{"id":"https://openalex.org/W2767028443","doi":"https://doi.org/10.48550/arxiv.1710.08336","title":"A Survey on Hardware Implementations of Elliptic Curve Cryptosystems","display_name":"A Survey on Hardware Implementations of Elliptic Curve Cryptosystems","publication_year":2017,"publication_date":"2017-10-19","ids":{"openalex":"https://openalex.org/W2767028443","doi":"https://doi.org/10.48550/arxiv.1710.08336","mag":"2767028443"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1710.08336","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.08336","pdf_url":"https://arxiv.org/pdf/1710.08336","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1710.08336","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017337821","display_name":"Bahram Rashidi","orcid":"https://orcid.org/0000-0002-3254-0891","observed_orcids":["https://orcid.org/0000-0002-3254-0891","https://orcid.org/0000-0001-9662-3197","https://orcid.org/0009-0005-6025-1543"]},"institutions":[{"id":"https://openalex.org/I4210129530","display_name":"Ayatollah Boroujerdi University","ror":"https://ror.org/0377qcz53","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210129530"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Rashidi, Bahram","raw_affiliation_strings":["Dept. of Elec. Eng. , University of Ayatollah ozma Boroujerdi Boroujerd , 69199-69411 , Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Elec. Eng. , University of Ayatollah ozma Boroujerdi Boroujerd , 69199-69411 , Iran","institution_ids":["https://openalex.org/I4210129530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017337821"],"corresponding_institution_ids":["https://openalex.org/I4210129530"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":1.0,"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":1.0,"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/T10951","display_name":"Cryptographic Implementations and Security","score":9.999999747378752e-05,"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/T11130","display_name":"Coding theory and cryptography","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"elliptic curve cryptography","score":0.9990000128746033},{"id":"https://openalex.org/keywords/hardware-implementation","display_name":"hardware implementation","score":0.9700000286102295},{"id":"https://openalex.org/keywords/binary-field-arithmetic","display_name":"binary field arithmetic","score":0.7549999952316284},{"id":"https://openalex.org/keywords/fpga","display_name":"FPGA","score":0.5649999976158142},{"id":"https://openalex.org/keywords/asic","display_name":"ASIC","score":0.7839999794960022},{"id":"https://openalex.org/keywords/smart-cards","display_name":"smart cards","score":0.6970000267028809},{"id":"https://openalex.org/keywords/wireless-sensor-networks","display_name":"wireless sensor networks","score":0.9229999780654907},{"id":"https://openalex.org/keywords/rfid-tags","display_name":"RFID tags","score":0.8529999852180481},{"id":"https://openalex.org/keywords/lightweight-cryptography","display_name":"lightweight cryptography","score":0.7950000166893005},{"id":"https://openalex.org/keywords/high-speed-implementation","display_name":"high-speed implementation","score":0.7279999852180481}],"concepts":[{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.7774919271469116},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7611017823219299},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.6580753326416016},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5807862877845764},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.5200545191764832},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.48644256591796875},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.4263896942138672},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.4178309142589569},{"id":"https://openalex.org/C197966572","wikidata":"https://www.wikidata.org/wiki/Q915079","display_name":"Elliptic Curve Digital Signature Algorithm","level":5,"score":0.4169250726699829},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.413017213344574},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21833503246307373},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.2152574360370636},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.18173140287399292},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.16074636578559875},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:1710.08336","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.08336","pdf_url":"https://arxiv.org/pdf/1710.08336","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1710.08336","doi":"https://doi.org/10.48550/arxiv.1710.08336","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.08336","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1710.08336","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.08336","pdf_url":"https://arxiv.org/pdf/1710.08336","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2767028443.pdf","grobid_xml":"https://content.openalex.org/works/W2767028443.grobid-xml"},"referenced_works_count":136,"referenced_works":["https://openalex.org/W19531220","https://openalex.org/W49133982","https://openalex.org/W109039816","https://openalex.org/W124286720","https://openalex.org/W127770406","https://openalex.org/W268239100","https://openalex.org/W1481041935","https://openalex.org/W1482218422","https://openalex.org/W1482481952","https://openalex.org/W1493251891","https://openalex.org/W1503069186","https://openalex.org/W1508696767","https://openalex.org/W1514429798","https://openalex.org/W1517364441","https://openalex.org/W1531476167","https://openalex.org/W1532610151","https://openalex.org/W1557126506","https://openalex.org/W1559075275","https://openalex.org/W1560281596","https://openalex.org/W1568138047","https://openalex.org/W1592482282","https://openalex.org/W1606269009","https://openalex.org/W1632631493","https://openalex.org/W1634503271","https://openalex.org/W1664139981","https://openalex.org/W1790731608","https://openalex.org/W1798101321","https://openalex.org/W1803812000","https://openalex.org/W1860992226","https://openalex.org/W1964698277","https://openalex.org/W1971605365","https://openalex.org/W1976525096","https://openalex.org/W1980304421","https://openalex.org/W1981856935","https://openalex.org/W1981998307","https://openalex.org/W1984097153","https://openalex.org/W1985361237","https://openalex.org/W1987496383","https://openalex.org/W1987524735","https://openalex.org/W1993446964","https://openalex.org/W2004814164","https://openalex.org/W2005575073","https://openalex.org/W2007751412","https://openalex.org/W2020207242","https://openalex.org/W2021211179","https://openalex.org/W2029128725","https://openalex.org/W2030413992","https://openalex.org/W2031993065","https://openalex.org/W2033234115","https://openalex.org/W2036378739","https://openalex.org/W2036527636","https://openalex.org/W2037213884","https://openalex.org/W2039371093","https://openalex.org/W2043445242","https://openalex.org/W2044568130","https://openalex.org/W2044785659","https://openalex.org/W2048246978","https://openalex.org/W2049277537","https://openalex.org/W2051032439","https://openalex.org/W2056966882","https://openalex.org/W2059168043","https://openalex.org/W2062530062","https://openalex.org/W2064534471","https://openalex.org/W2069863720","https://openalex.org/W2073835664","https://openalex.org/W2078731783","https://openalex.org/W2080546540","https://openalex.org/W2085540322","https://openalex.org/W2089927003","https://openalex.org/W2091649106","https://openalex.org/W2092442746","https://openalex.org/W2093610370","https://openalex.org/W2097524549","https://openalex.org/W2101533612","https://openalex.org/W2105103055","https://openalex.org/W2105832889","https://openalex.org/W2106010856","https://openalex.org/W2106776162","https://openalex.org/W2110487967","https://openalex.org/W2117539011","https://openalex.org/W2119688981","https://openalex.org/W2120658908","https://openalex.org/W2124421452","https://openalex.org/W2124489059","https://openalex.org/W2125123187","https://openalex.org/W2127115545","https://openalex.org/W2127806631","https://openalex.org/W2129139401","https://openalex.org/W2132494474","https://openalex.org/W2132886229","https://openalex.org/W2134046806","https://openalex.org/W2136689025","https://openalex.org/W2137153089","https://openalex.org/W2137461728","https://openalex.org/W2138461374","https://openalex.org/W2143032227","https://openalex.org/W2145280842","https://openalex.org/W2147227696","https://openalex.org/W2149568614","https://openalex.org/W2150897446","https://openalex.org/W2152910750","https://openalex.org/W2155526801","https://openalex.org/W2160037268","https://openalex.org/W2160895497","https://openalex.org/W2161531038","https://openalex.org/W2163208013","https://openalex.org/W2163604964","https://openalex.org/W2169155140","https://openalex.org/W2169383187","https://openalex.org/W2214868577","https://openalex.org/W2244200266","https://openalex.org/W2281229068","https://openalex.org/W2282799451","https://openalex.org/W2297160859","https://openalex.org/W2301890010","https://openalex.org/W2321801529","https://openalex.org/W2338349198","https://openalex.org/W2401718577","https://openalex.org/W2404213574","https://openalex.org/W2408518707","https://openalex.org/W2430735257","https://openalex.org/W2462802980","https://openalex.org/W2474056434","https://openalex.org/W2498349122","https://openalex.org/W2538739524","https://openalex.org/W2539628602","https://openalex.org/W2544689054","https://openalex.org/W2547988034","https://openalex.org/W2549318334","https://openalex.org/W2549863117","https://openalex.org/W2559812431","https://openalex.org/W2560618890","https://openalex.org/W2584189638","https://openalex.org/W2604743040","https://openalex.org/W2913989337","https://openalex.org/W3151447419"],"related_works":["https://openalex.org/W3097062724","https://openalex.org/W6927078831","https://openalex.org/W2512626181","https://openalex.org/W3116203889","https://openalex.org/W3208772028","https://openalex.org/W2462247954","https://openalex.org/W88866664","https://openalex.org/W1977844621","https://openalex.org/W1989727469","https://openalex.org/W3009403871"],"abstract_inverted_index":{"In":[0,28,204],"the":[1,67,85,124,142,168,209],"past":[2],"two":[3,90],"decades,":[4],"Elliptic":[5],"Curve":[6],"Cryptography":[7],"(ECC)":[8],"have":[9,118],"become":[10],"increasingly":[11],"advanced.":[12],"ECC,":[13],"with":[14],"much":[15],"smaller":[16],"key":[17],"sizes,":[18],"offers":[19],"equivalent":[20],"security":[21],"when":[22],"compared":[23],"to":[24,117,190,199],"other":[25],"asymmetric":[26],"cryptosystems.":[27],"this":[29],"survey,":[30],"an":[31,164],"comprehensive":[32],"overview":[33],"of":[34,37,77,84,98,133,152,159,208,214],"hardware":[35,70],"implementations":[36,83,105,125],"ECC":[38,78,86,169],"is":[39,163,221],"provided.":[40,222,236],"We":[41],"first":[42],"discuss":[43],"different":[44],"elliptic":[45],"curves,":[46],"point":[47],"multiplication":[48],"algorithms":[49],"and":[50,59,75,106,122,128,138,154,183,192,218,226],"underling":[51],"finite":[52,134],"field":[53,99],"operations":[54],"over":[55],"binary":[56],"fields":[57,61],"F2m":[58],"prime":[60],"Fp":[62],"which":[63],"are":[64,80,87,126,144,202,235],"used":[65],"in":[66,89,114,141,146,156,167,176,212],"literature":[68,143],"for":[69,149],"implementation.":[71],"Then":[72],"methods,":[73],"steps":[74],"considerations":[76],"implementation":[79,95,162,196],"presented.":[81],"The":[82,136],"categorized":[88],"main":[91],"groups":[92],"based":[93,104,130],"on":[94,131],"technologies":[96],"consist":[97],"programmable":[100],"gate":[101],"array":[102],"(FPGA)":[103],"application":[107],"specific":[108],"integrated":[109],"circuit":[110],"(ASIC)":[111],"implementations.":[112,160,194],"Therefore,":[113,195],"these":[115,200],"categories":[116],"a":[119,206],"better":[120],"presentation":[121,151],"comparison,":[123],"presented":[127],"distinguished":[129],"type":[132],"fields.":[135],"best":[137],"newest":[139],"structures":[140],"described":[145],"more":[147],"details":[148],"overall":[150],"architectures":[153],"approaches":[155],"each":[157],"group":[158],"High-speed":[161],"important":[165],"factor":[166],"applications":[170,201],"such":[171],"as":[172],"network":[173],"servers.":[174],"Also":[175],"smart":[177],"cards,":[178],"Wireless":[179],"Sensor":[180],"Networks":[181],"(WSN)":[182],"Radio":[184],"Frequency":[185],"Identification":[186],"(RFID)":[187],"tags":[188],"require":[189],"low-cost":[191],"lightweight":[193],"methods":[197],"related":[198],"explored.":[203],"addition,":[205],"classification":[207],"previous":[210],"works":[211,230],"terms":[213],"scalability,":[215],"flexibility,":[216],"performance":[217],"cost":[219],"effectiveness":[220],"Finally,":[223],"some":[224],"words":[225],"techniques":[227],"about":[228],"future":[229],"that":[231],"should":[232],"be":[233],"considered":[234]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2017-11-10T00:00:00"}