{"id":"https://openalex.org/W3213688930","doi":"https://doi.org/10.3934/amc.2021068","title":"Rectangular, range, and restricted AONTs: Three generalizations of all-or-nothing transforms","display_name":"Rectangular, range, and restricted AONTs: Three generalizations of all-or-nothing transforms","publication_year":2022,"publication_date":"2022-01-11","ids":{"openalex":"https://openalex.org/W3213688930","doi":"https://doi.org/10.3934/amc.2021068","mag":"3213688930"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2021068","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021068","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2021068","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040870755","display_name":"Navid Nasr Esfahani","orcid":"https://orcid.org/0000-0001-8146-3450"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Navid Nasr Esfahani","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5021938024","display_name":"Douglas R. Stinson","orcid":"https://orcid.org/0000-0001-5635-8122"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Douglas R. Stinson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5021938024"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00629589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"1","first_page":"26","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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":0.9995999932289124,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9973999857902527,"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/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.7599432468414307},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.7081828117370605},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6361619234085083},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5666855573654175},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5642058849334717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5399013161659241},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5301207900047302},{"id":"https://openalex.org/keywords/nothing","display_name":"Nothing","score":0.4792506694793701},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46420344710350037},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41396039724349976},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33481264114379883},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2966037094593048},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.25862962007522583}],"concepts":[{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.7599432468414307},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.7081828117370605},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6361619234085083},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5666855573654175},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5642058849334717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5399013161659241},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5301207900047302},{"id":"https://openalex.org/C136815107","wikidata":"https://www.wikidata.org/wiki/Q154242","display_name":"Nothing","level":2,"score":0.4792506694793701},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46420344710350037},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41396039724349976},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33481264114379883},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2966037094593048},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.25862962007522583},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3934/amc.2021068","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021068","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2111.05961","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.05961","pdf_url":"https://arxiv.org/pdf/2111.05961","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"mag:3213994942","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2111.05961.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"arXiv (Cornell University)","raw_type":null},{"id":"mag:3213688930","is_oa":false,"landing_page_url":"https://eprint.iacr.org/2021/1498.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764847869","display_name":"IACR Cryptology ePrint Archive","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4322614454"],"host_organization_lineage_names":["Cryptology ePrint Archive"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Cryptology ePrint Archive","raw_type":null},{"id":"doi:10.48550/arxiv.2111.05961","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2111.05961","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.3934/amc.2021068","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021068","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2963143529","https://openalex.org/W2963015159","https://openalex.org/W2610262450","https://openalex.org/W2800690885","https://openalex.org/W2475557115","https://openalex.org/W345902015","https://openalex.org/W2136616826","https://openalex.org/W2577266497","https://openalex.org/W2954802327","https://openalex.org/W2963681790","https://openalex.org/W3093581322","https://openalex.org/W2396523442","https://openalex.org/W3030123711","https://openalex.org/W1807095039","https://openalex.org/W1192941359","https://openalex.org/W1530355549","https://openalex.org/W3003979555","https://openalex.org/W2027528470","https://openalex.org/W151964062","https://openalex.org/W2063487992"],"abstract_inverted_index":{"<p":[0,111],"style='text-indent:20px;'>All-or-nothing":[1],"transforms":[2,52],"(AONTs)":[3],"were":[4],"originally":[5],"defined":[6],"by":[7,64,124],"Rivest":[8],"[<xref":[9,131,138],"ref-type=\"bibr\"":[10,132,139],"rid=\"b14\">14</xref>]":[11],"as":[12,229],"bijections":[13],"from":[14],"<inline-formula><tex-math":[15,22,77,90,101,171,183],"id=\"M1\">\\begin{document}$":[16],"s":[17,24],"$\\end{document}</tex-math></inline-formula>":[18,25,93,104],"input":[19,37,94],"blocks":[20,27,95],"to":[21,127,197],"id=\"M2\">\\begin{document}$":[23],"output":[26,44,105,205],"such":[28,228],"that":[29,121],"no":[30,83],"information":[31,69,84],"can":[32,85],"be":[33,86],"obtained":[34,87],"about":[35,88],"any":[36,43,89,100],"block":[38],"in":[39,56,67,81,96,151,188],"the":[40,97,155,162,170,192],"absence":[41,98],"of":[42,50,60,99,119,157,164,179,182,203],"block.":[45],"Numerous":[46],"generalizations":[47,118,144],"and":[48,134,147,210,212,215,237],"extensions":[49],"all-or-nothing":[51],"have":[53,107],"been":[54],"discussed":[55],"recent":[57],"years,":[58],"many":[59],"which":[61,82],"are":[62,122,195],"motivated":[63,123],"diverse":[65],"applications":[66,125],"cryptography,":[68],"security,":[70],"secure":[71],"distributed":[72],"storage,":[73],"etc.":[74],"In":[75],"particular,":[76],"id=\"M3\">\\begin{document}$":[78],"t":[79,92,103,173,185],"$\\end{document}</tex-math></inline-formula>-AONTs,":[80],"id=\"M4\">\\begin{document}$":[91],"id=\"M5\">\\begin{document}$":[102],"blocks,":[106],"received":[108],"considerable":[109],"study.":[110],"style='text-indent:20px;'>In":[112],"this":[113],"paper,":[114],"we":[115],"study":[116,208],"three":[117],"AONTs":[120],"due":[126],"Pham":[128],"et":[129,136],"al.":[130,137],"rid=\"b13\">13</xref>]":[133],"Oliveira":[135],"rid=\"b12\">12</xref>].":[140],"We":[141,207,220],"term":[142],"these":[143,218],"rectangular,":[145],"range,":[146],"restricted":[148,190],"AONTs.":[149],"Briefly,":[150],"a":[152,177,189,200],"rectangular":[153],"AONT,":[154,191],"number":[156,163],"outputs":[158,194],"is":[159],"greater":[160],"than":[161],"inputs.":[165],"A":[166],"range":[167,178],"AONT":[168],"satisfies":[169],"id=\"M6\">\\begin{document}$":[172],"$\\end{document}</tex-math></inline-formula>-AONT":[174],"property":[175],"for":[176,217],"consecutive":[180],"values":[181],"id=\"M7\">\\begin{document}$":[184],"$\\end{document}</tex-math></inline-formula>.":[186],"Finally,":[187],"unknown":[193],"assumed":[196],"occur":[198],"within":[199],"specified":[201],"set":[202],"\"secure\"":[204],"blocks.":[206],"existence":[209],"non-existence":[211],"provide":[213],"examples":[214],"constructions":[216],"generalizations.":[219],"also":[221],"demonstrate":[222],"interesting":[223],"connections":[224],"with":[225],"combinatorial":[226],"structures":[227],"orthogonal":[230,233],"arrays,":[231,234],"split":[232],"MDS":[235],"codes":[236],"difference":[238],"matrices.":[239]},"counts_by_year":[],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2023-03-20T00:00:00"}