{"id":"https://openalex.org/W2134044008","doi":"https://doi.org/10.1007/s10623-016-0277-5","title":"Higher order differentiation over finite fields with applications to generalising the cube attack","display_name":"Higher order differentiation over finite fields with applications to generalising the cube attack","publication_year":2016,"publication_date":"2016-09-21","ids":{"openalex":"https://openalex.org/W2134044008","doi":"https://doi.org/10.1007/s10623-016-0277-5","mag":"2134044008"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-016-0277-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-016-0277-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10623-016-0277-5.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs10623-016-0277-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052214880","display_name":"Ana S\u0103l\u0103gean","orcid":"https://orcid.org/0000-0002-8942-375X"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Ana S\u0103l\u0103gean","raw_affiliation_strings":["Department of Computer Science, Loughborough University, Loughborough, UK","Loughborough University ,"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Loughborough University, Loughborough, UK","institution_ids":["https://openalex.org/I143804889"]},{"raw_affiliation_string":"Loughborough University ,","institution_ids":["https://openalex.org/I143804889"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017072746","display_name":"Richard Winter","orcid":"https://orcid.org/0000-0002-2897-3256"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"R. Winter","raw_affiliation_strings":["Department of Computer Science, Loughborough University, Loughborough, UK","Loughborough University ,"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Loughborough University, Loughborough, UK","institution_ids":["https://openalex.org/I143804889"]},{"raw_affiliation_string":"Loughborough University ,","institution_ids":["https://openalex.org/I143804889"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052143778","display_name":"Matei Mandache-S\u0103l\u0103gean","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matei Mandache-S\u0103l\u0103gean","raw_affiliation_strings":["Trinity College, University of Cambridge, Cambridge, UK","University of Cambridge,"],"affiliations":[{"raw_affiliation_string":"Trinity College, University of Cambridge, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"University of Cambridge,","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066166428","display_name":"Rapha\u00ebl C.\u2010W. Phan","orcid":"https://orcid.org/0000-0001-7448-4595"},"institutions":[{"id":"https://openalex.org/I173029219","display_name":"Multimedia University","ror":"https://ror.org/04zrbnc33","country_code":"MY","type":"education","lineage":["https://openalex.org/I173029219"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Raphael C.-W. Phan","raw_affiliation_strings":["Faculty of Engineering, Multimedia University, Cyberjaya, Malaysia","Multimedia University"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Multimedia University, Cyberjaya, Malaysia","institution_ids":["https://openalex.org/I173029219"]},{"raw_affiliation_string":"Multimedia University","institution_ids":["https://openalex.org/I173029219"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5052214880"],"corresponding_institution_ids":["https://openalex.org/I143804889"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.00221855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"84","issue":"3","first_page":"425","last_page":"449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9987999796867371,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9945999979972839,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7943992614746094},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.7281497120857239},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6360529065132141},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6113783121109009},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6080780029296875},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5728740096092224},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5143340826034546},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48191359639167786},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48140978813171387},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4632936716079712},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.46213239431381226},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4426150918006897},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4343584179878235},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.36613568663597107},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23283988237380981},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19047769904136658},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07462024688720703}],"concepts":[{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7943992614746094},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.7281497120857239},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6360529065132141},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6113783121109009},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6080780029296875},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5728740096092224},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5143340826034546},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48191359639167786},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48140978813171387},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4632936716079712},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.46213239431381226},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4426150918006897},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4343584179878235},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.36613568663597107},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23283988237380981},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19047769904136658},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07462024688720703},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10623-016-0277-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-016-0277-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10623-016-0277-5.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:shdl.mmu.edu.my:6734","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196753","display_name":"Siti Hasmah Digital Library-MMU Institutiona Repository (Multimedia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I173029219","host_organization_name":"Multimedia University","host_organization_lineage":["https://openalex.org/I173029219"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"pmh:oai:arXiv.org:1410.4095","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1410.4095","pdf_url":"https://arxiv.org/pdf/1410.4095","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.743.8980","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.743.8980","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1410.4095.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.lboro.ac.uk:2134/22851","is_oa":true,"landing_page_url":"https://dspace.lboro.ac.uk/2134/22851","pdf_url":null,"source":{"id":"https://openalex.org/S4306401023","display_name":"Loughborough University Institutional Repository (Loughborough University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I143804889","host_organization_name":"Loughborough University","host_organization_lineage":["https://openalex.org/I143804889"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10623-016-0277-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-016-0277-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10623-016-0277-5.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2134044008.pdf","grobid_xml":"https://content.openalex.org/works/W2134044008.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W37385681","https://openalex.org/W1467319789","https://openalex.org/W1605116544","https://openalex.org/W1606480398","https://openalex.org/W1629301835","https://openalex.org/W1780696059","https://openalex.org/W1857402953","https://openalex.org/W1965754682","https://openalex.org/W1978695162","https://openalex.org/W2052078837","https://openalex.org/W2104120023","https://openalex.org/W2155600383","https://openalex.org/W2158695491","https://openalex.org/W2160494425","https://openalex.org/W2164455525","https://openalex.org/W2181873030","https://openalex.org/W2285305687","https://openalex.org/W2323793830","https://openalex.org/W2396403651","https://openalex.org/W2401625751","https://openalex.org/W2403571297","https://openalex.org/W2913594971","https://openalex.org/W3028939594","https://openalex.org/W4238783710"],"related_works":["https://openalex.org/W2177966018","https://openalex.org/W2964242841","https://openalex.org/W4302423208","https://openalex.org/W1992663735","https://openalex.org/W3087194925","https://openalex.org/W2467357782","https://openalex.org/W3152691454","https://openalex.org/W4288118777","https://openalex.org/W3104344759","https://openalex.org/W4324098889"],"abstract_inverted_index":{"Higher":[0],"order":[1,21],"differentiation":[2,51,151,168],"was":[3],"introduced":[4],"in":[5,16,52,88],"a":[6,64,174],"cryptographic":[7],"context":[8,18],"by":[9,120],"Lai.":[10],"Several":[11],"attacks":[12,185],"can":[13,91,164],"be":[14,92,165,181],"viewed":[15],"the":[17,25,33,40,46,57,73,86,110,138],"of":[19,28,36,39,61,125],"higher":[20,93],"differentiations,":[22],"amongst":[23],"them":[24],"cube":[26,74,112,175,184],"attack":[27,35,75,99,113,176],"Dinur":[29,121],"and":[30,32,67,96,114,122,160],"Shamir":[31],"AIDA":[34],"Vielhaber.":[37],"All":[38],"above":[41],"have":[42],"been":[43],"developed":[44],"for":[45],"binary":[47],"case.":[48],"We":[49],"examine":[50],"larger":[53,116],"fields,":[54],"starting":[55],"with":[56,104,131,157],"field":[58,117],"$$\\mathrm":[59,77,143,155,170,178,187],"{GF}(p)$$":[60,78,144,171,188],"integers":[62],"modulo":[63],"prime":[65],"p,":[66],"apply":[68],"these":[69],"techniques":[70],"to":[71,76,106,133,137,167,183],"generalising":[72],".":[79,189],"The":[80],"crucial":[81],"difference":[82],"is":[83],"that":[84,162],"now":[85],"degree":[87],"each":[89,107,134],"variable":[90,108],"than":[94],"one,":[95],"our":[97],"proposed":[98],"will":[100],"differentiate":[101,127],"several":[102],"times":[103],"respect":[105,132],"(unlike":[109],"classical":[111],"its":[115],"version":[118],"described":[119],"Shamir,":[123],"both":[124],"which":[126],"at":[128],"most":[129],"once":[130],"variable).":[135],"Connections":[136],"Moebius/Reed":[139],"Muller":[140],"Transform":[141],"over":[142,152,169,177,186],"are":[145],"also":[146],"examined.":[147],"Finally":[148],"we":[149],"describe":[150],"finite":[153],"fields":[154],"{GF}(p^s)$$":[156,179],"$$p^s$$":[158],"elements":[159],"show":[161],"it":[163],"reduced":[166],",":[172],"so":[173],"would":[180],"equivalent":[182]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
