{"id":"https://openalex.org/W2071256459","doi":"https://doi.org/10.1007/s11786-012-0121-x","title":"On the Comparison of Cryptographical Properties of Two Different Families of Graphs with Large Cycle Indicator","display_name":"On the Comparison of Cryptographical Properties of Two Different Families of Graphs with Large Cycle Indicator","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2071256459","doi":"https://doi.org/10.1007/s11786-012-0121-x","mag":"2071256459"},"language":"en","primary_location":{"id":"doi:10.1007/s11786-012-0121-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-012-0121-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-012-0121-x.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11786-012-0121-x.pdf","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/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]},{"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":["CZ","PL"],"is_corresponding":false,"raw_author_name":"Micha\u0142 Klisowski","raw_affiliation_strings":["Maria Curie-Sklodowska University, Institute of Mathematics, pl. M. Curie-Sk\u0142odowskiej 1, 20-031, Lublin, Poland","Maria Curie-Sklodowska University , Institute of Mathematics"],"raw_orcid":null,"affiliations":[{"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"]},{"raw_affiliation_string":"Maria Curie-Sklodowska University , Institute of Mathematics","institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210120266"]}]},{"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/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]},{"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":["CZ","PL"],"is_corresponding":true,"raw_author_name":"Vasyl Ustimenko","raw_affiliation_strings":["Maria Curie-Sklodowska University, Institute of Mathematics, pl. M. Curie-Sk\u0142odowskiej 1, 20-031, Lublin, Poland","Maria Curie-Sklodowska University , Institute of Mathematics"],"raw_orcid":null,"affiliations":[{"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"]},{"raw_affiliation_string":"Maria Curie-Sklodowska University , Institute of Mathematics","institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062430200"],"corresponding_institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210120266","https://openalex.org/I4210137370"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":3.2084,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.92208142,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"6","issue":"2","first_page":"181","last_page":"198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/T11476","display_name":"Graph theory and applications","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9975000023841858,"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":0.7132211923599243},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6885532736778259},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6567147970199585},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5513741374015808},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.5394258499145508},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5166902542114258}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7132211923599243},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6885532736778259},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6567147970199585},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5513741374015808},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.5394258499145508},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5166902542114258},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11786-012-0121-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-012-0121-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-012-0121-x.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11786-012-0121-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-012-0121-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-012-0121-x.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2071256459.pdf","grobid_xml":"https://content.openalex.org/works/W2071256459.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W157601813","https://openalex.org/W158450660","https://openalex.org/W162015597","https://openalex.org/W223331605","https://openalex.org/W1483897861","https://openalex.org/W1495591881","https://openalex.org/W1504871872","https://openalex.org/W1510730180","https://openalex.org/W1560594658","https://openalex.org/W1579329156","https://openalex.org/W1991809067","https://openalex.org/W1996462091","https://openalex.org/W2012280556","https://openalex.org/W2023307326","https://openalex.org/W2038111422","https://openalex.org/W2055888811","https://openalex.org/W2063989392","https://openalex.org/W2087806988","https://openalex.org/W2089513963","https://openalex.org/W2091826091","https://openalex.org/W2138064235","https://openalex.org/W2148726777","https://openalex.org/W2151951054","https://openalex.org/W2158681102","https://openalex.org/W2216961322","https://openalex.org/W2403344865","https://openalex.org/W2498463796","https://openalex.org/W2610547191","https://openalex.org/W2734731986","https://openalex.org/W2778635173","https://openalex.org/W2799004609","https://openalex.org/W2947567546","https://openalex.org/W2948469813","https://openalex.org/W3036237457","https://openalex.org/W4292508377","https://openalex.org/W4387298474","https://openalex.org/W4387301961"],"related_works":["https://openalex.org/W2399505800","https://openalex.org/W333749553","https://openalex.org/W1966623661","https://openalex.org/W2942288111","https://openalex.org/W2951675266","https://openalex.org/W2039516134","https://openalex.org/W1653027350","https://openalex.org/W1509594480","https://openalex.org/W2788737482","https://openalex.org/W2964302506"],"abstract_inverted_index":{"The":[0,108],"paper":[1],"is":[2,32,54,91,117],"devoted":[3],"to":[4],"the":[5,8,24,48,75,78,102,112,118],"implementations":[6],"of":[7,40,57,59,80,94,106,120,123],"public":[9,124],"key":[10],"algorithms":[11],"based":[12,135],"on":[13,136],"simple":[14],"algebraic":[15],"graphs":[16,41,58,96,137],"A(n,":[17,84,128],"K)":[18,21],"and":[19],"D(n,":[20,50,138],"defined":[22],"over":[23],"same":[25],"finite":[26,34],"commutative":[27],"ring":[28],"K.":[29],"If":[30],"K":[31],"a":[33,55,92],"field":[35],"both":[36],"families":[37,39],"are":[38],"with":[42,63,77,97,101,132],"large":[43,60,98],"cycle":[44,99],"indicator.":[45],"In":[46],"fact,":[47],"family":[49,56,93],"F":[51,71,87],"q":[52,72,88],")":[53,73],"girth":[61],"(f.g.l.g.)":[62],"c":[64],"=":[65],"1,":[66],"their":[67],"connected":[68,95],"components":[69],"CD(n,":[70],"form":[74],"f.g.l.g.":[76],"speed":[79,105],"growth":[81],"4/3.":[82],"Family":[83],"q),":[85],"char":[86],"\u2260":[89],"2":[90],"indicator":[100],"largest":[103],"possible":[104],"growth.":[107],"computer":[109],"simulation":[110],"demonstrates":[111],"advantage":[113],"(better":[114],"density":[115],"which":[116],"number":[119],"monomial":[121],"expressions)":[122],"rules":[125],"derived":[126],"from":[127],"q)":[129],"in":[130],"comparison":[131],"symbolic":[133],"algorithm":[134],"q).":[139]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
