{"id":"https://openalex.org/W4291653101","doi":"https://doi.org/10.1109/tcsii.2022.3197314","title":"Efficient High-Radix GF(p) Montgomery Modular Multiplication Via Deep Use Of Multipliers","display_name":"Efficient High-Radix GF(p) Montgomery Modular Multiplication Via Deep Use Of Multipliers","publication_year":2022,"publication_date":"2022-08-15","ids":{"openalex":"https://openalex.org/W4291653101","doi":"https://doi.org/10.1109/tcsii.2022.3197314"},"language":"en","primary_location":{"id":"doi:10.1109/tcsii.2022.3197314","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2022.3197314","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","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/A5025243127","display_name":"Ruoyu Wu","orcid":"https://orcid.org/0000-0002-4850-2267"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruoyu Wu","raw_affiliation_strings":["College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-4850-2267","affiliations":[{"raw_affiliation_string":"College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084382806","display_name":"Ming Xu","orcid":"https://orcid.org/0000-0002-8849-9656"},"institutions":[{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming Xu","raw_affiliation_strings":["Information School, NingboTech University, Ningbo, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information School, NingboTech University, Ningbo, China","institution_ids":["https://openalex.org/I159389169"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015705962","display_name":"Yingqing Yang","orcid":"https://orcid.org/0000-0003-4236-8543"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingqing Yang","raw_affiliation_strings":["College of Control Science and Engineering, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-4236-8543","affiliations":[{"raw_affiliation_string":"College of Control Science and Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014432572","display_name":"Guanzhong Tian","orcid":"https://orcid.org/0000-0002-7292-4056"},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanzhong Tian","raw_affiliation_strings":["Ningbo Research Institute, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-7292-4056","affiliations":[{"raw_affiliation_string":"Ningbo Research Institute, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I109935558","https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101551608","display_name":"Ping Yu","orcid":"https://orcid.org/0000-0001-8648-9799"},"institutions":[{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ping Yu","raw_affiliation_strings":["Information School, NingboTech University, Ningbo, China"],"raw_orcid":"https://orcid.org/0000-0001-8648-9799","affiliations":[{"raw_affiliation_string":"Information School, NingboTech University, Ningbo, China","institution_ids":["https://openalex.org/I159389169"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004316172","display_name":"Yangfan Zhao","orcid":"https://orcid.org/0009-0002-8565-0506"},"institutions":[{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yangfan Zhao","raw_affiliation_strings":["Information School, NingboTech University, Ningbo, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information School, NingboTech University, Ningbo, China","institution_ids":["https://openalex.org/I159389169"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017561052","display_name":"Bin Lian","orcid":"https://orcid.org/0000-0001-9363-5782"},"institutions":[{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bin Lian","raw_affiliation_strings":["Information School, NingboTech University, Ningbo, China"],"raw_orcid":"https://orcid.org/0000-0001-9363-5782","affiliations":[{"raw_affiliation_string":"Information School, NingboTech University, Ningbo, China","institution_ids":["https://openalex.org/I159389169"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056003654","display_name":"Longhua Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Longhua Ma","raw_affiliation_strings":["Information School, NingboTech University, Ningbo, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information School, NingboTech University, Ningbo, China","institution_ids":["https://openalex.org/I159389169"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":8,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.868,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.92270911,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"69","issue":"12","first_page":"5099","last_page":"5103"},"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":0.9945999979972839,"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":0.9793999791145325,"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/arithmetic","display_name":"Arithmetic","score":0.7440434694290161},{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.726965606212616},{"id":"https://openalex.org/keywords/radix","display_name":"Radix (gastropod)","score":0.6929965615272522},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6507354378700256},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.580072820186615},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.5766241550445557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5633417963981628},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.5523064732551575},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.500640869140625},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.4465067386627197},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39667147397994995},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3041210174560547},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.26028478145599365},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.189031720161438},{"id":"https://openalex.org/keywords/latency","display_name":"Latency (audio)","score":0.09470903873443604}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7440434694290161},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.726965606212616},{"id":"https://openalex.org/C2779091547","wikidata":"https://www.wikidata.org/wiki/Q287565","display_name":"Radix (gastropod)","level":2,"score":0.6929965615272522},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6507354378700256},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.580072820186615},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.5766241550445557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5633417963981628},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.5523064732551575},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.500640869140625},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.4465067386627197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39667147397994995},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3041210174560547},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.26028478145599365},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.189031720161438},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.09470903873443604},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsii.2022.3197314","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2022.3197314","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4080565995","display_name":null,"funder_award_id":"LY21F040004","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"}],"funders":[{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W2026445983","https://openalex.org/W2029487736","https://openalex.org/W2395191213","https://openalex.org/W2539628602","https://openalex.org/W2559812431","https://openalex.org/W2586653522","https://openalex.org/W2795031321","https://openalex.org/W2885098807","https://openalex.org/W2931078655","https://openalex.org/W2940460717","https://openalex.org/W2948829558","https://openalex.org/W2965690158","https://openalex.org/W2970769336","https://openalex.org/W3009403871","https://openalex.org/W3110374082","https://openalex.org/W3123229602","https://openalex.org/W3174403583","https://openalex.org/W3216468923","https://openalex.org/W4200271029","https://openalex.org/W4205198354","https://openalex.org/W4237773356"],"related_works":["https://openalex.org/W4390550886","https://openalex.org/W3217463396","https://openalex.org/W2516396101","https://openalex.org/W2790557758","https://openalex.org/W2361290373","https://openalex.org/W4302768783","https://openalex.org/W2782264914","https://openalex.org/W2353466882","https://openalex.org/W2904069009","https://openalex.org/W2355149595"],"abstract_inverted_index":{"High-radix":[0],"Montgomery":[1],"Modular":[2,34],"Multiplication":[3,35],"(MMM)":[4],"is":[5,65,107],"flexible":[6],"and":[7,47,57,67,84,91,125],"consumes":[8],"fewer":[9],"cycles,":[10,53],"but":[11],"turns":[12],"inefficient":[13],"especially":[14],"when":[15],"it":[16],"comes":[17],"to":[18,69,120],"low-bit":[19],"calculation.":[20],"In":[21],"this":[22],"brief,":[23],"we":[24],"propose":[25],"a":[26,115],"high-radix":[27],"MMM":[28,40],"algorithm,":[29],"called":[30],"Separated":[31],"Iterative":[32],"Digit-Digit":[33],"(S-IDDMM),":[36],"which":[37],"accelerates":[38],"the":[39,62,71],"by":[41,109],"taking":[42],"full":[43],"advantage":[44],"of":[45,55,59,79,123],"multipliers":[46,60,124],"adders.":[48],"The":[49],"relationship":[50],"among":[51],"clock":[52],"pipeline":[54],"multiplications":[56],"number":[58],"for":[61],"proposed":[63],"algorithm":[64],"derived":[66],"utilized":[68],"optimize":[70],"overall":[72],"efficiency":[73],"jointly.":[74],"Xilinx":[75],"Virtex-7":[76],"FPGA":[77],"implementations":[78],"S-IDDMM":[80],"in":[81],"256":[82],"bits":[83,86],"512":[85],"are":[87],"constructed":[88],"with":[89,95,114],"radix-32":[90],"radix-64,":[92],"respectively.":[93],"Compared":[94],"IDDMM":[96],"design":[97],"reported":[98],"elsewhere":[99],"(Amiet":[100],"et":[101],"al.,":[102],"2016),":[103],"our":[104],"calculation":[105],"time":[106],"reduced":[108],"more":[110],"than":[111],"2":[112],"times":[113],"similar":[116],"area":[117],"cost,":[118],"due":[119],"deep":[121],"use":[122],"higher":[126],"frequency.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}