{"id":"https://openalex.org/W2015257352","doi":"https://doi.org/10.2478/v10065-011-0014-7","title":"On the key expansion of D(n, K)-based cryptographical algorithm","display_name":"On the key expansion of D(n, K)-based cryptographical algorithm","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2015257352","doi":"https://doi.org/10.2478/v10065-011-0014-7","mag":"2015257352"},"language":"en","primary_location":{"id":"doi:10.2478/v10065-011-0014-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10065-011-0014-7","pdf_url":"https://journals.umcs.pl/ai/article/download/3313/2507","source":{"id":"https://openalex.org/S4210184648","display_name":"Annales Universitatis Mariae Curie-Sklodowska sectio AI \u2013 Informatica","issn_l":"1732-1360","issn":["1732-1360","2083-3628"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales UMCS, Informatica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://journals.umcs.pl/ai/article/download/3313/2507","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062430200","display_name":"Vasyl Ustimenko","orcid":"https://orcid.org/0000-0002-2138-2357"},"institutions":[{"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"]},{"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"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Vasyl Ustimenko","raw_affiliation_strings":["Institute of Mathematics, Maria Curie-Sklodowska University pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland","Institute of Mathematics Maria Curie-Sk\u0142odowska University Pl. M. Curie-Sk\u0142odowskiej 1 20-031 Lublin, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Maria Curie-Sklodowska University pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland","institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Institute of Mathematics Maria Curie-Sk\u0142odowska University 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/A5012596722","display_name":"Aneta Wr\u00f3blewska","orcid":"https://orcid.org/0000-0001-9724-4586"},"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/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"funder","lineage":["https://openalex.org/I99542240"]},{"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"]},{"id":"https://openalex.org/I4210119410","display_name":"Institute of Fundamental Technological Research","ror":"https://ror.org/03fs4aq04","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210119410","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Aneta Wr\u00f3blewska","raw_affiliation_strings":["Institute of Mathematics, Maria Curie-Sklodowska University pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland","Institute of Fundamental Technological Research Polish Academy of Sciences ul. Pawinskiego 5B; 02-106 Warszawa, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Maria Curie-Sklodowska University pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland","institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Institute of Fundamental Technological Research Polish Academy of Sciences ul. Pawinskiego 5B; 02-106 Warszawa, Poland","institution_ids":["https://openalex.org/I4210119410","https://openalex.org/I99542240"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062430200"],"corresponding_institution_ids":["https://openalex.org/I174183983","https://openalex.org/I4210137370"],"apc_list":null,"apc_paid":null,"fwci":1.7749,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.86729342,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"2","first_page":null,"last_page":null},"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/T10849","display_name":"Finite Group Theory Research","score":0.9979000091552734,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9898999929428101,"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":0.7226495742797852},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5761092901229858},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5354388356208801},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.46944212913513184}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7226495742797852},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5761092901229858},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5354388356208801},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.46944212913513184}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2478/v10065-011-0014-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10065-011-0014-7","pdf_url":"https://journals.umcs.pl/ai/article/download/3313/2507","source":{"id":"https://openalex.org/S4210184648","display_name":"Annales Universitatis Mariae Curie-Sklodowska sectio AI \u2013 Informatica","issn_l":"1732-1360","issn":["1732-1360","2083-3628"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales UMCS, Informatica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2478/v10065-011-0014-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10065-011-0014-7","pdf_url":"https://journals.umcs.pl/ai/article/download/3313/2507","source":{"id":"https://openalex.org/S4210184648","display_name":"Annales Universitatis Mariae Curie-Sklodowska sectio AI \u2013 Informatica","issn_l":"1732-1360","issn":["1732-1360","2083-3628"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales UMCS, Informatica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3998201246","display_name":null,"funder_award_id":"Social","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G5374134968","display_name":null,"funder_award_id":"European Social Fund","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2015257352.pdf","grobid_xml":"https://content.openalex.org/works/W2015257352.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W162015597","https://openalex.org/W610336853","https://openalex.org/W1483897861","https://openalex.org/W1510730180","https://openalex.org/W1579329156","https://openalex.org/W1598884337","https://openalex.org/W1996462091","https://openalex.org/W2012280556","https://openalex.org/W2054649237","https://openalex.org/W2082538734","https://openalex.org/W2138064235","https://openalex.org/W2148726777","https://openalex.org/W2158681102","https://openalex.org/W2319263775","https://openalex.org/W2403344865","https://openalex.org/W2498463796","https://openalex.org/W2602645338","https://openalex.org/W2610547191","https://openalex.org/W2947567546","https://openalex.org/W3035373793","https://openalex.org/W3139951841"],"related_works":["https://openalex.org/W2114124567","https://openalex.org/W1979597421","https://openalex.org/W2998724919","https://openalex.org/W161787318","https://openalex.org/W2007980826","https://openalex.org/W1997883919","https://openalex.org/W1968682565","https://openalex.org/W2963982375","https://openalex.org/W2042372008","https://openalex.org/W4245490552"],"abstract_inverted_index":{"The":[0,27,57,77,119,137,151],"family":[1],"of":[2,41,47,54,81,88,144,147,183,190],"algebraic":[3],"graphs":[4,64],"D(n,":[5,55,59,123,212],"K)":[6,53,60,80,124,140,159,204,213],"defined":[7],"over":[8,133],"finite":[9],"commutative":[10],"ring":[11,135],"K":[12],"have":[13,98],"been":[14],"used":[15],"in":[16],"different":[17],"cryptographical":[18],"algorithms":[19],"(private":[20],"and":[21,61,205],"public":[22,206],"keys,":[23],"key":[24,207],"exchange":[25],"protocols).":[26],"encryption":[28,42,89,117,127],"maps":[29,43,90],"correspond":[30],"to":[31,71,110],"special":[32],"walks":[33,72],"on":[34,93,168,210],"this":[35],"graph.":[36],"We":[37,162,193],"expand":[38],"the":[39,45,94,122,134,164,169,174,198,211],"class":[40],"via":[44],"use":[46],"edge":[48],"transitive":[49],"automorphism":[50,189],"group":[51,78,138,146,175],"G(n,":[52,79,139,158,203],"K).":[56],"graph":[58,125],"related":[62],"directed":[63],"are":[65],"disconnected.":[66],"So":[67],"private":[68],"keys":[69],"corresponding":[70],"preserve":[73],"each":[74],"connected":[75],"component.":[76],"transformations":[82],"generated":[83],"by":[84,115],"an":[85,111,116],"expanded":[86],"set":[87],"acts":[91],"transitively":[92],"plainspace.":[95],"Thus":[96],"we":[97],"a":[99,129,142,155],"great":[100],"difference":[101],"with":[102],"block":[103],"ciphers,":[104],"any":[105],"plaintexts":[106],"can":[107],"be":[108],"transformed":[109],"arbitrarily":[112],"chosen":[113],"ciphertex":[114],"map.":[118],"plainspace":[120],"for":[121,154,173,197,202],"based":[126,167,209],"is":[128,141,160,179],"free":[130,184],"module":[131,185],"P":[132,186],"K.":[136],"subgroup":[143],"Cremona":[145],"all":[148],"polynomial":[149,156,188],"automorphisms.":[150],"maximal":[152],"degree":[153,191],"from":[157],"3.":[161],"discuss":[163],"Diffie-Hellman":[165],"algorithm":[166,208],"discrete":[170,199],"logarithm":[171,200],"problem":[172,201],"\u03c4-1G\u03c4,":[176],"where":[177],"\u03c4":[178],"invertible":[180],"affine":[181],"transformation":[182],"i.e.":[187],"1.":[192],"consider":[194],"some":[195],"relations":[196],"graphs.":[214]},"counts_by_year":[{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}
