{"id":167580,"date":"2014-09-30T00:00:00","date_gmt":"2014-09-30T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/weak-instances-of-plwe\/"},"modified":"2018-10-16T21:59:45","modified_gmt":"2018-10-17T04:59:45","slug":"weak-instances-of-plwe","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/weak-instances-of-plwe\/","title":{"rendered":"Weak Instances of PLWE"},"content":{"rendered":"<div class=\"asset-content\">\n<p>In this paper we present a new attack on the polynomial version of the Ring-LWE assumption, for certain carefully chosen number fields. This variant of RLWE, introduced in [BV11] and called the PLWE assumption, is known to be as hard as the RLWE assumption for 2-power cyclotomic number fields, and for cyclotomic number fields in general with a small cost in terms of error growth. For general number fields, we articulate the relevant properties and prove security reductions for number fields with those properties. We then present an attack on PLWE for number fields satisfying certain properties.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper we present a new attack on the polynomial version of the Ring-LWE assumption, for certain carefully chosen number fields. This variant of RLWE, introduced in [BV11] and called the PLWE assumption, is known to be as hard as the RLWE assumption for 2-power cyclotomic number fields, and for cyclotomic number fields in [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13558],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-167580","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_publishername":"Springer","msr_edition":"Selected Areas in Cryptography 2014","msr_affiliation":"","msr_published_date":"2014-09-30","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"204647","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"ringlwe.pdf","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/ringlwe.pdf","id":204647,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":204647,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/ringlwe.pdf"}],"msr-author-ordering":[{"type":"text","value":"Kirsten Eisentrager","user_id":0,"rest_url":false},{"type":"text","value":"Sean Hallgren","user_id":0,"rest_url":false},{"type":"user_nicename","value":"klauter","user_id":32558,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=klauter"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[438444,170495],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":{"projects":[{"ID":438444,"post_title":"Microsoft SEAL","post_name":"microsoft-seal","post_type":"msr-project","post_date":"2017-11-07 10:24:35","post_modified":"2023-01-04 09:36:35","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/microsoft-seal\/","post_excerpt":"Microsoft SEAL\u2014powered by open-source homomorphic encryption technology\u2014provides a set of encryption libraries that allow computations to be performed directly on encrypted data.","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/438444"}]}},{"ID":170495,"post_title":"Lattice-based Cryptography","post_name":"lattice-based-cryptography","post_type":"msr-project","post_date":"2010-07-03 12:03:35","post_modified":"2018-11-08 15:25:21","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/lattice-based-cryptography\/","post_excerpt":"Lattices are geometric objects that have recently emerged as a powerful tool in cryptography. Lattice-based schemes have also proven to be remarkably resistant to sub-exponential and quantum attacks (in sharp contrast to their number-theoretic friends). Our goal is to use lattices to construct cryptographic primitives that are simultaneously highly efficient and highly functional. 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