{"id":"https://openalex.org/W1556393797","doi":"https://doi.org/10.1007/978-3-540-89255-7_2","title":"Strongly Multiplicative and 3-Multiplicative Linear Secret Sharing Schemes","display_name":"Strongly Multiplicative and 3-Multiplicative Linear Secret Sharing Schemes","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1556393797","doi":"https://doi.org/10.1007/978-3-540-89255-7_2","mag":"1556393797"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-89255-7_2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-89255-7_2","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-540-89255-7_2.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":null,"license_id":null,"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":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-540-89255-7_2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101849591","display_name":"Zhifang Zhang","orcid":"https://orcid.org/0000-0002-3824-7821"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"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":true,"raw_author_name":"Zhifang Zhang","raw_affiliation_strings":["Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028081738","display_name":"Mulan Liu","orcid":null},"institutions":[{"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"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mulan Liu","raw_affiliation_strings":["Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088037430","display_name":"Yeow Meng Chee","orcid":"https://orcid.org/0000-0001-7823-8068"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yeow Meng Chee","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore"],"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063268716","display_name":"San Ling","orcid":"https://orcid.org/0000-0002-1978-3557"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"San Ling","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore"],"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090841998","display_name":"Huaxiong Wang","orcid":"https://orcid.org/0000-0002-7669-8922"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["AU","SG"],"is_corresponding":false,"raw_author_name":"Huaxiong Wang","raw_affiliation_strings":["Centre for Advanced Computing - Algorithms and Cryptography Department of Computing, Macquarie University, Australia","Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore"],"affiliations":[{"raw_affiliation_string":"Centre for Advanced Computing - Algorithms and Cryptography Department of Computing, Macquarie University, Australia","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101849591"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.8346,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.72904339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"19","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9962999820709229,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/multiplicative-function","display_name":"Multiplicative function","score":0.8642312288284302},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.8346004486083984},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.49259859323501587},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.46650972962379456},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4551820456981659},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44859352707862854},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2262551486492157},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11315047740936279}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.8642312288284302},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.8346004486083984},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.49259859323501587},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46650972962379456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4551820456981659},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44859352707862854},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2262551486492157},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11315047740936279},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-89255-7_2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-89255-7_2","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-540-89255-7_2.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":null,"license_id":null,"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:10.1007/978-3-540-89255-7_2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-89255-7_2","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-540-89255-7_2.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":null,"license_id":null,"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/G1609537680","display_name":null,"funder_award_id":"NRF-CRP","funder_id":"https://openalex.org/F4320320709","funder_display_name":"National Research Foundation Singapore"},{"id":"https://openalex.org/G3926388264","display_name":"Secure Multi-Party Computation","funder_award_id":"DP0665035","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G5302094078","display_name":null,"funder_award_id":"NRF-CRP2-2007-03","funder_id":"https://openalex.org/F4320320709","funder_display_name":"National Research Foundation Singapore"},{"id":"https://openalex.org/G7641028097","display_name":null,"funder_award_id":"M58110040","funder_id":"https://openalex.org/F4320320766","funder_display_name":"Nanyang Technological University"},{"id":"https://openalex.org/G89056297","display_name":null,"funder_award_id":"CRP2-2007-03","funder_id":"https://openalex.org/F4320320709","funder_display_name":"National Research Foundation Singapore"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320709","display_name":"National Research Foundation Singapore","ror":"https://ror.org/03cpyc314"},{"id":"https://openalex.org/F4320320766","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1556393797.pdf","grobid_xml":"https://content.openalex.org/works/W1556393797.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1533708960","https://openalex.org/W1556155774","https://openalex.org/W1572181357","https://openalex.org/W1574535057","https://openalex.org/W1582236684","https://openalex.org/W1600683719","https://openalex.org/W1601879746","https://openalex.org/W2027471022","https://openalex.org/W2077315235","https://openalex.org/W2092422002","https://openalex.org/W2097167239","https://openalex.org/W2120551550","https://openalex.org/W2124844315","https://openalex.org/W2809548040","https://openalex.org/W3128663643","https://openalex.org/W3141585064","https://openalex.org/W4229826396"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2387449261","https://openalex.org/W2418518962","https://openalex.org/W2963377682","https://openalex.org/W2043159103","https://openalex.org/W2391769344","https://openalex.org/W2359260952","https://openalex.org/W4297790016","https://openalex.org/W2769269860","https://openalex.org/W1997156598"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
