{"id":"https://openalex.org/W3148220426","doi":"https://doi.org/10.1109/ipdps.2006.1639608","title":"Parallel calculation of volcanoes for cryptographic uses","display_name":"Parallel calculation of volcanoes for cryptographic uses","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W3148220426","doi":"https://doi.org/10.1109/ipdps.2006.1639608","mag":"3148220426"},"language":"en","primary_location":{"id":"doi:10.1109/ipdps.2006.1639608","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ipdps.2006.1639608","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 20th IEEE International Parallel &amp; Distributed Processing Symposium","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/A5067031180","display_name":"Santi Mart\u00ednez","orcid":"https://orcid.org/0000-0002-1031-6522"},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"S. Martinez","raw_affiliation_strings":["Department dInform\u00e0tica i Enginyer\u00eda Industrial, Universitat de Lleida, Lleida, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department dInform\u00e0tica i Enginyer\u00eda Industrial, Universitat de Lleida, Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062165731","display_name":"R. Tom\u00e0s","orcid":null},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"R. Tomas","raw_affiliation_strings":["Department de Matem\u00e0tica, Universitat de Lleida, Lleida, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department de Matem\u00e0tica, Universitat de Lleida, Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038914395","display_name":"Concepci\u00f3 Roig","orcid":"https://orcid.org/0000-0003-3029-3820"},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"C. Roig","raw_affiliation_strings":["Department dInform\u00e0tica i Enginyer\u00eda Industrial, Universitat de Lleida, Lleida, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department dInform\u00e0tica i Enginyer\u00eda Industrial, Universitat de Lleida, Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030020799","display_name":"Magda Valls","orcid":"https://orcid.org/0000-0003-1992-146X"},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. Valls","raw_affiliation_strings":["Department dInform\u00e0tica i Enginyer\u00eda Industrial, Universitat de Lleida, Lleida, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department dInform\u00e0tica i Enginyer\u00eda Industrial, Universitat de Lleida, Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075780050","display_name":"R. Pe\u00f1a-Moreno","orcid":"https://orcid.org/0000-0002-9971-7444"},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"R. Moreno","raw_affiliation_strings":["Department de Matem\u00e0tica, Universitat de Lleida, Lleida, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department de Matem\u00e0tica, Universitat de Lleida, Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I15766328"],"apc_list":null,"apc_paid":null,"fwci":1.7192,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.90573257,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":null,"first_page":"8 pp.","last_page":"8 pp."},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9739000201225281,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/speedup","display_name":"Speedup","score":0.8627960681915283},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7725876569747925},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.7050027847290039},{"id":"https://openalex.org/keywords/granularity","display_name":"Granularity","score":0.6973044276237488},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5785642266273499},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5152726173400879},{"id":"https://openalex.org/keywords/workstation","display_name":"Workstation","score":0.5101185441017151},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.47254061698913574},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37502896785736084},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.3443775773048401},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3252722918987274},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.18372699618339539},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.15268561244010925},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.10339531302452087}],"concepts":[{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.8627960681915283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7725876569747925},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.7050027847290039},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.6973044276237488},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5785642266273499},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5152726173400879},{"id":"https://openalex.org/C67953723","wikidata":"https://www.wikidata.org/wiki/Q192525","display_name":"Workstation","level":2,"score":0.5101185441017151},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.47254061698913574},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37502896785736084},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.3443775773048401},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3252722918987274},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.18372699618339539},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.15268561244010925},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.10339531302452087}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ipdps.2006.1639608","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ipdps.2006.1639608","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 20th IEEE International Parallel &amp; Distributed Processing Symposium","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":7,"referenced_works":["https://openalex.org/W1508193711","https://openalex.org/W1561740949","https://openalex.org/W1664377124","https://openalex.org/W1927343998","https://openalex.org/W1990024880","https://openalex.org/W2052322466","https://openalex.org/W2097595126"],"related_works":["https://openalex.org/W2058965144","https://openalex.org/W2164382479","https://openalex.org/W98480971","https://openalex.org/W2150291671","https://openalex.org/W2027972911","https://openalex.org/W2146343568","https://openalex.org/W2013643406","https://openalex.org/W2157978810","https://openalex.org/W2597809628","https://openalex.org/W1969153118"],"abstract_inverted_index":{"Elliptic":[0],"curve":[1,20],"crypto":[2],"systems":[3],"are":[4,31],"nowadays":[5],"widely":[6],"used":[7],"in":[8,75,111,118,156],"the":[9,37,67,97,108,112,116,126,133,139,142],"design":[10],"of":[11,36,40,69,100,121,128,135,141,149],"many":[12],"security":[13],"devices.":[14],"Nevertheless,":[15],"since":[16],"not":[17],"every":[18],"elliptic":[19,41],"is":[21,73,87],"useful":[22],"for":[23,27,66,89,95,125],"cryptographic":[24],"purposes,":[25],"mechanisms":[26],"providing":[28],"good":[29,48],"curves":[30,42],"highly":[32],"needed.":[33],"The":[34],"generation":[35,127],"volcano":[38,71,130],"graph":[39],"can":[43,153],"help":[44],"to":[45,55,80,102],"provide":[46],"such":[47,70],"curves.":[49],"However,":[50],"this":[51,76],"procedure":[52],"turns":[53],"out":[54],"be":[56,103,154],"very":[57],"expensive":[58],"when":[59,114],"performed":[60],"sequentially.":[61],"Hence,":[62],"a":[63,84,119,147],"parallel":[64],"application":[65,117],"calculation":[68],"graphs":[72],"proposed":[74],"paper.":[77],"In":[78],"order":[79],"obtain":[81],"high":[82],"efficiency,":[83],"theoretical":[85],"analysis":[86],"provided":[88],"obtaining":[90],"an":[91],"accurate":[92],"granularity":[93],"and":[94,144],"giving":[96],"appropriate":[98],"number":[99],"tasks":[101],"created.":[104],"Experimental":[105],"results":[106],"show":[107,145],"benefits":[109],"obtained":[110],"speedup":[113,148],"executing":[115],"cluster":[120],"workstations":[122],"with":[123],"message-passing":[124],"different":[129],"graphs.":[131],"By":[132],"use":[134],"simulation,":[136],"we":[137],"study":[138],"scalability":[140],"implementation":[143],"that":[146],"more":[150],"than":[151],"80":[152],"achieved":[155],"some":[157],"cases.":[158]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
