{"id":161373,"date":"2011-05-16T00:00:00","date_gmt":"2011-05-16T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/affine-pairings-on-arm\/"},"modified":"2018-10-16T20:12:28","modified_gmt":"2018-10-17T03:12:28","slug":"affine-pairings-on-arm","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/affine-pairings-on-arm\/","title":{"rendered":"Affine Pairings on ARM"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Pairings on elliptic curves are being used in an increasing number of cryptographic applications on many different devices and platforms, but few performance numbers for cryptographic pairings have been reported on embedded and mobile devices.<\/p>\n<p>In this paper we give performance numbers for affine and projective pairings on a dual-core Cortex A9 ARM processor and compare performance of the same implementation across three platforms: x86, x86-64 and ARM. Using a fast inversion in the base field and doing inversion in extension fields by using the norm map to convert to inversions in smaller fields, we find a very low ratio of inversion-to-multiplication costs on all three platforms. This favors using affine coordinates for pairing implementations, even for the current 128 bit minimum security level specified by NIST. Our implementation shows another platform where affine coordinates are a better choice. We compare with other reported performance numbers on ARM processors and find that our implementation of affine pairings compares favorably.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pairings on elliptic curves are being used in an increasing number of cryptographic applications on many different devices and platforms, but few performance numbers for cryptographic pairings have been reported on embedded and mobile devices. In this paper we give performance numbers for affine and projective pairings on a dual-core Cortex A9 ARM processor and [&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":[13552],"msr-publication-type":[193718],"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-161373","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-hardware-devices","msr-locale-en_us"],"msr_publishername":"International Association for Cryptologic Research","msr_edition":"Cryptology ePrint Archive, Report 2011\/243","msr_affiliation":"","msr_published_date":"2011-05-16","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"243","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"2011\/43","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"Cryptology ePrint Archive, Report 2011\/243","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":"457371","msr_publicationurl":"http:\/\/eprint.iacr.org\/2011\/243","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"Affine Pairings on ARM","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2011\/05\/Affine-Pairings-on-ARM.pdf","id":457371,"label_id":0},{"type":"url","title":"http:\/\/eprint.iacr.org\/2011\/243","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"http:\/\/eprint.iacr.org\/2011\/243"}],"msr-author-ordering":[{"type":"user_nicename","value":"tolga","user_id":34244,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=tolga"},{"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":"mnaehrig","user_id":32976,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=mnaehrig"},{"type":"user_nicename","value":"danshu","user_id":31538,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=danshu"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[239792],"publication":[],"video":[],"download":[],"msr_publication_type":"techreport","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. ECC has been standardized for use in key exchange and digital signatures. This project focuses on efficient generation of parameters and implementation of ECC and pairing-based crypto primitives, across architectures and platforms.","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/239792"}]}}]},"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/161373"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/161373\/revisions"}],"predecessor-version":[{"id":524606,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/161373\/revisions\/524606"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=161373"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=161373"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=161373"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=161373"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=161373"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=161373"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=161373"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=161373"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=161373"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=161373"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=161373"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=161373"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=161373"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=161373"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=161373"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=161373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}