{"id":"https://openalex.org/W4384471326","doi":"https://doi.org/10.1007/978-3-031-37709-9_16","title":"Certified Verification for\u00a0Algebraic Abstraction","display_name":"Certified Verification for\u00a0Algebraic Abstraction","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4384471326","doi":"https://doi.org/10.1007/978-3-031-37709-9_16"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-37709-9_16","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-37709-9_16","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-37709-9_16.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-37709-9_16.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103341619","display_name":"Ming-Hsien Tsai","orcid":"https://orcid.org/0009-0001-7621-7981"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ming-Hsien Tsai","raw_affiliation_strings":["National Institute of Cyber Security, Taipei, Taiwan"],"affiliations":[{"raw_affiliation_string":"National Institute of Cyber Security, Taipei, Taiwan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068622571","display_name":"Yu-Fu Fu","orcid":"https://orcid.org/0000-0002-2451-4431"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu-Fu Fu","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, USA"],"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"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/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiaxiang Liu","raw_affiliation_strings":["Shenzhen University, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"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/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"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaomu Shi","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]},{"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"],"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"],"affiliations":[{"raw_affiliation_string":"Academia Sinica, Taipei, Taiwan","institution_ids":["https://openalex.org/I84653119"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5000257041"],"corresponding_institution_ids":["https://openalex.org/I180726961"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.5209,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65101266,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"329","last_page":"349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9994999766349792,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9994999766349792,"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":0.9993000030517578,"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/T11424","display_name":"Security and Verification in Computing","score":0.9986000061035156,"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/soundness","display_name":"Soundness","score":0.8664777278900146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.769851803779602},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.6828722357749939},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6029820442199707},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5167204737663269},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.4850982427597046},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.4843122065067291},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.47385910153388977},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.45406150817871094},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4333404004573822},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42301827669143677},{"id":"https://openalex.org/keywords/certification","display_name":"Certification","score":0.41370266675949097},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36108487844467163},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.3320072889328003},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30743902921676636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1502688229084015}],"concepts":[{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.8664777278900146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.769851803779602},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.6828722357749939},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6029820442199707},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5167204737663269},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.4850982427597046},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.4843122065067291},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.47385910153388977},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.45406150817871094},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4333404004573822},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42301827669143677},{"id":"https://openalex.org/C46304622","wikidata":"https://www.wikidata.org/wiki/Q374814","display_name":"Certification","level":2,"score":0.41370266675949097},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36108487844467163},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.3320072889328003},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30743902921676636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1502688229084015},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-37709-9_16","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-37709-9_16","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-37709-9_16.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-37709-9_16","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-37709-9_16","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-37709-9_16.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1709975844","display_name":null,"funder_award_id":"2022A1515011","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G1762991518","display_name":null,"funder_award_id":"EP/V00252X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2041635355","display_name":null,"funder_award_id":"AS-IA-109-M01","funder_id":"https://openalex.org/F4320321041","funder_display_name":"Academia Sinica"},{"id":"https://openalex.org/G3700602200","display_name":null,"funder_award_id":"1501088","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3757194791","display_name":null,"funder_award_id":"JCYJ20","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G384178317","display_name":null,"funder_award_id":"02008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G42895381","display_name":null,"funder_award_id":"62002228","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4441624775","display_name":null,"funder_award_id":"51501145","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4488680036","display_name":null,"funder_award_id":"2022A15","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5881942141","display_name":null,"funder_award_id":"202103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6437360502","display_name":null,"funder_award_id":"2021032","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6782968491","display_name":null,"funder_award_id":"51501088","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7097245526","display_name":null,"funder_award_id":"61836005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8161904097","display_name":null,"funder_award_id":"202008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8527195007","display_name":null,"funder_award_id":"AS-KPQ-109-DSTCP","funder_id":"https://openalex.org/F4320321041","funder_display_name":"Academia Sinica"},{"id":"https://openalex.org/G8554118371","display_name":null,"funder_award_id":"2022A1515011458, 2022A1515010880","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321041","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null},{"id":"https://openalex.org/F4320325571","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70"},{"id":"https://openalex.org/F4320326705","display_name":"Science, Technology and Innovation Commission of Shenzhen Municipality","ror":null},{"id":"https://openalex.org/F4320331164","display_name":"National Science and Technology Council","ror":"https://ror.org/00wnb9798"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4384471326.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W565004971","https://openalex.org/W1553511155","https://openalex.org/W2003141394","https://openalex.org/W2004814164","https://openalex.org/W2050804394","https://openalex.org/W2158519138","https://openalex.org/W2734612968","https://openalex.org/W2766912712","https://openalex.org/W2866028610","https://openalex.org/W2928036819","https://openalex.org/W2984214499","https://openalex.org/W2997561197","https://openalex.org/W2998997824","https://openalex.org/W3183490041","https://openalex.org/W4294325602","https://openalex.org/W4300166240"],"related_works":["https://openalex.org/W1511249877","https://openalex.org/W2466303427","https://openalex.org/W1578828174","https://openalex.org/W2000943029","https://openalex.org/W2950376466","https://openalex.org/W4302559785","https://openalex.org/W4226437312","https://openalex.org/W2949331520","https://openalex.org/W2140496290","https://openalex.org/W2290698615"],"abstract_inverted_index":{"Abstract":[0],"We":[1,47,76],"present":[2],"a":[3],"certified":[4,80],"algebraic":[5,15],"abstraction":[6,53],"technique":[7,61],"for":[8,41],"verifying":[9],"bit-accurate":[10,42],"non-linear":[11,64],"integer":[12],"computations.":[13],"In":[14],"abstraction,":[16],"programs":[17,85],"are":[18,29,39],"lifted":[19],"to":[20,31,50],"polynomial":[21,34],"equations":[22],"in":[23,66],"the":[24,79,87],"abstract":[25,33],"domain.":[26],"Algebraic":[27],"techniques":[28],"employed":[30],"analyze":[32],"programs;":[35],"SMT":[36],"QF_BV":[37],"solvers":[38],"adopted":[40],"analysis":[43],"of":[44,82],"soundness":[45],"conditions.":[46],"explain":[48],"how":[49],"verify":[51],"our":[52],"algorithm":[54],"and":[55,73],"certify":[56],"verification":[57,81],"results.":[58],"Our":[59],"hybrid":[60],"has":[62],"verified":[63],"computations":[65],"various":[67],"security":[68],"libraries":[69],"such":[70],"as":[71],"Bitcoin":[72],"OpenSSL":[74],".":[75,91],"also":[77],"report":[78],"Number-Theoretic":[83],"Transform":[84],"from":[86],"post-quantum":[88],"cryptosystem":[89],"Kyber":[90]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}