{"id":"https://openalex.org/W2131946302","doi":"https://doi.org/10.1109/acssc.2008.5074513","title":"Parallel high-radix Montgomery multipliers","display_name":"Parallel high-radix Montgomery multipliers","publication_year":2008,"publication_date":"2008-10-01","ids":{"openalex":"https://openalex.org/W2131946302","doi":"https://doi.org/10.1109/acssc.2008.5074513","mag":"2131946302"},"language":"en","primary_location":{"id":"doi:10.1109/acssc.2008.5074513","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acssc.2008.5074513","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 42nd Asilomar Conference on Signals, Systems and Computers","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/A5070427395","display_name":"Philip Amberg","orcid":null},"institutions":[{"id":"https://openalex.org/I133543626","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45","country_code":"US","type":"education","lineage":["https://openalex.org/I133543626"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Philip Amberg","raw_affiliation_strings":["Harvey Mudd College, Claremont, CA, USA","Harvey Mudd College, Claremont, CA"],"affiliations":[{"raw_affiliation_string":"Harvey Mudd College, Claremont, CA, USA","institution_ids":["https://openalex.org/I133543626"]},{"raw_affiliation_string":"Harvey Mudd College, Claremont, CA","institution_ids":["https://openalex.org/I133543626"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050270997","display_name":"Nathaniel Pinckney","orcid":"https://orcid.org/0000-0001-6159-8964"},"institutions":[{"id":"https://openalex.org/I133543626","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45","country_code":"US","type":"education","lineage":["https://openalex.org/I133543626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nathaniel Pinckney","raw_affiliation_strings":["Harvey Mudd College, Claremont, CA, USA","Harvey Mudd College, Claremont, CA"],"affiliations":[{"raw_affiliation_string":"Harvey Mudd College, Claremont, CA, USA","institution_ids":["https://openalex.org/I133543626"]},{"raw_affiliation_string":"Harvey Mudd College, Claremont, CA","institution_ids":["https://openalex.org/I133543626"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101661944","display_name":"David Harris","orcid":"https://orcid.org/0000-0001-9075-5965"},"institutions":[{"id":"https://openalex.org/I133543626","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45","country_code":"US","type":"education","lineage":["https://openalex.org/I133543626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Money Harris","raw_affiliation_strings":["Harvey Mudd College, Claremont, CA"],"affiliations":[{"raw_affiliation_string":"Harvey Mudd College, Claremont, CA","institution_ids":["https://openalex.org/I133543626"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070427395"],"corresponding_institution_ids":["https://openalex.org/I133543626"],"apc_list":null,"apc_paid":null,"fwci":3.4991,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.93779587,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"772","last_page":"776"},"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":0.9984999895095825,"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":0.9851999878883362,"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-exponentiation","display_name":"Modular exponentiation","score":0.7554261684417725},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.754625141620636},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.6028438806533813},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.5832877159118652},{"id":"https://openalex.org/keywords/radix","display_name":"Radix (gastropod)","score":0.5500975847244263},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.547321617603302},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5440189242362976},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.5245963931083679},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.5222271680831909},{"id":"https://openalex.org/keywords/booths-multiplication-algorithm","display_name":"Booth's multiplication algorithm","score":0.5048568844795227},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.49955058097839355},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4801765978336334},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.45296430587768555},{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.2629336714744568},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.16800463199615479},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14902296662330627},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08460012078285217},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.08173123002052307},{"id":"https://openalex.org/keywords/latency","display_name":"Latency (audio)","score":0.08073529601097107}],"concepts":[{"id":"https://openalex.org/C152763109","wikidata":"https://www.wikidata.org/wiki/Q1228841","display_name":"Modular exponentiation","level":4,"score":0.7554261684417725},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.754625141620636},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.6028438806533813},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.5832877159118652},{"id":"https://openalex.org/C2779091547","wikidata":"https://www.wikidata.org/wiki/Q287565","display_name":"Radix (gastropod)","level":2,"score":0.5500975847244263},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.547321617603302},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5440189242362976},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5245963931083679},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.5222271680831909},{"id":"https://openalex.org/C72475854","wikidata":"https://www.wikidata.org/wiki/Q477049","display_name":"Booth's multiplication algorithm","level":4,"score":0.5048568844795227},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.49955058097839355},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4801765978336334},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.45296430587768555},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.2629336714744568},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.16800463199615479},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14902296662330627},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08460012078285217},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.08173123002052307},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.08073529601097107},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","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/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acssc.2008.5074513","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acssc.2008.5074513","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 42nd Asilomar Conference on Signals, Systems and Computers","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.158.5309","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.5309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www3.hmc.edu/~harris/research/asilomar08.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1608823649","https://openalex.org/W2004814164","https://openalex.org/W2026445983","https://openalex.org/W2110122313","https://openalex.org/W2111793257","https://openalex.org/W2118738175","https://openalex.org/W2122637726","https://openalex.org/W2126162217","https://openalex.org/W2129769654","https://openalex.org/W2140850958","https://openalex.org/W2160005544","https://openalex.org/W2164533233","https://openalex.org/W2245967636","https://openalex.org/W4237773356","https://openalex.org/W6678827218","https://openalex.org/W6679596785"],"related_works":["https://openalex.org/W4235485585","https://openalex.org/W670148","https://openalex.org/W1507420113","https://openalex.org/W4242613270","https://openalex.org/W2107014706","https://openalex.org/W28274153","https://openalex.org/W2736837562","https://openalex.org/W2020808628","https://openalex.org/W2767903583","https://openalex.org/W1508408889"],"abstract_inverted_index":{"This":[0,106],"paper":[1],"describes":[2],"the":[3,89,115,122],"algorithm":[4],"and":[5,29,46,52,72,75,103,127],"design":[6,60,107,123,136],"tradeoffs":[7],"for":[8,111],"multiple":[9],"hardware":[10,125],"implementations":[11,19],"of":[12,20,42,88,118],"parallel":[13],"high-radix":[14],"scalable":[15],"Montgomery":[16,21],"multipliers.":[17],"Hardware":[18],"multipliers":[22],"require":[23],"choosing":[24],"a":[25,62,93,142],"radix,":[26],"shift":[27],"direction,":[28],"whether":[30],"to":[31,77],"use":[32],"Booth":[33,53,85],"encoding.":[34,54],"Presented":[35],"are":[36],"processing":[37],"element":[38],"designs":[39],"exploring":[40],"combinations":[41],"radices":[43],"2,":[44],"4,":[45],"8,":[47],"right":[48],"vs.":[49],"left":[50],"shifting,":[51],"A":[55,84],"radix-4,":[56],"left-shifting,":[57],"non-Booth":[58],"encoded":[59,86],"performs":[61,92],"1024-bit":[63,94],"modular":[64,95],"exponentiation":[65,96],"in":[66,80,97],"9.4":[67],"ms":[68,99],"using":[69,100],"4997":[70],"LUTs":[71,102],"4051":[73],"REGs":[74],"appears":[76],"maximize":[78],"performance/hardware":[79,139],"an":[81],"FPGA":[82],"implementation.":[83],"version":[87],"above":[90],"multiplier":[91],"13":[98],"4852":[101],"2887":[104],"REGs.":[105],"may":[108],"be":[109],"beneficial":[110],"systems":[112],"constrained":[113],"by":[114],"cycle":[116],"time":[117],"other":[119],"elements":[120],"because":[121],"minimizes":[124],"usage":[126],"requires":[128],"no":[129,138],"precomputed":[130],"multiples.":[131],"The":[132],"radix-8,":[133],"right-shifting,":[134],"Booth-encoded":[135],"offers":[137],"advantage":[140],"over":[141],"comparable":[143],"radix-4":[144],"design.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}