{"id":"https://openalex.org/W4367050730","doi":"https://doi.org/10.1007/s12095-023-00639-1","title":"Differential and Linear properties of vectorial boolean functions based on chi","display_name":"Differential and Linear properties of vectorial boolean functions based on chi","publication_year":2023,"publication_date":"2023-04-26","ids":{"openalex":"https://openalex.org/W4367050730","doi":"https://doi.org/10.1007/s12095-023-00639-1","pmid":"https://pubmed.ncbi.nlm.nih.gov/37927823"},"language":"en","primary_location":{"id":"doi:10.1007/s12095-023-00639-1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s12095-023-00639-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-023-00639-1.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography and Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s12095-023-00639-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067049629","display_name":"Silvia Mella","orcid":"https://orcid.org/0000-0002-4664-3541"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Silvia Mella","raw_affiliation_strings":["Digital Security Group, Radboud University, Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security Group, Radboud University, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027799923","display_name":"Alireza Mehrdad","orcid":"https://orcid.org/0000-0001-6341-7944"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Alireza Mehrdad","raw_affiliation_strings":["Digital Security Group, Radboud University, Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security Group, Radboud University, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055847285","display_name":"Joan Daemen","orcid":"https://orcid.org/0000-0002-4102-0775"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Joan Daemen","raw_affiliation_strings":["Digital Security Group, Radboud University, Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security Group, Radboud University, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067049629"],"corresponding_institution_ids":["https://openalex.org/I145872427"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.1758,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.53200333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"15","issue":"6","first_page":"1087","last_page":"1116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","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/T11130","display_name":"Coding theory and cryptography","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/T10951","display_name":"Cryptographic Implementations and 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":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-cryptanalysis","display_name":"Linear cryptanalysis","score":0.8371363878250122},{"id":"https://openalex.org/keywords/differential-cryptanalysis","display_name":"Differential cryptanalysis","score":0.6876537799835205},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.6847356557846069},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6451279520988464},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6245695352554321},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5354832410812378},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4917779266834259},{"id":"https://openalex.org/keywords/cryptographic-primitive","display_name":"Cryptographic primitive","score":0.4783037304878235},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45062947273254395},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4179306626319885},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4022487998008728},{"id":"https://openalex.org/keywords/cryptanalysis","display_name":"Cryptanalysis","score":0.39175015687942505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3855651319026947},{"id":"https://openalex.org/keywords/cryptographic-protocol","display_name":"Cryptographic protocol","score":0.2895137071609497},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07703176140785217}],"concepts":[{"id":"https://openalex.org/C82424418","wikidata":"https://www.wikidata.org/wiki/Q1826463","display_name":"Linear cryptanalysis","level":4,"score":0.8371363878250122},{"id":"https://openalex.org/C36123800","wikidata":"https://www.wikidata.org/wiki/Q1224471","display_name":"Differential cryptanalysis","level":4,"score":0.6876537799835205},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.6847356557846069},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6451279520988464},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6245695352554321},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5354832410812378},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4917779266834259},{"id":"https://openalex.org/C15927051","wikidata":"https://www.wikidata.org/wiki/Q246593","display_name":"Cryptographic primitive","level":4,"score":0.4783037304878235},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45062947273254395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4179306626319885},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4022487998008728},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.39175015687942505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3855651319026947},{"id":"https://openalex.org/C33884865","wikidata":"https://www.wikidata.org/wiki/Q1254335","display_name":"Cryptographic protocol","level":3,"score":0.2895137071609497},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07703176140785217},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s12095-023-00639-1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s12095-023-00639-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-023-00639-1.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography and Communications","raw_type":"journal-article"},{"id":"pmid:37927823","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37927823","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography and communications : discrete structures, Boolean functions and sequences","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10624758","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10624758","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10624758/pdf/12095_2023_Article_639.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cryptogr Commun","raw_type":"Text"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/298020","is_oa":true,"landing_page_url":"https://hdl.handle.net/2066/298020","pdf_url":"https://repository.ubn.ru.nl//bitstream/handle/2066/298020/298020.pdf","source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article / Letter to editor"}],"best_oa_location":{"id":"doi:10.1007/s12095-023-00639-1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s12095-023-00639-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-023-00639-1.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography and Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2286086968","display_name":null,"funder_award_id":"ERC-2017-ADG Nr. 788980 ESCADA","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4367050730.pdf"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1572300106","https://openalex.org/W1587687098","https://openalex.org/W2024156986","https://openalex.org/W2173356534","https://openalex.org/W3088704016","https://openalex.org/W4210793868","https://openalex.org/W4213335922","https://openalex.org/W4232988949","https://openalex.org/W4240574532","https://openalex.org/W4282040101","https://openalex.org/W4311870646"],"related_works":["https://openalex.org/W1907974733","https://openalex.org/W2786560893","https://openalex.org/W2137326899","https://openalex.org/W321472610","https://openalex.org/W2541280449","https://openalex.org/W2390821355","https://openalex.org/W4378376555","https://openalex.org/W2552531143","https://openalex.org/W2086160109","https://openalex.org/W4387485962"],"abstract_inverted_index":{"To":[0],"evaluate":[1],"the":[2,29,78,84,145,170,216,219,231,250,257],"security":[3],"of":[4,31,41,48,70,81,90,141,150,157,176,193,206,221,224,233,237,252,260],"a":[5,42,46,139,166,190,234,241],"cryptographic":[6,20,60],"primitive,":[7],"investigating":[8],"its":[9],"resistance":[10],"against":[11],"differential":[12,86,146,174],"and":[13,45,65,77,87,147,184,200,230,262],"linear":[14,49,88,148,203],"cryptanalysis":[15],"is":[16,56,73],"required.":[17],"Many":[18],"modern":[19],"primitives":[21,61],"repeatedly":[22],"apply":[23,249],"similar":[24],"round":[25,32,37],"functions":[26],"alternated":[27],"with":[28,102,268],"addition":[30],"keys":[33],"or":[34,124],"constants.":[35],"A":[36],"function":[38],"usually":[39],"consists":[40],"non-linear":[43,52,79,171,258],"mapping":[44,53,94],"number":[47],"mappings.":[50],"The":[51,93],"<mml:math":[54,71,91,95,151,177,207,225,238,269],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c7</mml:mi></mml:math>":[55,72,96,152,178,226,239],"used":[57,74],"in":[58,75,116,133,182,185],"different":[59,103],"such":[62],"as":[63,115,132],"Keccak":[64],"Subterranean.":[66],"An":[67],"alternative":[68,155],"version":[69],"Ascon":[76,261],"layer":[80],"Simon":[82,263],"has":[83],"same":[85],"properties":[89,149,175,205],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c7</mml:mi></mml:math>.":[92,208,270],"can":[97,108,126,248],"be":[98,109,127],"applied":[99,111,128],"to":[100,112,129,162,164,210,256,265],"strings":[101,114,131,229],"lengths.":[104],"For":[105],"instance,":[106],"it":[107,119,125,136],"parallelly":[110],"small-length":[113,228],"Keccak,":[117],"where":[118,135],"works":[120,137],"on":[121,138,154,227,240],"5-bit":[122],"strings,":[123,158],"big-length":[130,242],"Subterranean,":[134],"string":[140],"length":[142],"257.":[143],"Investigating":[144],"working":[153],"lengths":[156],"provides":[159],"useful":[160],"information":[161],"designers":[163],"make":[165],"better":[167],"choice":[168],"for":[169],"layer.":[172],"Some":[173],"have":[179],"been":[180],"analyzed":[181],"[8]":[183],"this":[186,198,253],"work":[187],"we":[188,201,214,247],"provide":[189],"revised":[191],"presentation":[192],"them.":[194],"We":[195,244],"then":[196],"extend":[197,215],"study":[199,254],"analyze":[202],"propagation":[204],"Thanks":[209],"these":[211],"additional":[212],"results,":[213],"comparison":[217],"between":[218],"application":[220,232],"parallel":[222],"instances":[223],"single":[235],"instance":[236],"string.":[243],"show":[245],"how":[246],"results":[251],"also":[255],"layers":[259],"thanks":[264],"their":[266],"affine-equivalence":[267]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}