{"id":"https://openalex.org/W7225769693","doi":"https://doi.org/10.23939/csn2026.02.303","title":"UPPER BOUND ON THE COMPLEXITY OF A BITSLICED REPRESENTATION OF BIJECTIVE 4-BIT S-BOXES IN A TERNARY LOGIC BASIS","display_name":"UPPER BOUND ON THE COMPLEXITY OF A BITSLICED REPRESENTATION OF BIJECTIVE 4-BIT S-BOXES IN A TERNARY LOGIC BASIS","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225769693","doi":"https://doi.org/10.23939/csn2026.02.303"},"language":"en","primary_location":{"id":"doi:10.23939/csn2026.02.303","doi":"https://doi.org/10.23939/csn2026.02.303","is_oa":true,"landing_page_url":"https://doi.org/10.23939/csn2026.02.303","pdf_url":null,"source":{"id":"https://openalex.org/S4210238343","display_name":"Komp'\u00fbtern\u00ec sistemi ta mere\u017e\u00ec","issn_l":"2707-2371","issn":["2707-2371"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer systems and network","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.23939/csn2026.02.303","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016964479","display_name":"\u042f\u0440\u043e\u0441\u043b\u0430\u0432 \u0420\u043e\u043c\u0430\u043d\u043e\u0432\u0438\u0447 \u0421\u043e\u0432\u0438\u043d","orcid":"https://orcid.org/0000-0002-5023-8442","observed_orcids":["https://orcid.org/0000-0002-5023-8442"]},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Y. R. Sovyn","raw_affiliation_strings":["Lviv Polytechnic National University"],"raw_orcid":"https://orcid.org/0000-0002-5023-8442","affiliations":[{"raw_affiliation_string":"Lviv Polytechnic National University","institution_ids":["https://openalex.org/I98435010"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022056502","display_name":"Yuriy Nakonechnyy","orcid":"https://orcid.org/0000-0002-6046-6190","observed_orcids":["https://orcid.org/0000-0002-6046-6190"]},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Yu. M. Nakonechnyi","raw_affiliation_strings":["Lviv Polytechnic National University"],"raw_orcid":"https://orcid.org/0000-0002-6046-6190","affiliations":[{"raw_affiliation_string":"Lviv Polytechnic National University","institution_ids":["https://openalex.org/I98435010"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I98435010"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"2","first_page":"303","last_page":"314"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9990000128746033,"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":0.9990000128746033,"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":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":9.999999747378752e-05,"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":[],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7459999918937683},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6290000081062317},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.569100022315979},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5321000218391418},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.5164999961853027},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5052000284194946},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5009999871253967},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48890000581741333},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4458000063896179},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4325999915599823},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.35409998893737793},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3538999855518341},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3264999985694885},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.3206999897956848},{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.32019999623298645},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31529998779296875},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.3061000108718872},{"id":"https://openalex.org/C136726353","wikidata":"https://www.wikidata.org/wiki/Q903789","display_name":"Disjunctive normal form","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2955000102519989},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.2549999952316284}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23939/csn2026.02.303","doi":"https://doi.org/10.23939/csn2026.02.303","is_oa":true,"landing_page_url":"https://doi.org/10.23939/csn2026.02.303","pdf_url":null,"source":{"id":"https://openalex.org/S4210238343","display_name":"Komp'\u00fbtern\u00ec sistemi ta mere\u017e\u00ec","issn_l":"2707-2371","issn":["2707-2371"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer systems and network","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.23939/csn2026.02.303","doi":"https://doi.org/10.23939/csn2026.02.303","is_oa":true,"landing_page_url":"https://doi.org/10.23939/csn2026.02.303","pdf_url":null,"source":{"id":"https://openalex.org/S4210238343","display_name":"Komp'\u00fbtern\u00ec sistemi ta mere\u017e\u00ec","issn_l":"2707-2371","issn":["2707-2371"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer systems and network","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W194100104","https://openalex.org/W1523982624","https://openalex.org/W2497867845","https://openalex.org/W2499464388","https://openalex.org/W2737356556","https://openalex.org/W2905439514","https://openalex.org/W3089944233","https://openalex.org/W3171788119","https://openalex.org/W4205906257","https://openalex.org/W4240033684","https://openalex.org/W4312121310","https://openalex.org/W4387951849","https://openalex.org/W4387969477","https://openalex.org/W4390102969","https://openalex.org/W4405242230","https://openalex.org/W4413977839"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,56,60,66,70,91,104,113,125,155,186],"logical":[4,67,210],"complexity":[5,68,114,188,204],"of":[6,9,18,26,39,45,59,69,73,94,103,107,110,115,132,161,172,206],"bitsliced":[7,71,193],"representations":[8],"4-bit":[10,76],"bijective":[11,75,122],"S-boxes":[12,111,176,207],"\u2013":[13],"a":[14,49,86,138,145,170],"key":[15],"non-linear":[16],"component":[17],"lightweight":[19,175],"block":[20],"ciphers":[21],"used":[22,174],"to":[23,153,169,203],"secure":[24],"Internet":[25],"Things":[27],"devices":[28],"and":[29,119,182,191],"embedded":[30],"systems.":[31],"We":[32,63,135],"consider":[33],"ternary":[34,82,159],"logic":[35],"instructions,":[36,83],"operations":[37],"capable":[38],"computing":[40],"an":[41,101],"arbitrary":[42],"Boolean":[43],"function":[44],"three":[46],"variables":[47],"in":[48,54,208],"single":[50],"call,":[51],"hardware-supported":[52],"by,":[53],"particular,":[55],"vpternlogd":[57],"instruction":[58],"AVX-512":[61],"extension.":[62],"demonstrate":[64],"that":[65,150],"description":[72],"any":[74,162],"S-box":[77],"does":[78],"not":[79],"exceed":[80],"eight":[81],"thereby":[84],"establishing":[85],"guaranteed":[87,152],"upper":[88],"bound":[89],"for":[90,184],"entire":[92],"class":[93,109],"such":[95],"transformations.":[96],"The":[97,165,197],"proof":[98],"relies":[99],"on":[100,144],"analysis":[102],"structural":[105],"properties":[106],"this":[108],"through":[112],"individual":[116],"16-bit":[117],"vectors":[118],"their":[120],"mutually":[121],"pairs,":[123],"with":[124],"most":[126],"complex":[127],"cases":[128],"verified":[129],"by":[130],"means":[131],"GPU-accelerated":[133],"computation.":[134],"further":[136],"develop":[137],"computationally":[139],"efficient":[140],"software":[141],"tool,":[142],"based":[143],"decomposition-based":[146],"exhaustive":[147],"search":[148],"scheme,":[149],"is":[151,167,189],"find":[154],"optimal":[156],"(provably":[157],"minimal)":[158],"representation":[160],"given":[163],"S-box.":[164],"method":[166],"applied":[168],"number":[171],"widely":[173],"(Piccolo,":[177],"Present,":[178],"GIFT,":[179],"KLEIN,":[180],"MIBS,":[181],"others),":[183],"which":[185],"minimal":[187],"established":[190],"explicit":[192],"descriptions":[194],"are":[195],"provided.":[196],"proposed":[198],"approach":[199],"can":[200],"be":[201],"extended":[202],"evaluation":[205],"other":[209],"bases":[211],"as":[212],"well.":[213]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}