{"id":"https://openalex.org/W7225465610","doi":"https://doi.org/10.5281/zenodo.24044199","title":"Prime-order reduction at cryptographic heights: a pre-registered test of the refined Koblitz conjecture over consecutive primes","display_name":"Prime-order reduction at cryptographic heights: a pre-registered test of the refined Koblitz conjecture over consecutive primes","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225465610","doi":"https://doi.org/10.5281/zenodo.24044199"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24044199","doi":"https://doi.org/10.5281/zenodo.24044199","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24044199","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","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24044199","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024868042","display_name":"Matthew Gifford","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gifford, Matthew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5024868042"],"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.7387999892234802,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.7387999892234802,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.18690000474452972,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.02979999966919422,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/consecutive-primes","display_name":"consecutive primes","score":0.6669999957084656},{"id":"https://openalex.org/keywords/complex-multiplication","display_name":"complex multiplication","score":0.7089999914169312},{"id":"https://openalex.org/keywords/supersingular-primes","display_name":"supersingular primes","score":0.6359999775886536},{"id":"https://openalex.org/keywords/embedding-degree","display_name":"embedding degree","score":0.8730000257492065},{"id":"https://openalex.org/keywords/congruence-classes","display_name":"congruence classes","score":0.5350000262260437},{"id":"https://openalex.org/keywords/pre-registered-replication","display_name":"pre-registered replication","score":0.49399998784065247}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8064000010490417},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5690000057220459},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5426999926567078},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5274999737739563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5120000243186951},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.48069998621940613},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.46790000796318054},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.39899998903274536},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.3917999863624573},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C191421660","wikidata":"https://www.wikidata.org/wiki/Q829546","display_name":"Primality test","level":3,"score":0.3465000092983246},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3140000104904175},{"id":"https://openalex.org/C201866948","wikidata":"https://www.wikidata.org/wiki/Q228206","display_name":"Random number generation","level":2,"score":0.30559998750686646},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25839999318122864},{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24044199","doi":"https://doi.org/10.5281/zenodo.24044199","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24044199","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.24044200","doi":"https://doi.org/10.5281/zenodo.24044200","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24044200","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.24044199","doi":"https://doi.org/10.5281/zenodo.24044199","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24044199","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W7224997849"],"related_works":["https://openalex.org/W4409511201","https://openalex.org/W1594578326","https://openalex.org/W2083304150","https://openalex.org/W2085192447","https://openalex.org/W2006673603","https://openalex.org/W4244353648","https://openalex.org/W2805982196","https://openalex.org/W1570012314","https://openalex.org/W7098911046","https://openalex.org/W4409893780"],"abstract_inverted_index":{"Prime-order":[0,283],"reduction":[1],"at":[2,78,92,155,178,285],"cryptographic":[3],"heights:":[4],"a":[5,19,31,37,123,271,412],"pre-registered":[6,213],"test":[7],"of":[8,27,62,103,138,198,273,297,312,336,351,399],"the":[9,46,59,79,82,129,151,166,203,243,259,267,280,295,298,313,329,377,385,400,408,415,417,419,425,435,440,450,456],"refined":[10,58],"Koblitz":[11,16],"conjecture":[12],"over":[13,34,182],"consecutive":[14,139,286],"primes":[15,48,140,184,191,287],"(1988)":[17],"proposed":[18],"way":[20],"to":[21,73,294,310],"find":[22],"an":[23],"elliptic":[24],"curve":[25,32,153,168],"group":[26],"prime":[28,161,355],"order:":[29,356],"fix":[30],"E":[33],"Q,":[35],"pick":[36],"large":[38],"random":[39,117,143],"odd":[40],"M,":[41],"and":[42,95,101,109,149,157,164,180,228,234,238,277,384,394,411,424],"compute":[43],"#E(Fp)":[44,363],"for":[45,208,232,242,275,279,357],"successive":[47],"p":[49,185,263,337,352,369],"\u2265":[50],"M":[51],"until":[52],"it":[53,90],"is":[54,84,249,320,341,388],"prime.":[55,343],"Zywina":[56],"(2011)":[57],"predicted":[60],"rate":[61,222,260],"success.":[63],"That":[64],"prediction":[65,100],"had":[66],"been":[67],"tested":[68],"on":[69,251,262,303],"exhaustive":[70],"ranges":[71],"up":[72],"about":[74],"109,":[75],"but":[76],"not":[77],"sizes":[80],"where":[81],"procedure":[83],"actually":[85],"used.":[86],"This":[87,374,405],"paper":[88,134,345,409,430],"tests":[89,215],"there,":[91],"264,":[93],"2128":[94,179],"2256.":[96],"Design.":[97],"Every":[98],"test,":[99],"line":[102],"analysis":[104],"code":[105],"was":[106,119,224,442],"frozen,":[107],"hashed":[108],"made":[110],"public":[111],"before":[112],"any":[113,304],"data":[114],"existed.":[115],"The":[116,133,220,246,300,316,344,429],"seed":[118],"then":[120],"taken":[121],"from":[122,141,308,328,376,434],"drand":[124],"beacon":[125],"round":[126],"published":[127],"after":[128],"freeze":[130],"(round":[131],"6611336).":[132],"samples":[135],"fixed-length":[136],"runs":[137],"uniformly":[142],"starts,":[144],"in":[145,322,338,379,390,455],"four":[146,324,426],"arms:":[147],"A":[148],"B:":[150],"non-CM":[152],"37a1":[154,276],"264":[156],"2128,":[158],"with":[159,174,444],"every":[160],"eligible;":[162],"C":[163],"D:":[165],"CM":[167,244,281],"y2":[169,358],"=":[170,176,359],"x3":[171,360],"\u2212":[172,361],"x":[173],"t":[175],"8":[177],"2256,":[181],"ordinary":[183],"\u2261":[186,364,370],"1":[187,371],"(mod":[188,366,372],"4).":[189],"Supersingular":[190],"are":[192,288],"excluded":[193],"because":[194],"they":[195],"give":[196],"curves":[197],"embedding":[199],"degree":[200],"2,":[201],"which":[202,339,348],"MOV":[204],"attack":[205],"rules":[206],"out":[207,217,354],"cryptography.":[209],"Results.":[210],"All":[211],"12":[212],"decisive":[214],"came":[216],"as":[218,266,326,453],"predicted.":[219],"observed-to-predicted":[221],"ratio":[223,272],"0.9954":[225],"\u00b1":[226,230,236,240],"0.0046":[227],"0.9933":[229],"0.0059":[231],"37a1,":[233],"1.0001":[235],"0.0006":[237],"0.9983":[239],"0.0018":[241],"curve.":[245,282],"arm-C":[247],"figure":[248],"based":[250],"2.47":[252],"million":[253],"prime-order":[254],"events.":[255],"Among":[256],"eligible":[257],"primes,":[258],"depends":[261],"mod":[264],"3":[265],"Galois":[268],"images":[269],"predict:":[270],"5/4":[274],"3/4":[278],"events":[284],"correlated":[289],"only":[290],"through":[291,334],"congruence":[292,349],"classes,":[293],"precision":[296],"tests.":[299],"99%":[301],"bounds":[302],"extra":[305],"effect":[306],"run":[307],"2.4%":[309],"10.6%":[311],"base":[314],"rate.":[315],"raw":[317],"lag-1":[318],"correlation":[319],"negative":[321],"all":[323],"arms,":[325],"expected":[327],"Lemke":[330],"Oliver\u2013Soundararajan":[331],"bias":[332],"acting":[333],"classes":[335,350],"#E(Fp)/t":[340],"never":[342],"also":[346],"proves":[347],"rule":[353],"x,":[362],"0":[365],"16)":[367],"when":[368],"8).":[373],"follows":[375],"formula":[378],"Gauss's":[380],"last":[381],"diary":[382],"entry,":[383],"mod-16":[386],"step":[387],"checked":[389],"Lean":[391],"4.":[392],"Data":[393],"code:":[395],"doi:10.5281/zenodo.24026057":[396],"(all":[397],"versions":[398],"dataset).":[401],"Companion":[402],"paper:":[403],"doi:10.5281/zenodo.23843403.":[404],"upload":[406],"contains":[407],"(PDF)":[410],"source":[413],"bundle:":[414],"LaTeX,":[416],"figures,":[418],"scripts":[420],"that":[421],"regenerate":[422],"them,":[423],"results":[427],"files.":[428],"can":[431],"be":[432],"rebuilt":[433],"bundle":[436],"alone.":[437],"AI":[438,445],"use:":[439],"work":[441],"produced":[443],"assistance":[446],"(Claude,":[447],"Anthropic)":[448],"under":[449],"author's":[451],"direction,":[452],"described":[454],"paper.":[457]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-08T00:00:00"}
