{"id":"https://openalex.org/W4409168994","doi":"https://doi.org/10.3390/cryptography9020021","title":"Compact 8-Bit S-Boxes Based on Multiplication in a Galois Field GF(24)","display_name":"Compact 8-Bit S-Boxes Based on Multiplication in a Galois Field GF(24)","publication_year":2025,"publication_date":"2025-04-03","ids":{"openalex":"https://openalex.org/W4409168994","doi":"https://doi.org/10.3390/cryptography9020021"},"language":"en","primary_location":{"id":"doi:10.3390/cryptography9020021","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography9020021","pdf_url":"https://www.mdpi.com/2410-387X/9/2/21/pdf?version=1743694703","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2410-387X/9/2/21/pdf?version=1743694703","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039121427","display_name":"Phuc-Phan Duong","orcid":"https://orcid.org/0009-0004-4534-9879"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Phuc-Phan Duong","raw_affiliation_strings":["Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan"],"raw_orcid":"https://orcid.org/0009-0004-4534-9879","affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031277423","display_name":"Tuan-Kiet Dang","orcid":"https://orcid.org/0000-0003-2616-2510"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tuan-Kiet Dang","raw_affiliation_strings":["Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan"],"raw_orcid":"https://orcid.org/0000-0003-2616-2510","affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025387024","display_name":"Trong-Thuc Hoang","orcid":"https://orcid.org/0000-0002-4078-0836"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Trong-Thuc Hoang","raw_affiliation_strings":["Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042912660","display_name":"Cong\u2010Kha Pham","orcid":"https://orcid.org/0000-0001-5255-4919"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Cong-Kha Pham","raw_affiliation_strings":["Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan"],"raw_orcid":"https://orcid.org/0000-0001-5255-4919","affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039121427"],"corresponding_institution_ids":["https://openalex.org/I20529979"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1732},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1732},"fwci":6.5473,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.96023583,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"9","issue":"2","first_page":"21","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9987999796867371,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/gf","display_name":"GF(2)","score":0.8673275113105774},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7842525839805603},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.7055661678314209},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6482127904891968},{"id":"https://openalex.org/keywords/bit","display_name":"Bit (key)","score":0.5464566349983215},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.46783602237701416},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.46095114946365356},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4504354000091553},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42414340376853943},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28192099928855896},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11905351281166077},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11140018701553345},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.0694277286529541}],"concepts":[{"id":"https://openalex.org/C156350748","wikidata":"https://www.wikidata.org/wiki/Q5513324","display_name":"GF(2)","level":3,"score":0.8673275113105774},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7842525839805603},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.7055661678314209},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6482127904891968},{"id":"https://openalex.org/C117011727","wikidata":"https://www.wikidata.org/wiki/Q1278488","display_name":"Bit (key)","level":2,"score":0.5464566349983215},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.46783602237701416},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.46095114946365356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4504354000091553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42414340376853943},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28192099928855896},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11905351281166077},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11140018701553345},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0694277286529541}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/cryptography9020021","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography9020021","pdf_url":"https://www.mdpi.com/2410-387X/9/2/21/pdf?version=1743694703","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c333fa97083c470d8e3966b63384716e","is_oa":true,"landing_page_url":"https://doaj.org/article/c333fa97083c470d8e3966b63384716e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cryptography, Vol 9, Iss 2, p 21 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/cryptography9020021","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography9020021","pdf_url":"https://www.mdpi.com/2410-387X/9/2/21/pdf?version=1743694703","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409168994.pdf","grobid_xml":"https://content.openalex.org/works/W4409168994.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W1562542037","https://openalex.org/W1572300106","https://openalex.org/W1629301835","https://openalex.org/W1670558497","https://openalex.org/W1866546768","https://openalex.org/W2010870387","https://openalex.org/W2050685430","https://openalex.org/W2065383271","https://openalex.org/W2149174385","https://openalex.org/W2167720990","https://openalex.org/W2198140127","https://openalex.org/W2474422174","https://openalex.org/W2492167924","https://openalex.org/W2763003773","https://openalex.org/W2890717930","https://openalex.org/W2919954404","https://openalex.org/W2924233255","https://openalex.org/W2946410155","https://openalex.org/W3006740938","https://openalex.org/W3025712646","https://openalex.org/W3026248346","https://openalex.org/W3095289892","https://openalex.org/W3110691795","https://openalex.org/W3157623144","https://openalex.org/W3169066024","https://openalex.org/W3183821273","https://openalex.org/W3202060852","https://openalex.org/W3214450358","https://openalex.org/W4205779884","https://openalex.org/W4221048763","https://openalex.org/W4238134147","https://openalex.org/W4285217105","https://openalex.org/W4288044863","https://openalex.org/W4294577353","https://openalex.org/W4323050291","https://openalex.org/W4360866302","https://openalex.org/W4361799285","https://openalex.org/W4366201389","https://openalex.org/W4376874822","https://openalex.org/W4381798374","https://openalex.org/W4385194751","https://openalex.org/W4387951849","https://openalex.org/W4388513850","https://openalex.org/W4390119871","https://openalex.org/W4390234097","https://openalex.org/W4392397329","https://openalex.org/W4395467106","https://openalex.org/W4396817356","https://openalex.org/W4400973657","https://openalex.org/W6639307586","https://openalex.org/W6723381580","https://openalex.org/W6798804033","https://openalex.org/W6842516807"],"related_works":["https://openalex.org/W1825396486","https://openalex.org/W843373033","https://openalex.org/W2127172196","https://openalex.org/W2587136861","https://openalex.org/W2142116768","https://openalex.org/W1528972180","https://openalex.org/W2039812289","https://openalex.org/W1537813558","https://openalex.org/W172172592","https://openalex.org/W3128023985"],"abstract_inverted_index":{"Substitution":[0],"boxes":[1],"(S-Boxes)":[2],"function":[3],"as":[4,79],"essential":[5],"nonlinear":[6],"elements":[7],"in":[8,32,118],"contemporary":[9],"cryptographic":[10,53,76,154],"systems,":[11],"offering":[12],"robust":[13],"protection":[14],"against":[15],"cryptanalytic":[16],"attacks.":[17],"This":[18],"study":[19,164],"presents":[20],"a":[21,63,147],"novel":[22],"technique":[23],"for":[24,170],"generating":[25],"compact":[26],"8-bit":[27],"S-Boxes":[28,45,61],"based":[29],"on":[30],"multiplication":[31],"the":[33,59,69,80,85,106,121,125,151,163,166,172],"Galois":[34],"Field":[35],"GF(24).":[36],"The":[37],"goal":[38],"of":[39,66,124,128,150,177],"this":[40,144],"method":[41],"is":[42],"to":[43,103],"create":[44],"with":[46],"low":[47],"hardware":[48,112],"implementation":[49,122,160],"cost":[50,123],"while":[51],"ensuring":[52],"properties.":[54],"Experimental":[55],"results":[56],"indicate":[57],"that":[58],"suggested":[60],"achieve":[62],"nonlinearity":[64],"value":[65],"112,":[67],"matching":[68],"AES":[70],"S-Box.":[71],"They":[72],"also":[73],"maintain":[74],"other":[75],"properties,":[77,155],"such":[78],"Bit":[81],"Independence":[82],"Criterion":[83,88],"(BIC),":[84],"Strict":[86],"Avalanche":[87],"(SAC),":[89],"Differential":[90],"Approximation":[91,95],"Probability,":[92,96],"and":[93,140,159,180],"Linear":[94],"within":[97],"acceptable":[98],"security":[99],"thresholds.":[100],"Notably,":[101],"compared":[102],"existing":[104],"studies,":[105],"proposed":[107],"S-Box":[108,126],"architecture":[109],"demonstrates":[110],"enhanced":[111],"efficiency,":[113],"significantly":[114],"reducing":[115],"resource":[116,168],"utilization":[117],"implementations.":[119],"Specifically,":[120],"consists":[127],"31":[129],"XOR":[130],"gates,":[131,135,139],"32":[132],"two-input":[133,137],"AND":[134],"6":[136],"OR":[138],"2":[141],"MUX21s.":[142],"Moreover,":[143],"work":[145],"provides":[146],"thorough":[148],"assessment":[149],"S-Box,":[152,173],"covering":[153],"side":[156],"channel":[157],"attacks,":[158],"aspects.":[161],"Furthermore,":[162],"estimates":[165],"quantum":[167],"requirements":[169],"implementing":[171],"including":[174],"an":[175],"analysis":[176],"CNOT,":[178],"Toffoli,":[179],"NOT":[181],"gate":[182],"counts.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3}],"updated_date":"2026-06-29T08:53:18.405633","created_date":"2025-10-10T00:00:00"}