{"id":"https://openalex.org/W7136896622","doi":"https://doi.org/10.46586/tosc.v2026.i1.468-505","title":"Cryptanalytic Extraction of Neural Networks with Various Activation Functions","display_name":"Cryptanalytic Extraction of Neural Networks with Various Activation Functions","publication_year":2026,"publication_date":"2026-03-16","ids":{"openalex":"https://openalex.org/W7136896622","doi":"https://doi.org/10.46586/tosc.v2026.i1.468-505"},"language":"en","primary_location":{"id":"doi:10.46586/tosc.v2026.i1.468-505","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2026.i1.468-505","pdf_url":null,"source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.46586/tosc.v2026.i1.468-505","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129464200","display_name":"Xiaokang Qi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaokang Qi","raw_affiliation_strings":["School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I4210132990","https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129441811","display_name":"Hao Lei","orcid":null},"institutions":[{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Lei","raw_affiliation_strings":["School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I4210132990","https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048145450","display_name":"Longxiang Wei","orcid":null},"institutions":[{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Longxiang Wei","raw_affiliation_strings":["School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I4210132990","https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111662666","display_name":"Xiaohan Sun","orcid":"https://orcid.org/0009-0004-2724-4205"},"institutions":[{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohan Sun","raw_affiliation_strings":["School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I4210132990","https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100707460","display_name":"Mengdi Wang","orcid":"https://orcid.org/0000-0002-2101-9507"},"institutions":[{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Meiqin Wang","raw_affiliation_strings":["School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, 266237, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I4210132990","https://openalex.org/I80143920"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":23.4316,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.99283384,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"2026","issue":"1","first_page":"468","last_page":"505"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.6018999814987183,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.6018999814987183,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.07720000296831131,"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/T11241","display_name":"Advanced Malware Detection Techniques","score":0.05400000140070915,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/activation-function","display_name":"Activation function","score":0.7781000137329102},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6011000275611877},{"id":"https://openalex.org/keywords/scope","display_name":"Scope (computer science)","score":0.4392000138759613},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4043999910354614},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.39809998869895935},{"id":"https://openalex.org/keywords/extraction","display_name":"Extraction (chemistry)","score":0.39149999618530273}],"concepts":[{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.7781000137329102},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7354000210762024},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6011000275611877},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5357999801635742},{"id":"https://openalex.org/C2778012447","wikidata":"https://www.wikidata.org/wiki/Q1034415","display_name":"Scope (computer science)","level":2,"score":0.4392000138759613},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.39820000529289246},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C4725764","wikidata":"https://www.wikidata.org/wiki/Q844704","display_name":"Extraction (chemistry)","level":2,"score":0.39149999618530273},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C153604712","wikidata":"https://www.wikidata.org/wiki/Q7310755","display_name":"Relationship extraction","level":3,"score":0.31360000371932983},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.26010000705718994}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46586/tosc.v2026.i1.468-505","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2026.i1.468-505","pdf_url":null,"source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0abe18c151fc4bcbbb7b97147bac313f","is_oa":true,"landing_page_url":"https://doaj.org/article/0abe18c151fc4bcbbb7b97147bac313f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Transactions on Symmetric Cryptology, Vol 2026, Iss 1 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46586/tosc.v2026.i1.468-505","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2026.i1.468-505","pdf_url":null,"source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Originally":[0],"introduced":[1],"as":[2,14],"a":[3,15,73,81,97,163,235],"machine":[4,248],"learning":[5,249],"problem":[6],"in":[7,27,44,157,194],"1991,":[8],"model":[9,42,93,147,191,231],"extraction":[10,43,76,94,148,192,232],"was":[11],"explicitly":[12],"cast":[13],"cryptanalytic":[16],"challenge":[17],"at":[18],"CRYPTO":[19],"2020":[20],"and":[21,117,130,153,178,198,214,233,247],"has":[22],"since":[23],"gained":[24],"increasing":[25],"prominence":[26],"this":[28,140],"context.":[29],"While":[30],"early":[31],"work":[32,226],"focused":[33],"on":[34,53],"ReLU-based":[35],"neural":[36,211],"networks,":[37],"recent":[38],"studies":[39],"have":[40,240],"investigated":[41],"the":[45,90,131,135,142,158,168,196,204,245],"raw-output":[46,197],"setting":[47],"for":[48,75,100,149,154,210,243],"PReLU-based":[49,155],"models.":[50],"However,":[51],"research":[52],"other":[54,122],"activation":[55,64,85,111,123,151,172,208,220],"functions":[56,65,152,209,221],"remains":[57],"largely":[58],"unexplored.":[59],"In":[60,113],"modern":[61],"deep":[62],"learning,":[63],"beyond":[66],"ReLU":[67,116],"are":[68],"widely":[69],"used,":[70],"thereby":[71],"creating":[72],"need":[74],"techniques":[77],"that":[78,103,238],"can":[79],"accommodate":[80],"wider":[82],"variety":[83],"of":[84,92,110,137,167,170,185,207],"functions.":[86,112],"This":[87,225],"paper":[88],"broadens":[89],"scope":[91],"by":[95],"introducing":[96],"systematic":[98],"framework":[99,237],"parameter":[101],"recovery":[102],"is":[104,141,188],"specifically":[105],"tailored":[106],"to":[107,115,145],"different":[108],"categories":[109],"addition":[114],"PReLU,":[118],"we":[119,202],"investigate":[120],"several":[121],"functions,":[124],"including":[125],"Leaky":[126],"ReLU,":[127],"HardTanh,":[128],"ELU,":[129],"Step":[132],"function.":[133],"To":[134],"best":[136],"our":[138,186],"knowledge,":[139],"first":[143],"study":[144],"explore":[146,215],"these":[150],"models":[156],"hard-label":[159,199],"setting.":[160],"We":[161],"provide":[162],"detailed":[164],"theoretical":[165,181],"analysis":[166],"properties":[169],"each":[171],"function,":[173],"propose":[174],"novel":[175],"attack":[176],"strategies,":[177],"offer":[179],"new":[180],"insights.":[182],"The":[183],"effectiveness":[184],"approach":[187],"demonstrated":[189],"through":[190],"attacks":[193],"both":[195,244],"settings.":[200],"Moreover,":[201],"discuss":[203],"security":[205],"implications":[206,242],"network":[212],"design":[213],"how":[216],"composite":[217],"or":[218],"mixed":[219],"may":[222,239],"enhance":[223],"security.":[224],"provides":[227],"valuable":[228],"insights":[229],"into":[230],"introduces":[234],"flexible":[236],"meaningful":[241],"cryptographic":[246],"communities.":[250]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-08-13T07:04:57.449891","created_date":"2026-03-17T00:00:00"}