{"id":"https://openalex.org/W1966735860","doi":"https://doi.org/10.1007/s11432-009-0159-9","title":"Probability method for cryptanalysis of general multivariate modular linear equation","display_name":"Probability method for cryptanalysis of general multivariate modular linear equation","publication_year":2009,"publication_date":"2009-10-01","ids":{"openalex":"https://openalex.org/W1966735860","doi":"https://doi.org/10.1007/s11432-009-0159-9","mag":"1966735860"},"language":"en","primary_location":{"id":"doi:10.1007/s11432-009-0159-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11432-009-0159-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210224633","display_name":"Science in China Series F Information Sciences","issn_l":"1009-2757","issn":["1009-2757","1862-2836"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science in China Series F: Information Sciences","raw_type":"journal-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/A5022791383","display_name":"Haijian Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"HaiJian Zhou","raw_affiliation_strings":["Tsinghua National Laboratory for Information Science and Technology (TNlist), Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China","Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua National Laboratory for Information Science and Technology (TNlist), Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101643492","display_name":"Ping Luo","orcid":"https://orcid.org/0000-0002-8167-1900"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ping Luo","raw_affiliation_strings":["School of Software, Tsinghua University, Beijing, 100084, China","Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Software, Tsinghua University, Beijing, 100084, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":null,"display_name":"DaoShun Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"DaoShun Wang","raw_affiliation_strings":["Tsinghua National Laboratory for Information Science and Technology (TNlist), Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China","Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua National Laboratory for Information Science and Technology (TNlist), Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108446559","display_name":"Yiqi Dai","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YiQi Dai","raw_affiliation_strings":["Tsinghua National Laboratory for Information Science and Technology (TNlist), Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China","Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua National Laboratory for Information Science and Technology (TNlist), Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022791383"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0805237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"52","issue":"10","first_page":"1792","last_page":"1800"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9997000098228455,"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":0.9997000098228455,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9994999766349792,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6657283306121826},{"id":"https://openalex.org/keywords/cryptanalysis","display_name":"Cryptanalysis","score":0.5859012603759766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5727330446243286},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5281094312667847},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.45382675528526306},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.41891002655029297},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.4166661500930786},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.41476666927337646},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3923686742782593},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22699525952339172},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21327969431877136},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20606788992881775},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14589887857437134},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10062113404273987},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.07111239433288574}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6657283306121826},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.5859012603759766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5727330446243286},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5281094312667847},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.45382675528526306},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.41891002655029297},{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.4166661500930786},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.41476666927337646},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3923686742782593},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22699525952339172},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21327969431877136},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20606788992881775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14589887857437134},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10062113404273987},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.07111239433288574},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11432-009-0159-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11432-009-0159-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210224633","display_name":"Science in China Series F Information Sciences","issn_l":"1009-2757","issn":["1009-2757","1862-2836"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science in China Series F: Information Sciences","raw_type":"journal-article"},{"id":"mag:3146716742","is_oa":false,"landing_page_url":"https://en.cnki.com.cn/Article_en/CJFDTOTAL-JFXG200910010.htm","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"\u4e2d\u56fd\u79d1\u5b66(F\u8f91:\u4fe1\u606f\u79d1\u5b66)(\u82f1\u6587\u7248)","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1532770887","https://openalex.org/W1646776302","https://openalex.org/W1766548092","https://openalex.org/W1997888568","https://openalex.org/W2033785065","https://openalex.org/W2050689197","https://openalex.org/W2096221836","https://openalex.org/W2106287110","https://openalex.org/W2111416661","https://openalex.org/W2126483728","https://openalex.org/W2134863191","https://openalex.org/W2138880305","https://openalex.org/W2141040012","https://openalex.org/W2149789050","https://openalex.org/W2155178472","https://openalex.org/W6680765892"],"related_works":["https://openalex.org/W241127407","https://openalex.org/W2381035939","https://openalex.org/W1521824362","https://openalex.org/W2468477307","https://openalex.org/W2910645127","https://openalex.org/W162895179","https://openalex.org/W3177799343","https://openalex.org/W3119198325","https://openalex.org/W623642078","https://openalex.org/W3125085490"],"abstract_inverted_index":null,"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}