{"id":"https://openalex.org/W2467362426","doi":"https://doi.org/10.1109/tc.2015.2481408","title":"New Architectures for Digit-Level Single, Hybrid-Double, Hybrid-Triple Field Multiplications and Exponentiation Using Gaussian Normal Bases","display_name":"New Architectures for Digit-Level Single, Hybrid-Double, Hybrid-Triple Field Multiplications and Exponentiation Using Gaussian Normal Bases","publication_year":2015,"publication_date":"2015-09-23","ids":{"openalex":"https://openalex.org/W2467362426","doi":"https://doi.org/10.1109/tc.2015.2481408","mag":"2467362426"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2015.2481408","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2015.2481408","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","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/A5004053076","display_name":"Hayssam El-Razouk","orcid":"https://orcid.org/0000-0002-3452-5281"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Hayssam El-Razouk","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Western University, London, ON, Canada","Dept. of Electrical and Computer Engineering, Western University, London, ON, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Western University, London, ON, Canada","institution_ids":["https://openalex.org/I125749732"]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, Western University, London, ON, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073730333","display_name":"Arash Reyhani-Masoleh","orcid":"https://orcid.org/0000-0001-9743-6975"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Arash Reyhani-Masoleh","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Western University, London, ON, Canada","Dept. of Electrical and Computer Engineering, Western University, London, ON, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Western University, London, ON, Canada","institution_ids":["https://openalex.org/I125749732"]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, Western University, London, ON, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004053076"],"corresponding_institution_ids":["https://openalex.org/I125749732"],"apc_list":null,"apc_paid":null,"fwci":3.1784,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.93362893,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"65","issue":"8","first_page":"2495","last_page":"2509"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9997000098228455,"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":0.9836000204086304,"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/exponentiation","display_name":"Exponentiation","score":0.7545251846313477},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6459172964096069},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5703722238540649},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5658890008926392},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4847988188266754},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.46305274963378906},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37893033027648926},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20435062050819397}],"concepts":[{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.7545251846313477},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6459172964096069},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5703722238540649},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5658890008926392},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4847988188266754},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.46305274963378906},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37893033027648926},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20435062050819397},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.2015.2481408","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2015.2481408","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320337440","display_name":"Division of Administrative Services","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W101018159","https://openalex.org/W1566542142","https://openalex.org/W1569612250","https://openalex.org/W1577293358","https://openalex.org/W1764137175","https://openalex.org/W1889596231","https://openalex.org/W1894395730","https://openalex.org/W1963863611","https://openalex.org/W1968718173","https://openalex.org/W1978673726","https://openalex.org/W2024113859","https://openalex.org/W2027457414","https://openalex.org/W2036873162","https://openalex.org/W2049990610","https://openalex.org/W2071470870","https://openalex.org/W2099317248","https://openalex.org/W2102712964","https://openalex.org/W2114353618","https://openalex.org/W2115179918","https://openalex.org/W2128903967","https://openalex.org/W2144047299","https://openalex.org/W2145254449","https://openalex.org/W2153377676","https://openalex.org/W2156186849","https://openalex.org/W2162915244","https://openalex.org/W2167845685","https://openalex.org/W2169932713","https://openalex.org/W2249744080"],"related_works":["https://openalex.org/W821885883","https://openalex.org/W2365969810","https://openalex.org/W2905444740","https://openalex.org/W2034756930","https://openalex.org/W87836137","https://openalex.org/W2015737074","https://openalex.org/W2480811334","https://openalex.org/W1980003318","https://openalex.org/W3007839288","https://openalex.org/W2008443281"],"abstract_inverted_index":{"Gaussian":[0],"normal":[1,8],"bases":[2,9],"(GNBs)":[3],"are":[4],"special":[5],"set":[6],"of":[7,35,47,60,105],"(NBs)":[10],"which":[11,118],"yield":[12],"low":[13],"complexity":[14],"<inline-formula>":[15],"<tex-math":[16],"notation=\"LaTeX\">$GF\\left(2^{m}\\right)$</tex-math></inline-formula>":[17,37],"arithmetic":[18],"operations.":[19],"In":[20,108],"this":[21],"paper,":[22],"we":[23,110],"present":[24,111],"new":[25,113],"architectures":[26],"for":[27,44,72,97],"the":[28,41,69,93,103],"digit-level":[29,82,100],"single,":[30],"hybrid-double,":[31],"and":[32,64,80,88],"hybrid-triple":[33,81],"multiplication":[34,59],"<inline-formula><tex-math":[36,48],"elements":[38,63],"based":[39],"on":[40],"GNB":[42,83],"representation":[43],"odd":[45],"values":[46],"notation=\"LaTeX\">$m":[49],"&gt;":[50],"1$</tex-math></inline-formula>":[51],".":[52],"The":[53,77],"proposed":[54,78],"fully-serial-in":[55],"single":[56,99],"multipliers":[57,84],"perform":[58],"two":[61,87],"field":[62,90,115],"offer":[65],"high":[66],"throughput":[67],"when":[68],"data-path":[70],"capacity":[71],"entering":[73],"inputs":[74],"is":[75],"limited.":[76],"hybrid-double":[79],"perform,":[85],"respectively,":[86],"three":[89],"multiplications":[91],"using":[92],"same":[94],"latency":[95],"required":[96],"a":[98,112],"multiplier,":[101],"at":[102],"expense":[104],"increased":[106],"area.":[107],"addition,":[109],"eight-ary":[114],"exponentiation":[116],"architecture":[117],"does":[119],"not":[120],"require":[121],"precomputed":[122],"or":[123],"stored":[124],"intermediate":[125],"values.":[126]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
