{"id":"https://openalex.org/W1597125077","doi":"https://doi.org/10.1007/978-3-642-10838-9_18","title":"Quadratic Equations from a Kind of S-boxes","display_name":"Quadratic Equations from a Kind of S-boxes","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1597125077","doi":"https://doi.org/10.1007/978-3-642-10838-9_18","mag":"1597125077"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-10838-9_18","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-10838-9_18","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5113963319","display_name":"Jia Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia Xie","raw_affiliation_strings":["The state key laboratory of information securtity, Graduate School of Chinese Academy of Sciences,","The state key laboratory of information securtity, Institute of software, Chinese Academy of Science, Beijing, 100790, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The state key laboratory of information securtity, Graduate School of Chinese Academy of Sciences,","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"The state key laboratory of information securtity, Institute of software, Chinese Academy of Science, Beijing, 100790, China","institution_ids":["https://openalex.org/I4210128818"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101985834","display_name":"Weiwei Cao","orcid":"https://orcid.org/0000-0002-8991-9915"},"institutions":[{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiwei Cao","raw_affiliation_strings":["The state key laboratory of information securtity, Graduate School of Chinese Academy of Sciences,","The state key laboratory of information securtity, Institute of software, Chinese Academy of Science, Beijing, 100790, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The state key laboratory of information securtity, Graduate School of Chinese Academy of Sciences,","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"The state key laboratory of information securtity, Institute of software, Chinese Academy of Science, Beijing, 100790, China","institution_ids":["https://openalex.org/I4210128818"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103281554","display_name":"Tianze Wang","orcid":"https://orcid.org/0000-0003-2717-3596"},"institutions":[{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"TianZe Wang","raw_affiliation_strings":["The state key laboratory of information securtity, Graduate School of Chinese Academy of Sciences,","The state key laboratory of information securtity, Institute of software, Chinese Academy of Science, Beijing, 100790, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The state key laboratory of information securtity, Graduate School of Chinese Academy of Sciences,","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"The state key laboratory of information securtity, Institute of software, Chinese Academy of Science, Beijing, 100790, China","institution_ids":["https://openalex.org/I4210128818"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"239","last_page":"253"},"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":0.9998999834060669,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/s-box","display_name":"S-box","score":0.6596248745918274},{"id":"https://openalex.org/keywords/block-cipher","display_name":"Block cipher","score":0.6585336923599243},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6536386013031006},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6348088979721069},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5594585537910461},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4717232584953308},{"id":"https://openalex.org/keywords/block-size","display_name":"Block size","score":0.44448351860046387},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.44382381439208984},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4239479899406433},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.41847318410873413},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.41290995478630066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3819536864757538},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3726697266101837},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3566976487636566},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3215912878513336},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.29192835092544556},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28957608342170715},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18212971091270447},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15060874819755554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11424842476844788},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.08709505200386047},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0614071786403656}],"concepts":[{"id":"https://openalex.org/C45737032","wikidata":"https://www.wikidata.org/wiki/Q748364","display_name":"S-box","level":4,"score":0.6596248745918274},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.6585336923599243},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6536386013031006},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6348088979721069},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5594585537910461},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4717232584953308},{"id":"https://openalex.org/C41431624","wikidata":"https://www.wikidata.org/wiki/Q1053357","display_name":"Block size","level":3,"score":0.44448351860046387},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.44382381439208984},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4239479899406433},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.41847318410873413},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.41290995478630066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3819536864757538},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3726697266101837},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3566976487636566},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3215912878513336},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.29192835092544556},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28957608342170715},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18212971091270447},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15060874819755554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11424842476844788},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.08709505200386047},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0614071786403656},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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:10.1007/978-3-642-10838-9_18","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-10838-9_18","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1699105","https://openalex.org/W75090305","https://openalex.org/W123374790","https://openalex.org/W183907894","https://openalex.org/W1506034437","https://openalex.org/W1519490952","https://openalex.org/W1542020576","https://openalex.org/W1569612250","https://openalex.org/W1849095083","https://openalex.org/W1918243660","https://openalex.org/W2029031418","https://openalex.org/W2087896741","https://openalex.org/W2109394932","https://openalex.org/W2485957127","https://openalex.org/W2495889793","https://openalex.org/W2502627125","https://openalex.org/W2619633776","https://openalex.org/W4236509984"],"related_works":["https://openalex.org/W1985115047","https://openalex.org/W2986543571","https://openalex.org/W2534971686","https://openalex.org/W2919954404","https://openalex.org/W2955579865","https://openalex.org/W2387168119","https://openalex.org/W377307689","https://openalex.org/W2321159322","https://openalex.org/W2090210875","https://openalex.org/W4296872954"],"abstract_inverted_index":null,"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
