{"id":"https://openalex.org/W2538131460","doi":"https://doi.org/10.1145/2976749.2978400","title":"Attacking OpenSSL Implementation of ECDSA with a Few Signatures","display_name":"Attacking OpenSSL Implementation of ECDSA with a Few Signatures","publication_year":2016,"publication_date":"2016-10-24","ids":{"openalex":"https://openalex.org/W2538131460","doi":"https://doi.org/10.1145/2976749.2978400","mag":"2538131460"},"language":"en","primary_location":{"id":"doi:10.1145/2976749.2978400","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2976749.2978400","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security","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/A5109166613","display_name":"Shuqin Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shuqin Fan","raw_affiliation_strings":["State Key Laboratory of Cryptology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Cryptology, Beijing, China","institution_ids":["https://openalex.org/I4210132990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046054684","display_name":"Wenbo Wang","orcid":"https://orcid.org/0000-0002-7500-8723"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wenbo Wang","raw_affiliation_strings":["Luoyang University of Foreign Languages, Luoyang, Henan, China"],"affiliations":[{"raw_affiliation_string":"Luoyang University of Foreign Languages, Luoyang, Henan, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071194455","display_name":"Qingfeng Cheng","orcid":"https://orcid.org/0000-0001-6149-4807"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qingfeng Cheng","raw_affiliation_strings":["Xidian University, Xi'an, Shanxi, China"],"affiliations":[{"raw_affiliation_string":"Xidian University, Xi'an, Shanxi, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109166613"],"corresponding_institution_ids":["https://openalex.org/I4210132990"],"apc_list":null,"apc_paid":null,"fwci":9.9521,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.97988401,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1505","last_page":"1515"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9987999796867371,"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":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/elliptic-curve-digital-signature-algorithm","display_name":"Elliptic Curve Digital Signature Algorithm","score":0.799248218536377},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7629501819610596},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.6915998458862305},{"id":"https://openalex.org/keywords/side-channel-attack","display_name":"Side channel attack","score":0.5689414143562317},{"id":"https://openalex.org/keywords/lattice-reduction","display_name":"Lattice reduction","score":0.5214740037918091},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.431541383266449},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4263031780719757},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4216546416282654},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4023439586162567},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.3962210416793823},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.37030768394470215},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.3576608896255493},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35509192943573},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.33859872817993164},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.257706880569458},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.24900296330451965},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.17292547225952148},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.16914018988609314},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.15850287675857544},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.07185524702072144}],"concepts":[{"id":"https://openalex.org/C197966572","wikidata":"https://www.wikidata.org/wiki/Q915079","display_name":"Elliptic Curve Digital Signature Algorithm","level":5,"score":0.799248218536377},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7629501819610596},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.6915998458862305},{"id":"https://openalex.org/C49289754","wikidata":"https://www.wikidata.org/wiki/Q2267081","display_name":"Side channel attack","level":3,"score":0.5689414143562317},{"id":"https://openalex.org/C44274781","wikidata":"https://www.wikidata.org/wiki/Q6497132","display_name":"Lattice reduction","level":4,"score":0.5214740037918091},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.431541383266449},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4263031780719757},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4216546416282654},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4023439586162567},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.3962210416793823},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.37030768394470215},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.3576608896255493},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35509192943573},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.33859872817993164},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.257706880569458},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.24900296330451965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.17292547225952148},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.16914018988609314},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.15850287675857544},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.07185524702072144},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2976749.2978400","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2976749.2978400","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W50107694","https://openalex.org/W80562455","https://openalex.org/W590469213","https://openalex.org/W1427174644","https://openalex.org/W1485287820","https://openalex.org/W1510439863","https://openalex.org/W1520399166","https://openalex.org/W1521787982","https://openalex.org/W1547036183","https://openalex.org/W1554359822","https://openalex.org/W1576391039","https://openalex.org/W1584579923","https://openalex.org/W1592889082","https://openalex.org/W1766548092","https://openalex.org/W1964389195","https://openalex.org/W1992291252","https://openalex.org/W2013613544","https://openalex.org/W2056778557","https://openalex.org/W2058546698","https://openalex.org/W2069196751","https://openalex.org/W2103289002","https://openalex.org/W2115190247","https://openalex.org/W2141040012","https://openalex.org/W2154909745","https://openalex.org/W2159520802","https://openalex.org/W2210258279","https://openalex.org/W2403933547","https://openalex.org/W2475786860","https://openalex.org/W2561675875","https://openalex.org/W3150881812","https://openalex.org/W4211068006","https://openalex.org/W4248175462"],"related_works":["https://openalex.org/W2361273900","https://openalex.org/W1992593853","https://openalex.org/W2351744923","https://openalex.org/W1521649858","https://openalex.org/W2367688749","https://openalex.org/W2188111145","https://openalex.org/W2890691626","https://openalex.org/W2365294822","https://openalex.org/W2952185445","https://openalex.org/W4289130109"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,52,91,114],"give":[4],"a":[5,30,54],"lattice":[6,110],"attack":[7,132,159],"on":[8,75],"the":[9,13,20,43,48,65,85,93,100,116,129,136,141,153,157,170],"ECDSA":[10],"implementation":[11],"in":[12,81],"latest":[14],"version":[15],"of":[16,37,71,87,95,118],"OpenSSL,":[17],"which":[18,58,105],"implement":[19],"scalar":[21],"multiplication":[22],"by":[23,109],"windowed":[24],"Non-Adjacent":[25],"Form":[26],"method.":[27],"We":[28],"propose":[29],"totally":[31],"different":[32],"but":[33],"more":[34],"efficient":[35,56],"method":[36],"extracting":[38],"and":[39,125,140],"utilizing":[40],"information":[41,63,72],"from":[42,64],"side-channel":[44,66],"results,":[45,67],"remarkably":[46],"improving":[47],"previous":[49],"attacks.":[50],"First,":[51],"develop":[53],"new":[55],"method,":[57],"can":[59,106],"extract":[60],"almost":[61],"all":[62],"obtaining":[68],"105.8":[69],"bits":[70],"per":[73],"signature":[74],"average":[76],"for":[77],"256-bit":[78],"ECDSA.":[79],"Then":[80],"order":[82],"to":[83,99,127,135,151],"make":[84],"utmost":[86],"our":[88],"extracted":[89],"information,":[90],"translate":[92],"problem":[94],"recovering":[96,124],"secret":[97,154],"key":[98,155],"Extended":[101],"Hidden":[102],"Number":[103],"Problem,":[104],"be":[107,149],"solved":[108],"reduction":[111],"algorithms.":[112],"Finally,":[113],"introduce":[115],"methods":[117],"elimination,":[119],"merging,":[120],"most":[121],"significant":[122],"digit":[123],"enumeration":[126],"improve":[128],"attack.":[130],"Our":[131],"is":[133,160,166],"mounted":[134],"{series":[137],"secp256k1}":[138],"curve,":[139],"result":[142,173],"shows":[143],"that":[144],"only":[145],"4":[146],"signatures":[147],"would":[148],"enough":[150],"recover":[152],"if":[156],"Flush+Reload":[158],"implemented":[161],"perfectly":[162],"without":[163],"any":[164],"error,which":[165],"much":[167],"better":[168],"than":[169],"best":[171],"known":[172],"needing":[174],"at":[175],"least":[176],"13":[177],"signatures.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}