{"id":"https://openalex.org/W3217248132","doi":"https://doi.org/10.1007/s11047-022-09885-3","title":"Heuristic search of (semi-)bent functions based on cellular automata","display_name":"Heuristic search of (semi-)bent functions based on cellular automata","publication_year":2022,"publication_date":"2022-05-20","ids":{"openalex":"https://openalex.org/W3217248132","doi":"https://doi.org/10.1007/s11047-022-09885-3","mag":"3217248132"},"language":"en","primary_location":{"id":"doi:10.1007/s11047-022-09885-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-022-09885-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-022-09885-3.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"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":"Natural Computing","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/s11047-022-09885-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069577574","display_name":"Luca Mariot","orcid":"https://orcid.org/0000-0003-3089-6517"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Luca Mariot","raw_affiliation_strings":["Digital Security Group, Radboud University, PO Bus 9010, 6500 GL, Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security Group, Radboud University, PO Bus 9010, 6500 GL, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081081559","display_name":"Martina Saletta","orcid":"https://orcid.org/0000-0001-7250-8987"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Martina Saletta","raw_affiliation_strings":["Dipartimento di Informatica, Sistemistica e Comunicazione, Universit\u00e0 degli Studi di Milano-Bicocca, Viale Sarca 336/14, 20126, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Sistemistica e Comunicazione, Universit\u00e0 degli Studi di Milano-Bicocca, Viale Sarca 336/14, 20126, Milan, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083297323","display_name":"Alberto Leporati","orcid":"https://orcid.org/0000-0002-8105-4371"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Leporati","raw_affiliation_strings":["Dipartimento di Informatica, Sistemistica e Comunicazione, Universit\u00e0 degli Studi di Milano-Bicocca, Viale Sarca 336/14, 20126, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Sistemistica e Comunicazione, Universit\u00e0 degli Studi di Milano-Bicocca, Viale Sarca 336/14, 20126, Milan, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112710019","display_name":"Luca Manzoni","orcid":null},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luca Manzoni","raw_affiliation_strings":["Dipartimento di Matematica e Geoscienze, Universit\u00e0 degli Studi di Trieste, Via Valerio 12/1, 34127, Trieste, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Geoscienze, Universit\u00e0 degli Studi di Trieste, Via Valerio 12/1, 34127, Trieste, Italy","institution_ids":["https://openalex.org/I142444530"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069577574"],"corresponding_institution_ids":["https://openalex.org/I145872427"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.9538,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87376156,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"21","issue":"3","first_page":"377","last_page":"391"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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/T12029","display_name":"DNA and Biological Computing","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.736961305141449},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5720610022544861},{"id":"https://openalex.org/keywords/cellular-automaton","display_name":"Cellular automaton","score":0.5409444570541382},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5253866314888},{"id":"https://openalex.org/keywords/thread","display_name":"Thread (computing)","score":0.5012755393981934},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48999062180519104},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.48286062479019165},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.48272988200187683},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47860878705978394},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.46512413024902344},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4567478895187378},{"id":"https://openalex.org/keywords/bent-molecular-geometry","display_name":"Bent molecular geometry","score":0.45085564255714417},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4292408227920532},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.42225801944732666},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4171319007873535},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29710477590560913},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16159963607788086}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.736961305141449},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5720610022544861},{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.5409444570541382},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5253866314888},{"id":"https://openalex.org/C138101251","wikidata":"https://www.wikidata.org/wiki/Q213092","display_name":"Thread (computing)","level":2,"score":0.5012755393981934},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48999062180519104},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.48286062479019165},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.48272988200187683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47860878705978394},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.46512413024902344},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4567478895187378},{"id":"https://openalex.org/C138211643","wikidata":"https://www.wikidata.org/wiki/Q675211","display_name":"Bent molecular geometry","level":2,"score":0.45085564255714417},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4292408227920532},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.42225801944732666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4171319007873535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29710477590560913},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16159963607788086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s11047-022-09885-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-022-09885-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-022-09885-3.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"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":"Natural Computing","raw_type":"journal-article"},{"id":"pmh:oai:aisberg.unibg.it:10446/265013","is_oa":true,"landing_page_url":"https://hdl.handle.net/10446/265013","pdf_url":null,"source":{"id":"https://openalex.org/S4377196347","display_name":"Aisberg (University of Bergamo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11039511","host_organization_name":"University of Bergamo","host_organization_lineage":["https://openalex.org/I11039511"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arts.units.it:11368/3029202","is_oa":true,"landing_page_url":"http://hdl.handle.net/11368/3029202","pdf_url":null,"source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:boa.unimib.it:10281/408489","is_oa":true,"landing_page_url":"https://hdl.handle.net/10281/408489","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/253690","is_oa":false,"landing_page_url":"https://repository.ubn.ru.nl/handle/2066/253690","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article / Letter to editor"},{"id":"pmh:ru:oai:repository.ubn.ru.nl:2066/253690","is_oa":true,"landing_page_url":"http://hdl.handle.net/2066/253690","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Natural Computing, 21, 377 - 391","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11047-022-09885-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-022-09885-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-022-09885-3.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"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":"Natural Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3217248132.pdf","grobid_xml":"https://content.openalex.org/works/W3217248132.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W115326044","https://openalex.org/W140633939","https://openalex.org/W184356974","https://openalex.org/W601494766","https://openalex.org/W1279378592","https://openalex.org/W1517403092","https://openalex.org/W1527842484","https://openalex.org/W1571837880","https://openalex.org/W1605815326","https://openalex.org/W1981357736","https://openalex.org/W1983388978","https://openalex.org/W2001609288","https://openalex.org/W2004502213","https://openalex.org/W2013276354","https://openalex.org/W2036424138","https://openalex.org/W2050654845","https://openalex.org/W2073904033","https://openalex.org/W2083716409","https://openalex.org/W2090432705","https://openalex.org/W2108704847","https://openalex.org/W2109394932","https://openalex.org/W2117420234","https://openalex.org/W2144769627","https://openalex.org/W2274349130","https://openalex.org/W2293055178","https://openalex.org/W2294833267","https://openalex.org/W2396007476","https://openalex.org/W2397760753","https://openalex.org/W2605945904","https://openalex.org/W2787705702","https://openalex.org/W2804804260","https://openalex.org/W2888423035","https://openalex.org/W2888452529","https://openalex.org/W2888524838","https://openalex.org/W2903744383","https://openalex.org/W2949136830","https://openalex.org/W2949926214","https://openalex.org/W3002948307","https://openalex.org/W3027260415","https://openalex.org/W3093954335","https://openalex.org/W3094723618","https://openalex.org/W3098467670","https://openalex.org/W3135375768","https://openalex.org/W3135749679","https://openalex.org/W3170821075","https://openalex.org/W3198310217","https://openalex.org/W4205482204","https://openalex.org/W4249267162"],"related_works":["https://openalex.org/W1996794584","https://openalex.org/W1977927882","https://openalex.org/W2614614073","https://openalex.org/W1575067221","https://openalex.org/W2808103058","https://openalex.org/W3028718793","https://openalex.org/W2395115528","https://openalex.org/W2503515100","https://openalex.org/W2750816313","https://openalex.org/W2314418525"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"interesting":[2],"thread":[3],"in":[4],"the":[5,16,31,50,63,76,80,89,112,121,139],"research":[6],"of":[7,18,52,65,79,91,123],"Boolean":[8],"functions":[9],"for":[10],"cryptography":[11],"and":[12,67,83,102],"coding":[13],"theory":[14],"is":[15,33],"study":[17],"secondary":[19,54],"constructions":[20],":":[21],"given":[22],"a":[23,27,38,53],"known":[24],"function":[25,41],"with":[26,136],"good":[28],"cryptographic":[29],"profile,":[30],"aim":[32],"to":[34,37,88,116,138],"extend":[35,132],"it":[36],"(usually":[39],"larger)":[40],"possessing":[42],"analogous":[43],"properties.":[44],"In":[45],"this":[46],"work,":[47],"we":[48,84,110],"continue":[49],"investigation":[51],"construction":[55,74,129],"based":[56,97],"on":[57,62,98],"cellular":[58],"automata":[59],"(CA),":[60],"focusing":[61],"classes":[64,125],"bent":[66],"semi-bent":[68],"functions.":[69],"We":[70],"prove":[71],"that":[72,120,126],"our":[73,86,127],"preserves":[75],"algebraic":[77],"degree":[78],"local":[81],"rule,":[82],"narrow":[85],"attention":[87],"subclass":[90],"quadratic":[92],"functions,":[93],"performing":[94],"several":[95],"experiments":[96],"exhaustive":[99],"combinatorial":[100],"search":[101],"heuristic":[103],"optimization":[104],"through":[105],"Evolutionary":[106],"Strategies":[107],"(ES).":[108],"Finally,":[109],"classify":[111],"obtained":[113],"results":[114],"up":[115],"permutation":[117],"equivalence,":[118],"remarking":[119],"number":[122],"equivalence":[124],"CA-XOR":[128],"can":[130],"successfully":[131],"grows":[133],"very":[134],"quickly":[135],"respect":[137],"CA":[140],"diameter.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2021-12-06T00:00:00"}