{"id":"https://openalex.org/W2802728900","doi":"https://doi.org/10.1109/iscas.2018.8351614","title":"A Fast Modular Inversion FPGA Implementation over GF(2<sup>m</sup>) using Modified x<sup>2n</sup> Unit","display_name":"A Fast Modular Inversion FPGA Implementation over GF(2<sup>m</sup>) using Modified x<sup>2n</sup> Unit","publication_year":2018,"publication_date":"2018-05-01","ids":{"openalex":"https://openalex.org/W2802728900","doi":"https://doi.org/10.1109/iscas.2018.8351614","mag":"2802728900"},"language":"en","primary_location":{"id":"doi:10.1109/iscas.2018.8351614","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2018.8351614","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Circuits and Systems (ISCAS)","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/A5101637628","display_name":"Jiakun Li","orcid":"https://orcid.org/0000-0003-1487-4967"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiakun Li","raw_affiliation_strings":["Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100356634","display_name":"Zhe Li","orcid":"https://orcid.org/0000-0002-0475-9642"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhe Li","raw_affiliation_strings":["Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069616003","display_name":"Chengbo Xue","orcid":"https://orcid.org/0000-0002-4786-2586"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chengbo Xue","raw_affiliation_strings":["Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021087212","display_name":"Jingqi Zhang","orcid":"https://orcid.org/0000-0003-4140-7029"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingqi Zhang","raw_affiliation_strings":["Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010846765","display_name":"Wei Gao","orcid":"https://orcid.org/0000-0003-2257-5684"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Gao","raw_affiliation_strings":["Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Technology, School of Information and Electronics, Beijing 100081,China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044419947","display_name":"Shan Cao","orcid":"https://orcid.org/0000-0003-3713-8671"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shan Cao","raw_affiliation_strings":["Shanghai Institute for Advanced Communication and Data ScienceShanghai University, Key laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai 200444,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Institute for Advanced Communication and Data ScienceShanghai University, Key laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai 200444,China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2339,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.85376186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"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":0.9894000291824341,"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":0.9811000227928162,"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/modular-design","display_name":"Modular design","score":0.7277302742004395},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.6345280408859253},{"id":"https://openalex.org/keywords/clock-rate","display_name":"Clock rate","score":0.5951899886131287},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5629868507385254},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.5288856029510498},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5275518298149109},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.4437628388404846},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.42892494797706604},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.4134616553783417},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38676029443740845},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.3309277892112732},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.25288283824920654},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.09760111570358276},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.07532775402069092}],"concepts":[{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.7277302742004395},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.6345280408859253},{"id":"https://openalex.org/C178693496","wikidata":"https://www.wikidata.org/wiki/Q911691","display_name":"Clock rate","level":3,"score":0.5951899886131287},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5629868507385254},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5288856029510498},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5275518298149109},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.4437628388404846},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.42892494797706604},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.4134616553783417},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38676029443740845},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.3309277892112732},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.25288283824920654},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.09760111570358276},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.07532775402069092},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C165005293","wikidata":"https://www.wikidata.org/wiki/Q1074500","display_name":"Chip","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iscas.2018.8351614","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2018.8351614","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Circuits and Systems (ISCAS)","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":13,"referenced_works":["https://openalex.org/W1958293770","https://openalex.org/W1967989952","https://openalex.org/W1982862755","https://openalex.org/W1984792575","https://openalex.org/W2001498742","https://openalex.org/W2007751412","https://openalex.org/W2032492064","https://openalex.org/W2033203529","https://openalex.org/W2108882106","https://openalex.org/W2156822915","https://openalex.org/W2338349198","https://openalex.org/W2343583178","https://openalex.org/W2430735257"],"related_works":["https://openalex.org/W2069736719","https://openalex.org/W1549779101","https://openalex.org/W2792277736","https://openalex.org/W2140559439","https://openalex.org/W1568138047","https://openalex.org/W2113430197","https://openalex.org/W4378805983","https://openalex.org/W2045123001","https://openalex.org/W2353466882","https://openalex.org/W2531852525"],"abstract_inverted_index":{"Modular":[0],"inversion":[1,19,29,74],"is":[2,14,105],"an":[3],"important":[4],"step":[5],"in":[6,61,75,90],"Elliptic":[7],"Curve":[8],"Cryptography":[9],"(ECC).":[10],"Itoh-Tsujii's":[11],"algorithm":[12],"(ITA)":[13],"a":[15,24],"commonly":[16],"applied":[17],"modular":[18,28,35,73,88],"algorithm.":[20],"This":[21],"paper":[22],"proposes":[23],"novel":[25],"architecture":[26],"of":[27,101],"implementation":[30],"based":[31],"on":[32,68],"ITA.":[33],"The":[34,99],"multiplier":[36],"and":[37,53,107],"2":[38],"<sup":[39],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[40],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[41],"units":[42],"are":[43,56,66],"modified":[44],"into":[45],"non-iterative":[46],"logic":[47],"to":[48,58],"increase":[49],"clock":[50,77,81,92,96],"frequency.":[51],"Least-clock-cycle-ITA":[52],"High-speed-ITA":[54],"architectures":[55,65,104],"proposed":[57,103],"minimize":[59],"latency":[60],"different":[62],"situations.":[63],"Both":[64],"implemented":[67],"FPGA":[69],"Virtex-5.":[70],"LCC-ITA":[71],"completes":[72,86],"9":[76],"cycles":[78,93],"with":[79,94],"maximum":[80,95],"frequency":[82,97],"126.1MHz,":[83],"while":[84],"HS-ITA":[85],"two":[87],"inversions":[89],"20":[91],"177.6MHz.":[98],"performance":[100],"the":[102,111],"56%":[106],"134%":[108],"higher":[109],"than":[110],"best":[112],"work":[113],"before.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}