{"id":"https://openalex.org/W2031132945","doi":"https://doi.org/10.1007/s10623-007-9073-6","title":"Parallel Itoh\u2013Tsujii multiplicative inversion algorithm for a special class of trinomials","display_name":"Parallel Itoh\u2013Tsujii multiplicative inversion algorithm for a special class of trinomials","publication_year":2007,"publication_date":"2007-06-16","ids":{"openalex":"https://openalex.org/W2031132945","doi":"https://doi.org/10.1007/s10623-007-9073-6","mag":"2031132945"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-007-9073-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-007-9073-6","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-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/A5068036569","display_name":"Francisco Rodr\u00edguez\u2010Henr\u00edquez","orcid":"https://orcid.org/0000-0002-5916-6625"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Francisco Rodr\u00edguez-Henr\u00edquez","raw_affiliation_strings":["Computer Science Section, Electrical Engineering Department, CINVESTAV-IPN, Av. IPN No. 2508, 07300, Mexico City, Mexico","Computer Science Section, Electrical Engineering Department, CINVESTAV-IPN, Mexico City, Mexico 07300"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Section, Electrical Engineering Department, CINVESTAV-IPN, Av. IPN No. 2508, 07300, Mexico City, Mexico","institution_ids":["https://openalex.org/I68368234"]},{"raw_affiliation_string":"Computer Science Section, Electrical Engineering Department, CINVESTAV-IPN, Mexico City, Mexico 07300","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029172759","display_name":"Guillermo Morales-Luna","orcid":"https://orcid.org/0000-0001-6800-4081"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Guillermo Morales-Luna","raw_affiliation_strings":["Computer Science Section, Electrical Engineering Department, CINVESTAV-IPN, Av. IPN No. 2508, 07300, Mexico City, Mexico","Computer Science Section, Electrical Engineering Department, CINVESTAV-IPN, Mexico City, Mexico 07300"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Section, Electrical Engineering Department, CINVESTAV-IPN, Av. IPN No. 2508, 07300, Mexico City, Mexico","institution_ids":["https://openalex.org/I68368234"]},{"raw_affiliation_string":"Computer Science Section, Electrical Engineering Department, CINVESTAV-IPN, Mexico City, Mexico 07300","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049976562","display_name":"Nazar Abbas Saqib","orcid":"https://orcid.org/0000-0003-1976-0643"},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Nazar A. Saqib","raw_affiliation_strings":["Centre for Cyber Technology and Spectrum Management, (CCT & SM), NUST, Islamabad, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Cyber Technology and Spectrum Management, (CCT & SM), NUST, Islamabad, Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084757701","display_name":"Nareli Cruz-Cort\u00e9s","orcid":"https://orcid.org/0000-0003-4827-0184"},"institutions":[{"id":"https://openalex.org/I59361560","display_name":"Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/059sp8j34","country_code":"MX","type":"education","lineage":["https://openalex.org/I59361560"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Nareli Cruz-Cort\u00e9s","raw_affiliation_strings":["Center for Computing Research (CIC), National Polytechnic Institute (IPN), Av. Juan de Dios B\u00e1tiz s/n, Esq. Mendiz\u00e1bal, Col. Zacatenco, 07738, Mexico City, Mexico","Center for Computing Research (CIC), National Polytechnic Institute (IPN), Mexico City, Mexico 07738#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computing Research (CIC), National Polytechnic Institute (IPN), Av. Juan de Dios B\u00e1tiz s/n, Esq. Mendiz\u00e1bal, Col. Zacatenco, 07738, Mexico City, Mexico","institution_ids":["https://openalex.org/I59361560"]},{"raw_affiliation_string":"Center for Computing Research (CIC), National Polytechnic Institute (IPN), Mexico City, Mexico 07738#TAB#","institution_ids":["https://openalex.org/I59361560"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5068036569"],"corresponding_institution_ids":["https://openalex.org/I68368234"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":7.4579,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.96746057,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"1","first_page":"19","last_page":"37"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9775999784469604,"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/trinomial","display_name":"Trinomial","score":0.8877677917480469},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7206202149391174},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.6293949484825134},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6052514314651489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5987638235092163},{"id":"https://openalex.org/keywords/multiplicative-inverse","display_name":"Multiplicative inverse","score":0.5831634998321533},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5697824954986572},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5215518474578857},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4823690950870514},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.4676363468170166},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4606013894081116},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.43728888034820557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37027299404144287},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3289187550544739},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23944884538650513}],"concepts":[{"id":"https://openalex.org/C6791720","wikidata":"https://www.wikidata.org/wiki/Q1670509","display_name":"Trinomial","level":2,"score":0.8877677917480469},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7206202149391174},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.6293949484825134},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6052514314651489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5987638235092163},{"id":"https://openalex.org/C157351203","wikidata":"https://www.wikidata.org/wiki/Q216906","display_name":"Multiplicative inverse","level":3,"score":0.5831634998321533},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5697824954986572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5215518474578857},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4823690950870514},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.4676363468170166},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4606013894081116},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.43728888034820557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37027299404144287},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3289187550544739},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23944884538650513},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-007-9073-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-007-9073-6","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5199999809265137,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W129807151","https://openalex.org/W1589682573","https://openalex.org/W1660562555","https://openalex.org/W1964845253","https://openalex.org/W1984735869","https://openalex.org/W2007751412","https://openalex.org/W2024113859","https://openalex.org/W2045131863","https://openalex.org/W2059168043","https://openalex.org/W2096979168","https://openalex.org/W2114881946","https://openalex.org/W2121371977","https://openalex.org/W2136119832","https://openalex.org/W2139813613","https://openalex.org/W2144129711","https://openalex.org/W2156497760","https://openalex.org/W2160954489","https://openalex.org/W2161716369","https://openalex.org/W2161958080","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W3028810483","https://openalex.org/W4289127653","https://openalex.org/W6744529318"],"related_works":["https://openalex.org/W2591794433","https://openalex.org/W4312742439","https://openalex.org/W4313513739","https://openalex.org/W4285051586","https://openalex.org/W4233505935","https://openalex.org/W4313642433","https://openalex.org/W4313513695","https://openalex.org/W3175552624","https://openalex.org/W4313466780","https://openalex.org/W4295815789"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2025-10-10T00:00:00"}