{"id":"https://openalex.org/W2974724013","doi":"https://doi.org/10.1080/10586458.2021.1926009","title":"Adventures in Supersingularland","display_name":"Adventures in Supersingularland","publication_year":2021,"publication_date":"2021-10-21","ids":{"openalex":"https://openalex.org/W2974724013","doi":"https://doi.org/10.1080/10586458.2021.1926009","mag":"2974724013"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2021.1926009","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1926009","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/10586458.2021.1926009?needAccess=true","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"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":"Experimental Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.tandfonline.com/doi/pdf/10.1080/10586458.2021.1926009?needAccess=true","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035725284","display_name":"Sarah Arpin","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sarah Arpin","raw_affiliation_strings":["Department of Mathematics, University of Colorado, Boulder, CO, USA","Department of Mathematics, University of Colorado Boulder, CO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Department of Mathematics, University of Colorado Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051488534","display_name":"Catalina Camacho-Navarro","orcid":"https://orcid.org/0000-0001-7338-9051"},"institutions":[{"id":"https://openalex.org/I31944674","display_name":"Universidad de Costa Rica","ror":"https://ror.org/02yzgww51","country_code":"CR","type":"education","lineage":["https://openalex.org/I31944674"]}],"countries":["CR"],"is_corresponding":false,"raw_author_name":"Catalina Camacho-Navarro","raw_affiliation_strings":["Sede del Atl\u00e1ntico, Universidad de Costa Rica, Costa Rica"],"affiliations":[{"raw_affiliation_string":"Sede del Atl\u00e1ntico, Universidad de Costa Rica, Costa Rica","institution_ids":["https://openalex.org/I31944674"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002850656","display_name":"Kristin Lauter","orcid":"https://orcid.org/0000-0002-1320-696X"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kristin Lauter","raw_affiliation_strings":["Microsoft Research, Redmond, WA, USA","Microsoft Research, redmond, WA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, Redmond, WA, USA","institution_ids":["https://openalex.org/I1290206253"]},{"raw_affiliation_string":"Microsoft Research, redmond, WA, USA#TAB#","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085647891","display_name":"Joelle Lim","orcid":null},"institutions":[{"id":"https://openalex.org/I28490864","display_name":"DSO National Laboratories","ror":"https://ror.org/03e05fb06","country_code":"SG","type":"nonprofit","lineage":["https://openalex.org/I28490864"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Joelle Lim","raw_affiliation_strings":["DSO National Laboratories, Singapore, Singapore","DSO National Laboratories Singapore Singapore"],"affiliations":[{"raw_affiliation_string":"DSO National Laboratories, Singapore, Singapore","institution_ids":["https://openalex.org/I28490864"]},{"raw_affiliation_string":"DSO National Laboratories Singapore Singapore","institution_ids":["https://openalex.org/I28490864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112072886","display_name":"Kristina Nelson","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kristina Nelson","raw_affiliation_strings":["Department of Mathematics, University of California, Berkeley, CA, USA","DEPARTMENT OF MATHEMATICS,UNIVERSITY OF CALIFORNIA,BERKELEY,CA,USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS,UNIVERSITY OF CALIFORNIA,BERKELEY,CA,USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071644637","display_name":"Travis Scholl","orcid":"https://orcid.org/0000-0003-3039-4824"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Travis Scholl","raw_affiliation_strings":["Department of Mathematics, University of California, Irvine, CA, USA","Department of Mathematics , University of California , Irvine, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"Department of Mathematics , University of California , Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055077416","display_name":"Jana Sot\u00e1kov\u00e1","orcid":"https://orcid.org/0000-0003-2498-6399"},"institutions":[{"id":"https://openalex.org/I4210099082","display_name":"QuSoft","ror":"https://ror.org/00zq3ce72","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210099082"]},{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jana Sot\u00e1kov\u00e1","raw_affiliation_strings":["Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands","QuSoft and University of Amsterdam, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]},{"raw_affiliation_string":"QuSoft and University of Amsterdam, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I4210099082","https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5035725284"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":0.2844,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57440941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"32","issue":"2","first_page":"241","last_page":"268"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9993000030517578,"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":0.9993000030517578,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987999796867371,"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/T10237","display_name":"Cryptography and Data Security","score":0.9945999979972839,"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/isogeny","display_name":"Isogeny","score":0.8639508485794067},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7244257926940918},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6937589049339294},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.4782525599002838},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46892908215522766},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.467435747385025},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.21002894639968872},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.14024031162261963}],"concepts":[{"id":"https://openalex.org/C2779765290","wikidata":"https://www.wikidata.org/wiki/Q1674414","display_name":"Isogeny","level":3,"score":0.8639508485794067},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7244257926940918},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6937589049339294},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.4782525599002838},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46892908215522766},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.467435747385025},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.21002894639968872},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.14024031162261963}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1080/10586458.2021.1926009","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1926009","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/10586458.2021.1926009?needAccess=true","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"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":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/24154456-10c0-47fd-8c24-b4acb3c188bd","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/adventures-in-supersingularland(24154456-10c0-47fd-8c24-b4acb3c188bd).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Arpin, S, Camacho-Navarro, C, Lauter, K, Lim, J, Nelson, K, Scholl, T & Sot\u00e1kov\u00e1, J 2023, 'Adventures in Supersingularland', Experimental Mathematics, vol. 32, no. 2, pp. 241-268. https://doi.org/10.1080/10586458.2021.1926009","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1909.07779","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.07779","pdf_url":"https://arxiv.org/pdf/1909.07779","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2974724013","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1909.07779.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"mag:2982614747","is_oa":false,"landing_page_url":"https://eprint.iacr.org/2019/1056.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764847869","display_name":"IACR Cryptology ePrint Archive","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4322614454"],"host_organization_lineage_names":["Cryptology ePrint Archive"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Cryptology ePrint Archive","raw_type":null},{"id":"pmh:oai:dare.uva.nl:publications/24154456-10c0-47fd-8c24-b4acb3c188bd","is_oa":false,"landing_page_url":"https://hdl.handle.net/11245.1/24154456-10c0-47fd-8c24-b4acb3c188bd","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Arpin, S, Camacho-Navarro, C, Lauter, K, Lim, J, Nelson, K, Scholl, T & Sot\u00e1kov\u00e1, J 2023, 'Adventures in Supersingularland', Experimental Mathematics, vol. 32, no. 2, pp. 241-268. https://doi.org/10.1080/10586458.2021.1926009","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.48550/arxiv.1909.07779","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.07779","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1080/10586458.2021.1926009","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1926009","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/10586458.2021.1926009?needAccess=true","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"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":"Experimental Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1211560647","display_name":null,"funder_award_id":"24.003.037","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G249262831","display_name":null,"funder_award_id":"024.003.037","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G420050720","display_name":null,"funder_award_id":"024.003","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4418824033","display_name":null,"funder_award_id":"024.003.03","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G629491556","display_name":null,"funder_award_id":"(NWO)","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G691693794","display_name":null,"funder_award_id":"G-2014-13575","funder_id":"https://openalex.org/F4320306151","funder_display_name":"Alfred P. Sloan Foundation"}],"funders":[{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320308943","display_name":"Microsoft Research","ror":"https://ror.org/00d0nc645"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320323217","display_name":"Universidad de Costa Rica","ror":"https://ror.org/02yzgww51"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2974724013.pdf","grobid_xml":"https://content.openalex.org/works/W2974724013.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W189254053","https://openalex.org/W1495033848","https://openalex.org/W2137147061","https://openalex.org/W2166807717","https://openalex.org/W2205392500","https://openalex.org/W2552090562","https://openalex.org/W2592544948","https://openalex.org/W2609849511","https://openalex.org/W2791851483","https://openalex.org/W2794445524","https://openalex.org/W2811492100","https://openalex.org/W2953201355","https://openalex.org/W2953643502","https://openalex.org/W2963298745","https://openalex.org/W3037726112","https://openalex.org/W3115412413","https://openalex.org/W3123022554","https://openalex.org/W4235946010","https://openalex.org/W4292027090","https://openalex.org/W6767963694"],"related_works":["https://openalex.org/W2999617751","https://openalex.org/W2952370344","https://openalex.org/W3022810598","https://openalex.org/W2950811108","https://openalex.org/W3033784619","https://openalex.org/W2896217235","https://openalex.org/W1627240032","https://openalex.org/W3091801135","https://openalex.org/W2223422431","https://openalex.org/W1974893148","https://openalex.org/W3163276518","https://openalex.org/W2255729245","https://openalex.org/W2055203626","https://openalex.org/W2990819541","https://openalex.org/W2055736829","https://openalex.org/W2324654759","https://openalex.org/W2464813247","https://openalex.org/W782558809","https://openalex.org/W2953389245","https://openalex.org/W3166960035"],"abstract_inverted_index":{"In":[0],"this":[1,214,254],"paper,":[2],"we":[3,82,185],"study":[4,68,186,220],"isogeny":[5,12,66,153,246],"graphs":[6,13,86,247,262],"of":[7,30,57,64,100,176,179,182,197,224,227,244,260],"supersingular":[8,65,245],"elliptic":[9],"curves.":[10],"Supersingular":[11],"were":[14],"introduced":[15],"as":[16],"a":[17],"hard":[18,42],"problem":[19,43],"into":[20],"cryptography":[21],"by":[22,103,194,213],"Charles,":[23],"Goren,":[24],"and":[25,40,108,116,199,252,263],"Lauter":[26],"for":[27,50,139,232],"the":[28,41,58,91,93,98,104,109,129,132,151,165,177,187,195,221,242],"construction":[29],"cryptographic":[31],"hash":[32],"functions":[33],"[CGL06].":[34],"These":[35],"are":[36,157,211,230],"large":[37],"expander":[38],"graphs,":[39,67],"is":[44,97,137,147,168,192],"to":[45,78,126,131,160],"find":[46],"an":[47,174],"efficient":[48],"algorithm":[49],"routing,":[51],"or":[52],"path-finding,":[53],"between":[54,143,207],"two":[55,84,208],"vertices":[56,144],"graph.":[59,154],"We":[60,123,172,218,236],"consider":[61,83],"four":[62],"aspects":[63],"each":[69],"thoroughly":[70],"and,":[71],"where":[72],"appropriate,":[73],"discuss":[74],"how":[75,125,203],"they":[76],"relate":[77],"one":[79],"another.":[80],"First,":[81],"related":[85,222],"that":[87,191],"help":[88],"us":[89],"understand":[90],"structure:":[92],"`spine'":[94],"$\\mathcal{S}$,":[95],"which":[96,113,167],"subgraph":[99],"$\\mathcal{G}_\\ell(\\overline{\\mathbb{F}_p})$":[101,190],"given":[102,193],"$j$-invariants":[105,210,229],"in":[106,112,145,150,164],"$\\mathbb{F}_p$,":[107],"graph":[110,135],"$\\mathcal{G}_\\ell(\\mathbb{F}_p)$,":[111],"both":[114],"curves":[115],"isogenies":[117],"must":[118],"be":[119,161],"defined":[120],"over":[121],"$\\mathbb{F}_p$.":[122],"show":[124],"pass":[127],"from":[128,170],"latter":[130],"former.":[133],"The":[134,155],"$\\mathcal{S}$":[136],"relevant":[138],"cryptanalysis":[140],"because":[141],"routing":[142],"$\\mathbb{F}_p$":[146,198],"easier":[148],"than":[149],"full":[152],"$\\mathbb{F}_p$-vertices":[156],"typically":[158],"assumed":[159],"randomly":[162],"distributed":[163],"graph,":[166],"far":[169],"true.":[171],"provide":[173],"analysis":[175],"distances":[178],"connected":[180],"components":[181],"$\\mathcal{S}$.":[183],"Next,":[184],"involution":[188,215],"on":[189,202,241,258],"Frobenius":[196],"give":[200],"heuristics":[201],"often":[204],"shortest":[205],"paths":[206],"conjugate":[209,228],"preserved":[212],"(mirror":[216],"paths).":[217],"also":[219],"question":[223],"what":[225],"proportion":[226],"$\\ell$-isogenous":[231],"$\\ell":[233,249],"=":[234,250],"2,3$.":[235],"conclude":[237],"with":[238,255],"experimental":[239],"data":[240],"diameters":[243,259],"when":[248],"2$":[251],"compare":[253],"previous":[256],"results":[257],"LPS":[261],"random":[264],"Ramanujan":[265],"graphs.":[266]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}