{"id":"https://openalex.org/W4390942746","doi":"https://doi.org/10.1007/s10623-023-01349-8","title":"The state diagram of $$\\chi $$","display_name":"The state diagram of $$\\chi $$","publication_year":2024,"publication_date":"2024-01-17","ids":{"openalex":"https://openalex.org/W4390942746","doi":"https://doi.org/10.1007/s10623-023-01349-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-023-01349-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-023-01349-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-023-01349-8.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-023-01349-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001889799","display_name":"Jan Schoone","orcid":"https://orcid.org/0000-0002-0751-291X"},"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":"Jan Schoone","raw_affiliation_strings":["Digital Security, Radboud University, Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security, 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, Radboud University, Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Digital Security, Radboud University, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001889799"],"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":1.7376,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85622867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"92","issue":"5","first_page":"1393","last_page":"1421"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9991999864578247,"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/algorithm","display_name":"Algorithm","score":0.6257691383361816},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32730579376220703},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3238552212715149}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6257691383361816},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32730579376220703},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3238552212715149}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10623-023-01349-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-023-01349-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-023-01349-8.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/306186","is_oa":true,"landing_page_url":"https://hdl.handle.net/2066/306186","pdf_url":"https://repository.ubn.ru.nl//bitstream/handle/2066/306186/306186.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/s10623-023-01349-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-023-01349-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-023-01349-8.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5946328347","display_name":null,"funder_award_id":"788980","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390942746.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1976636244","https://openalex.org/W2033640124","https://openalex.org/W2064939672","https://openalex.org/W2072113533","https://openalex.org/W2078437472","https://openalex.org/W2164645101","https://openalex.org/W2334527086","https://openalex.org/W2531349903","https://openalex.org/W2794866029","https://openalex.org/W3105248407","https://openalex.org/W4213335922","https://openalex.org/W4240574532","https://openalex.org/W4301185346"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"Abstract":[0],"In":[1,152],"symmetric":[2],"cryptography,":[3],"block":[4],"ciphers,":[5],"stream":[6],"ciphers":[7],"and":[8,17,25,149],"permutations":[9],"often":[10,32],"make":[11],"use":[12],"of":[13,22,159,180,195,210,218,246,264,282,303,318],"a":[14,23,26,49,92,241,258,266,275,294],"round":[15,19],"function":[16],"many":[18,280],"functions":[20],"consist":[21],"linear":[24],"non-linear":[27],"layer.":[28],"One":[29],"that":[30,40,94,118,170],"is":[31,34,41,62,91,128,175,227],"used":[33,129],"based":[35],"on":[36,52,96,164,177,221,240],"the":[37,157,178,208,216,244,262,301,304,310,316],"cellular":[38],"automaton":[39],"denoted":[42],"by":[43,64],"$$\\chi":[44,87,107,124,160,171,196,211,247,283,319],"$$":[45,68,108,161,172,197,248,284,297,320],"<mml:math":[46,58,69,82,89,109,126,162,173,198,213,224,232,249,285,298,321,327],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c7</mml:mi></mml:math>":[47,110,163,174,199,250,286,322],"as":[48,257],"Boolean":[50],"map":[51,86,93,123],"bi-infinite":[53],"sequences,":[54],"$${\\mathbb":[55,222,324],"{F}}_2^{{\\mathbb":[56,325],"{Z}}}$$":[57,326],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msubsup><mml:mi>F</mml:mi><mml:mn>2</mml:mn><mml:mi>Z</mml:mi></mml:msubsup></mml:math>":[59,328],".":[60,84,121,200,234],"It":[61,167],"defined":[63],"$$\\sigma":[65,296],"\\mapsto":[66],"\\nu":[67],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>\u03c3</mml:mi><mml:mo>\u21a6</mml:mo><mml:mi>\u03bd</mml:mi></mml:mrow></mml:math>":[70],"where":[71],"each":[72],"$$\\nu":[73],"_i":[74,77],"=":[75],"\\sigma":[76],"+":[78],"(\\sigma":[79],"_{i+1}+1)\\sigma":[80],"_{i+2}$$":[81],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msub><mml:mi>\u03bd</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>\u03c3</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>\u03c3</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>\u03c3</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>":[83],"A":[85,235],"_n$$":[88,125,212],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>\u03c7</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>":[90,127,214],"operates":[95],"n":[97,120,206],"-bit":[98],"arrays":[99],"with":[100,106,116],"periodic":[101,113,165,182,237],"boundary":[102],"conditions.":[103],"This":[104,122],"corresponds":[105],"restricted":[111],"to":[112,323,331],"infinite":[114],"sequences":[115,188],"period":[117],"divides":[119],"in":[130,138,243,274,306,309],"various":[131],"permutations,":[132],"e.g.,":[133],"Keccak":[134],"-f":[135],"(the":[136,141],"permutation":[137],"SHA-3),":[139],"ASCON":[140],"NIST":[142],"standard":[143],"for":[144,204,293],"lightweight":[145],"cryptography),":[146],"Xoodoo,":[147],"Rasta":[148],"Subterranean":[150],"(2.0).":[151],"this":[153],"paper,":[154],"we":[155,290,314],"characterize":[156],"graph":[158,245],"sequences.":[166,183,334],"turns":[168],"out":[169],"surjective":[176],"set":[179],"all":[181],"We":[184,201],"will":[185,189],"show":[186],"what":[187],"give":[190],"collisions":[191],"after":[192,278],"one":[193,268],"application":[194],"prove":[202],"that,":[203],"odd":[205],",":[207,251,300,329],"order":[209],"(in":[215],"group":[217],"bijective":[219],"maps":[220],"{F}}_2^n$$":[223],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msubsup><mml:mi>F</mml:mi><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msubsup></mml:math>":[225],")":[226],"$$2^{\\lceil":[228],"{\\text":[229],"{lg}}(\\frac{n+1}{2})\\rceil":[230],"}$$":[231],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mo>\u2308</mml:mo><mml:mtext>lg</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>\u2309</mml:mo></mml:mrow></mml:msup></mml:math>":[233],"given":[236,295],"sequence":[238],"lies":[239,273],"cycle":[242,305],"or":[252,277],"it":[253,272,287],"can":[254,269,291],"be":[255],"represented":[256],"polynomial.":[259],"By":[260],"regarding":[261],"divisors":[263],"such":[265],"polynomial":[267],"see":[270],"whether":[271],"cycle,":[276],"how":[279],"iterations":[281],"will.":[288],"Furthermore,":[289],"see,":[292],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c3</mml:mi></mml:math>":[299],"length":[302],"its":[307],"component":[308],"state":[311],"diagram.":[312],"Finally,":[313],"extend":[315],"surjectivity":[317],"thus":[330],"include":[332],"non-periodic":[333]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2024-01-18T00:00:00"}