{"id":"https://openalex.org/W2951286680","doi":"https://doi.org/10.1561/0400000074","title":"A Decade of Lattice Cryptography","display_name":"A Decade of Lattice Cryptography","publication_year":2016,"publication_date":"2016-03-24","ids":{"openalex":"https://openalex.org/W2951286680","doi":"https://doi.org/10.1561/0400000074","mag":"2951286680"},"language":"en","primary_location":{"id":"doi:10.1561/0400000074","is_oa":false,"landing_page_url":"https://doi.org/10.1561/0400000074","pdf_url":null,"source":{"id":"https://openalex.org/S110848248","display_name":"Foundations and Trends\u00ae in Theoretical Computer Science","issn_l":"1551-305X","issn":["1551-305X","1551-3068"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Theoretical Computer Science","raw_type":"journal-article"},"type":"preprint","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/A5086535374","display_name":"Chris Peikert","orcid":"https://orcid.org/0000-0003-0419-7501"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chris Peikert","raw_affiliation_strings":["University of Michigan Computer Science and Engineering, ,","\u2020University of Michigan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Michigan Computer Science and Engineering, ,","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"\u2020University of Michigan","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086535374"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":7.0675,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.97107341,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"10","issue":"4","first_page":"283","last_page":"424"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9821000099182129,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9764999747276306,"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/lattice-based-cryptography","display_name":"Lattice-based cryptography","score":0.8883477449417114},{"id":"https://openalex.org/keywords/learning-with-errors","display_name":"Learning with errors","score":0.7970441579818726},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.7604131698608398},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5961036682128906},{"id":"https://openalex.org/keywords/post-quantum-cryptography","display_name":"Post-quantum cryptography","score":0.5942383408546448},{"id":"https://openalex.org/keywords/quantum-cryptography","display_name":"Quantum cryptography","score":0.4776971638202667},{"id":"https://openalex.org/keywords/lattice-problem","display_name":"Lattice problem","score":0.4653300642967224},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.46334418654441833},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.426106333732605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34650719165802},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.297750860452652},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.2800886034965515},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.22447600960731506},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19483837485313416},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.18889564275741577},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.12922126054763794},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07713228464126587},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07699370384216309}],"concepts":[{"id":"https://openalex.org/C137660015","wikidata":"https://www.wikidata.org/wiki/Q6497083","display_name":"Lattice-based cryptography","level":5,"score":0.8883477449417114},{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.7970441579818726},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.7604131698608398},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5961036682128906},{"id":"https://openalex.org/C108277079","wikidata":"https://www.wikidata.org/wiki/Q7233576","display_name":"Post-quantum cryptography","level":4,"score":0.5942383408546448},{"id":"https://openalex.org/C144901912","wikidata":"https://www.wikidata.org/wiki/Q471906","display_name":"Quantum cryptography","level":4,"score":0.4776971638202667},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.4653300642967224},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.46334418654441833},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.426106333732605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34650719165802},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.297750860452652},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.2800886034965515},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.22447600960731506},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19483837485313416},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.18889564275741577},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.12922126054763794},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07713228464126587},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07699370384216309},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1561/0400000074","is_oa":false,"landing_page_url":"https://doi.org/10.1561/0400000074","pdf_url":null,"source":{"id":"https://openalex.org/S110848248","display_name":"Foundations and Trends\u00ae in Theoretical Computer Science","issn_l":"1551-305X","issn":["1551-305X","1551-3068"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Theoretical Computer Science","raw_type":"journal-article"},{"id":"mag:2951286680","is_oa":false,"landing_page_url":"https://eprint.iacr.org/2015/939.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:CiteSeerX.psu:10.1.1.733.6846","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.733.6846","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprint.iacr.org/2015/939.pdf","raw_type":"text"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-028977382","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:cds.cern.ch:2761896","is_oa":false,"landing_page_url":"http://cds.cern.ch/record/2761896","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":175,"referenced_works":["https://openalex.org/W7540341","https://openalex.org/W17575016","https://openalex.org/W20286062","https://openalex.org/W31130112","https://openalex.org/W34386251","https://openalex.org/W39036742","https://openalex.org/W42080394","https://openalex.org/W56544557","https://openalex.org/W57039937","https://openalex.org/W65891367","https://openalex.org/W74973629","https://openalex.org/W80562455","https://openalex.org/W104209573","https://openalex.org/W121367636","https://openalex.org/W130395163","https://openalex.org/W139987668","https://openalex.org/W147447691","https://openalex.org/W149470655","https://openalex.org/W150064776","https://openalex.org/W150223756","https://openalex.org/W151792660","https://openalex.org/W155540543","https://openalex.org/W157865340","https://openalex.org/W174561455","https://openalex.org/W190530026","https://openalex.org/W607916523","https://openalex.org/W913176383","https://openalex.org/W1462154385","https://openalex.org/W1484751769","https://openalex.org/W1489617931","https://openalex.org/W1490468194","https://openalex.org/W1491861813","https://openalex.org/W1494049356","https://openalex.org/W1497981337","https://openalex.org/W1498316612","https://openalex.org/W1506156414","https://openalex.org/W1508077776","https://openalex.org/W1509320652","https://openalex.org/W1525451859","https://openalex.org/W1525538795","https://openalex.org/W1547036183","https://openalex.org/W1554247779","https://openalex.org/W1560474949","https://openalex.org/W1582043969","https://openalex.org/W1583834646","https://openalex.org/W1589034595","https://openalex.org/W1603256047","https://openalex.org/W1605712232","https://openalex.org/W1607264302","https://openalex.org/W1675339804","https://openalex.org/W1755636270","https://openalex.org/W1760474993","https://openalex.org/W1761303171","https://openalex.org/W1766548092","https://openalex.org/W1797206029","https://openalex.org/W1833653714","https://openalex.org/W1839785783","https://openalex.org/W1845765495","https://openalex.org/W1850468005","https://openalex.org/W1856342626","https://openalex.org/W1862721573","https://openalex.org/W1871739018","https://openalex.org/W1892798954","https://openalex.org/W1893972099","https://openalex.org/W1909955916","https://openalex.org/W1915197037","https://openalex.org/W1928000590","https://openalex.org/W1936753088","https://openalex.org/W1963071371","https://openalex.org/W1966731635","https://openalex.org/W1971053947","https://openalex.org/W1971286892","https://openalex.org/W1972050218","https://openalex.org/W1973079148","https://openalex.org/W1983370494","https://openalex.org/W1984153141","https://openalex.org/W1985439922","https://openalex.org/W1989510734","https://openalex.org/W1992226551","https://openalex.org/W1992282993","https://openalex.org/W1992938819","https://openalex.org/W1993060580","https://openalex.org/W1994790157","https://openalex.org/W1996360405","https://openalex.org/W2000956176","https://openalex.org/W2001093624","https://openalex.org/W2007466965","https://openalex.org/W2008701790","https://openalex.org/W2012589104","https://openalex.org/W2015880590","https://openalex.org/W2024697209","https://openalex.org/W2031533839","https://openalex.org/W2037426925","https://openalex.org/W2038761522","https://openalex.org/W2048994663","https://openalex.org/W2050689197","https://openalex.org/W2052267638","https://openalex.org/W2054904172","https://openalex.org/W2056492141","https://openalex.org/W2067107502","https://openalex.org/W2067264567","https://openalex.org/W2070189400","https://openalex.org/W2071676384","https://openalex.org/W2071825329","https://openalex.org/W2074196013","https://openalex.org/W2077244027","https://openalex.org/W2086042811","https://openalex.org/W2089477764","https://openalex.org/W2095708839","https://openalex.org/W2096221836","https://openalex.org/W2101444129","https://openalex.org/W2104952158","https://openalex.org/W2105994318","https://openalex.org/W2106121141","https://openalex.org/W2106970188","https://openalex.org/W2111416661","https://openalex.org/W2111809688","https://openalex.org/W2113717903","https://openalex.org/W2117362057","https://openalex.org/W2117376962","https://openalex.org/W2120030642","https://openalex.org/W2122086332","https://openalex.org/W2122973102","https://openalex.org/W2124218043","https://openalex.org/W2129580084","https://openalex.org/W2130410178","https://openalex.org/W2132172731","https://openalex.org/W2138001464","https://openalex.org/W2140256428","https://openalex.org/W2141040012","https://openalex.org/W2144593761","https://openalex.org/W2146689436","https://openalex.org/W2150624282","https://openalex.org/W2151237818","https://openalex.org/W2151241472","https://openalex.org/W2152688060","https://openalex.org/W2153886246","https://openalex.org/W2154059840","https://openalex.org/W2155178472","https://openalex.org/W2156030242","https://openalex.org/W2156186849","https://openalex.org/W2158911464","https://openalex.org/W2159486442","https://openalex.org/W2163469693","https://openalex.org/W2164761415","https://openalex.org/W2167236842","https://openalex.org/W2169690324","https://openalex.org/W2171001107","https://openalex.org/W2176745559","https://openalex.org/W2177209050","https://openalex.org/W2179033149","https://openalex.org/W2181114408","https://openalex.org/W2182904001","https://openalex.org/W2206688872","https://openalex.org/W2212077392","https://openalex.org/W2226167778","https://openalex.org/W2234439753","https://openalex.org/W2293813270","https://openalex.org/W2296067100","https://openalex.org/W2308457303","https://openalex.org/W2405203263","https://openalex.org/W2405984685","https://openalex.org/W2464308490","https://openalex.org/W2514326694","https://openalex.org/W2613413409","https://openalex.org/W2613674959","https://openalex.org/W2614049390","https://openalex.org/W2900370870","https://openalex.org/W2949731975","https://openalex.org/W2952119761","https://openalex.org/W2986959318","https://openalex.org/W3111297213","https://openalex.org/W3121827341","https://openalex.org/W3125094869","https://openalex.org/W3127778049"],"related_works":["https://openalex.org/W2061949491","https://openalex.org/W2038761522","https://openalex.org/W1489923862","https://openalex.org/W2031533839","https://openalex.org/W3165155389","https://openalex.org/W2766652244","https://openalex.org/W2883034031","https://openalex.org/W1996360405","https://openalex.org/W2372104937","https://openalex.org/W2335010064","https://openalex.org/W2796472420","https://openalex.org/W2007129452","https://openalex.org/W112021158","https://openalex.org/W2922252487","https://openalex.org/W3009843519","https://openalex.org/W2071825329","https://openalex.org/W74973629","https://openalex.org/W2142048307","https://openalex.org/W2092422002","https://openalex.org/W149470655"],"abstract_inverted_index":{"Lattice-based":[0],"cryptography":[1,25,66],"is":[2,75],"the":[3,15,61,68,77,99],"use":[4],"of":[5,23,60,102],"conjectured":[6],"hard":[7],"problems":[8,53,88],"on":[9,76],"point":[10],"lattices":[11],"in":[12,54,64],"\u211dn":[13],"as":[14],"foundation":[16],"for":[17],"secure":[18],"cryptographic":[19,109],"systems.":[20],"Attractive":[21],"features":[22],"lattice":[24,65,104],"include":[26],"apparent":[27],"resistance":[28],"to":[29,50],"quantum":[30],"attacks":[31],"(in":[32],"contrast":[33],"with":[34,85],"most":[35,59],"number-theoretic":[36],"cryptography),":[37],"high":[38],"asymptotic":[39],"efficiency":[40],"and":[41,48,83,106],"parallelism,":[42],"security":[43],"under":[44],"worst-case":[45,100],"intractability":[46,101],"assumptions,":[47],"solutions":[49],"long-standing":[51],"open":[52],"cryptography.":[55],"This":[56],"work":[57],"surveys":[58],"major":[62],"developments":[63],"over":[67],"past":[69],"ten":[70],"years.":[71],"The":[72],"main":[73],"focus":[74],"foundational":[78],"short":[79],"integer":[80],"solution":[81],"(SIS)":[82],"learning":[84],"errors":[86],"(LWE)":[87],"(and":[89],"their":[90,95,107],"more":[91],"efficient":[92],"ring-based":[93],"variants),":[94],"provable":[96],"hardness":[97],"assuming":[98],"standard":[103],"problems,":[105],"many":[108],"applications.":[110]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
