{"id":"https://openalex.org/W4312683657","doi":"https://doi.org/10.1007/978-3-031-22365-5_21","title":"PPAD is as\u00a0Hard as\u00a0LWE and\u00a0Iterated Squaring","display_name":"PPAD is as\u00a0Hard as\u00a0LWE and\u00a0Iterated Squaring","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4312683657","doi":"https://doi.org/10.1007/978-3-031-22365-5_21"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-22365-5_21","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-22365-5_21","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5065373891","display_name":"Nir Bitansky","orcid":"https://orcid.org/0000-0001-8361-6035"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Nir Bitansky","raw_affiliation_strings":["Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079980064","display_name":"Arka Rai Choudhuri","orcid":"https://orcid.org/0000-0003-0452-3426"},"institutions":[{"id":"https://openalex.org/I134446601","display_name":"Berkeley College","ror":"https://ror.org/02xewxa75","country_code":"US","type":"education","lineage":["https://openalex.org/I134446601"]},{"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":"Arka Rai Choudhuri","raw_affiliation_strings":["UC Berkeley, Berkeley, USA"],"affiliations":[{"raw_affiliation_string":"UC Berkeley, Berkeley, USA","institution_ids":["https://openalex.org/I134446601","https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022856374","display_name":"Justin Holmgren","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092597","display_name":"NTT (United States)","ror":"https://ror.org/004cn7092","country_code":"US","type":"company","lineage":["https://openalex.org/I2251713219","https://openalex.org/I4210092597"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Justin Holmgren","raw_affiliation_strings":["NTT Research, Palo Alto, USA"],"affiliations":[{"raw_affiliation_string":"NTT Research, Palo Alto, USA","institution_ids":["https://openalex.org/I4210092597"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012769677","display_name":"Chethan Kamath","orcid":"https://orcid.org/0009-0006-6812-7317"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Chethan Kamath","raw_affiliation_strings":["Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007205624","display_name":"Alex Lombardi","orcid":"https://orcid.org/0009-0007-0471-5379"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alex Lombardi","raw_affiliation_strings":["MIT, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, USA","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035828031","display_name":"Omer Paneth","orcid":"https://orcid.org/0000-0001-8561-1123"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Omer Paneth","raw_affiliation_strings":["Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049757682","display_name":"Ron D. Rothblum","orcid":"https://orcid.org/0000-0001-5481-7276"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ron D. Rothblum","raw_affiliation_strings":["Technion, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Technion, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5065373891"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":7.2004,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.97701149,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"593","last_page":"622"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","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/T10237","display_name":"Cryptography and Data Security","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/T10270","display_name":"Blockchain Technology Applications and Security","score":0.9983999729156494,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.6475856304168701},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.615649938583374},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.5603823065757751},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5579866766929626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5112977027893066},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.5081312656402588},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.48529237508773804},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.4783879518508911},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.45585310459136963},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4504866302013397},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4367968440055847},{"id":"https://openalex.org/keywords/computational-problem","display_name":"Computational problem","score":0.4183671176433563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41739022731781006},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.35502007603645325},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.269976407289505},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.2284412980079651},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12746942043304443}],"concepts":[{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.6475856304168701},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.615649938583374},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.5603823065757751},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5579866766929626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5112977027893066},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.5081312656402588},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.48529237508773804},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.4783879518508911},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45585310459136963},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4504866302013397},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4367968440055847},{"id":"https://openalex.org/C19754495","wikidata":"https://www.wikidata.org/wiki/Q3435924","display_name":"Computational problem","level":2,"score":0.4183671176433563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41739022731781006},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.35502007603645325},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.269976407289505},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2284412980079651},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12746942043304443},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-22365-5_21","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-22365-5_21","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1536074886","https://openalex.org/W1589034595","https://openalex.org/W1594319238","https://openalex.org/W1724472458","https://openalex.org/W1971297422","https://openalex.org/W1980813953","https://openalex.org/W2002373723","https://openalex.org/W2002930326","https://openalex.org/W2018738738","https://openalex.org/W2054904172","https://openalex.org/W2057913812","https://openalex.org/W2113244484","https://openalex.org/W2138698623","https://openalex.org/W2148888468","https://openalex.org/W2169359757","https://openalex.org/W2186160814","https://openalex.org/W2416431186","https://openalex.org/W2466495210","https://openalex.org/W2575553372","https://openalex.org/W2752822516","https://openalex.org/W2795247010","https://openalex.org/W2884026699","https://openalex.org/W2888119556","https://openalex.org/W2899466157","https://openalex.org/W2952338482","https://openalex.org/W2952604022","https://openalex.org/W2953744829","https://openalex.org/W2967898990","https://openalex.org/W2969529327","https://openalex.org/W3013660109","https://openalex.org/W3022089689","https://openalex.org/W3037017048","https://openalex.org/W3046921815","https://openalex.org/W3048764796","https://openalex.org/W3082337096","https://openalex.org/W3082860856","https://openalex.org/W3139003361","https://openalex.org/W3147459559","https://openalex.org/W3157193347","https://openalex.org/W3164947441","https://openalex.org/W3172178640","https://openalex.org/W4205765479","https://openalex.org/W4234761190","https://openalex.org/W4285136272","https://openalex.org/W4298227433","https://openalex.org/W4312753175"],"related_works":["https://openalex.org/W2109858088","https://openalex.org/W2949278206","https://openalex.org/W2166139242","https://openalex.org/W2990853482","https://openalex.org/W4235727887","https://openalex.org/W4205899062","https://openalex.org/W266537895","https://openalex.org/W2374430960","https://openalex.org/W1589381382","https://openalex.org/W2402664818"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}