{"id":"https://openalex.org/W3129647343","doi":"https://doi.org/10.1109/vlsi-soc46417.2020.9344069","title":"A Minimalistic Perspective on Koblitz Curve Scalar Multiplication for FPGA Platforms","display_name":"A Minimalistic Perspective on Koblitz Curve Scalar Multiplication for FPGA Platforms","publication_year":2020,"publication_date":"2020-10-05","ids":{"openalex":"https://openalex.org/W3129647343","doi":"https://doi.org/10.1109/vlsi-soc46417.2020.9344069","mag":"3129647343"},"language":"en","primary_location":{"id":"doi:10.1109/vlsi-soc46417.2020.9344069","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vlsi-soc46417.2020.9344069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IFIP/IEEE 28th International Conference on Very Large Scale Integration (VLSI-SOC)","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/A5089810331","display_name":"Siddhartha Chowdhury","orcid":null},"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":"Siddhartha Chowdhury","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, West Bengal, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, West Bengal, India","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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Debapriya Basu Roy","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Chair for Security in Information Technology, Technical Univeristy of Munich"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Chair for Security in Information Technology, Technical Univeristy of Munich","institution_ids":[]}]},{"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, West Bengal, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, West Bengal, India","institution_ids":["https://openalex.org/I145894827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089810331"],"corresponding_institution_ids":["https://openalex.org/I145894827"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.31909726,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"70","last_page":"75"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9891999959945679,"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":0.9807000160217285,"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/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.767391562461853},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6663142442703247},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.5218642950057983},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4839625656604767},{"id":"https://openalex.org/keywords/lookup-table","display_name":"Lookup table","score":0.4561866521835327},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.44287368655204773},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.41839587688446045},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.418239027261734},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.3872494101524353},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.35637253522872925},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.29790520668029785},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.2646142244338989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22820201516151428},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.19462496042251587}],"concepts":[{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.767391562461853},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6663142442703247},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.5218642950057983},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4839625656604767},{"id":"https://openalex.org/C134835016","wikidata":"https://www.wikidata.org/wiki/Q690265","display_name":"Lookup table","level":2,"score":0.4561866521835327},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.44287368655204773},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.41839587688446045},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.418239027261734},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.3872494101524353},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.35637253522872925},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.29790520668029785},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.2646142244338989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22820201516151428},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.19462496042251587},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/vlsi-soc46417.2020.9344069","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vlsi-soc46417.2020.9344069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IFIP/IEEE 28th International Conference on Very Large Scale Integration (VLSI-SOC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321024","display_name":"Defence Research and Development Organisation","ror":"https://ror.org/05k37v296"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W15239834","https://openalex.org/W1490721997","https://openalex.org/W1522228241","https://openalex.org/W1971605365","https://openalex.org/W1985205186","https://openalex.org/W2001180707","https://openalex.org/W2007751412","https://openalex.org/W2025482144","https://openalex.org/W2030413992","https://openalex.org/W2084002332","https://openalex.org/W2109801498","https://openalex.org/W2115190247","https://openalex.org/W2155526801","https://openalex.org/W2161531038","https://openalex.org/W2161958080","https://openalex.org/W2300226053","https://openalex.org/W2336615066","https://openalex.org/W2408518707","https://openalex.org/W6600620439","https://openalex.org/W6676681237","https://openalex.org/W6684373899","https://openalex.org/W6714074518"],"related_works":["https://openalex.org/W2946358183","https://openalex.org/W118355721","https://openalex.org/W2070976279","https://openalex.org/W2024574431","https://openalex.org/W2152593841","https://openalex.org/W3203056599","https://openalex.org/W2117300767","https://openalex.org/W2351744923","https://openalex.org/W2374017528","https://openalex.org/W3201415091"],"abstract_inverted_index":{"Koblitz":[0,106],"Curves":[1],"offer":[2],"excellent":[3],"optimization":[4],"opportunities":[5],"for":[6,105,118,126,158,164],"characteristic-2":[7,29,84],"Elliptic":[8],"Curve":[9],"Cryptosystems":[10],"(ECC).":[11],"However,":[12],"porting":[13],"such":[14],"choices":[15],"onto":[16],"a":[17,24,62,81,110,155,172,209,226,248],"lightweight":[18,82],"and":[19,70,193],"cost-effective":[20,227],"FPGA":[21,95,147,159],"platform":[22],"is":[23,31],"major":[25],"challenge.":[26],"The":[27,97,144,175,203,230],"underlying":[28,121],"algebra":[30],"not":[32,43],"aligned":[33],"with":[34,80,132,235],"the":[35,51,90,94,114,120,137,142,197,201,240,244],"on-chip":[36],"components":[37],"like":[38,149],"DSP":[39,122],"multipliers,":[40],"which":[41,108],"if":[42,72],"utilized":[44],"leads":[45,207],"to":[46,60,88,140,153,168,181,191,195,208,238],"large":[47],"LUT":[48],"counts":[49],"of":[50,93,136,200,243],"designs.":[52],"In":[53],"this":[54],"work,":[55],"we":[56],"develop":[57],"several":[58],"techniques":[59],"propose":[61],"minimal":[63,111,156],"instruction":[64,139],"set,":[65],"centered":[66],"around":[67],"ADDN":[68,101,138],"(Add":[69],"Branch":[71],"less":[73,216,221],"than":[74,217,222],"zero)":[75],"based":[76,102],"OISC":[77],"(One-Instruction-Set-Computing)":[78],"coupled":[79],"comba":[83],"finite":[85],"field":[86],"multiplier":[87,104],"ensure":[89],"aggressive":[91],"utilization":[92],"resources.":[96],"paper":[98],"develops":[99],"an":[100],"scalar":[103,183,213],"curves":[107],"has":[109,232],"footprint":[112],"on":[113,225],"LUTs,":[115,160],"leveraging":[116],"methods":[117],"utilizing":[119],"blocks":[123],"in":[124,130,171,215],"FPGAs":[125],"performing":[127,212],"GF(2)":[128],"operations,":[129],"conjunction":[131],"proposed":[133],"reduced":[134],"variants":[135],"perform":[141],"computations.":[143],"architecture":[145,211],"uses":[146],"resources":[148],"BRAMs,":[150],"DSPs":[151],"effectively":[152],"have":[154],"requirement":[157],"thus":[161],"leaving":[162],"room":[163],"other":[165],"peripheral":[166],"designs":[167],"be":[169,179],"hosted":[170],"single":[173],"FPGA.":[174,229],"same":[176],"design":[177,205,231],"can":[178],"configured":[180],"realize":[182],"multiplications":[184],"by":[185],"two":[186],"popular":[187],"strategies,":[188],"namely":[189],"due":[190],"Solinas":[192],"Montgomery,":[194],"demonstrate":[196],"modular":[198],"nature":[199],"design.":[202],"minimalistic":[204],"style":[206],"resource-constrained":[210],"multiplication":[214],"1000":[218],"slices,":[219],"needing":[220],"0.5":[223],"ms":[224],"Artix-7":[228],"been":[233],"compared":[234],"reported":[236],"literature":[237],"highlight":[239],"area":[241],"efficiency":[242],"design,":[245],"however":[246],"ensuring":[247],"competitive":[249],"AT":[250],"(area-time)":[251],"product.":[252]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}