{"id":"https://openalex.org/W2093675925","doi":"https://doi.org/10.1080/00207161003596708","title":"The invertibility of the XOR of rotations of a binary word","display_name":"The invertibility of the XOR of rotations of a binary word","publication_year":2010,"publication_date":"2010-12-04","ids":{"openalex":"https://openalex.org/W2093675925","doi":"https://doi.org/10.1080/00207161003596708","mag":"2093675925"},"language":"en","primary_location":{"id":"doi:10.1080/00207161003596708","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207161003596708","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051087399","display_name":"Ronald L. Rivest","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ronald L. Rivest","raw_affiliation_strings":["a   Computer Science and Artificial Intelligence Laboratory , Massachusetts Institute of Technology , Cambridge, MA, 02139,  USA","Computer Science and Artificial Intelligence Laboratory , Massachusetts Institute of Technology , Cambridge, MA, 02139, USA"],"affiliations":[{"raw_affiliation_string":"a   Computer Science and Artificial Intelligence Laboratory , Massachusetts Institute of Technology , Cambridge, MA, 02139,  USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Computer Science and Artificial Intelligence Laboratory , Massachusetts Institute of Technology , Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051087399"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":3.1573,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.92212295,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"88","issue":"2","first_page":"281","last_page":"284"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9991999864578247,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9991999864578247,"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/T11567","display_name":"semigroups and automata theory","score":0.9991000294685364,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.8126899600028992},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.8112330436706543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7367668151855469},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6688128709793091},{"id":"https://openalex.org/keywords/hash-function","display_name":"Hash function","score":0.6351731419563293},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5897996425628662},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.547887921333313},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4532838463783264},{"id":"https://openalex.org/keywords/binary-operation","display_name":"Binary operation","score":0.4408930838108063},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23775514960289001},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20751020312309265},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19667142629623413},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.05808049440383911}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.8126899600028992},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.8112330436706543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7367668151855469},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6688128709793091},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.6351731419563293},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5897996425628662},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.547887921333313},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4532838463783264},{"id":"https://openalex.org/C185529760","wikidata":"https://www.wikidata.org/wiki/Q164307","display_name":"Binary operation","level":2,"score":0.4408930838108063},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23775514960289001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20751020312309265},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19667142629623413},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.05808049440383911},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207161003596708","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207161003596708","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W106392311","https://openalex.org/W1552810527","https://openalex.org/W1623768750","https://openalex.org/W1763997349","https://openalex.org/W2010523529","https://openalex.org/W2047837169","https://openalex.org/W2158323850","https://openalex.org/W2212756535","https://openalex.org/W2330548796","https://openalex.org/W2900896801","https://openalex.org/W3151140615","https://openalex.org/W4240267682"],"related_works":["https://openalex.org/W4251428025","https://openalex.org/W4289867043","https://openalex.org/W2784467519","https://openalex.org/W2366459771","https://openalex.org/W1973736094","https://openalex.org/W2963453621","https://openalex.org/W2350707375","https://openalex.org/W2377881809","https://openalex.org/W2355516922","https://openalex.org/W1959408986"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,19,28,39],"following":[3],"result":[4,47],"regarding":[5],"operations":[6],"on":[7],"a":[8,14,22],"binary":[9],"word":[10,29],"whose":[11],"length":[12],"is":[13,30,44,48,52],"power":[15],"of":[16,21,24,27,41,68],"two:":[17],"computing":[18],"exclusive-or":[20],"number":[23,40],"rotated":[25],"versions":[26,42],"an":[31],"invertible":[32],"(one-to-one)":[33],"operation":[34],"if":[35,38],"and":[36],"only":[37],"combined":[43],"odd.":[45],"(This":[46],"not":[49],"new;":[50],"there":[51],"at":[53],"least":[54],"one":[55],"earlier":[56],"proof,":[57],"due":[58],"to":[59],"Thomsen":[60],"[Cryptographic":[61],"hash":[62],"functions,":[63],"PhD":[64],"thesis,":[65],"Technical":[66],"University":[67],"Denmark,":[69],"28":[70],"November":[71],"2008].":[72],"Our":[73],"proof":[74],"may":[75],"be":[76],"new.)":[77]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
