The security of many lattice-based cryptographic schemes relies on the hardness of finding short vectors in integral lattices. We propose a new variant of the parallel Gauss sieve algorithm to compute such short vectors. It combines favourable properties of previous approaches resulting in reduced run time and memory requirement per node. Our publicly available implementation outperforms all previous Gauss sieve approaches for dimensions 80, 88, and 96. When computing short vectors in ideal lattices, we show how to reduce the number of multiplications and comparisons by using a symbolic Fourier transform. We computed a short vector in a negacyclic ideal lattice of dimension 128 in less than nine days on 1,024 cores, more than twice as fast as the recent record computation for the same lattice on the same computer hardware.<\/p>\n","protected":false},"excerpt":{"rendered":"
The security of many lattice-based cryptographic schemes relies on the hardness of finding short vectors in integral lattices. We propose a new variant of the parallel Gauss sieve algorithm to compute such short vectors. It combines favourable properties of previous approaches resulting in reduced run time and memory requirement per node. Our publicly available implementation […]<\/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":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[250378,246691,254197,253393,254191,250426,254200,254203,254194,249685],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-633078","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us","msr-field-of-study-computation","msr-field-of-study-computer-science","msr-field-of-study-cryptography","msr-field-of-study-fourier-transform","msr-field-of-study-gauss","msr-field-of-study-lattice-order","msr-field-of-study-new-variant","msr-field-of-study-short-vector","msr-field-of-study-sieve","msr-field-of-study-topology"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2017-2-22","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"International Journal of Applied Cryptography","msr_volume":"3","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"4","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":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"doi","viewUrl":"false","id":"false","title":"10.1504\/IJACT.2017.10010312","label_id":"243106","label":0}],"msr_related_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"http:\/\/eprint.iacr.org\/2014\/880","label_id":"243118","label":0}],"msr_attachments":[],"msr-author-ordering":[{"type":"guest","value":"joppe-bos","user_id":480576,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=joppe-bos"},{"type":"user_nicename","value":"Michael Naehrig","user_id":32976,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Michael Naehrig"},{"type":"text","value":"Joop Van De Pol","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[428250],"publication":[],"video":[],"download":[],"msr_publication_type":"article","related_content":{"projects":[{"ID":428250,"post_title":"Post-quantum Cryptography","post_name":"post-quantum-cryptography","post_type":"msr-project","post_date":"2018-04-30 12:33:53","post_modified":"2024-09-30 21:14:11","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/post-quantum-cryptography\/","post_excerpt":"Cryptography in the era of quantum computers The private communication of individuals and organizations is protected online by cryptography. Cryptography protects our information as it travels over and is stored on the internet\u2014whether making a purchase from an online store, uploading data to the cloud, or accessing work email remotely. Our research and engineering work has focused on protecting private information and communication from the possible threat of future quantum computers. 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