{"id":"https://openalex.org/W4415353380","doi":"https://doi.org/10.1109/isit63088.2025.11195593","title":"A Fast Chinese Remaindering Transform Over Finite Fields","display_name":"A Fast Chinese Remaindering Transform Over Finite Fields","publication_year":2025,"publication_date":"2025-06-22","ids":{"openalex":"https://openalex.org/W4415353380","doi":"https://doi.org/10.1109/isit63088.2025.11195593"},"language":null,"primary_location":{"id":"doi:10.1109/isit63088.2025.11195593","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit63088.2025.11195593","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE International Symposium on Information Theory (ISIT)","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/A5100408343","display_name":"Chao Chen","orcid":"https://orcid.org/0000-0002-2855-7500"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chao Chen","raw_affiliation_strings":["Xidian University,State Key Laboratory of ISN,Xi&#x0027;an,China"],"affiliations":[{"raw_affiliation_string":"Xidian University,State Key Laboratory of ISN,Xi&#x0027;an,China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054764523","display_name":"Sian-Jheng Lin","orcid":"https://orcid.org/0000-0002-6309-2876"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sian-Jheng Lin","raw_affiliation_strings":["School of Cyber Science and Technology, University of Science and Technology of China,Hefei,China"],"affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, University of Science and Technology of China,Hefei,China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023807587","display_name":"Yunghsiang S. Han","orcid":"https://orcid.org/0000-0002-3592-1681"},"institutions":[{"id":"https://openalex.org/I4210145761","display_name":"Shenzhen Institutes of Advanced Technology","ror":"https://ror.org/04gh4er46","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210145761"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunghsiang S. Han","raw_affiliation_strings":["Shenzhen Institute for Advanced Study, UESTC,Shenzhen,China"],"affiliations":[{"raw_affiliation_string":"Shenzhen Institute for Advanced Study, UESTC,Shenzhen,China","institution_ids":["https://openalex.org/I4210145761"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063124926","display_name":"Baoming Bai","orcid":"https://orcid.org/0000-0002-6161-5493"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Baoming Bai","raw_affiliation_strings":["Xidian University,State Key Laboratory of ISN,Xi&#x0027;an,China"],"affiliations":[{"raw_affiliation_string":"Xidian University,State Key Laboratory of ISN,Xi&#x0027;an,China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100408343"],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.44667867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.986299991607666,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.986299991607666,"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/T10601","display_name":"Handwritten Text Recognition Techniques","score":0.9606000185012817,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9585999846458435,"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/chinese-remainder-theorem","display_name":"Chinese remainder theorem","score":0.8104000091552734},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.8084999918937683},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7254999876022339},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4846999943256378},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4812000095844269},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42410001158714294},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.41999998688697815},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4120999872684479}],"concepts":[{"id":"https://openalex.org/C151635116","wikidata":"https://www.wikidata.org/wiki/Q193878","display_name":"Chinese remainder theorem","level":2,"score":0.8104000091552734},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.8084999918937683},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7254999876022339},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5999000072479248},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4846999943256378},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4812000095844269},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46320000290870667},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.41999998688697815},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4120999872684479},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.37459999322891235},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36010000109672546},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C158457486","wikidata":"https://www.wikidata.org/wiki/Q17104301","display_name":"Multidimensional systems","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.32749998569488525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3127000033855438},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2928999960422516},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C2778648169","wikidata":"https://www.wikidata.org/wiki/Q967768","display_name":"Compatibility (geochemistry)","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2635999917984009},{"id":"https://openalex.org/C36605576","wikidata":"https://www.wikidata.org/wiki/Q273188","display_name":"Cantor set","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit63088.2025.11195593","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit63088.2025.11195593","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W39299451","https://openalex.org/W2001350036","https://openalex.org/W2006324729","https://openalex.org/W2016391699","https://openalex.org/W2028707966","https://openalex.org/W2049807270","https://openalex.org/W2060113672","https://openalex.org/W2068624242","https://openalex.org/W2101303074","https://openalex.org/W2129270830","https://openalex.org/W2136570131","https://openalex.org/W2154220188","https://openalex.org/W2165853100","https://openalex.org/W2167511540","https://openalex.org/W2170389905","https://openalex.org/W2519202371","https://openalex.org/W2540879644","https://openalex.org/W2737593932","https://openalex.org/W2894692820","https://openalex.org/W2898356255","https://openalex.org/W2963700143","https://openalex.org/W2964028050","https://openalex.org/W4231896027"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4],"a":[5,20,29,33,55,82,111,147],"fast":[6],"Chinese":[7],"remaindering":[8],"transform":[9],"(FCRT)":[10],"over":[11,160],"finite":[12],"fields":[13],"by":[14,25,40],"exploring":[15],"Lin-Chung-Han":[16],"(LCH)-FFT.":[17],"We":[18],"take":[19],"new":[21],"approach":[22],"to":[23,31,99],"LCHFFT":[24],"formulating":[26],"it":[27,152],"as":[28,109,125,141],"procedure":[30],"compute":[32],"remainder":[34,75],"tree.":[35],"It":[36],"is":[37,107],"demonstrated":[38],"that":[39,78,94],"adopting":[41],"the":[42,46,74,129,144],"Cantor":[43],"basis":[44],"for":[45],"underlying":[47],"field":[48],"<tex":[49,60,84,88,100,113,122,131,154,161],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[50,61,85,89,101,114,123,132,155,162],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathbb{F}_{2}":[51],"Q$</tex>":[52],"of":[53,58,118],"LCH-FFT,":[54,151],"special":[56],"set":[57],"moduli":[59],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\left\\{M_{i}(x):":[62],"0":[63,136],"\\leq":[64,66,137,139],"i":[65,138],"n-1\\right\\}$</tex>,":[67],"termed":[68],"\u201cFFT-moduli\u201d,":[69],"can":[70],"be":[71],"picked":[72],"from":[73],"tree,":[76],"satisfying":[77],"they":[79],"reside":[80],"in":[81,167],"subfield":[83,148],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathbb{F}_{2^{q}}$</tex>,":[86],"specifically":[87],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$M_{i}(x)":[90],"\\in":[91,116],"\\mathbb{F}_{2^{q}}[x]$</tex>,":[92],"and":[93,127,169],"their":[95],"degrees":[96],"sum":[97],"up":[98],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$N=\\sum_{i=0}^{n-1}":[102],"\\operatorname{deg}":[103],"M_{i}(x)=2^{Q}$</tex>.":[104],"The":[105],"FCRT":[106,145],"defined":[108],"taking":[110],"polynomial":[112],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$f(x)":[115],"\\mathbb{F}_{2^{q}}[x]$</tex>":[117],"degree":[119],"less":[120],"than":[121],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$N$</tex>":[124],"input":[126],"computing":[128],"remainders":[130],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\left\\{f(x)":[133],"\\bmod":[134],"M_{i}(x):":[135],"n-1\\right\\}$</tex>":[140],"output.":[142],"Since":[143],"realizes":[146],"subtree":[149],"within":[150],"requires":[153],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$O(N":[156],"\\log":[157],"N)$</tex>":[158],"operations":[159],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathbb{F}_{2":[163],"q}$</tex>.":[164],"Potential":[165],"applications":[166],"coding":[168],"secret":[170],"sharing":[171],"are":[172],"also":[173],"discussed.":[174]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-21T00:00:00"}
