{"id":"https://openalex.org/W3179241074","doi":"https://doi.org/10.3934/amc.2021025","title":"Four by four MDS matrices with the fewest XOR gates based on words","display_name":"Four by four MDS matrices with the fewest XOR gates based on words","publication_year":2021,"publication_date":"2021-07-09","ids":{"openalex":"https://openalex.org/W3179241074","doi":"https://doi.org/10.3934/amc.2021025","mag":"3179241074"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2021025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021025","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2021025","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101446311","display_name":"Shi Wang","orcid":"https://orcid.org/0000-0002-9719-2154"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100462231","display_name":"Yongqiang Li","orcid":"https://orcid.org/0000-0002-2551-2737"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yongqiang Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071722719","display_name":"Shizhu Tian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shizhu Tian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029996403","display_name":"Xiangyong Zeng","orcid":"https://orcid.org/0000-0002-8351-8766"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiangyong Zeng","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":0.6824,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.75093128,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"17","issue":"4","first_page":"845","last_page":"872"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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":0.9984999895095825,"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/mathematics","display_name":"Mathematics","score":0.7857486605644226},{"id":"https://openalex.org/keywords/xor-gate","display_name":"XOR gate","score":0.7741893529891968},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5145953893661499},{"id":"https://openalex.org/keywords/block-cipher","display_name":"Block cipher","score":0.4864189624786377},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4780234098434448},{"id":"https://openalex.org/keywords/bitwise-operation","display_name":"Bitwise operation","score":0.4671584665775299},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.45955216884613037},{"id":"https://openalex.org/keywords/stream-cipher","display_name":"Stream cipher","score":0.4553324580192566},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4386644959449768},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.393251895904541},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.32402920722961426},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2749289274215698},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16890016198158264},{"id":"https://openalex.org/keywords/logic-gate","display_name":"Logic gate","score":0.16396993398666382}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7857486605644226},{"id":"https://openalex.org/C28495749","wikidata":"https://www.wikidata.org/wiki/Q155516","display_name":"XOR gate","level":3,"score":0.7741893529891968},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5145953893661499},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.4864189624786377},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4780234098434448},{"id":"https://openalex.org/C134765980","wikidata":"https://www.wikidata.org/wiki/Q879126","display_name":"Bitwise operation","level":2,"score":0.4671584665775299},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.45955216884613037},{"id":"https://openalex.org/C92950451","wikidata":"https://www.wikidata.org/wiki/Q864718","display_name":"Stream cipher","level":3,"score":0.4553324580192566},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4386644959449768},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.393251895904541},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.32402920722961426},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2749289274215698},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16890016198158264},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.16396993398666382},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2021025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021025","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2021025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021025","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W35428663","https://openalex.org/W98521887","https://openalex.org/W1572300106","https://openalex.org/W1599175145","https://openalex.org/W1894646615","https://openalex.org/W1944544385","https://openalex.org/W2003858108","https://openalex.org/W2141124495","https://openalex.org/W2242540160","https://openalex.org/W2281317404","https://openalex.org/W2293947265","https://openalex.org/W2500084106","https://openalex.org/W2503098516","https://openalex.org/W2505213174","https://openalex.org/W2572813892","https://openalex.org/W2579400469","https://openalex.org/W2594061018","https://openalex.org/W2605101120","https://openalex.org/W2757403014","https://openalex.org/W2782477046","https://openalex.org/W2794903372","https://openalex.org/W2801742862","https://openalex.org/W2919480248","https://openalex.org/W2964867699","https://openalex.org/W2995132763","https://openalex.org/W3046498207"],"related_works":["https://openalex.org/W2362925226","https://openalex.org/W2903451324","https://openalex.org/W2504096904","https://openalex.org/W1598002630","https://openalex.org/W24612159","https://openalex.org/W2893407266","https://openalex.org/W1981170240","https://openalex.org/W4206055950","https://openalex.org/W118865363","https://openalex.org/W3029663907"],"abstract_inverted_index":{"MDS":[0,14,38,62,117,140,197],"matrices":[1,15,39,63,118,141],"play":[2],"an":[3,34],"important":[4],"role":[5],"in":[6,45],"the":[7,85,94,180,184],"design":[8],"of":[9,21,108,112,183],"block":[10],"ciphers,":[11],"and":[12,31,57,75,114,123,176],"constructing":[13],"with":[16,68,119,142],"fewer":[17],"xor":[18,73,79,127,151,186],"gates":[19,74,80,152],"is":[20,203],"significant":[22],"interest":[23],"for":[24,191],"lightweight":[25],"ciphers.":[26],"For":[27],"this":[28],"topic,":[29],"Duval":[30],"Leurent":[32],"proposed":[33],"approach":[35],"to":[36,90,172],"construct":[37],"by":[40],"using":[41],"three":[42,102,106],"linear":[43,103,110,174,201],"operations":[44,104,111],"ToSC":[46],"2018.":[47],"Taking":[48],"words":[49,190],"as":[50,97,105],"elements,":[51],"they":[52],"found":[53],"$":[54,56,58,61,65,67,70,72,76,78,120,122,124,126,132,134,136,138,144,146,148,150,154,156,192,196,204],"16\\times16":[55,133],"32\\times":[59],"32":[60],"over":[64,153,199],"\\mathbb{F}_2":[66,155],"only":[69,143],"35":[71,121],"67":[77,125],"respectively,":[81],"which":[82,160],"are":[83,157,161],"also":[84,158],"best":[86],"known":[87],"implementations":[88],"up":[89],"now.":[91],"Based":[92],"on":[93,189],"same":[95],"observation":[96],"their":[98],"work,":[99],"we":[100,177],"consider":[101],"kinds":[107],"elementary":[109],"matrices,":[113],"obtain":[115],"more":[116],"gates.":[128],"In":[129],"addition,":[130],"some":[131],"or":[135,147],"32\\times32":[137],"involutory":[139],"36":[145],"72":[149],"proposed,":[159],"better":[162],"than":[163],"previous":[164],"results.":[165],"Moreover,":[166],"our":[167],"method":[168],"can":[169],"be":[170],"extended":[171],"general":[173,200],"groups,":[175],"prove":[178],"that":[179],"lower":[181],"bound":[182],"sequential":[185],"count":[187],"based":[188],"4":[193,195],"\\times":[194],"matrix":[198],"groups":[202],"8n+2":[205],"$.":[206]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
