{"id":"https://openalex.org/W3092504708","doi":"https://doi.org/10.3934/amc.2020102","title":"On the diffusion of the Improved Generalized Feistel","display_name":"On the diffusion of the Improved Generalized Feistel","publication_year":2020,"publication_date":"2020-10-12","ids":{"openalex":"https://openalex.org/W3092504708","doi":"https://doi.org/10.3934/amc.2020102","mag":"3092504708"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2020102","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020102","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=8e2cdb4c-880e-4ec8-9094-034b02dcc361","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=8e2cdb4c-880e-4ec8-9094-034b02dcc361","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088591649","display_name":"Tsonka Baicheva","orcid":"https://orcid.org/0000-0002-6493-6188"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tsonka Baicheva","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054575522","display_name":"Svetlana Topalova","orcid":"https://orcid.org/0000-0003-3821-4672"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Svetlana Topalova","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088591649"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12847575,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"1","first_page":"95","last_page":"95"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9994999766349792,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.8103240132331848},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6961610913276672},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5277857184410095},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.47276097536087036},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4046822786331177},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4022620916366577}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8103240132331848},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6961610913276672},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5277857184410095},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.47276097536087036},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4046822786331177},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4022620916366577},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"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:10.3934/amc.2020102","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020102","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=8e2cdb4c-880e-4ec8-9094-034b02dcc361","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2020102","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020102","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=8e2cdb4c-880e-4ec8-9094-034b02dcc361","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3092504708.pdf","grobid_xml":"https://content.openalex.org/works/W3092504708.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1497721867","https://openalex.org/W1522919234","https://openalex.org/W1569252980","https://openalex.org/W1590392383","https://openalex.org/W1830378742","https://openalex.org/W2109394932","https://openalex.org/W2150381116","https://openalex.org/W2235214516","https://openalex.org/W2325193322","https://openalex.org/W2413890865","https://openalex.org/W2949226586"],"related_works":["https://openalex.org/W2371138613","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W2080152487","https://openalex.org/W2239445980","https://openalex.org/W2995553446","https://openalex.org/W2120455979","https://openalex.org/W4200527723","https://openalex.org/W3022347918"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>We":[1],"consider":[2,103,160],"the":[3,21,51,57,61,88,93,110,123],"Improved":[4],"Generalized":[5],"Feistel":[6,23,36],"Structure":[7],"(IGFS)":[8],"suggested":[9],"by":[10,126,146],"Suzaki":[11],"and":[12,46,71,83,92,184],"Minematsu":[13,84],"(LNCS,":[14,85],"2010).":[15],"It":[16],"is":[17,27,38,96],"a":[18,35,48,147,165],"generalization":[19],"of":[20,43,50,60,75,164,218],"classical":[22],"cipher.":[24,62],"The":[25],"message":[26],"divided":[28],"into":[29],"<inline-formula><tex-math":[30,67,132,138,152,169,179,185,208,222],"id=\"M1\">\\begin{document}$":[31],"k":[32,69,171,182,188],"$\\end{document}</tex-math></inline-formula>":[33,70,142,157,172,183,189],"subblocks,":[34,45],"transformation":[37],"applied":[39,97],"to":[40,198],"each":[41,99,206],"pair":[42],"successive":[44],"then":[47],"permutation":[49,55,95,118,166,176,200,219],"subblocks":[52,173,190],"follows.":[53],"This":[54],"affects":[56],"diffusion":[58,73,128,204],"property":[59],"IGFS":[63,104,121],"with":[64,105,122,202],"relatively":[65],"big":[66],"id=\"M2\">\\begin{document}$":[68],"good":[72,203],"are":[74,144],"particular":[76],"interest":[77],"for":[78,129,151,168,178,205,221],"light":[79],"weight":[80],"applications.</p><p":[81],"style='text-indent:20px;'>Suzaki":[82],"2010)":[86],"study":[87],"case":[89,115],"when":[90],"one":[91],"same":[94],"at":[98,109],"round,":[100],"while":[101,150],"we":[102,116,158,194,214],"possibly":[106],"different":[107,111],"permutations":[108],"rounds.":[112],"In":[113],"this":[114],"present":[117],"sequences":[119,177,201,220],"yielding":[120],"best":[124],"known":[125],"now":[127],"all":[130],"even":[131,207],"id=\"M3\">\\begin{document}$":[133],"k\\le":[134,140,155,210],"2048":[135,156,211],"$\\end{document}</tex-math></inline-formula>.":[136,212],"For":[137],"id=\"M4\">\\begin{document}$":[139],"16":[141],"they":[143],"found":[145],"computer-aided":[148],"search,":[149],"id=\"M5\">\\begin{document}$":[153],"18\\le":[154],"first":[159],"several":[161],"recursive":[162],"constructions":[163,197],"sequence":[167],"id=\"M6\">\\begin{document}$":[170],"from":[174],"two":[175],"id=\"M7\">\\begin{document}$":[180],"k_a<":[181],"id=\"M8\">\\begin{document}$":[186],"k_b<":[187],"respectively.":[191],"Using":[192],"computer,":[193],"apply":[195],"these":[196],"obtain":[199,215],"id=\"M9\">\\begin{document}$":[209],"Finally":[213],"infinite":[216],"families":[217],"id=\"M10\">\\begin{document}$":[223],"k>2048":[224],"$\\end{document}</tex-math></inline-formula>.</p>":[225]},"counts_by_year":[],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}