{"id":"https://openalex.org/W2582853162","doi":"https://doi.org/10.1109/asianhost.2016.7835562","title":"Inner collisions in ECC: Vulnerabilities of complete addition formulas for NIST curves","display_name":"Inner collisions in ECC: Vulnerabilities of complete addition formulas for NIST curves","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2582853162","doi":"https://doi.org/10.1109/asianhost.2016.7835562","mag":"2582853162"},"language":"en","primary_location":{"id":"doi:10.1109/asianhost.2016.7835562","is_oa":false,"landing_page_url":"https://doi.org/10.1109/asianhost.2016.7835562","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Asian Hardware-Oriented Security and Trust (AsianHOST)","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/A5101668689","display_name":"Poulami Das","orcid":"https://orcid.org/0000-0002-7404-8504"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Poulami Das","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102710760","display_name":"Debapriya Basu Roy","orcid":"https://orcid.org/0000-0003-4664-5237"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Debapriya Basu Roy","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015473813","display_name":"Harishma Boyapally","orcid":"https://orcid.org/0000-0002-2742-0772"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Harishma Boyapally","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078971402","display_name":"Debdeep Mukhopadhyay","orcid":"https://orcid.org/0000-0002-6499-8346"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Debdeep Mukhopadhyay","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur","institution_ids":["https://openalex.org/I145894827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101668689"],"corresponding_institution_ids":["https://openalex.org/I145894827"],"apc_list":null,"apc_paid":null,"fwci":1.327,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.87593699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"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":0.9972000122070312,"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":0.9966999888420105,"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/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.7109113931655884},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.680689811706543},{"id":"https://openalex.org/keywords/side-channel-attack","display_name":"Side channel attack","score":0.6679432392120361},{"id":"https://openalex.org/keywords/tripling-oriented-doche\u2013icart\u2013kohel-curve","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","score":0.6306280493736267},{"id":"https://openalex.org/keywords/jacobian-curve","display_name":"Jacobian curve","score":0.5997571349143982},{"id":"https://openalex.org/keywords/nist","display_name":"NIST","score":0.5802363753318787},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.5801237225532532},{"id":"https://openalex.org/keywords/hessian-form-of-an-elliptic-curve","display_name":"Hessian form of an elliptic curve","score":0.5413922667503357},{"id":"https://openalex.org/keywords/curve25519","display_name":"Curve25519","score":0.5305082201957703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5209309458732605},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5027613639831543},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4972882568836212},{"id":"https://openalex.org/keywords/edwards-curve","display_name":"Edwards curve","score":0.4620726704597473},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.43725013732910156},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4236389398574829},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3126232624053955},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2800810933113098},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.24290713667869568},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1440022885799408},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.12057119607925415}],"concepts":[{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.7109113931655884},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.680689811706543},{"id":"https://openalex.org/C49289754","wikidata":"https://www.wikidata.org/wiki/Q2267081","display_name":"Side channel attack","level":3,"score":0.6679432392120361},{"id":"https://openalex.org/C37055786","wikidata":"https://www.wikidata.org/wiki/Q7843607","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","level":5,"score":0.6306280493736267},{"id":"https://openalex.org/C79993320","wikidata":"https://www.wikidata.org/wiki/Q6119657","display_name":"Jacobian curve","level":5,"score":0.5997571349143982},{"id":"https://openalex.org/C111219384","wikidata":"https://www.wikidata.org/wiki/Q6954384","display_name":"NIST","level":2,"score":0.5802363753318787},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.5801237225532532},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.5413922667503357},{"id":"https://openalex.org/C198690329","wikidata":"https://www.wikidata.org/wiki/Q15702839","display_name":"Curve25519","level":5,"score":0.5305082201957703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5209309458732605},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5027613639831543},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4972882568836212},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.4620726704597473},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.43725013732910156},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4236389398574829},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3126232624053955},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2800810933113098},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.24290713667869568},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1440022885799408},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.12057119607925415},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"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/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.0},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/asianhost.2016.7835562","is_oa":false,"landing_page_url":"https://doi.org/10.1109/asianhost.2016.7835562","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Asian Hardware-Oriented Security and Trust (AsianHOST)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W7125584","https://openalex.org/W60689211","https://openalex.org/W1531102506","https://openalex.org/W1565369953","https://openalex.org/W1576488632","https://openalex.org/W1579766512","https://openalex.org/W1591503962","https://openalex.org/W1832880052","https://openalex.org/W1880212920","https://openalex.org/W1910751411","https://openalex.org/W1976677460","https://openalex.org/W2095423754","https://openalex.org/W2096133993","https://openalex.org/W2104841597","https://openalex.org/W2111978877","https://openalex.org/W2134258244","https://openalex.org/W2151279347","https://openalex.org/W2154290215","https://openalex.org/W2167078981","https://openalex.org/W2168356719","https://openalex.org/W2295000628","https://openalex.org/W2395369561","https://openalex.org/W2400247270","https://openalex.org/W2951379724","https://openalex.org/W3029756576","https://openalex.org/W6633902989","https://openalex.org/W6634817591","https://openalex.org/W6639789869","https://openalex.org/W6674513603","https://openalex.org/W6679573670","https://openalex.org/W6684692440","https://openalex.org/W6711601790","https://openalex.org/W6945000925"],"related_works":["https://openalex.org/W2006528304","https://openalex.org/W28923676","https://openalex.org/W2188057592","https://openalex.org/W2121110380","https://openalex.org/W2924530095","https://openalex.org/W2131587162","https://openalex.org/W1175355266","https://openalex.org/W2397131319","https://openalex.org/W4225299977","https://openalex.org/W2376262033"],"abstract_inverted_index":{"Elliptic":[0],"curve":[1,24,32,38],"cryptosystems":[2],"are":[3,43],"built":[4],"on":[5,34],"an":[6,11,30],"underlying":[7,36],"additive":[8],"group,":[9],"with":[10],"addition":[12,25,49,65,76,95,138],"operation":[13,26],"defined":[14],"as":[15,45],"the":[16,22,35,64,98,129,133,163,170,198],"group":[17],"operation.":[18],"The":[19,75,110],"aim":[20],"of":[21,100,112,131],"elliptic":[23,31,37],"is":[27,144,158,189],"to":[28,69,146,197],"render":[29],"point":[33,119],"when":[39],"two":[40,122,180],"ECC":[41,48,118],"points":[42],"taken":[44],"inputs.":[46],"However":[47],"formula":[50,66,77,96,135,178],"may":[51,58,67,194],"not":[52,86,159],"be":[53,147,195],"complete":[54,94],"in":[55,84,105,162],"nature,":[56],"and":[57,126,139],"contain":[59],"exceptional":[60],"points,":[61,125],"for":[62,78,97,120,136,173],"which":[63,201],"fail":[68],"produce":[70],"a":[71,93,115],"valid":[72,116],"third":[73,117],"point.":[74],"prime":[79,101],"order":[80,102],"NIST":[81,103],"curves":[82,104],"were":[83],"fact":[85],"complete,":[87],"till":[88],"Renes":[89],"et.":[90],"al.":[91],"proposed":[92],"class":[99],"their":[106],"Eurocrypt":[107],"2016":[108],"paper.":[109],"property":[111],"completeness":[113],"ensures":[114],"any":[121,152],"chosen":[123],"input":[124],"thus":[127],"provides":[128],"advantage":[130],"using":[132],"same":[134],"both":[137],"doubling":[140],"operations.":[141,208],"Consequently":[142],"it":[143,193],"assumed":[145],"inherently":[148],"side-channel":[149,156,171],"secure,":[150],"however":[151],"practical":[153],"validation":[154],"against":[155,179,191],"protection":[157,172],"yet":[160],"present":[161],"literature.":[164],"In":[165],"this":[166,174,186],"work":[167],"we":[168],"analyse":[169],"newly":[175],"constructed":[176],"unified":[177],"horizontal":[181],"attacks.":[182],"We":[183],"show":[184],"although":[185],"new":[187],"construction":[188],"resistant":[190],"HCCA,":[192],"vulnerable":[196],"ROSETTA":[199],"attack,":[200],"exploits":[202],"inner":[203],"collisions":[204],"within":[205],"field":[206],"multiplication":[207]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}