{"id":"https://openalex.org/W1688895763","doi":"https://doi.org/10.2478/forma-2014-0027","title":"Difference of Function on Vector Space over F","display_name":"Difference of Function on Vector Space over F","publication_year":2014,"publication_date":"2014-03-31","ids":{"openalex":"https://openalex.org/W1688895763","doi":"https://doi.org/10.2478/forma-2014-0027","mag":"1688895763"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2014-0027","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2014-0027","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2014-0027","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/forma-2014-0027","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047236261","display_name":"K.I. Arai","orcid":"https://orcid.org/0000-0003-3226-3035"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kenichi Arai","raw_affiliation_strings":["Tokyo University of Science Chiba, Japan","[Tokyo University of Science, Chiba, Japan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokyo University of Science Chiba, Japan","institution_ids":["https://openalex.org/I161296585"]},{"raw_affiliation_string":"[Tokyo University of Science, Chiba, Japan]","institution_ids":["https://openalex.org/I161296585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109889245","display_name":"Ken Wakabayashi","orcid":null},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ken Wakabayashi","raw_affiliation_strings":["Shinshu University Nagano, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048322538","display_name":"Hiroyuki Okazaki","orcid":"https://orcid.org/0009-0000-1022-361X"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroyuki Okazaki","raw_affiliation_strings":["Shinshu University Nagano, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03877618,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"3","first_page":"269","last_page":"275"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9997000098228455,"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":0.9997000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7823286056518555},{"id":"https://openalex.org/keywords/differential-cryptanalysis","display_name":"Differential cryptanalysis","score":0.6156212091445923},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5889703631401062},{"id":"https://openalex.org/keywords/block-cipher","display_name":"Block cipher","score":0.5473780632019043},{"id":"https://openalex.org/keywords/cryptanalysis","display_name":"Cryptanalysis","score":0.5257343053817749},{"id":"https://openalex.org/keywords/significant-difference","display_name":"Significant difference","score":0.4877544045448303},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.4617794454097748},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44721296429634094},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4122350513935089},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38448256254196167},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3468037247657776},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21963143348693848},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18003851175308228},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08842220902442932}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7823286056518555},{"id":"https://openalex.org/C36123800","wikidata":"https://www.wikidata.org/wiki/Q1224471","display_name":"Differential cryptanalysis","level":4,"score":0.6156212091445923},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5889703631401062},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.5473780632019043},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.5257343053817749},{"id":"https://openalex.org/C3018023364","wikidata":"https://www.wikidata.org/wiki/Q425265","display_name":"Significant difference","level":2,"score":0.4877544045448303},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4617794454097748},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44721296429634094},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4122350513935089},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38448256254196167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3468037247657776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21963143348693848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18003851175308228},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08842220902442932}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/forma-2014-0027","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2014-0027","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2014-0027","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:98ec484eca0c4ade9d97cb84ff70e66c","is_oa":false,"landing_page_url":"https://doaj.org/article/98ec484eca0c4ade9d97cb84ff70e66c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 22, Iss 3, Pp 269-275 (2014)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3723","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/3723","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2014-0027","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2014-0027","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2014-0027","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G306341369","display_name":"Computer-based Evaluation of Cryptographic Protocol Security","funder_award_id":"26730067","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1688895763.pdf","grobid_xml":"https://content.openalex.org/works/W1688895763.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W180239714","https://openalex.org/W192809544","https://openalex.org/W260340778","https://openalex.org/W1527545029","https://openalex.org/W1629301835","https://openalex.org/W2062624044","https://openalex.org/W2102333608","https://openalex.org/W2105559527","https://openalex.org/W2138253682","https://openalex.org/W2140950626","https://openalex.org/W2159772409","https://openalex.org/W2160628721","https://openalex.org/W2163641194","https://openalex.org/W2296232473","https://openalex.org/W2504160609","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W57168481","https://openalex.org/W2003194200","https://openalex.org/W1410349837","https://openalex.org/W1998022504","https://openalex.org/W2949235530","https://openalex.org/W1489035426","https://openalex.org/W2383171198","https://openalex.org/W4230315357","https://openalex.org/W2509111091","https://openalex.org/W1849484603"],"abstract_inverted_index":{"Summary":[0],"In":[1,44,79],"[11],":[2],"the":[3,23,53,84],"definitions":[4,24,47,85],"of":[5,25,55,86],"forward":[6,26,87],"difference,":[7,9,27,29,88,90],"backward":[8,28,89],"and":[10,30,91],"central":[11,31,92],"difference":[12,14,32,93],"as":[13],"operations":[15],"for":[16,33,94],"functions":[17,34,95],"on":[18,35,96],"R":[19],"were":[20],"formalized.":[21,43],"However,":[22],"vector":[36,97],"spaces":[37,98],"over":[38,99],"F":[39],"have":[40],"not":[41],"been":[42],"cryptology,":[45],"these":[46,77,107],"are":[48],"very":[49],"important":[50],"in":[51],"evaluating":[52],"security":[54],"cryptographic":[56],"systems":[57],"[3],":[58],"[10].":[59],"Differential":[60],"cryptanalysis":[61],"[4]":[62],"that":[63],"undertakes":[64],"a":[65],"general":[66],"purpose":[67],"attack":[68],"against":[69],"block":[70],"ciphers":[71],"[13]":[72],"can":[73],"be":[74],"formalized":[75],"using":[76],"definitions.":[78,108],"this":[80],"article,":[81],"we":[82,102],"formalize":[83,103],"F.":[100],"Moreover,":[101],"some":[104],"facts":[105],"about":[106]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
