109/fpt.2004.1393277","mag":"2098530776"},"language":"en","primary_location":{"id":"doi:10.1109/fpt.2004.1393277","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fpt.2004.1393277","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 2004 IEEE International Conference on Field- Programmable Technology (IEEE Cat. No.04EX921)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075293951","display_name":"Sashisu Bajracharya","orcid":null},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. Bajracharya","raw_affiliation_strings":["ECE Department, 4400 University Drive, Fairfax, VA, USA","ECE Department, George Mason University, Fairfax, VA, USA"],"affiliations":[{"raw_affiliation_string":"ECE Department, 4400 University Drive, Fairfax, VA, USA","institution_ids":[]},{"raw_affiliation_string":"ECE Department, George Mason University, Fairfax, VA, USA","institution_ids":["https://openalex.org/I162714631"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087896503","display_name":"Anuranjan Misra","orcid":"https://orcid.org/0000-0003-0458-0180"},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Misra","raw_affiliation_strings":["ECE Department, 4400 University Drive, Fairfax, VA, USA","ECE Department, George Mason University, Fairfax, VA, USA"],"affiliations":[{"raw_affiliation_string":"ECE Department, 4400 University Drive, Fairfax, VA, USA","institution_ids":[]},{"raw_affiliation_string":"ECE Department, George Mason University, Fairfax, VA, USA","institution_ids":["https://openalex.org/I162714631"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004924763","display_name":"Kris Gaj","orcid":"https://orcid.org/0000-0002-5050-8748"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Gaj","raw_affiliation_strings":["ECE Department, 4400 University Drive, Fairfax, VA, USA"],"affiliations":[{"raw_affiliation_string":"ECE Department, 4400 University Drive, Fairfax, VA, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001914825","display_name":"Tarek El\u2010Ghazawi","orcid":"https://orcid.org/0000-0001-9687-7939"},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. El-Ghazawi","raw_affiliation_strings":["ECE Department, George Washington University, Washington, DC, USA"],"affiliations":[{"raw_affiliation_string":"ECE Department, George Washington University, Washington, DC, USA","institution_ids":["https://openalex.org/I193531525"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5075293951"],"corresponding_institution_ids":["https://openalex.org/I162714631"],"apc_list":null,"apc_paid":null,"fwci":0.6733,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72537915,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2894","issue":null,"first_page":"263","last_page":"270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6712826490402222},{"id":"https://openalex.org/keywords/virtex","display_name":"Virtex","score":0.5768814086914062},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5656225681304932},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.5043920278549194},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.48184096813201904},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.47248902916908264},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4704899787902832},{"id":"https://openalex.org/keywords/integer-factorization","display_name":"Integer factorization","score":0.4566788077354431},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45156174898147583},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.42742589116096497},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.20427241921424866},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.1792716681957245},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.1399545669555664},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.12515899538993835},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.08757323026657104}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6712826490402222},{"id":"https://openalex.org/C2777674469","wikidata":"https://www.wikidata.org/wiki/Q20741011","display_name":"Virtex","level":3,"score":0.5768814086914062},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5656225681304932},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.5043920278549194},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.48184096813201904},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.47248902916908264},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4704899787902832},{"id":"https://openalex.org/C119677069","wikidata":"https://www.wikidata.org/wiki/Q4846249","display_name":"Integer factorization","level":4,"score":0.4566788077354431},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45156174898147583},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.42742589116096497},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.20427241921424866},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.1792716681957245},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.1399545669555664},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.12515899538993835},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.08757323026657104}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/fpt.2004.1393277","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fpt.2004.1393277","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 2004 IEEE International Conference on Field- Programmable Technology (IEEE Cat. No.04EX921)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.130.8611","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.130.8611","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cpe02.gmu.edu/rcm/publications/SHARCS_2005_paper.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1480297755","https://openalex.org/W1560262363","https://openalex.org/W1563304405","https://openalex.org/W1993840452","https://openalex.org/W1996266453","https://openalex.org/W1998079848","https://openalex.org/W2070735382","https://openalex.org/W2071483197","https://openalex.org/W2113005412","https://openalex.org/W2142367315","https://openalex.org/W2179025976","https://openalex.org/W2179504188","https://openalex.org/W2594245479","https://openalex.org/W2918128759","https://openalex.org/W3194229933","https://openalex.org/W4285719527","https://openalex.org/W6628639792","https://openalex.org/W6676995177"],"related_works":["https://openalex.org/W2544043553","https://openalex.org/W2546284597","https://openalex.org/W2348562861","https://openalex.org/W2540393334","https://openalex.org/W1983570530","https://openalex.org/W2390042878","https://openalex.org/W2062932566","https://openalex.org/W2271847574","https://openalex.org/W2746234147","https://openalex.org/W2085828379"],"abstract_inverted_index":{"Factorization":[0],"of":[1,9,33,45,71,95,100,114,124],"large":[2,19],"numbers":[3,20,115],"has":[4],"been":[5],"a":[6,72,96],"constant":[7],"source":[8],"interest":[10],"in":[11,50,78,117,134],"cryptanalysis.":[12],"The":[13,27],"fastest":[14],"known":[15],"algorithm":[16],"for":[17,92,102,111],"factoring":[18],"is":[21,55],"the":[22,47,58,68,89,93,121],"number":[23],"field":[24],"sieve":[25],"(NFS).":[26],"two":[28],"most":[29],"time":[30,91],"consuming":[31],"phases":[32],"NFS":[34],"are":[35],"sieving":[36],"and":[37,104],"matrix":[38,48,122],"step.":[39],"We":[40,66,86,108],"propose":[41],"an":[42],"efficient":[43],"way":[44],"implementing":[46],"step":[49,123],"reconfigurable":[51],"hardware.":[52],"Our":[53],"solution":[54],"based":[56],"on":[57],"mesh-routing":[59],"method":[60],"proposed":[61],"by":[62],"Lenstra":[63],"et":[64],"al.":[65],"determine":[67],"practical":[69,112],"size":[70],"partial":[73],"mesh":[74],"that":[75,110],"can":[76,126],"fit":[77],"one":[79],"FFGA":[80],"device,":[81],"Xilinx":[82],"Virtex":[83,131],"II":[84,132],"XC2V6000.":[85],"further":[87],"extrapolate":[88],"computation":[90],"case":[94],"square":[97],"systolic":[98],"array":[99],"FFGAs":[101,133],"512-bit":[103],"1024-bit":[105],"numbers'":[106],"factorization.":[107],"demonstrate":[109],"sizes":[113],"used":[116],"cryptography,":[118],"1024":[119,130],"bits,":[120],"factorization":[125],"be":[127],"performed":[128],"using":[129],"less":[135],"than":[136],"40":[137],"days.":[138]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}