{"id":"https://openalex.org/W2012770528","doi":"https://doi.org/10.1504/ijact.2012.045590","title":"Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction","display_name":"Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2012770528","doi":"https://doi.org/10.1504/ijact.2012.045590","mag":"2012770528"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1504/ijact.2012.045590","pdf_url":null,"source":{"id":"https://openalex.org/S55392106","display_name":"International Journal of Applied Cryptography","issn_l":"1753-0563","issn":["1753-0563","1753-0571"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310317825","host_organization_name":"Inderscience Publishers","host_organization_lineage":["https://openalex.org/P4310317825"],"host_organization_lineage_names":["Inderscience Publishers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://infoscience.epfl.ch/record/164550/files/164550.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012762741","display_name":"Joppe W. Bos","orcid":"https://orcid.org/0000-0003-1010-8157"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Joppe W. Bos","raw_affiliation_strings":["Laboratory for Cryptologic Algorithms, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 14, CH-1015 Lausanne, Switzerland.#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory for Cryptologic Algorithms, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 14, CH-1015 Lausanne, Switzerland.#TAB#","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023006207","display_name":"Marcelo E. Kaihara","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Marcelo E. Kaihara","raw_affiliation_strings":["Laboratory for Cryptologic Algorithms, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 14, CH-1015 Lausanne, Switzerland.#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory for Cryptologic Algorithms, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 14, CH-1015 Lausanne, Switzerland.#TAB#","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013956683","display_name":"Thorsten Kleinjung","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Thorsten Kleinjung","raw_affiliation_strings":["Laboratory for Cryptologic Algorithms, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 14, CH-1015 Lausanne, Switzerland.#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory for Cryptologic Algorithms, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 14, CH-1015 Lausanne, Switzerland.#TAB#","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109240185","display_name":"Arjen K. Lenstra","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Arjen K. Lenstra","raw_affiliation_strings":["Laboratory for Cryptologic Algorithms, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 14, CH-1015 Lausanne, Switzerland.#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory for Cryptologic Algorithms, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 14, CH-1015 Lausanne, Switzerland.#TAB#","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053924378","display_name":"Peter L. Montgomery","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter L. Montgomery","raw_affiliation_strings":["One Microsoft Way, Microsoft Research, Redmond, WA 98052, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"One Microsoft Way, Microsoft Research, Redmond, WA 98052, USA#TAB#","institution_ids":["https://openalex.org/I1290206253"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":30.641,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":65,"citation_normalized_percentile":{"value":0.993299,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"2","issue":"3","first_page":"212","last_page":"212"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9999,"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":0.9999,"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":0.9916,"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":0.9861,"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/discrete-logarithm","display_name":"Discrete logarithm","score":0.6526603},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.44588953}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6526603},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.64966565},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.58263224},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5611998},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5471446},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5115743},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.44588953},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44558915},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.44239488},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.43784535},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35008413},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18913203},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.13986471},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.131854},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10320699},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.093752384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08578721},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1504/ijact.2012.045590","pdf_url":null,"source":{"id":"https://openalex.org/S55392106","display_name":"International Journal of Applied Cryptography","issn_l":"1753-0563","issn":["1753-0563","1753-0571"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310317825","host_organization_name":"Inderscience Publishers","host_organization_lineage":["https://openalex.org/P4310317825"],"host_organization_lineage_names":["Inderscience Publishers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/164550","pdf_url":"https://infoscience.epfl.ch/record/164550/files/164550.pdf","source":{"id":"https://openalex.org/S4306400488","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/164550","pdf_url":"https://infoscience.epfl.ch/record/164550/files/164550.pdf","source":{"id":"https://openalex.org/S4306400488","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":50,"referenced_works":["https://openalex.org/W100509257","https://openalex.org/W1480958376","https://openalex.org/W1506559511","https://openalex.org/W1520933837","https://openalex.org/W1535283406","https://openalex.org/W1538333734","https://openalex.org/W1559075275","https://openalex.org/W1560663560","https://openalex.org/W1600795850","https://openalex.org/W1681176638","https://openalex.org/W1786760088","https://openalex.org/W1881382661","https://openalex.org/W1910751411","https://openalex.org/W1971605365","https://openalex.org/W1972442530","https://openalex.org/W1981663184","https://openalex.org/W1985265065","https://openalex.org/W2003736153","https://openalex.org/W2004814164","https://openalex.org/W2005317356","https://openalex.org/W2008272678","https://openalex.org/W2019816098","https://openalex.org/W2027028382","https://openalex.org/W2036378739","https://openalex.org/W2042173287","https://openalex.org/W2078234463","https://openalex.org/W2088492907","https://openalex.org/W2121904840","https://openalex.org/W2127075094","https://openalex.org/W2141836061","https://openalex.org/W2142863519","https://openalex.org/W2144004675","https://openalex.org/W2146923862","https://openalex.org/W2154290215","https://openalex.org/W2157672296","https://openalex.org/W2159535674","https://openalex.org/W2161531038","https://openalex.org/W2166957790","https://openalex.org/W2169716076","https://openalex.org/W2179025976","https://openalex.org/W2240200916","https://openalex.org/W2732984990","https://openalex.org/W2752853835","https://openalex.org/W2761924357","https://openalex.org/W3029006342","https://openalex.org/W3198160809","https://openalex.org/W4237773356","https://openalex.org/W4241373120","https://openalex.org/W4245047333","https://openalex.org/W4246140522"],"related_works":["https://openalex.org/W4300498183","https://openalex.org/W2944491272","https://openalex.org/W2656095712","https://openalex.org/W2577600644","https://openalex.org/W2321282558","https://openalex.org/W2299507895","https://openalex.org/W2012392278","https://openalex.org/W1900540279","https://openalex.org/W1866724006","https://openalex.org/W1555245969"],"abstract_inverted_index":{"We":[0,39],"describe":[1],"a":[2,27,36],"cell":[3],"processor":[4],"implementation":[5,23],"of":[6,16,29],"Pollard's":[7],"rho":[8],"method":[9],"to":[10,34],"solve":[11],"discrete":[12],"logarithms":[13],"in":[14,41],"groups":[15],"elliptic":[17],"curves":[18],"over":[19],"prime":[20],"fields.":[21],"The":[22],"was":[24],"used":[25],"on":[26],"cluster":[28],"PlayStation":[30],"3":[31],"game":[32],"consoles":[33],"set":[35],"new":[37],"record.":[38],"present":[40],"detail":[42],"the":[43],"underlying":[44],"single":[45],"instruction":[46],"multiple":[47],"data":[48],"modular":[49],"arithmetic.":[50]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2012770528","counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":8}],"updated_date":"2025-01-19T14:29:05.453428","created_date":"2016-06-24"}