{"id":"https://openalex.org/W4311870639","doi":"https://doi.org/10.46586/tosc.v2022.i4.266-290","title":"On the Lower Bound of Cost of MDS Matrices","display_name":"On the Lower Bound of Cost of MDS Matrices","publication_year":2022,"publication_date":"2022-12-07","ids":{"openalex":"https://openalex.org/W4311870639","doi":"https://doi.org/10.46586/tosc.v2022.i4.266-290"},"language":"en","primary_location":{"id":"doi:10.46586/tosc.v2022.i4.266-290","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2022.i4.266-290","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/9979/9477","source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://tosc.iacr.org/index.php/ToSC/article/download/9979/9477","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013219977","display_name":"Ayineedi Venkateswarlu","orcid":"https://orcid.org/0000-0003-3178-0727"},"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":"Ayineedi Venkateswarlu","raw_affiliation_strings":["Indian Statistical Institute, Chennai Centre, Chennai, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Statistical Institute, Chennai Centre, Chennai, India","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047180976","display_name":"Abhishek Kesarwani","orcid":"https://orcid.org/0000-0001-8488-6811"},"institutions":[{"id":"https://openalex.org/I94234084","display_name":"Indian Institute of Technology Kanpur","ror":"https://ror.org/05pjsgx75","country_code":"IN","type":"education","lineage":["https://openalex.org/I94234084"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Abhishek Kesarwani","raw_affiliation_strings":["IHUB NTIHAC FOUNDATION, IIT Kanpur, Kanpur, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IHUB NTIHAC FOUNDATION, IIT Kanpur, Kanpur, India","institution_ids":["https://openalex.org/I94234084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046539794","display_name":"Sumanta Sarkar","orcid":"https://orcid.org/0000-0002-6303-617X"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sumanta Sarkar","raw_affiliation_strings":["University of Warwick, Coventry, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warwick, Coventry, United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4641,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.69485701,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"266","last_page":"290"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9983999729156494,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9830999970436096,"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/bitwise-operation","display_name":"Bitwise operation","score":0.7357697486877441},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6266459822654724},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5955492854118347},{"id":"https://openalex.org/keywords/xor-gate","display_name":"XOR gate","score":0.5164123177528381},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5155560970306396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5099211931228638},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4603654146194458},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4593852162361145},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41829192638397217},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3547534942626953},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3213270902633667},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3000026345252991},{"id":"https://openalex.org/keywords/logic-gate","display_name":"Logic gate","score":0.06683158874511719},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.054440200328826904}],"concepts":[{"id":"https://openalex.org/C134765980","wikidata":"https://www.wikidata.org/wiki/Q879126","display_name":"Bitwise operation","level":2,"score":0.7357697486877441},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6266459822654724},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5955492854118347},{"id":"https://openalex.org/C28495749","wikidata":"https://www.wikidata.org/wiki/Q155516","display_name":"XOR gate","level":3,"score":0.5164123177528381},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5155560970306396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5099211931228638},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4603654146194458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4593852162361145},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41829192638397217},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3547534942626953},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3213270902633667},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3000026345252991},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.06683158874511719},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.054440200328826904},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.46586/tosc.v2022.i4.266-290","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2022.i4.266-290","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/9979/9477","source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:172320","is_oa":false,"landing_page_url":"https://wrap.warwick.ac.uk/172320/1/WRAP-on-the-lower-bound-cost-MDS-matrices-Sarkar-2022.pdf","pdf_url":"https://wrap.warwick.ac.uk/172320/1/WRAP-on-the-lower-bound-cost-MDS-matrices-Sarkar-2022.pdf","source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:cea9df7d0b884230b7241c06df474fbf","is_oa":true,"landing_page_url":"https://doaj.org/article/cea9df7d0b884230b7241c06df474fbf","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":"IACR Transactions on Symmetric Cryptology, Vol 2022, Iss 4 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46586/tosc.v2022.i4.266-290","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2022.i4.266-290","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/9979/9477","source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4311870639.pdf","grobid_xml":"https://content.openalex.org/works/W4311870639.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W35428663","https://openalex.org/W163970851","https://openalex.org/W1499906440","https://openalex.org/W1556212265","https://openalex.org/W1600295433","https://openalex.org/W2169932713","https://openalex.org/W2242540160","https://openalex.org/W2293947265","https://openalex.org/W2409722729","https://openalex.org/W2474422174","https://openalex.org/W2500084106","https://openalex.org/W2503098516","https://openalex.org/W2505213174","https://openalex.org/W2572813892","https://openalex.org/W2574259888","https://openalex.org/W2594061018","https://openalex.org/W2605101120","https://openalex.org/W2620219640","https://openalex.org/W2757403014","https://openalex.org/W2782477046","https://openalex.org/W2795253480","https://openalex.org/W2908427070","https://openalex.org/W2970895760","https://openalex.org/W2978013943","https://openalex.org/W3046498207","https://openalex.org/W3159567446","https://openalex.org/W3179241074","https://openalex.org/W3196338412","https://openalex.org/W3198844536","https://openalex.org/W3207692244","https://openalex.org/W4213347158","https://openalex.org/W4213437024","https://openalex.org/W4229881016","https://openalex.org/W4240983141","https://openalex.org/W4246856544","https://openalex.org/W4250572011","https://openalex.org/W4251216631","https://openalex.org/W4289604192","https://openalex.org/W4301621763"],"related_works":["https://openalex.org/W2362925226","https://openalex.org/W1981170240","https://openalex.org/W4206055950","https://openalex.org/W2404035422","https://openalex.org/W264971478","https://openalex.org/W2350295618","https://openalex.org/W3141649954","https://openalex.org/W2356469264","https://openalex.org/W2083409928","https://openalex.org/W3193950766"],"abstract_inverted_index":{"Ever":[0],"since":[1],"lightweight":[2],"cryptography":[3],"emerged":[4],"as":[5,135],"one":[6],"of":[7,19,27,78,93,121,146,163],"the":[8,16,25,44,56,72,91,94,105,119,131,144,157,167],"trending":[9],"topics":[10],"in":[11,24,76],"symmetric":[12],"key":[13],"cryptography,":[14],"optimizing":[15],"implementation":[17],"cost":[18,80,139],"MDS":[20,58,74,99],"matrices":[21,59,100,123,136],"has":[22],"been":[23,40,51],"center":[26],"attention.":[28],"In":[29,86],"this":[30,87],"direction,":[31],"various":[32],"metrics":[33],"like":[34],"d-XOR,":[35],"s-XOR":[36,173],"and":[37,130,141,150,174],"g-XOR":[38,175],"have":[39,50],"proposed":[41,107],"to":[42,53,63,67,172],"mimic":[43],"hardware":[45,79],"cost.":[46],"Consequently,":[47],"efforts":[48],"also":[49],"made":[52],"search":[54],"for":[55,60,143,160],"optimal":[57,73,95],"dimensions":[61],"relevant":[62],"cryptographic":[64],"applications":[65],"according":[66,171],"these":[68,161],"metrics.":[69,176],"However,":[70],"finding":[71],"matrix":[75],"terms":[77],"still":[81],"remains":[82],"an":[83],"unsolved":[84],"problem.":[85],"paper,":[88],"we":[89],"settle":[90],"question":[92],"4":[96,98,149],"x":[97],"over":[101],"GL(n,":[102],"F2)":[103],"under":[104],"recently":[106],"metric":[108],"sequential":[109],"XOR":[110],"count":[111],"based":[112],"on":[113],"words":[114],"(sw-XOR).":[115],"We":[116],"prove":[117],"that":[118],"sw-XOR":[120,138],"such":[122],"is":[124,133],"at":[125],"least":[126],"8n":[127],"+":[128],"3,":[129],"bound":[132,159],"tight":[134],"with":[137,166],"35":[140],"67":[142],"values":[145,162],"n":[147,164],"=":[148],"8,":[151],"respectively,":[152],"were":[153],"already":[154],"known.":[155],"Moreover,":[156],"lower":[158,169],"matches":[165],"known":[168],"bounds":[170]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}