{"id":"https://openalex.org/W4408676936","doi":"https://doi.org/10.1080/01611194.2025.2449711","title":"On computing the double point multiplication in elliptic curve cryptography","display_name":"On computing the double point multiplication in elliptic curve cryptography","publication_year":2025,"publication_date":"2025-03-19","ids":{"openalex":"https://openalex.org/W4408676936","doi":"https://doi.org/10.1080/01611194.2025.2449711"},"language":"en","primary_location":{"id":"doi:10.1080/01611194.2025.2449711","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01611194.2025.2449711","pdf_url":null,"source":{"id":"https://openalex.org/S185196701","display_name":"Cryptologia","issn_l":"0161-1194","issn":["0161-1194","1558-1586"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptologia","raw_type":"journal-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/A5115407832","display_name":"Fadila Nait-Abdesselam","orcid":"https://orcid.org/0000-0002-9606-955X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fadila Nait-Abdesselam","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9606-955X","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023220437","display_name":"Abdelkrim K. Oudjida","orcid":"https://orcid.org/0000-0003-2923-7258"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Abdelkrim Kamel Oudjida","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2923-7258","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Abdelkrim Kamel Oudjida","orcid":"https://orcid.org/0000-0003-2923-7258"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abdelkrim Kamel Oudjida","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2923-7258","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013279731","display_name":"Abdelhakim Khouas","orcid":"https://orcid.org/0000-0002-0921-289X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abdelhakim Khouas","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0921-289X","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013279731","display_name":"Abdelhakim Khouas","orcid":"https://orcid.org/0000-0002-0921-289X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Abdelhakim Khouas","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0921-289X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037309390","display_name":"Ahmed Liacha","orcid":"https://orcid.org/0000-0001-9142-4973"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ahmed Liacha","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9142-4973","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5013279731","https://openalex.org/A5023220437"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7886,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.92472861,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"50","issue":"2","first_page":"97","last_page":"128"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9714999794960022,"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":0.9645000100135803,"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-cryptography","display_name":"Elliptic curve cryptography","score":0.7925809621810913},{"id":"https://openalex.org/keywords/elliptic-curve-digital-signature-algorithm","display_name":"Elliptic Curve Digital Signature Algorithm","score":0.6582664847373962},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6566761136054993},{"id":"https://openalex.org/keywords/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.6494719982147217},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6290383338928223},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5722795128822327},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5628470182418823},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5364627838134766},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45956164598464966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3702145218849182},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34470534324645996},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.2540024518966675},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.24549531936645508},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.16826552152633667},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10409301519393921},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08419641852378845},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07493406534194946}],"concepts":[{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.7925809621810913},{"id":"https://openalex.org/C197966572","wikidata":"https://www.wikidata.org/wiki/Q915079","display_name":"Elliptic Curve Digital Signature Algorithm","level":5,"score":0.6582664847373962},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6566761136054993},{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.6494719982147217},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6290383338928223},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5722795128822327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5628470182418823},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5364627838134766},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45956164598464966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3702145218849182},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34470534324645996},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.2540024518966675},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.24549531936645508},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.16826552152633667},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10409301519393921},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08419641852378845},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07493406534194946}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/01611194.2025.2449711","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01611194.2025.2449711","pdf_url":null,"source":{"id":"https://openalex.org/S185196701","display_name":"Cryptologia","issn_l":"0161-1194","issn":["0161-1194","1558-1586"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptologia","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1487297807","https://openalex.org/W1504378831","https://openalex.org/W1507106163","https://openalex.org/W1515496055","https://openalex.org/W1521856420","https://openalex.org/W1522228241","https://openalex.org/W1523099545","https://openalex.org/W1526011068","https://openalex.org/W1537809712","https://openalex.org/W1565378600","https://openalex.org/W1613874182","https://openalex.org/W1638546798","https://openalex.org/W1660562555","https://openalex.org/W1880212920","https://openalex.org/W1957825227","https://openalex.org/W1994429123","https://openalex.org/W2038091128","https://openalex.org/W2066437741","https://openalex.org/W2072656343","https://openalex.org/W2105114022","https://openalex.org/W2121110380","https://openalex.org/W2134899616","https://openalex.org/W2144952508","https://openalex.org/W2146443249","https://openalex.org/W2154290215","https://openalex.org/W2154777362","https://openalex.org/W2155244510","https://openalex.org/W2505763232","https://openalex.org/W2775178453","https://openalex.org/W2791516576","https://openalex.org/W2904585189","https://openalex.org/W2906446416","https://openalex.org/W2943126371","https://openalex.org/W2991680843","https://openalex.org/W3034816776","https://openalex.org/W3046142497","https://openalex.org/W3108038120","https://openalex.org/W3125524301","https://openalex.org/W3126560502","https://openalex.org/W3136748529","https://openalex.org/W3164170653","https://openalex.org/W4241373120","https://openalex.org/W4245047333","https://openalex.org/W4250656566","https://openalex.org/W4289127653","https://openalex.org/W4300184098","https://openalex.org/W4390698913"],"related_works":["https://openalex.org/W1565266559","https://openalex.org/W2037734447","https://openalex.org/W2013613544","https://openalex.org/W2782833818","https://openalex.org/W3201596224","https://openalex.org/W2392460858","https://openalex.org/W2393578887","https://openalex.org/W2182900437","https://openalex.org/W1521649858","https://openalex.org/W1577956677"],"abstract_inverted_index":{"The":[0,91,128],"double":[1],"point-multiplication":[2],"(DPM)":[3],"operation":[4,31],"on":[5,25,68],"elliptic":[6],"curves,":[7,174],"denoted":[8],"as":[9,175,177],"u.P":[10],"+":[11],"v.Q,":[12],"where":[13],"u":[14,88,105],"and":[15,20,49,89,106,108,123,142,147,154,180],"v":[16,107],"are":[17,23,131],"nonnegative":[18],"integers":[19],"P,":[21],"Q":[22],"points":[24],"the":[26,102],"curve,":[27],"is":[28,166],"a":[29,54,95],"critical":[30],"in":[32,43],"digital":[33],"signature":[34],"verification.":[35],"Its":[36],"computational":[37],"scheme":[38],"significantly":[39],"impacts":[40],"system":[41],"performances":[42],"terms":[44],"of":[45,56],"speed,":[46,139],"memory":[47,121,140],"usage,":[48,141],"security.":[50,143],"This":[51,71,114],"article":[52],"introduces":[53],"range":[55],"straightforward":[57],"algorithms":[58,93,130],"for":[59,138],"DPM,":[60,119],"which":[61],"leverage":[62],"an":[63],"iterative":[64],"uniform":[65],"pattern":[66],"based":[67],"constant-time":[69],"arithmetic.":[70],"approach":[72],"mitigates":[73],"side-channel":[74],"attacks":[75],"(SCA)":[76],"that":[77],"exploit":[78],"timing":[79],"or":[80],"power":[81],"consumption":[82],"measurements":[83],"to":[84,99,157],"compromise":[85],"secret":[86],"keys":[87],"v.":[90],"proposed":[92],"employ":[94],"w-bit":[96],"windowing":[97],"method":[98],"simultaneously":[100],"recode":[101],"binary":[103],"strings":[104],"evaluate":[109],"DPM":[110],"on-the-fly":[111],"from":[112],"left-to-right.":[113],"one-pass":[115],"recode/evaluation":[116],"process":[117],"accelerates":[118],"reduces":[120],"overhead,":[122],"enhances":[124],"resilience":[125],"against":[126,163],"SCA.":[127],"new":[129],"systematically":[132],"evaluated":[133],"using":[134,171],"precise":[135],"analytic":[136],"formulas":[137],"They":[144],"prioritize":[145],"simplicity":[146],"flexibility,":[148],"enabling":[149],"easy":[150],"adjustments":[151],"between":[152],"speed-memory":[153],"speed-security":[155],"trade-offs":[156],"meet":[158],"various":[159],"constraints.":[160],"Comparative":[161],"analysis":[162],"state-of-the-art":[164],"methods":[165],"conducted,":[167],"comprehensively":[168],"examining":[169],"complexities":[170],"NIST-recommended":[172],"GF(2l)":[173],"well":[176],"twisted":[178],"Edwards":[179],"Montgomery":[181],"GF(p)":[182],"curves.":[183]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
