{"id":"https://openalex.org/W3177342323","doi":"https://doi.org/10.1007/s10836-021-05951-3","title":"Resistance of the Montgomery Ladder Against Simple SCA: Theory and Practice","display_name":"Resistance of the Montgomery Ladder Against Simple SCA: Theory and Practice","publication_year":2021,"publication_date":"2021-06-01","ids":{"openalex":"https://openalex.org/W3177342323","doi":"https://doi.org/10.1007/s10836-021-05951-3","mag":"3177342323"},"language":"en","primary_location":{"id":"doi:10.1007/s10836-021-05951-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10836-021-05951-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10836-021-05951-3.pdf","source":{"id":"https://openalex.org/S200807567","display_name":"Journal of Electronic Testing","issn_l":"0923-8174","issn":["0923-8174","1573-0727"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Electronic Testing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10836-021-05951-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056603264","display_name":"Ievgen Kabin","orcid":"https://orcid.org/0000-0002-3838-6493"},"institutions":[{"id":"https://openalex.org/I92894754","display_name":"Innovations for High Performance Microelectronics","ror":"https://ror.org/0489gab80","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I92894754"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ievgen Kabin","raw_affiliation_strings":["IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany"],"affiliations":[{"raw_affiliation_string":"IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany","institution_ids":["https://openalex.org/I92894754"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039434509","display_name":"Zoya Dyka","orcid":"https://orcid.org/0000-0002-6819-0467"},"institutions":[{"id":"https://openalex.org/I92894754","display_name":"Innovations for High Performance Microelectronics","ror":"https://ror.org/0489gab80","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I92894754"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Zoya Dyka","raw_affiliation_strings":["IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany"],"affiliations":[{"raw_affiliation_string":"IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany","institution_ids":["https://openalex.org/I92894754"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045906012","display_name":"Dan Klann","orcid":null},"institutions":[{"id":"https://openalex.org/I92894754","display_name":"Innovations for High Performance Microelectronics","ror":"https://ror.org/0489gab80","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I92894754"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dan Klann","raw_affiliation_strings":["IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany"],"affiliations":[{"raw_affiliation_string":"IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany","institution_ids":["https://openalex.org/I92894754"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043815462","display_name":"Marcin Aftowicz","orcid":"https://orcid.org/0000-0002-2975-2615"},"institutions":[{"id":"https://openalex.org/I92894754","display_name":"Innovations for High Performance Microelectronics","ror":"https://ror.org/0489gab80","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I92894754"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Marcin Aftowicz","raw_affiliation_strings":["IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany"],"affiliations":[{"raw_affiliation_string":"IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany","institution_ids":["https://openalex.org/I92894754"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042352640","display_name":"Peter Langend\u00f6erfer","orcid":"https://orcid.org/0000-0002-6209-9048"},"institutions":[{"id":"https://openalex.org/I92894754","display_name":"Innovations for High Performance Microelectronics","ror":"https://ror.org/0489gab80","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I92894754"]},{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Langendoerfer","raw_affiliation_strings":["BTU Cottbus-Senftenberg, Cottbus, Germany","IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany"],"affiliations":[{"raw_affiliation_string":"BTU Cottbus-Senftenberg, Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]},{"raw_affiliation_string":"IHP \u2013 Leibniz-Institut f\u00fcr innovative Mikroelektronik, Frankfurt (Oder), Germany","institution_ids":["https://openalex.org/I92894754"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5056603264"],"corresponding_institution_ids":["https://openalex.org/I92894754"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.4787,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.90768585,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"37","issue":"3","first_page":"289","last_page":"303"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9993000030517578,"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":0.996399998664856,"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/compiler","display_name":"Compiler","score":0.7205023169517517},{"id":"https://openalex.org/keywords/vhdl","display_name":"VHDL","score":0.710167407989502},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6681796908378601},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.6314535737037659},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.47396987676620483},{"id":"https://openalex.org/keywords/power-analysis","display_name":"Power analysis","score":0.42677462100982666},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.40263086557388306},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.37113505601882935},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32960307598114014},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.32833486795425415},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22335276007652283},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1513240933418274}],"concepts":[{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.7205023169517517},{"id":"https://openalex.org/C36941000","wikidata":"https://www.wikidata.org/wiki/Q209455","display_name":"VHDL","level":3,"score":0.710167407989502},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6681796908378601},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.6314535737037659},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.47396987676620483},{"id":"https://openalex.org/C71743495","wikidata":"https://www.wikidata.org/wiki/Q2845210","display_name":"Power analysis","level":3,"score":0.42677462100982666},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.40263086557388306},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.37113505601882935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32960307598114014},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.32833486795425415},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22335276007652283},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1513240933418274},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10836-021-05951-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10836-021-05951-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10836-021-05951-3.pdf","source":{"id":"https://openalex.org/S200807567","display_name":"Journal of Electronic Testing","issn_l":"0923-8174","issn":["0923-8174","1573-0727"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Electronic Testing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10836-021-05951-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10836-021-05951-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10836-021-05951-3.pdf","source":{"id":"https://openalex.org/S200807567","display_name":"Journal of Electronic Testing","issn_l":"0923-8174","issn":["0923-8174","1573-0727"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Electronic Testing","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.800000011920929,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3177342323.pdf","grobid_xml":"https://content.openalex.org/works/W3177342323.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1522228241","https://openalex.org/W1860992226","https://openalex.org/W1880212920","https://openalex.org/W1994429123","https://openalex.org/W2096133993","https://openalex.org/W2119769175","https://openalex.org/W2168356719","https://openalex.org/W2478327424","https://openalex.org/W2528382571","https://openalex.org/W2562672356","https://openalex.org/W2787237253","https://openalex.org/W2794544459","https://openalex.org/W2914391081","https://openalex.org/W3006254592","https://openalex.org/W3025374379","https://openalex.org/W3140739796","https://openalex.org/W4206595402","https://openalex.org/W6723422928"],"related_works":["https://openalex.org/W2016389538","https://openalex.org/W2479014312","https://openalex.org/W1583465708","https://openalex.org/W2351405704","https://openalex.org/W3094426418","https://openalex.org/W2028730298","https://openalex.org/W3215234104","https://openalex.org/W2368451485","https://openalex.org/W2573624673","https://openalex.org/W2380045081"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Montgomery":[2,7,45],"kP":[3,46,89,140],"algorithm":[4,47],"i.e.":[5,96],"the":[6,20,23,31,37,44,53,61,73,79,88,92,111,128,139,144,160,173,186,191,205,216,220,257,262,265,269,273,277,287,296,306,309,318,323],"ladder":[8],"is":[9,34,199,280],"reported":[10],"in":[11,286],"literature":[12],"as":[13,153,170,172,235,237],"resistant":[14],"against":[15,167,180,276],"simple":[16,163,176,212],"SCA":[17],"due":[18],"to":[19,226,242,294,315],"fact":[21],"that":[22,159],"processing":[24],"of":[25,30,40,69,87,124,131,138,162,175,215,219,268,311],"each":[26,132],"key":[27,297,319],"bit":[28],"value":[29],"scalar":[32,97,146,206],"k":[33,98,147,207],"done":[35],"using":[36,48,78,91,143],"same":[38,62,74,80,93,112,145],"sequence":[39],"operations.":[41],"We":[42,59,83,126,252],"implemented":[43,194],"Lopez-Dahab":[49],"projective":[50],"coordinates":[51],"for":[52,65,72,115,120,189,222,261],"NIST":[54],"elliptic":[55,100,149],"curve":[56,101,150],"B-233":[57],".":[58],"instantiated":[60],"VHDL":[63,113],"code":[64,114],"a":[66,121,283],"wide":[67],"range":[68],"clock":[70],"frequencies":[71,223,308],"target":[75,187],"FPGA":[76,168,221],"and":[77,99,105,148,195,301],"compiler":[81],"options.":[82],"measured":[84],"electromagnetic":[85,164,217],"traces":[86,218,259,288],"executions":[90],"input":[94],"data,":[95],"point":[102,151],"P":[103,152],",":[104],"measurement":[106],"setup.":[107],"Additionally,":[108],"we":[109],"synthesized":[110,133,181],"two":[116],"IHP":[117],"CMOS":[118],"technologies,":[119],"broad":[122],"spectrum":[123],"frequencies.":[125,304],"simulated":[127,260],"power":[129,177,258],"consumption":[130],"design":[134,192],"during":[135],"an":[136],"execution":[137],"operation,":[141],"always":[142],"inputs.":[154],"Our":[155],"experiments":[156,204],"clearly":[157],"show":[158],"success":[161],"analysis":[165,178],"attacks":[166,179,278],"implementations":[169],"well":[171,236],"one":[174],"ASIC":[182],"designs":[183],"depends":[184],"on":[185],"frequency":[188],"which":[190,197,313],"was":[193,208],"at":[196,298],"it":[198],"executed":[200],"significantly.":[201],"In":[202],"our":[203],"successfully":[209,316],"revealed":[210],"via":[211],"visual":[213],"inspection":[214],"from":[224,238],"40":[225],"100":[227],"MHz":[228,240,244],"when":[229,245,321],"standard":[230],"compile":[231,248],"options":[232,249],"were":[233,250],"used":[234],"50":[239],"up":[241],"240":[243],"performance":[246],"optimizing":[247],"used.":[251],"obtained":[253],"similar":[254],"results":[255],"attacking":[256],"ASIC.":[263],"Despite":[264],"significant":[266],"differences":[267],"here":[270],"investigated":[271],"technologies":[272],"designs\u2019":[274],"resistance":[275],"performed":[279],"similar:":[281],"only":[282],"few":[284],"points":[285,312],"represent":[289],"strong":[290],"leakage":[291],"sources":[292],"allowing":[293],"reveal":[295,317],"very":[299,302],"low":[300],"high":[303],"For":[305],"\u201cmiddle\u201d":[307],"number":[310],"allow":[314],"increases":[320],"increasing":[322],"frequency.":[324]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}