{"id":"https://openalex.org/W2172160110","doi":"https://doi.org/10.1109/icmlc.2011.6016898","title":"On cryptography properties of algebraic thickness","display_name":"On cryptography properties of algebraic thickness","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W2172160110","doi":"https://doi.org/10.1109/icmlc.2011.6016898","mag":"2172160110"},"language":"en","primary_location":{"id":"doi:10.1109/icmlc.2011.6016898","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icmlc.2011.6016898","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 International Conference on Machine Learning and Cybernetics","raw_type":"proceedings-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/A5041316526","display_name":"Yu Zhou","orcid":"https://orcid.org/0000-0003-1777-9439"},"institutions":[{"id":"https://openalex.org/I4210139481","display_name":"Science and Technology Department of Sichuan Province","ror":"https://ror.org/04323m874","country_code":"CN","type":"funder","lineage":["https://openalex.org/I4210139481"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu Zhou","raw_affiliation_strings":["Science and Technology on Communication Security Laboratory, Chengdu, Sichuan, China"],"affiliations":[{"raw_affiliation_string":"Science and Technology on Communication Security Laboratory, Chengdu, Sichuan, China","institution_ids":["https://openalex.org/I4210139481"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101542456","display_name":"Xianguo Zhang","orcid":"https://orcid.org/0009-0004-9487-3693"},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xian-Guo Zhang","raw_affiliation_strings":["North China Institute of Computing Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"North China Institute of Computing Technology, Beijing, China","institution_ids":["https://openalex.org/I4210090176"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013404222","display_name":"Chuan Lun Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuan_Lun Ren","raw_affiliation_strings":["North China Institute of Computing Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"North China Institute of Computing Technology, Beijing, China","institution_ids":["https://openalex.org/I4210090176"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111994830","display_name":"Xiang Gen Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang_Gen Wang","raw_affiliation_strings":["North China Institute of Computing Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"North China Institute of Computing Technology, Beijing, China","institution_ids":["https://openalex.org/I4210090176"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100405562","display_name":"Jia Jia","orcid":"https://orcid.org/0000-0001-8013-7290"},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia Jia","raw_affiliation_strings":["North China Institute of Computing Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"North China Institute of Computing Technology, Beijing, China","institution_ids":["https://openalex.org/I4210090176"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004921726","display_name":"Yun-Ling Su","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yun-Ling Su","raw_affiliation_strings":["North China Institute of Computing Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"North China Institute of Computing Technology, Beijing, China","institution_ids":["https://openalex.org/I4210090176"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5041316526"],"corresponding_institution_ids":["https://openalex.org/I4210139481"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14375117,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":null,"first_page":"1290","last_page":"1295"},"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":0.9988999962806702,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/boolean-function","display_name":"Boolean function","score":0.7630783319473267},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6687400341033936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6251594424247742},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.576383650302887},{"id":"https://openalex.org/keywords/algebraic-function","display_name":"Algebraic function","score":0.5639539957046509},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.5547317266464233},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.546684980392456},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.5380712151527405},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49430251121520996},{"id":"https://openalex.org/keywords/function-field-of-an-algebraic-variety","display_name":"Function field of an algebraic variety","score":0.489510178565979},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4662194848060608},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.4565713703632355},{"id":"https://openalex.org/keywords/boolean-network","display_name":"Boolean network","score":0.4486824572086334},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.44748103618621826},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.4289737939834595},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2758709788322449},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20153024792671204},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.09132680296897888},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.056844890117645264}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7630783319473267},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6687400341033936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6251594424247742},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.576383650302887},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.5639539957046509},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.5547317266464233},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.546684980392456},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.5380712151527405},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49430251121520996},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.489510178565979},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4662194848060608},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.4565713703632355},{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.4486824572086334},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.44748103618621826},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.4289737939834595},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2758709788322449},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20153024792671204},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.09132680296897888},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.056844890117645264},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icmlc.2011.6016898","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icmlc.2011.6016898","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 International Conference on Machine Learning and Cybernetics","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1552757548","https://openalex.org/W1583499453","https://openalex.org/W1587697857","https://openalex.org/W1606480398","https://openalex.org/W1966164580","https://openalex.org/W2010368681","https://openalex.org/W2024900297","https://openalex.org/W2065465262","https://openalex.org/W2069465266","https://openalex.org/W2121925267","https://openalex.org/W2356791622"],"related_works":["https://openalex.org/W1499231756","https://openalex.org/W98542587","https://openalex.org/W47695625","https://openalex.org/W2030362615","https://openalex.org/W2150272262","https://openalex.org/W4256012180","https://openalex.org/W2382077753","https://openalex.org/W2093517305","https://openalex.org/W2356791622","https://openalex.org/W2372501073"],"abstract_inverted_index":{"Algebraic":[0],"thickness":[1,18,46,62,87],"is":[2],"an":[3],"important":[4],"property":[5],"of":[6,19,34,44,63,88],"Boolean":[7,20,36,48,52,64,73,90],"functions.":[8,37,91],"In":[9],"this":[10,55],"paper":[11],"we":[12,39,78],"give":[13],"the":[14,41,57],"relationship":[15,43],"between":[16,47],"algebraic":[17,27,32,45,61,86],"functions":[21,65,74],"with":[22,66],"disjoint":[23],"variables":[24],"and":[25,29,50,70],"their":[26,71],"thickness,":[28],"derive":[30],"some":[31,80],"thicknesses":[33],"special":[35],"Furthermore,":[38],"prove":[40],"restrictive":[42],"function":[49],"complement":[51,72],"function,":[53],"by":[54],"result":[56],"upper":[58,83],"bounds":[59,84],"on":[60,85],"small":[67],"hamming":[68],"weights":[69],"are":[75],"given.":[76],"Finally,":[77],"summarize":[79],"lower":[81],"or":[82],"common":[89]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}