{"id":"https://openalex.org/W2138064235","doi":"https://doi.org/10.1109/imcsit.2010.5679687","title":"On the implementation of public keys algorithms based on algebraic graphs over finite commutative rings","display_name":"On the implementation of public keys algorithms based on algebraic graphs over finite commutative rings","publication_year":2010,"publication_date":"2010-10-01","ids":{"openalex":"https://openalex.org/W2138064235","doi":"https://doi.org/10.1109/imcsit.2010.5679687","mag":"2138064235"},"language":"en","primary_location":{"id":"doi:10.1109/imcsit.2010.5679687","is_oa":false,"landing_page_url":"https://doi.org/10.1109/imcsit.2010.5679687","pdf_url":null,"source":{"id":"https://openalex.org/S4210192132","display_name":"Proceedings of the International Multiconference on Computer Science and Information Technology","issn_l":"1896-7094","issn":["1896-7094","2157-5525","2157-5533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the International Multiconference on Computer Science and Information Technology","raw_type":"proceedings-article"},"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/A5041293006","display_name":"Micha\u0142 Klisowski","orcid":"https://orcid.org/0000-0002-2817-8404"},"institutions":[{"id":"https://openalex.org/I174183983","display_name":"Maria Curie-Sk\u0142odowska University","ror":"https://ror.org/015h0qg34","country_code":"PL","type":"education","lineage":["https://openalex.org/I174183983"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Michal Klisowski","raw_affiliation_strings":["Institute of Mathematics, Maria Curie Sk\u013aodowska University, Lublin, Poland","Maria Curie-Sklodowska University, Institute of Mathematics, pl. M. Curie-Sk\u0142odowskiej 1, 20-031 Lublin, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Maria Curie Sk\u013aodowska University, Lublin, Poland","institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Maria Curie-Sklodowska University, Institute of Mathematics, pl. M. Curie-Sk\u0142odowskiej 1, 20-031 Lublin, Poland","institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210137370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062430200","display_name":"Vasyl Ustimenko","orcid":"https://orcid.org/0000-0002-2138-2357"},"institutions":[{"id":"https://openalex.org/I174183983","display_name":"Maria Curie-Sk\u0142odowska University","ror":"https://ror.org/015h0qg34","country_code":"PL","type":"education","lineage":["https://openalex.org/I174183983"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Vasyl Ustimenko","raw_affiliation_strings":["Institute of Mathematics, Maria Curie Sk\u013aodowska University, Lublin, Poland","Maria Curie-Sklodowska University, Institute of Mathematics, pl. M. Curie-Sk\u0142odowskiej 1, 20-031 Lublin, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Maria Curie Sk\u013aodowska University, Lublin, Poland","institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Maria Curie-Sklodowska University, Institute of Mathematics, pl. M. Curie-Sk\u0142odowskiej 1, 20-031 Lublin, Poland","institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4522,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.90615965,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"303","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","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/T11130","display_name":"Coding theory and cryptography","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/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/girth","display_name":"Girth (graph theory)","score":0.6110206842422485},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5907312631607056},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5843941569328308},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5128660202026367},{"id":"https://openalex.org/keywords/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.49829840660095215},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4730754792690277},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4546315371990204},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.43873706459999084},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.3185168504714966},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.30754584074020386},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20855900645256042}],"concepts":[{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.6110206842422485},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5907312631607056},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5843941569328308},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5128660202026367},{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.49829840660095215},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4730754792690277},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4546315371990204},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.43873706459999084},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.3185168504714966},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.30754584074020386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20855900645256042}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/imcsit.2010.5679687","is_oa":false,"landing_page_url":"https://doi.org/10.1109/imcsit.2010.5679687","pdf_url":null,"source":{"id":"https://openalex.org/S4210192132","display_name":"Proceedings of the International Multiconference on Computer Science and Information Technology","issn_l":"1896-7094","issn":["1896-7094","2157-5525","2157-5533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the International Multiconference on Computer Science and Information Technology","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W162015597","https://openalex.org/W1483897861","https://openalex.org/W1510730180","https://openalex.org/W1579329156","https://openalex.org/W1996462091","https://openalex.org/W2063989392","https://openalex.org/W2087806988","https://openalex.org/W2091826091","https://openalex.org/W2403344865","https://openalex.org/W2498463796","https://openalex.org/W2799004609","https://openalex.org/W2947567546","https://openalex.org/W3139951841","https://openalex.org/W4292508377","https://openalex.org/W4387298474","https://openalex.org/W4387301961","https://openalex.org/W6856655358"],"related_works":["https://openalex.org/W2355522437","https://openalex.org/W1428391281","https://openalex.org/W2111868903","https://openalex.org/W4308298797","https://openalex.org/W4281261571","https://openalex.org/W3087272834","https://openalex.org/W4255963200","https://openalex.org/W2280116234","https://openalex.org/W2384360959","https://openalex.org/W2360590989"],"abstract_inverted_index":{"We":[0,51,70,86,107],"will":[1,71],"consider":[2,138],"balanced":[3,117],"directed":[4,34,74,97],"graphs,":[5],"i.e.,":[6],"graphs":[7,118,148],"of":[8,15,19,48,56,62,67,76,83,95,103,112,119,142,147,149,156,168],"binary":[9],"relations,":[10],"for":[11,24,36,125],"which":[12,37],"the":[13,22,38,45,54,57,65,68,88,96,100,110,139,154,157,169],"number":[14,18,61],"inputs":[16],"and":[17,41,152],"outputs":[20],"are":[21],"same":[23,39],"each":[25,126],"vertex.":[26],"The":[27],"commutative":[28,81,105,128],"diagram":[29,82],"is":[30],"formed":[31],"by":[32],"two":[33,134],"paths":[35],"starting":[40],"ending":[42],"points":[43],"form":[44],"full":[46],"list":[47],"common":[49],"vertices.":[50],"refer":[52],"to":[53,116,166],"length":[55,77],"maximal":[58],"path":[59],"(the":[60],"arrows)":[63],"as":[64,79,99],"rank":[66,84,102],"diagram.":[69,106],"count":[72],"a":[73,80],"cycle":[75],"m":[78],"m.":[85],"define":[87],"girth":[89,121,151],"indicator":[90],"gi,":[91],"gi":[92],"\u2265":[93],"2":[94],"graph":[98],"minimal":[101],"its":[104],"observe":[108],"briefly":[109],"applications":[111],"finite":[113,127,163],"automata":[114,164],"related":[115],"high":[120,150],"in":[122],"Cryptography.":[123],"Finally,":[124],"ring":[129],"K":[130,145],"with":[131],"more":[132],"than":[133],"regular":[135],"elements":[136],"we":[137],"explicit":[140],"construction":[141],"algebraic":[143],"over":[144],"family":[146],"discuss":[153],"implementation":[155],"public":[158],"key":[159],"algorithm":[160],"based":[161],"on":[162],"corresponding":[165],"members":[167],"family.":[170]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}