We apply Scholten’s construction to give explicit isogenies between the Weil restriction of supersingular Montgomery curves with full rational 2-torsion over GF(p^2) and corresponding abelian surfaces over GF(p). Subsequently, we show that isogeny-based public key cryptography can exploit the fast Kummer surface arithmetic that arises from the theory of theta functions. In particular, we show that chains of 2-isogenies between elliptic curves can instead be computed as chains of Richelot (2,2)-isogenies between Kummer surfaces. This gives rise to new possibilities for efficient supersingular isogeny-based cryptography.<\/p>\n","protected":false},"excerpt":{"rendered":"
We apply Scholten’s construction to give explicit isogenies between the Weil restriction of supersingular Montgomery curves with full rational 2-torsion over GF(p^2) and corresponding abelian surfaces over GF(p). Subsequently, we show that isogeny-based public key cryptography can exploit the fast Kummer surface arithmetic that arises from the theory of theta functions. In particular, we show […]<\/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":[13546],"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-504989","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_publishername":"Springer","msr_edition":"ASIACRYPT 2018","msr_affiliation":"","msr_published_date":"2018-12-08","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":"504992","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"sidh-kummer","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2018\/09\/sidh-kummer.pdf","id":504992,"label_id":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"user_nicename","value":"Craig Costello","user_id":31476,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Craig Costello"}],"msr_impact_theme":[],"msr_research_lab":[199565],"msr_event":[],"msr_group":[],"msr_project":[428250],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","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. 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