{"id":"https://openalex.org/W1481596910","doi":"https://doi.org/10.1007/3-540-68339-9_10","title":"Efficient Multiplicative Sharing Schemes","display_name":"Efficient Multiplicative Sharing Schemes","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W1481596910","doi":"https://doi.org/10.1007/3-540-68339-9_10","mag":"1481596910"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-68339-9_10","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-68339-9_10","pdf_url":"https://link.springer.com/content/pdf/10.1007/3-540-68339-9_10.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/10.1007/3-540-68339-9_10.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044763974","display_name":"Simon R. Blackburn\u22c6","orcid":"https://orcid.org/0000-0003-0762-031X"},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Simon R. Blackburn","raw_affiliation_strings":["Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK","institution_ids":["https://openalex.org/I184558857"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053202585","display_name":"Mike Burmester","orcid":"https://orcid.org/0000-0001-5094-5668"},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mike Burmester","raw_affiliation_strings":["Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK","institution_ids":["https://openalex.org/I184558857"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008979622","display_name":"Yvo Desmedt","orcid":"https://orcid.org/0000-0002-6679-7484"},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yvo Desmedt","raw_affiliation_strings":["Dept. EE & CS, Univ. of Wisconsin \u2014 Milwaukee, P.O. Box 784, WI, 53201, Milwaukee, USA"],"affiliations":[{"raw_affiliation_string":"Dept. EE & CS, Univ. of Wisconsin \u2014 Milwaukee, P.O. Box 784, WI, 53201, Milwaukee, USA","institution_ids":["https://openalex.org/I43579087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081238744","display_name":"Peter Wild","orcid":"https://orcid.org/0000-0002-7344-1742"},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Peter R. Wild","raw_affiliation_strings":["Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK","institution_ids":["https://openalex.org/I184558857"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5044763974"],"corresponding_institution_ids":["https://openalex.org/I184558857"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":3.0523,"has_fulltext":true,"cited_by_count":49,"citation_normalized_percentile":{"value":0.89649753,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"107","last_page":"118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"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":1.0,"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":0.9988999962806702,"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":0.9947999715805054,"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":0.717221200466156},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6317988634109497},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6172673106193542},{"id":"https://openalex.org/keywords/secret-sharing","display_name":"Secret sharing","score":0.5864044427871704},{"id":"https://openalex.org/keywords/chinese-remainder-theorem","display_name":"Chinese remainder theorem","score":0.5231203436851501},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5206224918365479},{"id":"https://openalex.org/keywords/multiplicative-inverse","display_name":"Multiplicative inverse","score":0.5105444192886353},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.492471307516098},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.4921411871910095},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.4736144244670868},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.47306716442108154},{"id":"https://openalex.org/keywords/access-structure","display_name":"Access structure","score":0.46623915433883667},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.4509182274341583},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.43379220366477966},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32446175813674927},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32169657945632935},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.18015113472938538},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.15715578198432922},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.14119523763656616},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.13341718912124634}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.717221200466156},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6317988634109497},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6172673106193542},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.5864044427871704},{"id":"https://openalex.org/C151635116","wikidata":"https://www.wikidata.org/wiki/Q193878","display_name":"Chinese remainder theorem","level":2,"score":0.5231203436851501},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5206224918365479},{"id":"https://openalex.org/C157351203","wikidata":"https://www.wikidata.org/wiki/Q216906","display_name":"Multiplicative inverse","level":3,"score":0.5105444192886353},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.492471307516098},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.4921411871910095},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.4736144244670868},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.47306716442108154},{"id":"https://openalex.org/C2778950925","wikidata":"https://www.wikidata.org/wiki/Q4672474","display_name":"Access structure","level":4,"score":0.46623915433883667},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.4509182274341583},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.43379220366477966},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32446175813674927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32169657945632935},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.18015113472938538},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.15715578198432922},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.14119523763656616},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.13341718912124634},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-68339-9_10","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-68339-9_10","pdf_url":"https://link.springer.com/content/pdf/10.1007/3-540-68339-9_10.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:10.1007/3-540-68339-9_10","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-68339-9_10","pdf_url":"https://link.springer.com/content/pdf/10.1007/3-540-68339-9_10.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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1481596910.pdf","grobid_xml":"https://content.openalex.org/works/W1481596910.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W648970207","https://openalex.org/W1482427796","https://openalex.org/W1495826104","https://openalex.org/W1497802087","https://openalex.org/W1557783852","https://openalex.org/W1558225230","https://openalex.org/W1607430658","https://openalex.org/W1883290937","https://openalex.org/W1970606468","https://openalex.org/W1972339028","https://openalex.org/W2009432965","https://openalex.org/W2017557672","https://openalex.org/W2019573778","https://openalex.org/W2043613477","https://openalex.org/W2050687505","https://openalex.org/W2141420453","https://openalex.org/W2159401786","https://openalex.org/W2912577494","https://openalex.org/W2970097841"],"related_works":["https://openalex.org/W2968534096","https://openalex.org/W2400235324","https://openalex.org/W2355820377","https://openalex.org/W2397026637","https://openalex.org/W1556126392","https://openalex.org/W1520180051","https://openalex.org/W2147096936","https://openalex.org/W3152626823","https://openalex.org/W1574442789","https://openalex.org/W2397781788"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
