{"id":"https://openalex.org/W4399666316","doi":"https://doi.org/10.1109/tcad.2024.3415017","title":"Area-Efficient Barrett Modular Multiplication With Optimized Karatsuba Algorithm","display_name":"Area-Efficient Barrett Modular Multiplication With Optimized Karatsuba Algorithm","publication_year":2024,"publication_date":"2024-06-14","ids":{"openalex":"https://openalex.org/W4399666316","doi":"https://doi.org/10.1109/tcad.2024.3415017"},"language":"en","primary_location":{"id":"doi:10.1109/tcad.2024.3415017","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2024.3415017","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"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 Computer-Aided Design of Integrated Circuits and Systems","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/A5100335386","display_name":"Bo Zhang","orcid":"https://orcid.org/0000-0003-3215-8745"},"institutions":[{"id":"https://openalex.org/I4210121321","display_name":"ANT Foundation Italy Onlus","ror":"https://ror.org/02zf60s91","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210121321"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Bo Zhang","raw_affiliation_strings":["Computing Systems Lab, Ant Research, Ant Group Co Ltd., Hangzhou, China","Computing Systems Lab, Ant Research, Ant Group, China"],"raw_orcid":"https://orcid.org/0000-0003-3215-8745","affiliations":[{"raw_affiliation_string":"Computing Systems Lab, Ant Research, Ant Group Co Ltd., Hangzhou, China","institution_ids":["https://openalex.org/I4210121321"]},{"raw_affiliation_string":"Computing Systems Lab, Ant Research, Ant Group, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049135681","display_name":"Shoumeng Yan","orcid":"https://orcid.org/0009-0007-9580-5395"},"institutions":[{"id":"https://openalex.org/I4210121321","display_name":"ANT Foundation Italy Onlus","ror":"https://ror.org/02zf60s91","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210121321"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Shoumeng Yan","raw_affiliation_strings":["Computing Systems Lab, Ant Research, Ant Group Co Ltd., Hangzhou, China","Computing Systems Lab, Ant Research, Ant Group, China"],"raw_orcid":"https://orcid.org/0009-0007-9580-5395","affiliations":[{"raw_affiliation_string":"Computing Systems Lab, Ant Research, Ant Group Co Ltd., Hangzhou, China","institution_ids":["https://openalex.org/I4210121321"]},{"raw_affiliation_string":"Computing Systems Lab, Ant Research, Ant Group, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210121321"],"apc_list":null,"apc_paid":null,"fwci":5.1355,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.96714797,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"43","issue":"12","first_page":"4626","last_page":"4639"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9434999823570251,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9434999823570251,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9376999735832214,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.933899998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.6295651197433472},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6145320534706116},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5824764370918274},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5385153889656067},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.500025749206543},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.47400081157684326},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.4156048893928528},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3901156783103943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29416587948799133},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.06841966509819031},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.05843207240104675}],"concepts":[{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.6295651197433472},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6145320534706116},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5824764370918274},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5385153889656067},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.500025749206543},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.47400081157684326},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.4156048893928528},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3901156783103943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29416587948799133},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.06841966509819031},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.05843207240104675},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcad.2024.3415017","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2024.3415017","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"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 Computer-Aided Design of Integrated Circuits and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1498685334","https://openalex.org/W2004814164","https://openalex.org/W2052363354","https://openalex.org/W2107953479","https://openalex.org/W2129745589","https://openalex.org/W2177209050","https://openalex.org/W2768174108","https://openalex.org/W2904069009","https://openalex.org/W2942691585","https://openalex.org/W2966077459","https://openalex.org/W3016585670","https://openalex.org/W3047409455","https://openalex.org/W3183042014","https://openalex.org/W3189815475","https://openalex.org/W3212490035","https://openalex.org/W4213435507","https://openalex.org/W4226334377","https://openalex.org/W4232836212","https://openalex.org/W4245047333","https://openalex.org/W4385348894","https://openalex.org/W4386608731","https://openalex.org/W4386825228","https://openalex.org/W4392309401","https://openalex.org/W6636949950","https://openalex.org/W6778434676"],"related_works":["https://openalex.org/W2113213955","https://openalex.org/W2057797376","https://openalex.org/W2090319426","https://openalex.org/W2225983048","https://openalex.org/W2016520453","https://openalex.org/W2506252583","https://openalex.org/W2372139915","https://openalex.org/W2361290373","https://openalex.org/W2904069009","https://openalex.org/W2355149595"],"abstract_inverted_index":{"This":[0],"article":[1],"presents":[2],"an":[3,66,68,92],"area-efficient":[4],"Barrett":[5],"modular":[6,49],"multiplication":[7,35,38,50,70,88],"(BMM)":[8],"algorithm,":[9],"facilitating":[10],"the":[11,61,157],"development":[12],"of":[13,20,159,165],"cryptosystems":[14],"like":[15],"fully":[16],"homomorphic":[17],"encryption.":[18],"Instead":[19],"implementing":[21],"three":[22],"normal":[23],"multiplications":[24,103,116],"required":[25],"by":[26],"classic":[27],"BMM,":[28],"our":[29,113,160],"proposed":[30,161],"BMM":[31,146,162],"introduces":[32],"optimizations":[33],"for":[34,86],"AB,":[36],"truncated":[37,87],"<inline-formula":[39,52,76,97,105],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[40,53,77,98,106],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[41,54,78,99,107],"<tex-math":[42,55,79,100,108],"notation=\"LaTeX\">$\\lfloor":[43],"AB/2^{f}":[44],"\\rfloor":[45],"$":[46],"</tex-math></inline-formula>,":[47],"and":[48,89,130,147,167],"(MM)":[51],"notation=\"LaTeX\">$AB":[56],"~\\text":[57],"{mod}~2^{f}$":[58],"</tex-math></inline-formula>.":[59,111],"Taking":[60],"4-term":[62],"Karatsuba":[63,115],"algorithm":[64,139],"as":[65],"example,":[67],"N-bit":[69],"AB":[71],"can":[72],"be":[73],"decomposed":[74],"into":[75],"notation=\"LaTeX\">$9~(N/4)$":[80],"</tex-math></inline-formula>-bit":[81,102],"multiplications.":[82],"Our":[83],"optimized":[84,114],"approaches":[85],"MM":[90],"require":[91],"area":[93,124,168],"equivalent":[94],"to":[95,140],"only":[96],"notation=\"LaTeX\">$6.5~(N/4)$":[101],"when":[104],"notation=\"LaTeX\">$f\\approx":[109],"N$":[110],"Furthermore,":[112],"introduce":[117],"efficient":[118],"(E,":[119],"I)":[120],"matrix":[121],"pairs,":[122],"circumventing":[123],"overhead":[125],"from":[126],"complex":[127],"I":[128],"matrices":[129],"sign":[131],"extension":[132],"in":[133,145,163],"multiplication.":[134],"We":[135],"also":[136],"employ":[137],"encode":[138],"eliminate":[141],"many":[142],"additions":[143],"needed":[144],"inside":[148],"multiplications,":[149],"significantly":[150],"shortening":[151],"critical":[152],"path.":[153],"Experimental":[154],"results":[155],"demonstrate":[156],"advantages":[158],"terms":[164],"throughput":[166],"efficiency.":[169]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}