{"id":"https://openalex.org/W2136650617","doi":"https://doi.org/10.1007/978-3-642-16318-0_73","title":"Accelerated Modular Multiplication Algorithm of Large Word Length Numbers with a Fixed Module","display_name":"Accelerated Modular Multiplication Algorithm of Large Word Length Numbers with a Fixed Module","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2136650617","doi":"https://doi.org/10.1007/978-3-642-16318-0_73","mag":"2136650617"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-16318-0_73","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-16318-0_73","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5041069957","display_name":"Nikolaos Bardis","orcid":"https://orcid.org/0000-0002-2259-7077"},"institutions":[{"id":"https://openalex.org/I203474044","display_name":"National Centre of Scientific Research \"Demokritos\"","ror":"https://ror.org/038jp4m40","country_code":"GR","type":"facility","lineage":["https://openalex.org/I203474044"]},{"id":"https://openalex.org/I24897511","display_name":"Hellenic Military Academy","ror":"https://ror.org/01esc8r67","country_code":"GR","type":"education","lineage":["https://openalex.org/I24897511"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"N. G. Bardis","raw_affiliation_strings":["Department of Mathematics and Engineering Science, Hellenic Army Academy, Vari, Greece","Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \u201dDemokritos\u201d, 27, Ag.Paraskevi, Athens, 15310, Greece","Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \"Demokritos\", 27, Ag.Paraskevi, Athens, 15310, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Engineering Science, Hellenic Army Academy, Vari, Greece","institution_ids":["https://openalex.org/I24897511"]},{"raw_affiliation_string":"Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \u201dDemokritos\u201d, 27, Ag.Paraskevi, Athens, 15310, Greece","institution_ids":["https://openalex.org/I203474044"]},{"raw_affiliation_string":"Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \"Demokritos\", 27, Ag.Paraskevi, Athens, 15310, Greece","institution_ids":["https://openalex.org/I203474044"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079688616","display_name":"Athanasios Drigas","orcid":"https://orcid.org/0000-0001-5637-9601"},"institutions":[{"id":"https://openalex.org/I203474044","display_name":"National Centre of Scientific Research \"Demokritos\"","ror":"https://ror.org/038jp4m40","country_code":"GR","type":"facility","lineage":["https://openalex.org/I203474044"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"A. Drigas","raw_affiliation_strings":["Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \u201dDemokritos\u201d, 27, Ag.Paraskevi, Athens, 15310, Greece","Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \"Demokritos\", 27, Ag.Paraskevi, Athens, 15310, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \u201dDemokritos\u201d, 27, Ag.Paraskevi, Athens, 15310, Greece","institution_ids":["https://openalex.org/I203474044"]},{"raw_affiliation_string":"Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \"Demokritos\", 27, Ag.Paraskevi, Athens, 15310, Greece","institution_ids":["https://openalex.org/I203474044"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016681829","display_name":"A. P. Markovskyy","orcid":null},"institutions":[{"id":"https://openalex.org/I202483615","display_name":"National Technical University of Ukraine \u201cIgor Sikorsky Kyiv Polytechnic Institute\u201d","ror":"https://ror.org/00syn5v21","country_code":"UA","type":"education","lineage":["https://openalex.org/I202483615"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"A. P. Markovskyy","raw_affiliation_strings":["Department of Computer Engineering, National Technical University of Ukraine, 37, Peremohy, pr. Kiev 252056, KPI, 2003, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, National Technical University of Ukraine, 37, Peremohy, pr. Kiev 252056, KPI, 2003, Ukraine","institution_ids":["https://openalex.org/I202483615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069221010","display_name":"I. Vrettaros","orcid":null},"institutions":[{"id":"https://openalex.org/I203474044","display_name":"National Centre of Scientific Research \"Demokritos\"","ror":"https://ror.org/038jp4m40","country_code":"GR","type":"facility","lineage":["https://openalex.org/I203474044"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"I. Vrettaros","raw_affiliation_strings":["Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \u201dDemokritos\u201d, 27, Ag.Paraskevi, Athens, 15310, Greece","Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \"Demokritos\", 27, Ag.Paraskevi, Athens, 15310, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \u201dDemokritos\u201d, 27, Ag.Paraskevi, Athens, 15310, Greece","institution_ids":["https://openalex.org/I203474044"]},{"raw_affiliation_string":"Institute of Informatics &, Telecommunications - Net Media Lab, Terma Patriarchou Grigoriou & Neapoleos, National Centre for Scientific Research \"Demokritos\", 27, Ag.Paraskevi, Athens, 15310, Greece","institution_ids":["https://openalex.org/I203474044"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2188,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.54182951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"573","last_page":"581"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.9943000078201294,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9690999984741211,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.8228933811187744},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.819163978099823},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.7976305484771729},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.730748176574707},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.677280604839325},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5821359157562256},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5642330646514893},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.5273600220680237},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.525322675704956},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4980497360229492},{"id":"https://openalex.org/keywords/word-length","display_name":"Word length","score":0.4848285913467407},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4770966172218323},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40870723128318787},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.37677696347236633},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20298650860786438},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.13139259815216064}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.8228933811187744},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.819163978099823},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.7976305484771729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.730748176574707},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.677280604839325},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5821359157562256},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5642330646514893},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.5273600220680237},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.525322675704956},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4980497360229492},{"id":"https://openalex.org/C3019641298","wikidata":"https://www.wikidata.org/wiki/Q625642","display_name":"Word length","level":2,"score":0.4848285913467407},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4770966172218323},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40870723128318787},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.37677696347236633},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20298650860786438},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.13139259815216064},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-642-16318-0_73","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-16318-0_73","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.4539","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.4539","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://imm.demokritos.gr/publications/Accelerated_Modular_Multiplication.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":16,"referenced_works":["https://openalex.org/W32238348","https://openalex.org/W1496801598","https://openalex.org/W1498685334","https://openalex.org/W1564551543","https://openalex.org/W1573824426","https://openalex.org/W1660562555","https://openalex.org/W2004814164","https://openalex.org/W2046404735","https://openalex.org/W2145428071","https://openalex.org/W2480498986","https://openalex.org/W2488547546","https://openalex.org/W2491896407","https://openalex.org/W2503514047","https://openalex.org/W2561675875","https://openalex.org/W3039948875","https://openalex.org/W3043060850"],"related_works":["https://openalex.org/W2113213955","https://openalex.org/W2225983048","https://openalex.org/W2016520453","https://openalex.org/W2372139915","https://openalex.org/W2070298508","https://openalex.org/W2361290373","https://openalex.org/W2367658296","https://openalex.org/W2904069009","https://openalex.org/W2355149595","https://openalex.org/W2162200818"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}