{"id":"https://openalex.org/W2613080092","doi":"https://doi.org/10.1515/jmc-2016-0013","title":"Applications of design theory for the constructions of MDS matrices for lightweight cryptography","display_name":"Applications of design theory for the constructions of MDS matrices for lightweight cryptography","publication_year":2017,"publication_date":"2017-05-11","ids":{"openalex":"https://openalex.org/W2613080092","doi":"https://doi.org/10.1515/jmc-2016-0013","mag":"2613080092"},"language":"en","primary_location":{"id":"doi:10.1515/jmc-2016-0013","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jmc-2016-0013","pdf_url":null,"source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doaj.org/article/c75052ec444b4df2ad0c5b41e5652bed","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102051987","display_name":"Kishan Chand Gupta","orcid":null},"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":"Kishan Chand Gupta","raw_affiliation_strings":["Applied Statistics Unit , Indian Statistical Institute , 203, B.T. Road , Kolkata 700108 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Statistics Unit , Indian Statistical Institute , 203, B.T. Road , Kolkata 700108 , India","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051709851","display_name":"Sumit Pandey","orcid":"https://orcid.org/0000-0003-2532-6587"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Sumit Kumar Pandey","raw_affiliation_strings":["School of Physical and Mathematical Sciences , Nanyang Technological University , Singapore , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences , Nanyang Technological University , Singapore , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036058781","display_name":"Indranil Ghosh Ray","orcid":"https://orcid.org/0000-0002-4156-8247"},"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":"Indranil Ghosh Ray","raw_affiliation_strings":["Applied Statistics Unit , Indian Statistical Institute , 203, B.T. Road , Kolkata 700108 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Statistics Unit , Indian Statistical Institute , 203, B.T. Road , Kolkata 700108 , India","institution_ids":["https://openalex.org/I6498739"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051709851"],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.0441955,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"11","issue":"2","first_page":"85","last_page":"116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9998000264167786,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9998000264167786,"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":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9991999864578247,"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/invertible-matrix","display_name":"Invertible matrix","score":0.6877118945121765},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.5446091294288635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5421465635299683},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5234826803207397},{"id":"https://openalex.org/keywords/hash-function","display_name":"Hash function","score":0.5193942189216614},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5085417032241821},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.494184285402298},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46209660172462463},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.44445738196372986},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41824087500572205},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3830932378768921},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3735870122909546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20575305819511414},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18936115503311157},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1524975597858429}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6877118945121765},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.5446091294288635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5421465635299683},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5234826803207397},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.5193942189216614},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5085417032241821},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.494184285402298},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46209660172462463},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.44445738196372986},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41824087500572205},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3830932378768921},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3735870122909546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20575305819511414},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18936115503311157},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1524975597858429},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jmc-2016-0013","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jmc-2016-0013","pdf_url":null,"source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c75052ec444b4df2ad0c5b41e5652bed","is_oa":true,"landing_page_url":"https://doaj.org/article/c75052ec444b4df2ad0c5b41e5652bed","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Cryptology, Vol 11, Iss 2, Pp 85-116 (2017)","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:doaj.org/article:c75052ec444b4df2ad0c5b41e5652bed","is_oa":true,"landing_page_url":"https://doaj.org/article/c75052ec444b4df2ad0c5b41e5652bed","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Cryptology, Vol 11, Iss 2, Pp 85-116 (2017)","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W35428663","https://openalex.org/W44079947","https://openalex.org/W66229595","https://openalex.org/W98521887","https://openalex.org/W147005573","https://openalex.org/W157243396","https://openalex.org/W179815912","https://openalex.org/W910200028","https://openalex.org/W1484622934","https://openalex.org/W1542662906","https://openalex.org/W1572300106","https://openalex.org/W1710218451","https://openalex.org/W1945671855","https://openalex.org/W1979946760","https://openalex.org/W2109265351","https://openalex.org/W2117420234","https://openalex.org/W2120464016","https://openalex.org/W2127908002","https://openalex.org/W2131792049","https://openalex.org/W2156775578","https://openalex.org/W2519262867","https://openalex.org/W2725380599","https://openalex.org/W4229888879","https://openalex.org/W4285719527","https://openalex.org/W6838408783"],"related_works":["https://openalex.org/W2387449261","https://openalex.org/W2418518962","https://openalex.org/W2963377682","https://openalex.org/W2043159103","https://openalex.org/W2391769344","https://openalex.org/W4297790016","https://openalex.org/W2359260952","https://openalex.org/W2769269860","https://openalex.org/W2388752733","https://openalex.org/W2560325964"],"abstract_inverted_index":{"Abstract":[0],"In":[1,58,279,305],"this":[2,280,306],"paper,":[3,281,307],"we":[4,282,333],"observe":[5],"simple":[6],"yet":[7],"subtle":[8],"interconnections":[9],"among":[10],"design":[11,37],"theory,":[12],"coding":[13,27],"theory":[14,28],"and":[15,41,65,89,176,295],"cryptography.":[16,57],"Maximum":[17],"distance":[18],"separable":[19],"(MDS)":[20],"matrices":[21,50,69,79,82,108,125,294,298],"have":[22],"applications":[23],"not":[24,116],"only":[25],"in":[26,35,55,173,200,215,292],"but":[29,112,248],"are":[30,71,80,87,104,109,309],"also":[31],"of":[32,38,84,91,122,132,169,171,197,210,290,299,338],"great":[33],"importance":[34],"the":[36,59,113,120,128,167,195,207,284,287,296],"block":[39],"ciphers":[40],"hash":[42],"functions.":[43],"It":[44],"is":[45,115],"nontrivial":[46],"to":[47,74,246,311],"find":[48],"MDS":[49,76,107,124],"which":[51,70],"could":[52],"be":[53],"used":[54],"lightweight":[56],"SAC":[60],"2004":[61],"paper":[62],"[12],":[63],"Junod":[64],"Vaudenay":[66],"considered":[67],"bi-regular":[68,110,144,227,293,349],"useful":[72],"objects":[73],"build":[75],"matrices.":[77],"Bi-regular":[78],"those":[81],"all":[83,90],"whose":[85,92],"entries":[86],"nonzero":[88],"<m:math":[93,134,149,177,217,230,253,267,313,339,357],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[94,135,150,178,218,231,254,268,314,340,358],"<m:mrow>":[95,136,151,157,179,185,219,235,258,269,318,341,362],"<m:mn>2</m:mn>":[96,98],"<m:mo>\u00d7</m:mo>":[97,138,221,343],"</m:mrow>":[99,140,161,162,189,190,223,239,262,273,322,345,366],"</m:math>":[100,141,163,191,224,241,264,274,324,346],"{2\\times":[101],"2}":[102],"submatrices":[103],"nonsingular.":[105],"Therefore":[106],"matrices,":[111,228,350,355],"converse":[114],"true.":[117],"They":[118,205],"proposed":[119],"constructions":[121],"efficient":[123],"by":[126,352],"studying":[127],"two":[129],"major":[130],"aspects":[131],"a":[133,216,335],"<m:mi>d</m:mi>":[137,139,220,222,236,238,259,261,270,319,321,342,344,363,365],"{d\\times":[142,225,347],"d}":[143,226,348],"matrix":[145],"M":[146,174,201],",":[147,165,175,193],"namely":[148],"<m:msub>":[152,180],"<m:mi>v</m:mi>":[153,233,256,316,360],"<m:mn>1</m:mn>":[154,182,234,257,317,361],"</m:msub>":[155,183],"<m:mo>\u2062</m:mo>":[156,184],"<m:mo>(</m:mo>":[158,186],"<m:mi>M</m:mi>":[159,187],"<m:mo>)</m:mo>":[160,188],"{v_{1}(M)}":[164],"i.e.":[166,194,229],"number":[168,196,209,289],"occurrences":[170],"1":[172],"<m:mi>c</m:mi>":[181],"{c_{1}(M)}":[192],"distinct":[198],"elements":[199],"other":[202],"than":[203],"1.":[204],"calculated":[206],"maximum":[208,288],"ones":[211,291],"that":[212],"can":[213],"occur":[214],"<m:msubsup>":[232,255,315,359],"<m:mo>,</m:mo>":[237,260,320,364],"</m:msubsup>":[240,263,323,367],"{v_{1}^{d,d}}":[242,265,325],"for":[243,266,326],"d":[244,328],"up":[245],"8,":[247],"with":[249],"their":[250],"approach,":[251],"finding":[252],"<m:mo>\u2265</m:mo>":[271],"<m:mn>9</m:mn>":[272],"{d\\geq":[275],"9}":[276],"seems":[277],"difficult.":[278],"explore":[283],"connection":[285],"between":[286],"incidence":[297],"Balanced":[300],"Incomplete":[301],"Block":[302],"Design":[303],"(BIBD).":[304],"tools":[308],"developed":[310],"compute":[312],"arbitrary":[327],".":[329],"Using":[330],"these":[331],"results,":[332],"construct":[334],"restrictive":[336],"version":[337],"introducing":[351],"calling":[353],"almost-bi-regular":[354],"having":[356]},"counts_by_year":[{"year":2023,"cited_by_count":3}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2017-05-19T00:00:00"}