{"id":"https://openalex.org/W2023249969","doi":"https://doi.org/10.1155/2013/768384","title":"Shannon's Random-Cipher Result and the Generalized<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math>-Norm Entropy of Type<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><mml:mrow><mml:mi>\u03b2</mml:mi></mml:mrow></mml:math>","display_name":"Shannon's Random-Cipher Result and the Generalized<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math>-Norm Entropy of Type<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><mml:mrow><mml:mi>\u03b2</mml:mi></mml:mrow></mml:math>","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2023249969","doi":"https://doi.org/10.1155/2013/768384","mag":"2023249969"},"language":"lv","primary_location":{"id":"doi:10.1155/2013/768384","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/768384","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/768384.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2013/768384.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100727659","display_name":"Satish Kumar","orcid":"https://orcid.org/0000-0003-3758-6853"},"institutions":[{"id":"https://openalex.org/I42869670","display_name":"Arba Minch University","ror":"https://ror.org/00ssp9h11","country_code":"ET","type":"education","lineage":["https://openalex.org/I42869670"]}],"countries":["ET"],"is_corresponding":false,"raw_author_name":"Satish Kumar","raw_affiliation_strings":["Department of Mathematics, College of Natural Sciences, Arba Minch University, Arba Minch, Ethiopia"],"raw_orcid":"https://orcid.org/0000-0003-3758-6853","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Natural Sciences, Arba Minch University, Arba Minch, Ethiopia","institution_ids":["https://openalex.org/I42869670"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021117385","display_name":"Arun Choudhary","orcid":"https://orcid.org/0000-0003-3226-8848"},"institutions":[{"id":"https://openalex.org/I105094715","display_name":"National Institute of Technology Kurukshetra","ror":"https://ror.org/04909p852","country_code":"IN","type":"education","lineage":["https://openalex.org/I105094715"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Arun Choudhary","raw_affiliation_strings":["Department of Mathematics, Geeta Institute of Management & Technology, Kanipla, Kurukshetra, Haryana 136131, India"],"raw_orcid":"https://orcid.org/0000-0003-3226-8848","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Geeta Institute of Management & Technology, Kanipla, Kurukshetra, Haryana 136131, India","institution_ids":["https://openalex.org/I105094715"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021117385"],"corresponding_institution_ids":["https://openalex.org/I105094715"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.24,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.60334223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.986299991607666,"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"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.986299991607666,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9663000106811523,"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/algorithm","display_name":"Algorithm","score":0.5976821780204773},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5222295522689819},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3376442492008209}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5976821780204773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5222295522689819},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3376442492008209}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2013/768384","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/768384","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/768384.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:af053946eee24f1986abbe76fdb38d82","is_oa":true,"landing_page_url":"https://doaj.org/article/af053946eee24f1986abbe76fdb38d82","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/768384","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/768384","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/768384.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.550000011920929,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2023249969.pdf","grobid_xml":"https://content.openalex.org/works/W2023249969.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2042690201","https://openalex.org/W2049279961","https://openalex.org/W2078210981","https://openalex.org/W2085178416","https://openalex.org/W2109394932","https://openalex.org/W2171545223","https://openalex.org/W2263958071"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Using":[0],"the":[1,5,25],"Fano":[2],"inequality":[3],"for":[4],"generalized<mml:math":[6,26],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,27,32],"id=\"M3\"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math>-norm":[8],"entropy":[9,29],"and":[10],"Bayess":[11],"probability":[12],"of":[13,30],"error,":[14],"a":[15],"generalized":[16],"random-cipher":[17],"result":[18],"is":[19],"proved":[20],"by":[21],"taking":[22],"into":[23],"account":[24],"id=\"M4\"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math>-norm":[28],"type<mml:math":[31],"id=\"M5\"><mml:mrow><mml:mi>\u03b2</mml:mi></mml:mrow></mml:math>.":[33]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
