{"id":"https://openalex.org/W4383816887","doi":"https://doi.org/10.1007/s12095-023-00651-5","title":"An infinite family of 0-APN monomials with two parameters","display_name":"An infinite family of 0-APN monomials with two parameters","publication_year":2023,"publication_date":"2023-07-10","ids":{"openalex":"https://openalex.org/W4383816887","doi":"https://doi.org/10.1007/s12095-023-00651-5"},"language":"en","primary_location":{"id":"doi:10.1007/s12095-023-00651-5","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s12095-023-00651-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-023-00651-5.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","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":"Cryptography and Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s12095-023-00651-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007946957","display_name":"Nikolay Kaleyski","orcid":"https://orcid.org/0000-0002-9695-1454"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Nikolay Kaleyski","raw_affiliation_strings":["Department of Informatics, University of Bergen, 5020, Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, 5020, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016236384","display_name":"Kjetil Nesheim","orcid":null},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Kjetil Nesheim","raw_affiliation_strings":["Department of Informatics, University of Bergen, 5020, Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, 5020, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021290362","display_name":"Pantelimon St\u0103nic\u0103","orcid":"https://orcid.org/0000-0002-8622-7120"},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pantelimon St\u0103nic\u0103","raw_affiliation_strings":["Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, 93943-5212, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, 93943-5212, USA","institution_ids":["https://openalex.org/I35364215"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007946957"],"corresponding_institution_ids":["https://openalex.org/I4432739"],"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":0,"citation_normalized_percentile":{"value":0.07126374,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"6","first_page":"1139","last_page":"1169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9934999942779541,"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"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5465055704116821},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5293835997581482},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5275209546089172},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2978503704071045},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13251826167106628},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0786004364490509}],"concepts":[{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5465055704116821},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5293835997581482},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5275209546089172},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2978503704071045},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13251826167106628},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0786004364490509},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12095-023-00651-5","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s12095-023-00651-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-023-00651-5.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","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":"Cryptography and Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s12095-023-00651-5","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s12095-023-00651-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-023-00651-5.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","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":"Cryptography and Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323078","display_name":"Universitetet i Bergen","ror":"https://ror.org/03zga2b32"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4383816887.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1493063799","https://openalex.org/W1528065150","https://openalex.org/W1531334709","https://openalex.org/W1554932142","https://openalex.org/W1571322537","https://openalex.org/W1587687098","https://openalex.org/W1629301835","https://openalex.org/W1976677460","https://openalex.org/W2015894712","https://openalex.org/W2024483577","https://openalex.org/W2080593599","https://openalex.org/W2087896741","https://openalex.org/W2123531143","https://openalex.org/W2153676672","https://openalex.org/W2594294946","https://openalex.org/W2947669364","https://openalex.org/W3007668722","https://openalex.org/W3020944523","https://openalex.org/W3091945005","https://openalex.org/W3210873239","https://openalex.org/W4205482204","https://openalex.org/W4210841065"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2467119940","https://openalex.org/W3194077685","https://openalex.org/W2152758797","https://openalex.org/W2382762871","https://openalex.org/W2544423928","https://openalex.org/W2950599922","https://openalex.org/W2062219402","https://openalex.org/W4286787881"],"abstract_inverted_index":{"Abstract":[0],"We":[1,93,128,158,200,260],"consider":[2],"an":[3,63],"infinite":[4,64],"family":[5],"of":[6,58,66,106,156,205,215,273],"exponents":[7,109],"e":[8,26,116,134,161,194,206],"(":[9,27,117,135,162,195,207],"l":[10,17,28,59,118,124,136,163,196,208,216],",":[11,20,29,62,119,137,164,197,209,244],"k":[12,19,30,61,120,126,138,165,198,210,218],")":[13,31,121,139,166,211],"with":[14],"two":[15],"parameters,":[16],"and":[18,21,60,98,125,153,181,217,245],"derive":[22],"sufficient":[23],"conditions":[24,50],"for":[25,55,122,212,232],"to":[32,53,144,193,249],"be":[33,111,141,254],"0-APN":[34,86],"over":[35,219],"$${\\mathbb":[36,220],"F}_{2^n}$$":[37,221],"<mml:math":[38,71,222,236],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[39,72,223,237],"<mml:msub>":[40,224],"<mml:mi>F</mml:mi>":[41,225],"<mml:msup>":[42,73,226],"<mml:mn>2</mml:mn>":[43,227],"<mml:mi>n</mml:mi>":[44,228,239],"</mml:msup>":[45,83,229],"</mml:msub>":[46,230],"</mml:math>":[47,84,231,243],".":[48,127],"These":[49],"allow":[51],"us":[52],"generate,":[54],"each":[56],"choice":[57],"list":[65],"dimensions":[67],"n":[68],"where":[69],"$$x^{e(l,k)}$$":[70],"<mml:mi>x</mml:mi>":[74],"<mml:mrow>":[75,238],"<mml:mi>e</mml:mi>":[76],"<mml:mo>(</mml:mo>":[77],"<mml:mi>l</mml:mi>":[78],"<mml:mo>,</mml:mo>":[79],"<mml:mi>k</mml:mi>":[80],"<mml:mo>)</mml:mo>":[81],"</mml:mrow>":[82,242],"is":[85,190],"much":[87],"more":[88],"efficiently":[89],"than":[90],"in":[91,113,132,169],"general.":[92],"observe":[94],"that":[95,186,262],"the":[96,104,107,114,148,170,175,187,203,247,269,274],"Gold":[97,108],"Inverse":[99,154],"exponents,":[100],"as":[101,103,174],"well":[102],"inverses":[105],"can":[110,140,167,253],"expressed":[112],"form":[115],"suitable":[123],"characterize":[129,159],"all":[130],"cases":[131],"which":[133,250],"cyclotomic":[142,172],"equivalent":[143,192],"a":[145],"representative":[146],"from":[147],"Gold,":[149],"Kasami,":[150],"Welch,":[151],"Niho,":[152],"families":[155],"exponents.":[157],"when":[160],"lie":[168],"same":[171],"coset":[173],"Dobbertin":[176,188],"exponent":[177],"(without":[178],"considering":[179],"inverses)":[180],"provide":[182],"computational":[183],"data":[184],"showing":[185],"inverse":[189],"never":[191],").":[199],"computationally":[201],"test":[202],"APN-ness":[204],"small":[213],"values":[214],"$$n":[233],"\\le":[234],"100$$":[235],"<mml:mo>\u2264</mml:mo>":[240],"<mml:mn>100</mml:mn>":[241],"sketch":[246],"limits":[248],"such":[251],"tests":[252],"performed":[255],"using":[256],"currently":[257],"available":[258],"technology.":[259],"conclude":[261],"there":[263],"are":[264],"no":[265],"APN":[266],"monomials":[267],"among":[268],"tested":[270],"functions,":[271],"outside":[272],"known":[275],"classes.":[276]},"counts_by_year":[],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}