We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8% to 8.5% over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P +Q from given points P, Q on the curve. We give applications to simultaneous multiple scalar multiplication and to the Elliptic Curve Method of factorization. We show how this improvement together with another idea can speed the computation of the Weil and Tate pairings by up to 7.8%.<\/p>\n","protected":false},"excerpt":{"rendered":"
We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8% to 8.5% over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P +Q from given points P, Q on the curve. We give applications to simultaneous […]<\/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-163979","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_publishername":"Springer Verlag","msr_edition":"LNCS 2612, Topics in Cryptology - CT-RSA 2003","msr_affiliation":"","msr_published_date":"2003-01-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"Topics in Cryptology - CT-RSA 2003","msr_pages_string":"343-354","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"2612","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":"270810","msr_publicationurl":"http:\/\/eprint.iacr.org\/2002\/112","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"rsa3","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2003\/01\/rsa3.pdf","id":270810,"label_id":0},{"type":"url","title":"http:\/\/eprint.iacr.org\/2002\/112","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"http:\/\/eprint.iacr.org\/2002\/112"}],"msr-author-ordering":[{"type":"text","value":"Kirsten Eisentr\u00e4ger","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"},{"type":"user_nicename","value":"petmon","user_id":33245,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=petmon"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[239792],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":{"projects":[{"ID":239792,"post_title":"Elliptic Curve Cryptography (ECC)","post_name":"elliptic-curve-cryptography-ecc","post_type":"msr-project","post_date":"2016-06-29 20:49:17","post_modified":"2020-03-31 12:25:10","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/elliptic-curve-cryptography-ecc\/","post_excerpt":"In the last 25 years, Elliptic Curve Cryptography (ECC) has become a mainstream primitive for cryptographic protocols and applications. 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