{"id":"https://openalex.org/W2118296400","doi":"https://doi.org/10.1145/1858378.1858388","title":"Improving multiplication and reminder using implementation based on word and index","display_name":"Improving multiplication and reminder using implementation based on word and index","publication_year":2010,"publication_date":"2010-09-16","ids":{"openalex":"https://openalex.org/W2118296400","doi":"https://doi.org/10.1145/1858378.1858388","mag":"2118296400"},"language":"en","primary_location":{"id":"doi:10.1145/1858378.1858388","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1858378.1858388","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 1st Amrita ACM-W Celebration on Women in Computing in India","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/A5062349749","display_name":"Najmeh Danesh","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086811","display_name":"Islamic Azad University Sari Branch","ror":"https://ror.org/0032wgp28","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210086811"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Najmeh Danesh","raw_affiliation_strings":["Islamic Azad University, Sari Branch, Sari, Iran"],"affiliations":[{"raw_affiliation_string":"Islamic Azad University, Sari Branch, Sari, Iran","institution_ids":["https://openalex.org/I4210086811"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039687461","display_name":"Malihe Danesh","orcid":null},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Malihe Danesh","raw_affiliation_strings":["Ferdowsi University of Mashhad, Mashhad, Iran"],"affiliations":[{"raw_affiliation_string":"Ferdowsi University of Mashhad, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072164576","display_name":"Hossein Shirgahi","orcid":"https://orcid.org/0000-0001-9034-3549"},"institutions":[{"id":"https://openalex.org/I110525433","display_name":"Islamic Azad University, Tehran","ror":"https://ror.org/01kzn7k21","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hossein Shirgahi","raw_affiliation_strings":["Islamic Azad University, Jouybar Branch, jouybar, Iran","Islamic Azad University - Jouybar Branch, Jouybar, Iran"],"affiliations":[{"raw_affiliation_string":"Islamic Azad University, Jouybar Branch, jouybar, Iran","institution_ids":["https://openalex.org/I110525433"]},{"raw_affiliation_string":"Islamic Azad University - Jouybar Branch, Jouybar, Iran","institution_ids":["https://openalex.org/I110525433"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005598798","display_name":"Abbas Ghaemi B.","orcid":null},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Abbas Ghaemi B.","raw_affiliation_strings":["Ferdowsi University of Mashhad, Mashhad, Iran"],"affiliations":[{"raw_affiliation_string":"Ferdowsi University of Mashhad, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5062349749"],"corresponding_institution_ids":["https://openalex.org/I4210086811"],"apc_list":null,"apc_paid":null,"fwci":0.6937,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.83367877,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"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":0.9986000061035156,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9973000288009644,"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":0.8046703338623047},{"id":"https://openalex.org/keywords/modular-exponentiation","display_name":"Modular exponentiation","score":0.7991963624954224},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.7441211938858032},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.7173424363136292},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6943540573120117},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.651382565498352},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.629047155380249},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.5810837149620056},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.5595803260803223},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.4868444800376892},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.46724438667297363},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4523431360721588},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4303736686706543},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.34804052114486694},{"id":"https://openalex.org/keywords/computer-engineering","display_name":"Computer engineering","score":0.32311829924583435},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28370174765586853},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.25581687688827515},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1815173625946045},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.14665979146957397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14028608798980713},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.12415146827697754},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.09375247359275818}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8046703338623047},{"id":"https://openalex.org/C152763109","wikidata":"https://www.wikidata.org/wiki/Q1228841","display_name":"Modular exponentiation","level":4,"score":0.7991963624954224},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.7441211938858032},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.7173424363136292},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6943540573120117},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.651382565498352},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.629047155380249},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.5810837149620056},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5595803260803223},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.4868444800376892},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.46724438667297363},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4523431360721588},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4303736686706543},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.34804052114486694},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.32311829924583435},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28370174765586853},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.25581687688827515},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1815173625946045},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.14665979146957397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14028608798980713},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.12415146827697754},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.09375247359275818},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1858378.1858388","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1858378.1858388","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 1st Amrita ACM-W Celebration on Women in Computing in India","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1498685334","https://openalex.org/W1501341705","https://openalex.org/W1517725369","https://openalex.org/W1540582803","https://openalex.org/W1544243968","https://openalex.org/W1972014440","https://openalex.org/W1981663184","https://openalex.org/W2004814164","https://openalex.org/W2026445983","https://openalex.org/W2051575897","https://openalex.org/W2053166349","https://openalex.org/W2053464283","https://openalex.org/W2055515093","https://openalex.org/W2056005357","https://openalex.org/W2063884927","https://openalex.org/W2124063495","https://openalex.org/W2156186849","https://openalex.org/W2165816141","https://openalex.org/W2407894843","https://openalex.org/W2752853835"],"related_works":["https://openalex.org/W2107014706","https://openalex.org/W2076621334","https://openalex.org/W2543318645","https://openalex.org/W2516936488","https://openalex.org/W2148643256","https://openalex.org/W2351661629","https://openalex.org/W2292159208","https://openalex.org/W1977356083","https://openalex.org/W2137988767","https://openalex.org/W2104685162"],"abstract_inverted_index":{"asynchronous":[0],"cryptography":[1,22],"is":[2,26],"one":[3,27],"of":[4,20,28,47,55,69,77,90,92,95,106,108],"the":[5,29,67,88,104],"most":[6,45],"widely":[7],"used":[8],"cryptographic":[9],"algorithms.":[10,34,57],"Much":[11],"research":[12],"has":[13],"been":[14],"done":[15],"to":[16,38,60,83,98],"find":[17],"other":[18],"applications":[19],"this":[21,109,112],"method.":[23],"Modular":[24],"exponentiation":[25],"primitive":[30],"operations":[31],"in":[32,111],"these":[33,48,56,70],"Since":[35,58],"we":[36,81],"need":[37],"perform":[39],"multiplication,":[40],"square":[41],"and":[42,79,102],"modular":[43],"division,":[44,80],"aspects":[46],"studies":[49],"were":[50],"based":[51],"on":[52],"optimizing":[53],"each":[54],"access":[59],"faster":[61],"software":[62,93],"or":[63],"hardware":[64],"techniques":[65],"was":[66],"objective":[68],"studies,":[71],"after":[72],"studying":[73],"optimized":[74],"implementation":[75,94,100],"methods":[76,91],"multiplication":[78],"tried":[82],"take":[84],"a":[85],"step":[86],"toward":[87],"application":[89],"some":[96],"examples":[97],"decrease":[99],"time":[101],"increase":[103],"efficiency":[105],"algorithms":[107],"type":[110],"paper.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
