{"id":"https://openalex.org/W4395683508","doi":"https://doi.org/10.1007/s12095-024-00711-4","title":"Propagation properties of a non-linear mapping based on squaring in odd characteristic","display_name":"Propagation properties of a non-linear mapping based on squaring in odd characteristic","publication_year":2024,"publication_date":"2024-04-26","ids":{"openalex":"https://openalex.org/W4395683508","doi":"https://doi.org/10.1007/s12095-024-00711-4","pmid":"https://pubmed.ncbi.nlm.nih.gov/39679387"},"language":"en","primary_location":{"id":"doi:10.1007/s12095-024-00711-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12095-024-00711-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-024-00711-4.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/s12095-024-00711-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":true,"raw_author_name":"Joan Daemen","raw_affiliation_strings":["Digital Security, Radboud University, Toernooiveld 212, Nijmegen, 6525 EC The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security, Radboud University, Toernooiveld 212, Nijmegen, 6525 EC The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067553258","display_name":"Dani\u00ebl Kuijsters","orcid":"https://orcid.org/0000-0002-5651-6431"},"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":"Dani\u00ebl Kuijsters","raw_affiliation_strings":["Digital Security, Radboud University, Toernooiveld 212, Nijmegen, 6525 EC The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security, Radboud University, Toernooiveld 212, Nijmegen, 6525 EC The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"middle","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":false,"raw_author_name":"Silvia Mella","raw_affiliation_strings":["Digital Security, Radboud University, Toernooiveld 212, Nijmegen, 6525 EC The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security, Radboud University, Toernooiveld 212, Nijmegen, 6525 EC The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080623318","display_name":"Denise Verbakel","orcid":null},"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":"Denise Verbakel","raw_affiliation_strings":["Digital Security, Radboud University, Toernooiveld 212, Nijmegen, 6525 EC The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security, Radboud University, Toernooiveld 212, Nijmegen, 6525 EC The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055847285"],"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":1.022,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.79103603,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"16","issue":"5","first_page":"997","last_page":"1011"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9955999851226807,"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/invertible-matrix","display_name":"Invertible matrix","score":0.6514544486999512},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6096054315567017},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5982182025909424},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5062002539634705},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44632643461227417},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4189378619194031},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34039801359176636},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33008724451065063},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1351357400417328},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0783630907535553}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6514544486999512},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6096054315567017},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5982182025909424},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5062002539634705},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44632643461227417},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4189378619194031},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34039801359176636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33008724451065063},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1351357400417328},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0783630907535553},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s12095-024-00711-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12095-024-00711-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-024-00711-4.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:39679387","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39679387","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:11639138","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11639138","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11639138/pdf/12095_2024_Article_711.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:2066/309713","is_oa":true,"landing_page_url":"https://hdl.handle.net/2066/309713","pdf_url":"https://repository.ubn.ru.nl//bitstream/handle/2066/309713/309713.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/s12095-024-00711-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12095-024-00711-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-024-00711-4.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/G1219913396","display_name":null,"funder_award_id":"ERC-2017","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G1255872072","display_name":"Energy-optimized Symmetric Cryptography by Algebraic Duality Analysis","funder_award_id":"788980","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5246431558","display_name":null,"funder_award_id":"805031","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G55441724","display_name":null,"funder_award_id":"788980","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4395683508.pdf","grobid_xml":"https://content.openalex.org/works/W4395683508.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W156355313","https://openalex.org/W1471103927","https://openalex.org/W1485341243","https://openalex.org/W1553650484","https://openalex.org/W1625275637","https://openalex.org/W2064939672","https://openalex.org/W2157570430","https://openalex.org/W2522644321","https://openalex.org/W2552640487","https://openalex.org/W2923280693","https://openalex.org/W2947157832","https://openalex.org/W2971081319","https://openalex.org/W3133710726","https://openalex.org/W4205482204","https://openalex.org/W4240505175","https://openalex.org/W4241072010","https://openalex.org/W4241617894","https://openalex.org/W4308269287","https://openalex.org/W4381429703"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4251428025","https://openalex.org/W2784467519","https://openalex.org/W4289867043","https://openalex.org/W2366459771","https://openalex.org/W1973736094","https://openalex.org/W2350707375","https://openalex.org/W2377881809","https://openalex.org/W2355516922","https://openalex.org/W1959408986"],"abstract_inverted_index":{"Many":[0],"modern":[1],"cryptographic":[2,19,104,189],"primitives":[3],"for":[4,100,130,171],"hashing":[5],"and":[6,51,67,123,136,143,174,206,217],"(authenticated)":[7],"encryption":[8],"make":[9],"use":[10,81],"of":[11,28,31,40,47,82,88,93,97,140,155,197,212],"constructions":[12,56],"that":[13,21,60,90,113,118,145,184,219],"are":[14,36,91,221],"instantiated":[15],"with":[16,202],"an":[17,29,160],"iterated":[18],"permutation":[20,66,190],"operates":[22],"on":[23,73,86,126,200,207],"a":[24,41,48,52,65,74,94,111,120,153],"fixed-width":[25],"state":[26],"consisting":[27,46],"array":[30],"bits.":[32],"Often,":[33],"such":[34],"permutations":[35],"the":[37,61,80,131,134,148,156,175,188,195,210,213],"repeated":[38],"application":[39],"relatively":[42],"simple":[43,121],"round":[44],"function":[45,63],"linear":[49,137],"layer":[50],"non-linear":[53],"layer.":[54],"These":[55],"do":[57],"not":[58],"require":[59],"underlying":[62],"is":[64,124,159,185],"they":[68,220,225],"can":[69,226],"plausibly":[70],"be":[71],"based":[72,125],"non-invertible":[75,83],"transformation.":[76],"Recently,":[77],"Grassi":[78],"proposed":[79],"mappings":[84],"operating":[85],"arrays":[87],"digits":[89],"elements":[92],"finite":[95],"field":[96],"odd":[98],"characteristic":[99],"so-called":[101],"MPC-/FHE-/ZK-friendly":[102],"symmetric":[103],"primitives.":[105],"In":[106],"this":[107],"work,":[108],"we":[109,114,167,193],"consider":[110],"mapping":[112,177,216],"call":[115],"<mml:math":[116,141,172,178,214],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03b3</mml:mi></mml:math>":[117,142,173,215],"has":[119],"expression":[122],"squaring.":[127],"We":[128],"discuss,":[129],"first":[132],"time,":[133],"differential":[135],"propagation":[138],"properties":[139],"observe":[144],"these":[146],"follow":[147],"same":[149],"rules":[150],"up":[151],"to":[152],"relabeling":[154],"digits.":[157],"This":[158],"intriguing":[161],"property":[162],"that,":[163],"as":[164,166,222,224],"far":[165],"know,":[168],"only":[169],"exists":[170],"binary":[176],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>\u03c7</mml:mi>":[179],"<mml:msub><mml:mrow></mml:mrow>":[180],"<mml:mn>3</mml:mn></mml:msub>":[181],"</mml:msub>":[182],"</mml:math>":[183],"used":[186],"in":[187],"Xoodoo.":[191],"Moreover,":[192],"study":[194],"implications":[196],"its":[198],"non-invertibility":[199],"differentials":[201],"zero":[203],"output":[204,211],"difference":[205],"biases":[208],"at":[209],"show":[218],"small":[223],"possibly":[227],"be.":[228]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}