{"id":"https://openalex.org/W2972726575","doi":"https://doi.org/10.3390/info10090285","title":"Low-Cost, Low-Power FPGA Implementation of ED25519 and CURVE25519 Point Multiplication","display_name":"Low-Cost, Low-Power FPGA Implementation of ED25519 and CURVE25519 Point Multiplication","publication_year":2019,"publication_date":"2019-09-14","ids":{"openalex":"https://openalex.org/W2972726575","doi":"https://doi.org/10.3390/info10090285","mag":"2972726575"},"language":"en","primary_location":{"id":"doi:10.3390/info10090285","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info10090285","pdf_url":"https://www.mdpi.com/2078-2489/10/9/285/pdf?version=1568948986","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2078-2489/10/9/285/pdf?version=1568948986","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069657593","display_name":"Ali Mehrabi","orcid":"https://orcid.org/0000-0003-3984-5361"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Mohamad Ali Mehrabi","raw_affiliation_strings":["Department of computing, Macquarie University, Sydney 2109, Australia","Macquarie University (Balaclava Road, North Ryde , NSW, 2109, Australia - Australia)"],"raw_orcid":"https://orcid.org/0000-0003-3984-5361","affiliations":[{"raw_affiliation_string":"Department of computing, Macquarie University, Sydney 2109, Australia","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Macquarie University (Balaclava Road, North Ryde , NSW, 2109, Australia - Australia)","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008443234","display_name":"Christophe Doche","orcid":null},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Christophe Doche","raw_affiliation_strings":["Optus Macquarie University Cyber Security Hub, Sydney 2109, Australia","Macquarie University (Balaclava Road, North Ryde , NSW, 2109, Australia - Australia)","GAATI - Laboratoire de G\u00e9om\u00e9trie Alg\u00e9brique et Applications \u00e0 la Th\u00e9orie de l'Information (Universit\u00e9 de la Polyn\u00e9sie fran\u00e7aise 98702 Faa'a Tahiti - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Optus Macquarie University Cyber Security Hub, Sydney 2109, Australia","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Macquarie University (Balaclava Road, North Ryde , NSW, 2109, Australia - Australia)","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"GAATI - Laboratoire de G\u00e9om\u00e9trie Alg\u00e9brique et Applications \u00e0 la Th\u00e9orie de l'Information (Universit\u00e9 de la Polyn\u00e9sie fran\u00e7aise 98702 Faa'a Tahiti - France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069657593"],"corresponding_institution_ids":["https://openalex.org/I99043593"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.5263,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.93839872,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"10","issue":"9","first_page":"285","last_page":"285"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9232000112533569,"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/scalar-multiplication","display_name":"Scalar multiplication","score":0.7451979517936707},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7219126224517822},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.705808162689209},{"id":"https://openalex.org/keywords/curve25519","display_name":"Curve25519","score":0.6807451248168945},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.6554277539253235},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5219285488128662},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.47343209385871887},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.46197450160980225},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4263705909252167},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.3781486749649048},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3619726598262787},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.3149278461933136},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.31049591302871704},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22029656171798706},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.20749765634536743},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.17566466331481934},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.08905303478240967},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.08750930428504944}],"concepts":[{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.7451979517936707},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7219126224517822},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.705808162689209},{"id":"https://openalex.org/C198690329","wikidata":"https://www.wikidata.org/wiki/Q15702839","display_name":"Curve25519","level":5,"score":0.6807451248168945},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.6554277539253235},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5219285488128662},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.47343209385871887},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.46197450160980225},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4263705909252167},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.3781486749649048},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3619726598262787},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.3149278461933136},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.31049591302871704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22029656171798706},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.20749765634536743},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.17566466331481934},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.08905303478240967},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.08750930428504944},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/info10090285","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info10090285","pdf_url":"https://www.mdpi.com/2078-2489/10/9/285/pdf?version=1568948986","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03602232v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03602232","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information, 2019, 10 (9), pp.285. &#x27E8;10.3390/info10090285&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:e4bbe33dc8d8478596f54d2aeecb438f","is_oa":true,"landing_page_url":"https://doaj.org/article/e4bbe33dc8d8478596f54d2aeecb438f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information, Vol 10, Iss 9, p 285 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2078-2489/10/9/285/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/info10090285","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/info10090285","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info10090285","pdf_url":"https://www.mdpi.com/2078-2489/10/9/285/pdf?version=1568948986","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320591","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2972726575.pdf","grobid_xml":"https://content.openalex.org/works/W2972726575.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W179459262","https://openalex.org/W1514429798","https://openalex.org/W1516510761","https://openalex.org/W1910751411","https://openalex.org/W1971605365","https://openalex.org/W1972442530","https://openalex.org/W1972461879","https://openalex.org/W2072600659","https://openalex.org/W2097848615","https://openalex.org/W2118678344","https://openalex.org/W2126703276","https://openalex.org/W2134258244","https://openalex.org/W2154290215","https://openalex.org/W2487840540","https://openalex.org/W2544689054","https://openalex.org/W2594174595","https://openalex.org/W2731579764","https://openalex.org/W2926472889","https://openalex.org/W2951379724","https://openalex.org/W6630737135"],"related_works":["https://openalex.org/W1568138047","https://openalex.org/W1995438231","https://openalex.org/W1911636251","https://openalex.org/W3009023388","https://openalex.org/W2946358183","https://openalex.org/W2347341077","https://openalex.org/W3112900045","https://openalex.org/W2070976279","https://openalex.org/W2356198393","https://openalex.org/W2234636045"],"abstract_inverted_index":{"Twisted":[0],"Edwards":[1],"curves":[2],"have":[3],"been":[4],"at":[5],"the":[6,65,96,115,118,128,137,146,149,168],"center":[7],"of":[8,72,95,108,114,139,148,162,170],"attention":[9],"since":[10],"their":[11],"introduction":[12],"by":[13,64],"Bernstein":[14],"et":[15],"al.":[16],"in":[17,78,126],"2007.":[18],"The":[19,39,112],"curve":[20,44],"ED25519,":[21],"used":[22,63,77],"for":[23,106],"Edwards-curve":[24],"Digital":[25],"Signature":[26],"Algorithm":[27],"(EdDSA),":[28],"provides":[29,52],"faster":[30],"digital":[31],"signatures":[32],"than":[33],"existing":[34],"schemes":[35],"without":[36],"sacrificing":[37],"security.":[38],"CURVE25519":[40,99],"is":[41,46,62,103,165],"a":[42,53,90,154],"Montgomery":[43],"that":[45,102],"closely":[47],"related":[48],"to":[49,136,166],"ED25519.":[50],"It":[51],"simple,":[54],"constant":[55],"time,":[56],"and":[57,74,82,98,131,142],"fast":[58],"point":[59],"multiplication,":[60,133],"which":[61],"key":[66,135],"exchange":[67],"protocol":[68],"X25519.":[69,143],"Software":[70],"implementations":[71],"EdDSA":[73,141],"X25519":[75],"are":[76,134],"many":[79],"web-based":[80],"PC":[81],"Mobile":[83],"applications.":[84,111],"In":[85],"this":[86,163],"paper,":[87],"we":[88,152],"introduce":[89],"low-power,":[91],"low-area":[92],"FPGA":[93,175],"implementation":[94],"ED25519":[97],"scalar":[100],"multiplication":[101,158],"particularly":[104],"relevant":[105],"Internet":[107],"Things":[109],"(IoT)":[110],"efficiency":[113,138],"arithmetic":[116],"modulo":[117],"prime":[119],"number":[120],"2":[121],"255":[122],"\u2212":[123],"19":[124],",":[125],"particular":[127],"modular":[129,132,157],"reduction":[130],"both":[140],"To":[144],"reduce":[145],"complexity":[147],"hardware":[150],"implementation,":[151],"propose":[153],"high-radix":[155],"interleaved":[156],"algorithm.":[159],"One":[160],"benefit":[161],"architecture":[164],"avoid":[167],"use":[169],"large-integer":[171],"multipliers":[172],"relying":[173],"on":[174],"DSP":[176],"modules.":[177]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
