{"id":"https://openalex.org/W2009514860","doi":"https://doi.org/10.1007/s10623-010-9475-8","title":"On the equivalence of quadratic APN functions","display_name":"On the equivalence of quadratic APN functions","publication_year":2010,"publication_date":"2010-12-29","ids":{"openalex":"https://openalex.org/W2009514860","doi":"https://doi.org/10.1007/s10623-010-9475-8","mag":"2009514860"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-010-9475-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-010-9475-8","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005728627","display_name":"Carl Bracken","orcid":null},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Carl Bracken","raw_affiliation_strings":["School of Mathematical Sciences, University College, Dublin, Ireland","School of Mathematical Sciences, University College, Dublin, Ireland#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University College, Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]},{"raw_affiliation_string":"School of Mathematical Sciences, University College, Dublin, Ireland#TAB#","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025217200","display_name":"Eimear Byrne","orcid":"https://orcid.org/0000-0002-1857-0365"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Eimear Byrne","raw_affiliation_strings":["School of Mathematical Sciences, University College, Dublin, Ireland","School of Mathematical Sciences, University College, Dublin, Ireland#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University College, Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]},{"raw_affiliation_string":"School of Mathematical Sciences, University College, Dublin, Ireland#TAB#","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049086257","display_name":"Gary McGuire","orcid":"https://orcid.org/0000-0003-2105-9792"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Gary McGuire","raw_affiliation_strings":["School of Mathematical Sciences, University College, Dublin, Ireland","School of Mathematical Sciences, University College, Dublin, Ireland#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University College, Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]},{"raw_affiliation_string":"School of Mathematical Sciences, University College, Dublin, Ireland#TAB#","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029375442","display_name":"Gabriele Nebe","orcid":"https://orcid.org/0000-0002-5297-5542"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gabriele Nebe","raw_affiliation_strings":["Lehrstuhl D f\u00fcr Mathematik, RWTH Aachen University, 52056, Aachen, Germany","Lehrstuhl D f\u00fcr Mathematik, RWTH Aachen University, Aachen, Germany 52056#TAB#"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl D f\u00fcr Mathematik, RWTH Aachen University, 52056, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"Lehrstuhl D f\u00fcr Mathematik, RWTH Aachen University, Aachen, Germany 52056#TAB#","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5005728627"],"corresponding_institution_ids":["https://openalex.org/I100930933"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":3.7239,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.93091832,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"61","issue":"3","first_page":"261","last_page":"272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.994700014591217,"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":0.9865000247955322,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.7939952611923218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6811767220497131},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6484556794166565},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.593767523765564},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5926041603088379},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.5282900333404541},{"id":"https://openalex.org/keywords/trinomial","display_name":"Trinomial","score":0.5245409607887268},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.48804771900177},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43201470375061035},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41914913058280945},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.30697667598724365},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0904061496257782}],"concepts":[{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.7939952611923218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6811767220497131},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6484556794166565},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.593767523765564},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5926041603088379},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.5282900333404541},{"id":"https://openalex.org/C6791720","wikidata":"https://www.wikidata.org/wiki/Q1670509","display_name":"Trinomial","level":2,"score":0.5245409607887268},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.48804771900177},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43201470375061035},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41914913058280945},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.30697667598724365},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0904061496257782},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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/s10623-010-9475-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-010-9475-8","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:eprints.maynoothuniversity.ie:2690","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401432","display_name":"Maynooth University ePrints and eTheses Archive (Maynooth University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157286207","host_organization_name":"National University of Ireland, Maynooth","host_organization_lineage":["https://openalex.org/I157286207"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.4221","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.4221","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.rwth-aachen.de/~Gabriele.Nebe/papers/bbmnfinal1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.745.6442","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.745.6442","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/1101.1508.pdf","raw_type":"text"},{"id":"pmh:oai:publications.rwth-aachen.de:195606","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-070974%22","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Designs, codes and cryptography 61(3), 261-272 (2011). doi:10.1007/s10623-010-9475-8","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"},{"id":"https://openalex.org/F4320321056","display_name":"Irish Research Council","ror":"https://ror.org/051xex213"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1528065150","https://openalex.org/W1543877612","https://openalex.org/W1587687098","https://openalex.org/W1603420037","https://openalex.org/W1606480398","https://openalex.org/W1977206724","https://openalex.org/W2163447078"],"related_works":["https://openalex.org/W3028761860","https://openalex.org/W1970042430","https://openalex.org/W2946560706","https://openalex.org/W2028694851","https://openalex.org/W2894743532","https://openalex.org/W4289422580","https://openalex.org/W3001002862","https://openalex.org/W2603026053","https://openalex.org/W2122699041","https://openalex.org/W2360596780"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
