{"id":"https://openalex.org/W4200348167","doi":"https://doi.org/10.1080/01611194.2021.1920070","title":"On latin squares, invariant differentials, random permutations and historical Enigma rotors","display_name":"On latin squares, invariant differentials, random permutations and historical Enigma rotors","publication_year":2021,"publication_date":"2021-12-07","ids":{"openalex":"https://openalex.org/W4200348167","doi":"https://doi.org/10.1080/01611194.2021.1920070"},"language":"en","primary_location":{"id":"doi:10.1080/01611194.2021.1920070","is_oa":true,"landing_page_url":"https://doi.org/10.1080/01611194.2021.1920070","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/01611194.2021.1920070?needAccess=true","source":{"id":"https://openalex.org/S185196701","display_name":"Cryptologia","issn_l":"0161-1194","issn":["0161-1194","1558-1586"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptologia","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.tandfonline.com/doi/pdf/10.1080/01611194.2021.1920070?needAccess=true","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085287860","display_name":"Nicolas T. Courtois","orcid":"https://orcid.org/0000-0003-0736-431X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nicolas T. Courtois","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0736-431X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056568482","display_name":"Marek Grajek","orcid":null},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Marek Grajek","raw_affiliation_strings":["Switzerland , Japan , Hungary , Croatia , Poland , Czechoslovakia , Russia University College London , Gower Street , London , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Switzerland , Japan , Hungary , Croatia , Poland , Czechoslovakia , Russia University College London , Gower Street , London , UK","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085287860"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19727756,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"5","first_page":"387","last_page":"421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9957000017166138,"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":0.9957000017166138,"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/T11130","display_name":"Coding theory and cryptography","score":0.9937999844551086,"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":0.9890000224113464,"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/block-cipher","display_name":"Block cipher","score":0.6197733879089355},{"id":"https://openalex.org/keywords/cipher","display_name":"Cipher","score":0.5209394693374634},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4701882600784302},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.45966964960098267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.429002046585083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36032065749168396},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1920507252216339},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.14414694905281067},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.06199786067008972}],"concepts":[{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.6197733879089355},{"id":"https://openalex.org/C2780221543","wikidata":"https://www.wikidata.org/wiki/Q4681865","display_name":"Cipher","level":3,"score":0.5209394693374634},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4701882600784302},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.45966964960098267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.429002046585083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36032065749168396},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1920507252216339},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.14414694905281067},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.06199786067008972},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/01611194.2021.1920070","is_oa":true,"landing_page_url":"https://doi.org/10.1080/01611194.2021.1920070","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/01611194.2021.1920070?needAccess=true","source":{"id":"https://openalex.org/S185196701","display_name":"Cryptologia","issn_l":"0161-1194","issn":["0161-1194","1558-1586"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptologia","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1080/01611194.2021.1920070","is_oa":true,"landing_page_url":"https://doi.org/10.1080/01611194.2021.1920070","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/01611194.2021.1920070?needAccess=true","source":{"id":"https://openalex.org/S185196701","display_name":"Cryptologia","issn_l":"0161-1194","issn":["0161-1194","1558-1586"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptologia","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200348167.pdf","grobid_xml":"https://content.openalex.org/works/W4200348167.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W345902015","https://openalex.org/W1530798571","https://openalex.org/W1974066067","https://openalex.org/W1984897840","https://openalex.org/W1988015188","https://openalex.org/W1991068735","https://openalex.org/W2011575828","https://openalex.org/W2013763930","https://openalex.org/W2029439483","https://openalex.org/W2069896120","https://openalex.org/W2077881181","https://openalex.org/W2083872127","https://openalex.org/W2094900471","https://openalex.org/W2113446244","https://openalex.org/W2398836113","https://openalex.org/W2502555207","https://openalex.org/W2584878234","https://openalex.org/W2791790212","https://openalex.org/W2902144589","https://openalex.org/W2972710075","https://openalex.org/W3024706617","https://openalex.org/W4206025803","https://openalex.org/W4231916902","https://openalex.org/W6631653303","https://openalex.org/W6697325266"],"related_works":["https://openalex.org/W1638546798","https://openalex.org/W2117179505","https://openalex.org/W4390979909","https://openalex.org/W4389575897","https://openalex.org/W1524307340","https://openalex.org/W3080116368","https://openalex.org/W2150878966","https://openalex.org/W140343426","https://openalex.org/W2092816212","https://openalex.org/W1980393268"],"abstract_inverted_index":{"In":[0],"this":[1,75,103],"article":[2],"we":[3],"study":[4],"the":[5,26,55,59,105,146],"quality":[6],"of":[7,70,81,107],"permutations":[8,82],"in":[9,38,67,93,98,104,136],"historical":[10,109,147],"cipher":[11,113,138,149],"machines":[12,114],"from":[13,54],"Germany,":[14],"Spain,":[15],"Italy,":[16],"Norway,":[17],"Switzerland,":[18],"Japan,":[19],"Hungary,":[20],"Croatia,":[21],"Poland,":[22],"Czechoslovakia,":[23],"Russia":[24],"and":[25,58,115,122,130],"United":[27],"States.":[28],"We":[29,73,100,125],"show":[30],"that":[31],"numerous":[32],"real-life":[33],"rotors":[34],"have":[35,62,117],"been":[36],"made":[37],"order":[39],"to":[40,44,50,91],"imitate":[41],"or":[42,88],"tend":[43],"a":[45,94,141],"certain":[46],"ideal":[47],"property":[48,143],"related":[49],"latin":[51],"squares.":[52],"Rotors":[53],"same":[56,60,134],"source":[57],"period":[61],"consistent":[63],"properties":[64],"deeply":[65],"rooted":[66],"classical":[68],"cryptography":[69],"polyalphabetical":[71],"ciphers.":[72],"demonstrate":[74],"based":[76],"on":[77,111,119],"probabilities:":[78],"random":[79],"occurrence":[80],"having":[83],"such":[84],"features":[85],"is":[86],"unlikely,":[87],"would":[89],"amount":[90],"winning":[92],"lottery":[95],"several":[96],"times":[97],"row.":[99],"put":[101],"all":[102],"context":[106],"known":[108],"sources":[110],"how":[112],"cryptanalysis":[116],"developed":[118],"both":[120],"German":[121],"Allied":[123],"sides.":[124],"also":[126],"exhibit":[127],"strong":[128],"linear":[129],"differential":[131],"properties.":[132],"The":[133],"occurs":[135],"Fialka":[137],"machines.":[139],"Finally,":[140],"stronger":[142],"holds":[144],"for":[145],"block":[148],"T-310.":[150]},"counts_by_year":[],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}