{"id":238111,"date":"2015-10-01T00:00:00","date_gmt":"2015-10-01T07:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/attacks-on-search-rlwe\/"},"modified":"2018-10-16T21:52:00","modified_gmt":"2018-10-17T04:52:00","slug":"attacks-on-search-rlwe","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/attacks-on-search-rlwe\/","title":{"rendered":"Attacks on search RLWE"},"content":{"rendered":"

We describe a new attack on the Search Ring Learning-With-Errors (RLWE) problem based on the chi-square statistical test, and give examples of RLWE instances in Galois number fields which are vulnerable to our attack. We prove a search-to-decision reduction for Galois fields which applies for any unramified prime modulus q<\/span><\/span><\/span><\/span>, regardless of the residue degree f<\/span><\/span><\/span><\/span> of q<\/span><\/span><\/span><\/span>, and we use this in our attacks. The time complexity of our attack is O<\/span>(<\/span>q<\/span>2<\/span>f<\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>, where f<\/span><\/span><\/span><\/span> is the {\\it residue degree} of q<\/span><\/span><\/span><\/span> in K<\/span><\/span><\/span><\/span>.<\/p>\n

We also show an attack on the RLWE problem in general cyclotomic rings (non 2<\/span><\/span><\/span><\/span>-power cyclotomic rings) which works when the modulus is a ramified prime. We demonstrate the attacks in practice by finding many vulnerable instances and successfully attacking them. We include the code for all attacks.<\/p>\n","protected":false},"excerpt":{"rendered":"

We describe a new attack on the Search Ring Learning-With-Errors (RLWE) problem based on the chi-square statistical test, and give examples of RLWE instances in Galois number fields which are vulnerable to our attack. We prove a search-to-decision reduction for Galois fields which applies for any unramified prime modulus q, regardless of the residue degree […]<\/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":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-2015-93","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Hao Chen, Katherine E 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