{"id":"https://openalex.org/W2965269076","doi":"https://doi.org/10.1109/tit.2019.2932739","title":"Analysis on Boolean Function in a Restricted (Biased) Domain","display_name":"Analysis on Boolean Function in a Restricted (Biased) Domain","publication_year":2019,"publication_date":"2019-08-02","ids":{"openalex":"https://openalex.org/W2965269076","doi":"https://doi.org/10.1109/tit.2019.2932739","mag":"2965269076"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2932739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2932739","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083439545","display_name":"Subhamoy Maitra","orcid":"https://orcid.org/0000-0002-8348-7971"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Subhamoy Maitra","raw_affiliation_strings":["Indian Statistical Institute, Kolkata, India","Indian Statistical Institute [Kolkata] (No. 203, Barrackpore Trunk Road, Kolkata, West Bengal 700108 - India)"],"raw_orcid":"https://orcid.org/0000-0002-8348-7971","affiliations":[{"raw_affiliation_string":"Indian Statistical Institute, Kolkata, India","institution_ids":["https://openalex.org/I6498739"]},{"raw_affiliation_string":"Indian Statistical Institute [Kolkata] (No. 203, Barrackpore Trunk Road, Kolkata, West Bengal 700108 - India)","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103985991","display_name":"Bimal Mandal","orcid":"https://orcid.org/0000-0002-9874-0087"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bimal Mandal","raw_affiliation_strings":["CARAMBA, INRIA Nancy-Grand Est, Villersl\u00e8s-Nancy, France","CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms (615 rue du Jardin Botanique\r\n54600 Villers-l\u00e8s-Nancy - France)"],"raw_orcid":"https://orcid.org/0000-0002-9874-0087","affiliations":[{"raw_affiliation_string":"CARAMBA, INRIA Nancy-Grand Est, Villersl\u00e8s-Nancy, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms (615 rue du Jardin Botanique\r\n54600 Villers-l\u00e8s-Nancy - France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040299399","display_name":"Thor Martinsen","orcid":null},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thor Martinsen","raw_affiliation_strings":["Naval Postgraduate School, Monterey, USA","NPS - Naval Postgraduate School (Monterey, California  93943 - United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Naval Postgraduate School, Monterey, USA","institution_ids":["https://openalex.org/I35364215"]},{"raw_affiliation_string":"NPS - Naval Postgraduate School (Monterey, California  93943 - United States)","institution_ids":["https://openalex.org/I35364215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102938117","display_name":"Dibyendu Roy","orcid":"https://orcid.org/0000-0002-3077-1143"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dibyendu Roy","raw_affiliation_strings":["ERTL(E), STQC, Kolkata, India","STQC - Standardisation Testing and Quality Certification (6 CGO Complex, New Delhi - 110 003 - India)"],"raw_orcid":"https://orcid.org/0000-0002-3077-1143","affiliations":[{"raw_affiliation_string":"ERTL(E), STQC, Kolkata, India","institution_ids":[]},{"raw_affiliation_string":"STQC - Standardisation Testing and Quality Certification (6 CGO Complex, New Delhi - 110 003 - India)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021290362","display_name":"Pantelimon St\u0103nic\u0103","orcid":"https://orcid.org/0000-0002-8622-7120"},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pantelimon Stanica","raw_affiliation_strings":["Naval Postgraduate School, Monterey, USA","NPS - Naval Postgraduate School (Monterey, California  93943 - United States)"],"raw_orcid":"https://orcid.org/0000-0002-8622-7120","affiliations":[{"raw_affiliation_string":"Naval Postgraduate School, Monterey, USA","institution_ids":["https://openalex.org/I35364215"]},{"raw_affiliation_string":"NPS - Naval Postgraduate School (Monterey, California  93943 - United States)","institution_ids":["https://openalex.org/I35364215"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.723,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78641602,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"66","issue":"2","first_page":"1219","last_page":"1231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9998999834060669,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9984999895095825,"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/boolean-function","display_name":"Boolean function","score":0.7724869251251221},{"id":"https://openalex.org/keywords/stream-cipher","display_name":"Stream cipher","score":0.7677179574966431},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5534374117851257},{"id":"https://openalex.org/keywords/keystream","display_name":"Keystream","score":0.5235837697982788},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5217055678367615},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4749370217323303},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4297371506690979},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42917656898498535},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4041328430175781},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3776697814464569},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.21629270911216736}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7724869251251221},{"id":"https://openalex.org/C92950451","wikidata":"https://www.wikidata.org/wiki/Q864718","display_name":"Stream cipher","level":3,"score":0.7677179574966431},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5534374117851257},{"id":"https://openalex.org/C2776132008","wikidata":"https://www.wikidata.org/wiki/Q1509893","display_name":"Keystream","level":4,"score":0.5235837697982788},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5217055678367615},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4749370217323303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4297371506690979},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42917656898498535},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4041328430175781},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3776697814464569},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.21629270911216736},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2019.2932739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2932739","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02374194v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-02374194","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2020, 66 (2), pp.1219-1231. &#x27E8;10.1109/TIT.2019.2932739&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:calhoun.nps.edu:10945/64445","is_oa":false,"landing_page_url":"https://hdl.handle.net/10945/64445","pdf_url":null,"source":{"id":"https://openalex.org/S4306400952","display_name":"Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35364215","host_organization_name":"Naval Postgraduate School","host_organization_lineage":["https://openalex.org/I35364215"],"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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2269930284","https://openalex.org/W2469100438","https://openalex.org/W2504631490","https://openalex.org/W2594834629","https://openalex.org/W2770809732","https://openalex.org/W2790824722","https://openalex.org/W2902740472","https://openalex.org/W4205562629"],"related_works":["https://openalex.org/W2163846246","https://openalex.org/W2103272980","https://openalex.org/W2950325680","https://openalex.org/W3001214808","https://openalex.org/W2130959496","https://openalex.org/W2614608824","https://openalex.org/W1901549827","https://openalex.org/W3029464614","https://openalex.org/W1583325060","https://openalex.org/W1446717654"],"abstract_inverted_index":{"Boolean":[0,35,56,149],"functions":[1,78,150],"are":[2],"usually":[3],"studied":[4,73],"under":[5],"the":[6,20,90,116,137,145,148,158,167,179,182],"assumption":[7],"that":[8,98],"each":[9,119],"input":[10],"bit":[11,28],"is":[12,29],"considered":[13],"independent":[14],"and":[15,79],"identically":[16],"distributed.":[17],"However,":[18],"in":[19,89,136],"case":[21],"of":[22,65,76,86,147,169,181,186,198],"some":[23],"stream":[24,48],"ciphers,":[25],"a":[26,33,40,55,100,133,153,175,191],"keystream":[27],"generated":[30],"by":[31,151],"using":[32],"nonlinear":[34,183],"function":[36,57,185],"with":[37,63],"inputs":[38,64,117],"from":[39],"restricted":[41,91,138,201],"domain.":[42,92,139,202],"At":[43],"Eurocrypt":[44],"2016,":[45],"one":[46],"such":[47,77],"cipher":[49],"(FLIP)":[50],"has":[51],"been":[52],"proposed,":[53],"where":[54],"on":[58,83,157,178],"n":[59],"variables":[60],"was":[61],"exploited":[62],"weight":[66],"n/2":[67],"only.":[68],"Recently,":[69],"Carlet":[70],"et":[71],"al.":[72],"several":[74,163],"properties":[75,146],"obtained":[80],"certain":[81],"bounds":[82,164],"linear":[84],"approximations":[85],"direct":[87,101,170],"sum":[88,102],"In":[93,140],"this":[94,141],"paper,":[95],"we":[96,143,173],"observe":[97],"for":[99],"like":[103],"f":[104,106,111,121,126],"=":[105],"<sub":[107,112,122,127],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[108,113,123,128],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[109,124],"+":[110],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[114,129],",":[115,125],"to":[118,166,194],"sub-function":[120],"do":[130],"not":[131],"follow":[132],"uniform":[134],"distribution":[135,156],"regard,":[142],"study":[144,195],"considering":[152],"general":[154,192],"probability":[155],"inputs.":[159],"We":[160],"further":[161],"obtain":[162,174],"related":[165],"biases":[168],"sums.":[171],"Finally,":[172],"lower":[176],"bound":[177],"bias":[180],"filter":[184],"FLIP.":[187],"Our":[188],"results":[189],"provide":[190],"framework":[193],"security":[196],"parameters":[197],"ciphers":[199],"over":[200]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}