{"id":"https://openalex.org/W4211203168","doi":"https://doi.org/10.1109/sin54109.2021.9699310","title":"On the Number of Arithmetic Operations in NTT-based Polynomial Multiplication in Kyber and Dilithium Cryptosystems","display_name":"On the Number of Arithmetic Operations in NTT-based Polynomial Multiplication in Kyber and Dilithium Cryptosystems","publication_year":2021,"publication_date":"2021-12-15","ids":{"openalex":"https://openalex.org/W4211203168","doi":"https://doi.org/10.1109/sin54109.2021.9699310"},"language":"en","primary_location":{"id":"doi:10.1109/sin54109.2021.9699310","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sin54109.2021.9699310","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 14th International Conference on Security of Information and Networks (SIN)","raw_type":"proceedings-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/A5086632547","display_name":"Murat Burhan \u0130lter","orcid":"https://orcid.org/0000-0002-4399-2594"},"institutions":[{"id":"https://openalex.org/I4210093841","display_name":"Institute of Applied Mathematics","ror":"https://ror.org/00h9jx107","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210093841","https://openalex.org/I4210124601","https://openalex.org/I4210148470"]},{"id":"https://openalex.org/I56303344","display_name":"Aselsan (Turkey)","ror":"https://ror.org/04knh8e66","country_code":"TR","type":"company","lineage":["https://openalex.org/I56303344"]}],"countries":["RU","TR"],"is_corresponding":false,"raw_author_name":"Murat Burhan Ilter","raw_affiliation_strings":["ASELSAN Inc., Ankara, TURKEY","Institute of Applied Mathematics, METU, Ankara, TURKEY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ASELSAN Inc., Ankara, TURKEY","institution_ids":["https://openalex.org/I56303344"]},{"raw_affiliation_string":"Institute of Applied Mathematics, METU, Ankara, TURKEY","institution_ids":["https://openalex.org/I4210093841"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044309845","display_name":"Ne\u015fe Ko\u00e7ak","orcid":null},"institutions":[{"id":"https://openalex.org/I56303344","display_name":"Aselsan (Turkey)","ror":"https://ror.org/04knh8e66","country_code":"TR","type":"company","lineage":["https://openalex.org/I56303344"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Nese Kocak","raw_affiliation_strings":["ASELSAN Inc., Ankara, TURKEY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ASELSAN Inc., Ankara, TURKEY","institution_ids":["https://openalex.org/I56303344"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008200304","display_name":"Erkan Uslu","orcid":"https://orcid.org/0000-0002-6971-981X"},"institutions":[{"id":"https://openalex.org/I4210093841","display_name":"Institute of Applied Mathematics","ror":"https://ror.org/00h9jx107","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210093841","https://openalex.org/I4210124601","https://openalex.org/I4210148470"]},{"id":"https://openalex.org/I56303344","display_name":"Aselsan (Turkey)","ror":"https://ror.org/04knh8e66","country_code":"TR","type":"company","lineage":["https://openalex.org/I56303344"]}],"countries":["RU","TR"],"is_corresponding":false,"raw_author_name":"Erkan Uslu","raw_affiliation_strings":["ASELSAN Inc., Ankara, TURKEY","Institute of Applied Mathematics, METU, Ankara, TURKEY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ASELSAN Inc., Ankara, TURKEY","institution_ids":["https://openalex.org/I56303344"]},{"raw_affiliation_string":"Institute of Applied Mathematics, METU, Ankara, TURKEY","institution_ids":["https://openalex.org/I4210093841"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016964880","display_name":"O\u011fuz Yayla","orcid":"https://orcid.org/0000-0001-8945-2780"},"institutions":[{"id":"https://openalex.org/I4210093841","display_name":"Institute of Applied Mathematics","ror":"https://ror.org/00h9jx107","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210093841","https://openalex.org/I4210124601","https://openalex.org/I4210148470"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Oguz Yayla","raw_affiliation_strings":["Institute of Applied Mathematics, METU, Ankara, TURKEY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, METU, Ankara, TURKEY","institution_ids":["https://openalex.org/I4210093841"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065391466","display_name":"Nergiz Yuca","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093841","display_name":"Institute of Applied Mathematics","ror":"https://ror.org/00h9jx107","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210093841","https://openalex.org/I4210124601","https://openalex.org/I4210148470"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Nergiz Yuca","raw_affiliation_strings":["Institute of Applied Mathematics, METU, Ankara, TURKEY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, METU, Ankara, TURKEY","institution_ids":["https://openalex.org/I4210093841"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2799,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66496689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"19","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9995999932289124,"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/T10237","display_name":"Cryptography and Data Security","score":0.9995999932289124,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.9991000294685364,"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/cryptosystem","display_name":"Cryptosystem","score":0.8007650375366211},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.7303385138511658},{"id":"https://openalex.org/keywords/dilithium","display_name":"Dilithium","score":0.5750739574432373},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5520522594451904},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5294271111488342},{"id":"https://openalex.org/keywords/cryptanalysis","display_name":"Cryptanalysis","score":0.5247578620910645},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5219144821166992},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4398495554924011},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.42012789845466614},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3791760802268982},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3027113080024719},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11599990725517273},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11063823103904724}],"concepts":[{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.8007650375366211},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7303385138511658},{"id":"https://openalex.org/C2775951159","wikidata":"https://www.wikidata.org/wiki/Q1189242","display_name":"Dilithium","level":4,"score":0.5750739574432373},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5520522594451904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5294271111488342},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.5247578620910645},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5219144821166992},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4398495554924011},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.42012789845466614},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3791760802268982},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3027113080024719},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11599990725517273},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11063823103904724},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C118629725","wikidata":"https://www.wikidata.org/wiki/Q2686738","display_name":"Deprotonation","level":3,"score":0.0},{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/sin54109.2021.9699310","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sin54109.2021.9699310","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 14th International Conference on Security of Information and Networks (SIN)","raw_type":"proceedings-article"},{"id":"pmh:oai:https://open.metu.edu.tr:11511/100330","is_oa":false,"landing_page_url":"https://hdl.handle.net/11511/100330","pdf_url":null,"source":{"id":"https://openalex.org/S4306402495","display_name":"OpenMETU (Middle East Technical University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I201799495","host_organization_name":"Middle East Technical University","host_organization_lineage":["https://openalex.org/I201799495"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"14th International Conference on Security of Information and Networks (SIN)","raw_type":"Conference Paper"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"},{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1985439922","https://openalex.org/W2061171222","https://openalex.org/W2061949491","https://openalex.org/W2069441027","https://openalex.org/W2098290658","https://openalex.org/W2751110934","https://openalex.org/W2791664942"],"related_works":["https://openalex.org/W4312813683","https://openalex.org/W1531522605","https://openalex.org/W4384027664","https://openalex.org/W2011670317","https://openalex.org/W2095023645","https://openalex.org/W2099770555","https://openalex.org/W4400224514","https://openalex.org/W2239154762","https://openalex.org/W1553510179","https://openalex.org/W4200446781"],"abstract_inverted_index":{"National":[0],"Institute":[1],"of":[2,16,58,79,94,112,154,157],"Standards":[3],"and":[4,14,28,39,103,114,132,146,159,173],"Technology":[5],"(NIST)":[6],"initiated":[7],"a":[8,126],"post-quantum":[9],"standardization":[10],"process":[11],"in":[12,63,98,117],"2016,":[13],"as":[15],"July":[17],"2020,":[18],"Round":[19],"3":[20],"candidates":[21],"were":[22],"announced.":[23],"Among":[24],"these":[25],"candidates,":[26],"Crystals-Kyber":[27],"Crystals-Dilithium":[29],"are":[30,68,161],"the":[31,45,59,80,92,110,121,143,149,168],"most":[32,60,81],"promising":[33],"lattice-based":[34,122],"key":[35],"encapsulation":[36],"mechanism":[37],"(KEM)":[38],"signature":[40],"algorithm":[41],"that":[42],"rely":[43],"on":[44,109,163],"module":[46],"learning":[47],"with":[48],"errors":[49],"(Module-LWE)":[50],"problem.":[51],"In":[52],"general,":[53],"polynomial":[54,70],"multiplication":[55,71,100],"is":[56,84,134,142,148],"one":[57],"time-consuming":[61],"operations":[62,96,156],"Module-LWE":[64],"based":[65],"cryptosystems.":[66,105],"There":[67],"several":[69],"methods":[72,83],"for":[73,101,120,136],"multiplying":[74],"two":[75],"polynomials":[76],"effectively.":[77],"One":[78],"efficient":[82],"Number":[85],"Theoretic":[86],"Transform":[87],"(NTT).":[88],"This":[89],"paper":[90],"analyzes":[91],"number":[93,111],"arithmetic":[95,155],"occupied":[97],"NTT":[99,118],"Kyber":[102,131,158],"Dilithium":[104,133,160],"The":[106],"general":[107],"formula":[108],"multiplications":[113],"additions":[115],"used":[116],"operation":[119],"algorithms":[123],"which":[124],"have":[125],"ring":[127],"structure":[128],"similar":[129],"to":[130,166],"given":[135],"<tex>$q":[137],"&lt;":[138],"2^{w-1}$</tex>":[139],"where":[140],"<tex>$w$</tex>":[141],"word":[144],"size":[145],"<tex>$q$</tex>":[147],"modulus.":[150],"Also,":[151],"cycle":[152,174],"counts":[153],"calculated":[162],"reference":[164],"implementations":[165],"determine":[167],"relationship":[169],"between":[170],"our":[171],"formulations":[172],"counts.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
