{"id":"https://openalex.org/W4410412760","doi":"https://doi.org/10.32604/cmc.2025.065085","title":"Polynomial Commitment in a Verkle Tree Based on a Non-Positional Polynomial Notation","display_name":"Polynomial Commitment in a Verkle Tree Based on a Non-Positional Polynomial Notation","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4410412760","doi":"https://doi.org/10.32604/cmc.2025.065085"},"language":"en","primary_location":{"id":"doi:10.32604/cmc.2025.065085","is_oa":true,"landing_page_url":"https://doi.org/10.32604/cmc.2025.065085","pdf_url":null,"source":{"id":"https://openalex.org/S4210191605","display_name":"Computers, materials & continua/Computers, materials & continua (Print)","issn_l":"1546-2218","issn":["1546-2218","1546-2226"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers, Materials & Continua","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.32604/cmc.2025.065085","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000411485","display_name":"\u041a\u0443\u043d\u0431\u043e\u043b\u0430\u0442 \u0410\u043b\u0433\u0430\u0437\u044b","orcid":"https://orcid.org/0000-0003-3670-2170"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kunbolat T. Algazy","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058839405","display_name":"Kairat Sakan","orcid":"https://orcid.org/0000-0002-6812-6000"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kairat S. Sakan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006925601","display_name":"Saule E. Nyssanbayeva","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saule E. Nyssanbayeva","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081628522","display_name":"\u0410\u0440\u0434\u0430\u0431\u0435\u043a \u0425\u043e\u043c\u043f\u044b\u0448","orcid":"https://orcid.org/0000-0002-0702-9346"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ardabek Khompysh","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5000411485"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14165666,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"84","issue":"1","first_page":"1581","last_page":"1595"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.7681999802589417,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11106","display_name":"Data Management and Algorithms","score":0.7681999802589417,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/notation","display_name":"Notation","score":0.6489429473876953},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6223584413528442},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5852881669998169},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.4995543956756592},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.49066269397735596},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37879565358161926},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35815396904945374},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2677823603153229},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1821686029434204},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06971356272697449}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6489429473876953},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6223584413528442},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5852881669998169},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.4995543956756592},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.49066269397735596},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37879565358161926},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35815396904945374},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2677823603153229},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1821686029434204},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06971356272697449}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.32604/cmc.2025.065085","is_oa":true,"landing_page_url":"https://doi.org/10.32604/cmc.2025.065085","pdf_url":null,"source":{"id":"https://openalex.org/S4210191605","display_name":"Computers, materials & continua/Computers, materials & continua (Print)","issn_l":"1546-2218","issn":["1546-2218","1546-2226"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers, Materials & Continua","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.32604/cmc.2025.065085","is_oa":true,"landing_page_url":"https://doi.org/10.32604/cmc.2025.065085","pdf_url":null,"source":{"id":"https://openalex.org/S4210191605","display_name":"Computers, materials & continua/Computers, materials & continua (Print)","issn_l":"1546-2218","issn":["1546-2218","1546-2226"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers, Materials & Continua","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.46000000834465027,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W33646188","https://openalex.org/W1909324101","https://openalex.org/W3035286518","https://openalex.org/W3096061848","https://openalex.org/W3189233848","https://openalex.org/W4286214339","https://openalex.org/W4308207204","https://openalex.org/W4375928292","https://openalex.org/W4389391360","https://openalex.org/W4390906665","https://openalex.org/W4391430481","https://openalex.org/W4392427204","https://openalex.org/W4399745991","https://openalex.org/W4400228954","https://openalex.org/W4402949791","https://openalex.org/W4403936938","https://openalex.org/W4406167468","https://openalex.org/W4407252204","https://openalex.org/W4408423125"],"related_works":["https://openalex.org/W2056024401","https://openalex.org/W2149734642","https://openalex.org/W4311251537","https://openalex.org/W3216258873","https://openalex.org/W2185931218","https://openalex.org/W4320917455","https://openalex.org/W2617044949","https://openalex.org/W4298079332","https://openalex.org/W4205471980","https://openalex.org/W2365733060"],"abstract_inverted_index":{"This":[0,96],"paper":[1],"examines":[2],"the":[3,6,27,44,70,130,184,198,204],"application":[4,145],"of":[5,129,162,186],"Verkle":[7,28,52,116,211],"tree\u2014an":[8],"efficient":[9,77,230],"data":[10,78,84,100],"structure":[11],"that":[12,191,207],"leverages":[13],"commitments":[14],"and":[15,37,80,93,112,134,147,158,165,183,223,229],"a":[16,59,64,148],"novel":[17],"proof":[18,113],"technique":[19,97],"in":[20,106,115,121,197],"cryptographic":[21,107],"solutions.":[22],"Unlike":[23],"traditional":[24],"Merkle":[25],"trees,":[26,117],"tree":[29],"significantly":[30],"reduces":[31],"signature":[32],"size":[33],"by":[34,82],"utilizing":[35],"polynomial":[36,66],"vector":[38],"commitments.":[39],"Compact":[40],"proofs":[41],"also":[42],"accelerate":[43],"verification":[45,81],"process,":[46],"reducing":[47,91],"computational":[48,125],"overhead,":[49,92],"which":[50,102],"makes":[51],"trees":[53,212],"particularly":[54],"useful.":[55],"The":[56],"study":[57,205],"proposes":[58],"new":[60],"approach":[61,218],"based":[62,154],"on":[63,155],"non-positional":[65],"notation":[67],"(NPN)":[68],"employing":[69],"Chinese":[71],"Remainder":[72],"Theorem":[73],"(CRT).":[74],"CRT":[75,209],"enables":[76],"representation":[79],"decomposing":[83],"into":[85],"smaller,":[86],"independent":[87],"components,":[88],"simplifying":[89],"computations,":[90],"enhancing":[94],"scalability.":[95],"facilitates":[98],"parallel":[99],"processing,":[101],"is":[103],"especially":[104],"advantageous":[105],"applications":[108],"such":[109],"as":[110,118,120],"commitment":[111],"construction":[114],"well":[119],"systems":[122,222,226],"with":[123,151,210],"constrained":[124],"resources.":[126],"Theoretical":[127],"foundations":[128],"approach,":[131],"its":[132],"advantages,":[133],"practical":[135],"implementation":[136],"aspects":[137],"are":[138],"explored,":[139],"including":[140,167],"resistance":[141],"to":[142],"potential":[143,163],"attacks,":[144,172],"domains,":[146],"comparative":[149],"analysis":[150,161],"existing":[152],"methods":[153],"well-known":[156],"parameters":[157],"characteristics.":[159],"An":[160],"attacks":[164,175],"vulnerabilities,":[166],"greatest":[168],"common":[169],"divisor":[170],"(GCD)":[171],"approximate":[173],"multiple":[174],"(LLL":[176],"lattice-based),":[177],"brute-force":[178],"search":[179],"for":[180,220],"irreducible":[181],"polynomials,":[182],"estimation":[185],"their":[187],"total":[188],"number,":[189],"indicates":[190],"no":[192],"vulnerabilities":[193],"have":[194],"been":[195],"identified":[196],"proposed":[199],"method":[200],"thus":[201],"far.":[202],"Furthermore,":[203],"demonstrates":[206],"integrating":[208],"ensures":[213],"high":[214],"scalability,":[215],"making":[216],"this":[217],"promising":[219],"blockchain":[221],"other":[224],"distributed":[225],"requiring":[227],"compact":[228],"proofs.":[231]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}