{"id":"https://openalex.org/W7130435621","doi":"https://doi.org/10.1007/s10623-025-01796-5","title":"Security analysis of the P-SPN structure with a class of linear layer matrix against invariant subspace attack","display_name":"Security analysis of the P-SPN structure with a class of linear layer matrix against invariant subspace attack","publication_year":2026,"publication_date":"2026-02-18","ids":{"openalex":"https://openalex.org/W7130435621","doi":"https://doi.org/10.1007/s10623-025-01796-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-025-01796-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-025-01796-5","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"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":"Designs, Codes and Cryptography","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/A5035683782","display_name":"E Duan","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"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/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ee Duan","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","University of Chinese Academy of Sciences, Beijing, 100049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022492800","display_name":"Wenling Wu","orcid":"https://orcid.org/0000-0002-7974-5544"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"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/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenling Wu","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","University of Chinese Academy of Sciences, Beijing, 100049, China","Zhongguancun Laboratory, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, 100049, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Zhongguancun Laboratory, Beijing, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022492800"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818","https://openalex.org/I4210165038"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16793301,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"94","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.503000020980835,"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":0.503000020980835,"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":0.1687999963760376,"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/T11130","display_name":"Coding theory and cryptography","score":0.1509999930858612,"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/invariant-subspace","display_name":"Invariant subspace","score":0.49410000443458557},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4846999943256378},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.47920000553131104},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.47130000591278076},{"id":"https://openalex.org/keywords/matrix-analysis","display_name":"Matrix analysis","score":0.4593999981880188},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42590001225471497},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4068000018596649},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.382999986410141},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.3822999894618988},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.3693000078201294}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7432000041007996},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5054000020027161},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.49410000443458557},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4846999943256378},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.47920000553131104},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.47130000591278076},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.4593999981880188},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42590001225471497},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4068000018596649},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.3822999894618988},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.3693000078201294},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.35350000858306885},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35100001096725464},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.3506999909877777},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.3359000086784363},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2946999967098236},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2922999858856201},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2694999873638153},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26840001344680786},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.26579999923706055},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.26339998841285706},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2524999976158142},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-025-01796-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-025-01796-5","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"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":"Designs, Codes and Cryptography","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.6800382137298584}],"awards":[{"id":"https://openalex.org/G7838409408","display_name":null,"funder_award_id":"62072445","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W83473285","https://openalex.org/W584705194","https://openalex.org/W632399495","https://openalex.org/W1611243483","https://openalex.org/W2234480126","https://openalex.org/W2295458874","https://openalex.org/W2469100438","https://openalex.org/W2485873601","https://openalex.org/W2537089202","https://openalex.org/W2552640487","https://openalex.org/W2728494734","https://openalex.org/W2770809732","https://openalex.org/W2794866029","https://openalex.org/W2947157832","https://openalex.org/W2977846258","https://openalex.org/W3011201404","https://openalex.org/W3013174546","https://openalex.org/W3091014139","https://openalex.org/W3133710726","https://openalex.org/W3170477465","https://openalex.org/W3205150321","https://openalex.org/W4246457644","https://openalex.org/W4285241375","https://openalex.org/W4308361277","https://openalex.org/W4308391475","https://openalex.org/W4384010359","https://openalex.org/W4385654519","https://openalex.org/W4385654699","https://openalex.org/W4400866137","https://openalex.org/W4416010281","https://openalex.org/W6904191344"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-02-20T06:14:18.993340","created_date":"2026-02-19T00:00:00"}
