{"id":"https://openalex.org/W2042985742","doi":"https://doi.org/10.1137/s0895480199366251","title":"Nonlinearity of Boolean Functions and Hyperelliptic Curves","display_name":"Nonlinearity of Boolean Functions and Hyperelliptic Curves","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2042985742","doi":"https://doi.org/10.1137/s0895480199366251","mag":"2042985742"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480199366251","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480199366251","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5044011121","display_name":"Jung Hee Cheon","orcid":"https://orcid.org/0000-0002-7085-2220"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jung Hee Cheon.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073685419","display_name":"Shiaw Phin Chee","orcid":"https://orcid.org/0000-0003-4382-4870"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Seongtaek Chee","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4645,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.74225219,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"3","first_page":"354","last_page":"365"},"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":0.9977999925613403,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.8443746566772461},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.7385026216506958},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7170403003692627},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6486215591430664},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.583942174911499},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5476254224777222},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5268955230712891},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.47377490997314453},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2703908383846283},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19379469752311707}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8443746566772461},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7385026216506958},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7170403003692627},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6486215591430664},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.583942174911499},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5476254224777222},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5268955230712891},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.47377490997314453},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2703908383846283},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19379469752311707},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480199366251","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480199366251","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W21535682","https://openalex.org/W1486898453","https://openalex.org/W1528065150","https://openalex.org/W1531334709","https://openalex.org/W1565237252","https://openalex.org/W1569612250","https://openalex.org/W1588408025","https://openalex.org/W1597815045","https://openalex.org/W1606480398","https://openalex.org/W1776788878","https://openalex.org/W1964723977","https://openalex.org/W2065871941","https://openalex.org/W2128718974","https://openalex.org/W2138238405","https://openalex.org/W3151140615","https://openalex.org/W4253892719"],"related_works":["https://openalex.org/W2075328823","https://openalex.org/W3129818589","https://openalex.org/W2384505037","https://openalex.org/W2212615093","https://openalex.org/W2999312112","https://openalex.org/W2346253477","https://openalex.org/W1909384579","https://openalex.org/W3155691820","https://openalex.org/W2952185983","https://openalex.org/W1604438253"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,27,44,59,76],"novel":[3],"relationship":[4],"between":[5],"the":[6,14,19,31,48,80],"nonlinearity":[7,32,49,81],"of":[8,16,18,53],"rational":[9,34,65],"functions":[10,35,66],"over":[11,36,68],"$\\mathbb{F}_{2^n}$":[12],"and":[13],"number":[15],"points":[17],"associated":[20],"hyperelliptic":[21],"curve.":[22],"Using":[23],"this,":[24],"we":[25,74],"obtain":[26],"lower":[28,45,77],"bound":[29,46,61,78],"on":[30,47,79],"for":[33,51,82],"$\\mathbb{F}_{2^n}$.":[37,69],"Compared":[38],"to":[39,63],"previous":[40],"work":[41],"that":[42],"provides":[43],"only":[50],"monomials":[52],"special":[54],"types,":[55],"our":[56],"result":[57],"gives":[58],"general":[60],"applicable":[62],"all":[64],"defined":[67],"By":[70],"applying":[71],"this":[72],"result,":[73],"get":[75],"various":[83],"n":[84],"\u00d7":[85],"kn":[86],"S-boxes.":[87]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}