{"id":"https://openalex.org/W7223828397","doi":"https://doi.org/10.5281/zenodo.23680528","title":"A Three-Bit Boundary for Cyclic Boolean\u2013Modular Inversion","display_name":"A Three-Bit Boundary for Cyclic Boolean\u2013Modular Inversion","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7223828397","doi":"https://doi.org/10.5281/zenodo.23680528"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23680528","doi":"https://doi.org/10.5281/zenodo.23680528","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23680528","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23680528","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159976007","display_name":"lmtlssss\ud83d\udf10","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"lmtlssss\ud83d\udf10","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159976007"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.6068999767303467,"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":0.6068999767303467,"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":0.2890999913215637,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.05469999834895134,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/carry-propagation","display_name":"carry propagation","score":0.5889999866485596},{"id":"https://openalex.org/keywords/closure-equations","display_name":"closure equations","score":0.6159999966621399},{"id":"https://openalex.org/keywords/bit-rotation","display_name":"bit rotation","score":0.531000018119812},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"modular arithmetic","score":0.4059999883174896},{"id":"https://openalex.org/keywords/combinatorial-bounds","display_name":"combinatorial bounds","score":0.4300000071525574}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7347999811172485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7221999764442444},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6690000295639038},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6581000089645386},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5716999769210815},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5386000275611877},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5144000053405762},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4884999990463257},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.46540001034736633},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.45410001277923584},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.4519999921321869},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3328999876976013},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26980000734329224},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.26019999384880066},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23680528","doi":"https://doi.org/10.5281/zenodo.23680528","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23680528","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23680529","doi":"https://doi.org/10.5281/zenodo.23680529","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23680529","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23680528","doi":"https://doi.org/10.5281/zenodo.23680528","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23680528","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7223980947","https://openalex.org/W2135034264","https://openalex.org/W7005642746","https://openalex.org/W2887761912","https://openalex.org/W1564773445","https://openalex.org/W7223971076","https://openalex.org/W7208268068","https://openalex.org/W10922151","https://openalex.org/W2620934168","https://openalex.org/W2093675925"],"abstract_inverted_index":{"For":[0,21],"fixed":[1],"w-bit":[2],"words":[3],"c":[4],"and":[5,54,70,98],"k,":[6],"consider":[7],"F(x)":[8],"=":[9],"((ROR1(x)":[10],"XOR":[11],"ROR3(x))":[12],"+":[13,17],"(x":[14],"AND":[15],"c)":[16],"k)":[18],"modulo":[19],"2^w.":[20],"every":[22,84],"w":[23,50,101],"at":[24,33,83],"least":[25],"four,":[26],"each":[27,47,67],"inverse":[28],"fiber":[29],"is":[30],"determined":[31],"by":[32,87],"most":[34],"eight":[35,75],"choices":[36],"of":[37,74,91],"the":[38,60,81],"first":[39],"three":[40,55],"input":[41],"bits.":[42],"A":[43,89],"carry":[44],"recurrence":[45],"reconstructs":[46],"candidate":[48],"in":[49],"local":[51],"bit":[52],"updates,":[53],"closure":[56],"equations":[57],"select":[58],"exactly":[59],"preimages.":[61,76],"We":[62],"prove":[63],"completeness,":[64],"uniqueness":[65],"within":[66],"boundary":[68,97],"choice,":[69],"a":[71,99],"sharp":[72],"bound":[73,82],"An":[77],"explicit":[78],"family":[79],"attains":[80],"width":[85],"divisible":[86],"seven.":[88],"rotation":[90],"r":[92],"positions":[93],"gives":[94],"an":[95],"r-bit":[96],"2^r":[100],"update":[102],"bound.":[103]},"counts_by_year":[],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2026-10-28T00:00:00"}