{"id":"https://openalex.org/W4411158044","doi":"https://doi.org/10.46586/tches.v2025.i3.668-692","title":"Algebraic Linear Analysis for Number Theoretic Transform in Lattice-Based Cryptography","display_name":"Algebraic Linear Analysis for Number Theoretic Transform in Lattice-Based Cryptography","publication_year":2025,"publication_date":"2025-06-05","ids":{"openalex":"https://openalex.org/W4411158044","doi":"https://doi.org/10.46586/tches.v2025.i3.668-692"},"language":"en","primary_location":{"id":"doi:10.46586/tches.v2025.i3.668-692","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i3.668-692","pdf_url":"https://moving-the-social.ub.rub.de/index.php/TCHES/article/download/12230/12037","source":{"id":"https://openalex.org/S4210207404","display_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","issn_l":"2569-2925","issn":["2569-2925"],"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 Cryptographic Hardware and Embedded Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://moving-the-social.ub.rub.de/index.php/TCHES/article/download/12230/12037","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066663646","display_name":"Chun-Ming Chiu","orcid":null},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chun-Ming Chiu","raw_affiliation_strings":["National Taiwan University, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Taiwan University, Taipei, Taiwan","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000257041","display_name":"Jiaxiang Liu","orcid":"https://orcid.org/0000-0002-6725-8167"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaxiang Liu","raw_affiliation_strings":["Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103341619","display_name":"Ming-Hsien Tsai","orcid":"https://orcid.org/0009-0001-7621-7981"},"institutions":[{"id":"https://openalex.org/I154864474","display_name":"National Taiwan University of Science and Technology","ror":"https://ror.org/00q09pe49","country_code":"TW","type":"education","lineage":["https://openalex.org/I154864474"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Ming-Hsien Tsai","raw_affiliation_strings":["National Taiwan University of Science and Technology, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Taiwan University of Science and Technology, Taipei, Taiwan","institution_ids":["https://openalex.org/I154864474"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054753413","display_name":"Xiaomu Shi","orcid":"https://orcid.org/0000-0001-6277-2813"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaomu Shi","raw_affiliation_strings":["Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023111671","display_name":"Bow-Yaw Wang","orcid":"https://orcid.org/0000-0002-5757-545X"},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Bow-Yaw Wang","raw_affiliation_strings":["Academia Sinica, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academia Sinica, Taipei, Taiwan","institution_ids":["https://openalex.org/I84653119"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016631189","display_name":"Bo\u2010Yin Yang","orcid":"https://orcid.org/0000-0002-9362-5282"},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Bo-Yin Yang","raw_affiliation_strings":["Academia Sinica, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academia Sinica, Taipei, Taiwan","institution_ids":["https://openalex.org/I84653119"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.059,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.82954454,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"2025","issue":"3","first_page":"668","last_page":"692"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.991599977016449,"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"}},{"id":"https://openalex.org/T10388","display_name":"Advanced Steganography and Watermarking Techniques","score":0.9811999797821045,"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/algebraic-number","display_name":"Algebraic number","score":0.6067250967025757},{"id":"https://openalex.org/keywords/lattice-based-cryptography","display_name":"Lattice-based cryptography","score":0.5808701515197754},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5729423761367798},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5003714561462402},{"id":"https://openalex.org/keywords/algebraic-analysis","display_name":"Algebraic analysis","score":0.4632806181907654},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4536338746547699},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34922274947166443},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33804917335510254},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3320753574371338},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26708847284317017},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22623476386070251},{"id":"https://openalex.org/keywords/quantum-cryptography","display_name":"Quantum cryptography","score":0.149619460105896},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13983601331710815},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13312506675720215},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12927737832069397},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.07030421495437622},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.06164601445198059}],"concepts":[{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6067250967025757},{"id":"https://openalex.org/C137660015","wikidata":"https://www.wikidata.org/wiki/Q6497083","display_name":"Lattice-based cryptography","level":5,"score":0.5808701515197754},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5729423761367798},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5003714561462402},{"id":"https://openalex.org/C554573382","wikidata":"https://www.wikidata.org/wiki/Q4723988","display_name":"Algebraic analysis","level":5,"score":0.4632806181907654},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4536338746547699},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34922274947166443},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33804917335510254},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3320753574371338},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26708847284317017},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22623476386070251},{"id":"https://openalex.org/C144901912","wikidata":"https://www.wikidata.org/wiki/Q471906","display_name":"Quantum cryptography","level":4,"score":0.149619460105896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13983601331710815},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13312506675720215},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12927737832069397},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.07030421495437622},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.06164601445198059},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46586/tches.v2025.i3.668-692","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i3.668-692","pdf_url":"https://moving-the-social.ub.rub.de/index.php/TCHES/article/download/12230/12037","source":{"id":"https://openalex.org/S4210207404","display_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","issn_l":"2569-2925","issn":["2569-2925"],"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 Cryptographic Hardware and Embedded Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9619f7dde6ae4a9d87f2831e5fa3b311","is_oa":true,"landing_page_url":"https://doaj.org/article/9619f7dde6ae4a9d87f2831e5fa3b311","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":"Transactions on Cryptographic Hardware and Embedded Systems, Vol 2025, Iss 3 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46586/tches.v2025.i3.668-692","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i3.668-692","pdf_url":"https://moving-the-social.ub.rub.de/index.php/TCHES/article/download/12230/12037","source":{"id":"https://openalex.org/S4210207404","display_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","issn_l":"2569-2925","issn":["2569-2925"],"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 Cryptographic Hardware and Embedded Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321041","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784"},{"id":"https://openalex.org/F4320331164","display_name":"National Science and Technology Council","ror":"https://ror.org/00wnb9798"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411158044.pdf","grobid_xml":"https://content.openalex.org/works/W4411158044.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2315723423","https://openalex.org/W1489923862","https://openalex.org/W5819577","https://openalex.org/W2188587181","https://openalex.org/W2096221836","https://openalex.org/W4232705780","https://openalex.org/W2359831739","https://openalex.org/W4288674537","https://openalex.org/W2497843319","https://openalex.org/W2249849083"],"abstract_inverted_index":{"The":[0],"topic":[1],"of":[2],"verifying":[3,44],"postquantum":[4,18,31],"cryptographic":[5,46,62],"software":[6,47],"has":[7],"never":[8],"been":[9,70],"more":[10,119],"pressing":[11],"than":[12],"today":[13],"between":[14],"the":[15,51,65,97,101,107],"new":[16],"NIST":[17],"cryptosystem":[19],"standards":[20],"being":[21],"finalized":[22],"and":[23,87,115,125,129],"various":[24],"countries":[25],"issuing":[26],"directives":[27],"to":[28,30,84,96,117],"switch":[29],"or":[32],"at":[33],"least":[34],"hybrid":[35],"cryptography":[36],"in":[37,43,50,59],"a":[38],"decade.":[39],"One":[40],"critical":[41],"issue":[42],"lattice-based":[45],"is":[48,134],"range-checking":[49],"finite-field":[52,127],"arithmetic":[53,86,120],"assembly":[54],"code":[55],"which":[56,111],"occurs":[57],"frequently":[58],"highly":[60],"optimized":[61],"software.":[63],"For":[64],"most":[66],"part":[67],"these":[68],"have":[69],"handled":[71],"by":[72],"Satisfiability":[73],"Modulo":[74],"Theory":[75],"(SMT)":[76],"but":[77],"so":[78],"far":[79],"they":[80],"mostly":[81],"are":[82],"restricted":[83],"Montgomery":[85],"16-bit":[88],"precision.":[89],"We":[90],"add":[91],"semi-automatic":[92],"range-check":[93],"reasoning":[94],"capability":[95],"CryptoLine":[98],"toolkit":[99],"via":[100,106],"Integer":[102],"Set":[103],"Library":[104],"(wrapped":[105],"python":[108],"package":[109],"islpy)":[110],"makes":[112],"it":[113],"easier":[114],"faster":[116],"verify":[118],"crypto":[121],"code,":[122],"including":[123],"Barrett":[124],"Plantard":[126],"arithmetic,":[128],"show":[130],"experimentally":[131],"that":[132],"this":[133],"viable":[135],"on":[136],"production":[137],"code.":[138]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}